trying to RECOGNIZE REPUNIT FACTORS BY HAND INSPECTION

[barker]

(a) n > m > 0
(b) n and m are positive integers

Unless you provide an example of a positive integer <= 0, either " > 0"
or "positive" is redundant. Therefore I must apply Rule 1:

Rule 1: Always stop at the first error or anomaly.

Juniors or clerks (eg, Pubkeybreaker <***@aol.com>) can show
you how to apply the Taylor expansion to solve what I guess this little
problem was meant to be, had it been correctly formulated (more serious
errors in its exposition followed the first one I showed above).

Now, in contrast, here is a real problem, with something valuable to
learn while attempting to solve it.

With everything shown in base-10, consider the two primes:
113136621886721
and
617431748093238554410874808506989442264783116181403206744221352101186333
which when multiplied yield
698541422248819000939556056942681614546383342970851314130956479402221733
63516839384093
What prime, when multiplied by this last number, will yield a repunit?
And how did you find it? No cheating, please.

There is a valuable lesson within the structures of these prime and
nearly-
prime factors.

Notation for non-mathematicians:
A base-10 repunit is (10^n -1)/9 where n is a positive integer. e.g., 111,
1.
A nearly-prime number is a product of two primes. e.g. 111, 4
Warning: 1 is not a prime.

Thank you,

"barker" (associate of the late falsified Dr Pertti Lounesto)

[quasi]

Post by barker
113136621886721
and
61743174809323855441087480850698944226478311618140
3206744221352101186333
which when multiplied yield
69854142224881900093955605694268161454638334297085
131413095647940222173363516839384093
What prime, when multiplied by this last number, will
yield a repunit?
And how did you find it? No cheating, please.

Let p,q be the two given primes, with p the smaller one.

Factoring p-1 yields

p-1 = (2^8)(5)(29)(173)(227)(77611)

Let e = p-1.

We can find the order of 10 mod p by starting with

10^(p-1) = 1 (mod p)

and successively removing prime factors of p-1 from the
exponent while testing the new exponent to make sure 10
to that power is still congruent to 1 mod p.

We end up with 10^227 = 1 mod p.

We can do the same with the prime q since q-1 factors
easily as

q-1 = (2^2)(3)(41)(227)(5273)*h

where h is the prime

10484318980370298149714985666207150440923314817650
24061012157551

It turns out that 10 has order 227 mod q, hence

(10^227 - 1)/9 is a multiple of p*q

Letting r = ((10^227 - 1)/9)/(p*q), we test r and find
that r is prime.

Hence r is a prime such that p*q*r is a repunit, as required.

As to how you found p,q, I'm not sure.

Perhaps you factored x = (10^227 - 1)/9?

Is x in the range of fast factoring algorithms?

It might be.

quasi

[Pubkeybreaker]

Post by quasi
As to how you found p,q, I'm not sure.

Table lookup. The Cunningham tables......

Post by quasi
Perhaps you factored x = (10^227 - 1)/9?
Is x in the range of fast factoring algorithms?

10^281-1 is the smallest integer of the form 10^n-1 that is not
fully factored.

[barker]

quasi, you are allocated full marks for mechanistic reasoning. The
prime is:
159061592587323425117771471330677165732172663157935428592494153340689013
866064831389024866905836001165382255194784215933028413820020114354227
and its product with Y is:
111111111111111111111111111111111111111111111111111111111111111111111111
111111111111111111111111111111111111111111111111111111111111111111111111
111111111111111111111111111111111111111111111111111111111111111111111111
11111111111 = (10^227-1)/9

Post by Pubkeybreaker

Post by quasi
As to how you found p,q, I'm not sure.

Let me explain how to generate potential repunit prime or nearly-prime
factors with an efficiency far greater than "suck it and see".

You may be familiar with the concept of a normal number. A normal number,
written in the form of an infinite decimal (e.g., so 2 = 2.000...) is one
in which each digit or sequence of digits occurs the statistically
expected
proportion of times. Normality is very hard to prove. When I last looked,
neither sqrt(2), the base of natural logs nor pi has been proven normal,
though each is suspected to be. Normality is hard to prove. An example of
a normal number is 0.12345678910111213.....99100101.....999910001001...
Normality is clearly related to randomness. Random decimal numbers would
be normal, loosely speaking. The reverse is not true, as the normal number
I quoted is clearly not "random", in any sense of that concept.

Now, forget about normality, but think about the likelihood of certain
combinations of digits occurring within a number. While primes cannot be
normal (they are integers!), if you disregard the last digit, their digit
sequences meet quasi-normal criteria re sequence-likelihoods. Loosely
speaking, their digits apart from the last one appear to be "random."
This has been statistically shown in many studies, though not proven.

But not so primes OR nearly-primes which are factors of repunits,
especially repunits where the number of digits is prime (hint: 227 is
prime). They DO include digit sequences in other than what would be
expected to be their statistically expected frequencies, as far as we
know. All repunit prime or nearly-prime factors known so far have been
examined.

Note again, this is an unproven conjecture, merely supported by the
limited information available so far. If true, there is a secret to do
with the structure of primes that is hitherto unknown.

Post by Pubkeybreaker

Post by quasi
Is (10^227-1)/9 in the range of fast factoring algorithms?

No.

Post by Pubkeybreaker
10^281-1 is the smallest integer of the form 10^n-1 that is not
fully factored.

No.

It is the smallest one whose prime factors have not been published.

There is a difference... Reading between the lines, would you like a
decomposition of this nearly-prime number:
149757228779144917176204260591184175807079292786053093556159199041982349
206415406540332144366189548551670508994053634039049939359298138323011269
238802598321754298938863469321281048841531709492264740073694039201
(yes, it has exactly two prime factors).

For reference, here are all six prime or nearly-prime factors of the
repunit originally in question:

113136621886721

617431748093238554410874808506989442264783116181403206744221352101186333

698541422248819000939556056942681614546383342970851314130956479402221733
63516839384093

159061592587323425117771471330677165732172663157935428592494153340689013
866064831389024866905836001165382255194784215933028413820020114354227

179956912572516741925952061604066250026043931734578797752092356481864249
850378246546198832808085293596132153154665017233714517729376660209728956
67261519667

982096771656856179669463016916734637917878564200109112194769888316291158
929000525607255285131063773103221026560885703118320809283587891336782742
67239942357743229610071851165137671683769570402913782212648893179591

Look carefully...

Thank you,

"barker" (associate of the late falsified Dr Pertti Lounesto)

[quasi]

Pubkeybreaker wrote...
Let me explain how to generate potential repunit prime or >nearly-prime factors with an efficiency far greater than
"suck it and see".
You may be familiar with the concept of a normal number.
A normal number, written in the form of an infinite decimal
(e.g., so 2 = 2.000...) is one in which each digit or
sequence of digits occurs the statistically expected
proportion of times. Normality is very hard to prove. When
I last looked, neither sqrt(2), the base of natural logs
nor pi has been proven normal, though each is suspected to
be. Normality is hard to prove. An example of a normal
number is
0.12345678910111213.....99100101.....999910001001...
Normality is clearly related to randomness. Random decimal
numbers would be normal, loosely speaking. The reverse is
not true, as the normal number I quoted is clearly not
"random", in any sense of that concept.
Now, forget about normality, but think about the likelihood
of certain combinations of digits occurring within a number.
While primes cannot be normal (they are integers!), if you
disregard the last digit, their digit sequences meet
quasi-normal criteria re sequence-likelihoods. Loosely
speaking, their digits apart from the last one appear to be
"random." This has been statistically shown in many studies,
though not proven.
But not so primes OR nearly-primes which are factors of
repunits, especially repunits where the number of digits
is prime (hint: 227 is prime). They DO include digit
sequences in other than what would be expected to be their
statistically expected frequencies, as far as we know. All
repunit prime or nearly-prime factors known so far have been
examined.
Note again, this is an unproven conjecture, merely supported
by the limited information available so far. If true, there
is a secret to do with the structure of primes that is
hitherto unknown.

Post by Pubkeybreaker

Post by quasi
Is (10^227-1)/9 in the range of fast factoring algorithms?

No.

So then was it factored using some of the ideas you describe?

Post by Pubkeybreaker
10^281-1 is the smallest integer of the form 10^n-1 that is
not fully factored.

No.
It is the smallest one whose prime factors have not been
published. There is a difference...
Reading between the lines, would you like a decomposition of
14975722877914491717620426059118417580707929278605
30935561591990419823492064154065403321443661895485
51670508994053634039049939359298138323011269238802
59832175429893886346932128104884153170949226474007
3694039201
(yes, it has exactly two prime factors).

The problem with that is how do we know that it wasn't
obtained simply by multiplying two large primes?

For reference, here are all six prime or nearly-prime
113136621886721
61743174809323855441087480850698944226478311618140
3206744221352101186333
69854142224881900093955605694268161454638334297085
131413095647940222173363516839384093
15906159258732342511777147133067716573217266315793
54285924941533406890138660648313890248669058360011
65382255194784215933028413820020114354227
17995691257251674192595206160406625002604393173457
87977520923564818642498503782465461988328080852935
96132153154665017233714517729376660209728956672615
19667
98209677165685617966946301691673463791787856420010
91121947698883162911589290005256072552851310637731
03221026560885703118320809283587891336782742672399
42357743229610071851165137671683769570402913782212
648893179591
Look carefully...

I don't see the pattern (but maybe I didn't look as
closely as I should have).

But suppose the factors of a repunit have digit patterns
which appear with greater frequency than what would occur
in a random digit string. Now what? Does it cut down the
search space when looking for factors? If so, by how much?

quasi

[Tonico]

Post by quasi

Pubkeybreaker wrote...
Let me explain how to generate potential repunit prime or >nearly-prime factors with an efficiency far greater than
"suck it and see".
You may be familiar with the concept of a normal number.
A normal number, written in the form of an infinite decimal
(e.g., so 2 = 2.000...) is one in which each digit or
sequence of digits occurs the statistically expected
proportion of times. Normality is very hard to prove. When
I last looked, neither sqrt(2), the base of natural logs
nor pi has been proven normal, though each is suspected to
be. Normality is hard to prove. An example of a normal
number is
0.12345678910111213.....99100101.....999910001001...
Normality is clearly related to randomness. Random decimal
numbers would be normal, loosely speaking. The reverse is
not true, as the normal number I quoted is clearly not
"random", in any sense of that concept.
Now, forget about normality, but think about the likelihood
of certain combinations of digits occurring within a number.
While primes cannot be normal (they are integers!), if you
disregard the last digit, their digit sequences meet
quasi-normal criteria re sequence-likelihoods. Loosely
speaking, their digits apart from the last one appear to be
"random." This has been statistically shown in many studies,
though not proven.
But not so primes OR nearly-primes which are factors of
repunits, especially repunits where the number of digits
is prime (hint: 227 is prime). They DO include digit
sequences in other than what would be expected to be their
statistically expected frequencies, as far as we know. All
repunit prime or nearly-prime factors known so far have been
examined.
Note again, this is an unproven conjecture, merely supported
by the limited information available so far. If true, there
is a secret to do with the structure of primes that is
hitherto unknown.

Post by Pubkeybreaker

Post by quasi
Is (10^227-1)/9 in the range of fast factoring algorithms?

No.

So then was it factored using some of the ideas you describe?

Post by Pubkeybreaker
10^281-1 is the smallest integer of the form 10^n-1 that is
not fully factored.

No.
It is the smallest one whose prime factors have not been
published. There is a difference...
Reading between the lines, would you like a decomposition of
14975722877914491717620426059118417580707929278605
30935561591990419823492064154065403321443661895485
51670508994053634039049939359298138323011269238802
59832175429893886346932128104884153170949226474007
3694039201
(yes, it has exactly two prime factors).

The problem with that is how do we know that it wasn't
obtained simply by multiplying two large primes?

For reference, here are all six prime or nearly-prime
113136621886721
61743174809323855441087480850698944226478311618140
3206744221352101186333
69854142224881900093955605694268161454638334297085
131413095647940222173363516839384093
15906159258732342511777147133067716573217266315793
54285924941533406890138660648313890248669058360011
65382255194784215933028413820020114354227
17995691257251674192595206160406625002604393173457
87977520923564818642498503782465461988328080852935
96132153154665017233714517729376660209728956672615
19667
98209677165685617966946301691673463791787856420010
91121947698883162911589290005256072552851310637731
03221026560885703118320809283587891336782742672399
42357743229610071851165137671683769570402913782212
648893179591
Look carefully...

I don't see the pattern (but maybe I didn't look as
closely as I should have).
But suppose the factors of a repunit have digit patterns
which appear with greater frequency than what would occur
in a random digit string. Now what? Does it cut down the
search space when looking for factors? If so, by how much?
quasi-

Watch it: this barker is the same idiot that trolled around some 2-3
weeks ago with his alter ego praising him and stating barker 1 -
sci.math 0 and etc.

Don'ty feed the troll...

Tonio

[quasi]

Post by Tonico
Watch it: this barker is the same idiot that trolled around
some 2-3 weeks ago with his alter ego praising him and
stating barker 1 - sci.math 0 and etc.
Don't feed the troll...

Yep, a troll he surely is.

Thanks for the alert.

quasi

[quasi]

Post by quasi

Pubkeybreaker wrote...
Let me explain how to generate potential repunit prime or >nearly-prime factors with an efficiency far greater than
"suck it and see".
You may be familiar with the concept of a normal number.
A normal number, written in the form of an infinite decimal
(e.g., so 2 = 2.000...) is one in which each digit or
sequence of digits occurs the statistically expected
proportion of times. Normality is very hard to prove. When
I last looked, neither sqrt(2), the base of natural logs
nor pi has been proven normal, though each is suspected to
be. Normality is hard to prove. An example of a normal
number is
0.12345678910111213.....99100101.....999910001001...
Normality is clearly related to randomness. Random decimal
numbers would be normal, loosely speaking. The reverse is
not true, as the normal number I quoted is clearly not
"random", in any sense of that concept.
Now, forget about normality, but think about the likelihood
of certain combinations of digits occurring within a number.
While primes cannot be normal (they are integers!), if you
disregard the last digit, their digit sequences meet
quasi-normal criteria re sequence-likelihoods. Loosely
speaking, their digits apart from the last one appear to be
"random." This has been statistically shown in many studies,
though not proven.
But not so primes OR nearly-primes which are factors of
repunits, especially repunits where the number of digits
is prime (hint: 227 is prime). They DO include digit
sequences in other than what would be expected to be their
statistically expected frequencies, as far as we know. All
repunit prime or nearly-prime factors known so far have been
examined.
Note again, this is an unproven conjecture, merely supported
by the limited information available so far. If true, there
is a secret to do with the structure of primes that is
hitherto unknown.

Post by Pubkeybreaker

Post by quasi
Is (10^227-1)/9 in the range of fast factoring algorithms?

No.

So then was it factored using some of the ideas you describe?

Post by Pubkeybreaker
10^281-1 is the smallest integer of the form 10^n-1 that is
not fully factored.

No.
It is the smallest one whose prime factors have not been
published. There is a difference...
Reading between the lines, would you like a decomposition of
14975722877914491717620426059118417580707929278605
30935561591990419823492064154065403321443661895485
51670508994053634039049939359298138323011269238802
59832175429893886346932128104884153170949226474007
3694039201
(yes, it has exactly two prime factors).

The problem with that is how do we know that it wasn't
obtained simply by multiplying two large primes?

For reference, here are all six prime or nearly-prime
113136621886721
61743174809323855441087480850698944226478311618140
3206744221352101186333
69854142224881900093955605694268161454638334297085
131413095647940222173363516839384093
15906159258732342511777147133067716573217266315793
54285924941533406890138660648313890248669058360011
65382255194784215933028413820020114354227
17995691257251674192595206160406625002604393173457
87977520923564818642498503782465461988328080852935
96132153154665017233714517729376660209728956672615
19667
98209677165685617966946301691673463791787856420010
91121947698883162911589290005256072552851310637731
03221026560885703118320809283587891336782742672399
42357743229610071851165137671683769570402913782212
648893179591
Look carefully...

I don't see the pattern (but maybe I didn't look as
closely as I should have).
But suppose the factors of a repunit have digit patterns
which appear with greater frequency than what would occur
in a random digit string. Now what? Does it cut down the
search space when looking for factors? If so, by how much?

I just came to my senses (and Tonico's reply made it even
more clear).

It's all smoke and mirrors, barker.

Let's see you factor some repunit whose factors are not yet
published.

Short of that, how about specifying an actual digit pattern
such that factors of repunits have that pattern with a
frequency greater than that of random digit strings.

That's how I came to my senses. If there was such a pattern,
an analogous patterns should hold for any specified base,
not just base 10. So what's the anomalous pattern of digits
for factors of repunits base 2? The obvious answer is there's
no such pattern.

I'll admit I'm sometimes naive, and you did manage to fool me
for a while -- until I had time to think it through. But I
won't be fooled again -- at least not by you.

quasi

[barker]

Post by quasi

Post by barker

Post by Pubkeybreaker
10^281-1 is the smallest integer of the form 10^n-1 that is
not fully factored.

No.
It is the smallest one whose prime factors have not been
published. There is a difference...
Reading between the lines, would you like a decomposition of
14975722877914491717620426059118417580707929278605
30935561591990419823492064154065403321443661895485
51670508994053634039049939359298138323011269238802
59832175429893886346932128104884153170949226474007
3694039201
(yes, it has exactly two prime factors).

The problem with that is how do we know that it wasn't
obtained simply by multiplying two large primes?

You have contrived to confuse yourself.

Pubkeybreaker <***@aol.com> mentioned the repunit 10^281-1,
attributing a property incorrectly to it. I never mentioned it until
he did. I am not he. Thereafter, I have provided a large factor of
this number, and can, if properly motivated, provide all its prime
factors (i.e., decompose the number:
149757228779144917176204260591184175807079292786053093556159199041982349
206415406540332144366189548551670508994053634039049939359298138323011269
238802598321754298938863469321281048841531709492264740073694039201 )
Google, Pubkeybreaker's admitted tool of the trade, wouldn't help here.

Divide 10^281-1 by this number, and you will find what I say is true.
The other factor is relatively small and easy to decompose.

I could not, therefore, have arrived at this 200+ digit number simply by
coming up with two primes and multiplying them! It is, instead, a factor
of the number 10^281-1 produced as some form of challenge by the other
poster, Pubkeybreaker <***@aol.com>, who appears, in common
with many AO Lusers, to be a troll. Irrelevant references to the axion
of choice are a way of knowing them by their works.

Post by quasi

Post by barker
For reference, here are all six prime or nearly-prime
113136621886721
61743174809323855441087480850698944226478311618140
3206744221352101186333
69854142224881900093955605694268161454638334297085
131413095647940222173363516839384093
15906159258732342511777147133067716573217266315793
54285924941533406890138660648313890248669058360011
65382255194784215933028413820020114354227
17995691257251674192595206160406625002604393173457
87977520923564818642498503782465461988328080852935
96132153154665017233714517729376660209728956672615
19667
98209677165685617966946301691673463791787856420010
91121947698883162911589290005256072552851310637731
03221026560885703118320809283587891336782742672399
42357743229610071851165137671683769570402913782212
648893179591
Look carefully...

I don't see the pattern (but maybe I didn't look as
closely as I should have).

Let me start you on your voyage of discovery. Please do not assume
this is true except that it is a good point to begin your voyage.

A repunit is a string of "1"s. In decimal notation, the digit-
complement of "1" is "9". "0" has its obvious role within repunit
factor strings.

Look for "9"s in the numbers above, and see how frequently they
are adjacent to "0"s. Look for "1"s, and see how frequently they
are adjacent to "1"s. Then even see how frequently "9"s are
adjacent to "0"s. Assume pseudo-normality, compute what expected
frequencies are, and be startled at how much higher these are.
"90009" - there for sure.

Small sample, I hear? Skewed because I chosed the 227th repunit
(10^227-1)/9? Try it with as many others as you can, at least
partially decomposing them and examining the results of part-
decomposition (warning! consider only prime or near-prime factors,
as defined earlier).

You will soon be a convert.

Just do a frequency expectation chart. It will jump out at you.

Decide whether the patterns found in the prime or nearly-prime
factors of (10^n-1)/9 are stronger (= more frequent) if n is prime.

Should you need assistance with factorizations, there are AO-Lusers
with large computing power and limited brain power (Pubkeybreaker
<***@aol.com> serves well) who can help you, but whose
mathematical intuition is either insignificant or absent.

Working out WHY these factors are far from pseudo-normal, and why
these sequences are so common, now that is another matter altogether.

Post by quasi
But suppose the factors of a repunit have digit patterns
which appear with greater frequency than what would occur
in a random digit string. Now what? Does it cut down the
search space when looking for factors? If so, by how much?

Step by step. Learn first to walk. Consider what would the position
be in a lower notational base. 2 and 3 are no use because the concept
of adjacency breaks down and we are left with having to look for more
complex patterns. In fact, restating all numbers in a much larger base
- for example, base 31 - will illustrate the principle clearer.

There are some deep truths in number theory buried within here.

Post by quasi
trolling

As appeared Galois, Leibnitz etc., no doubt. To the
Confederacy, that is.

Post by quasi
quasi

Thank you,

"barker" (associate of the late falsified Dr Pertti Lounesto)

[quasi]

On Mon, 16 Apr 2012 04:43:12 +0200, barker

Post by barker

Post by quasi

Post by barker

Post by Pubkeybreaker
10^281-1 is the smallest integer of the form 10^n-1 that is
not fully factored.

No.
It is the smallest one whose prime factors have not been
published. There is a difference...
Reading between the lines, would you like a decomposition of
14975722877914491717620426059118417580707929278605
30935561591990419823492064154065403321443661895485
51670508994053634039049939359298138323011269238802
59832175429893886346932128104884153170949226474007
3694039201
(yes, it has exactly two prime factors).

The problem with that is how do we know that it wasn't
obtained simply by multiplying two large primes?

You have contrived to confuse yourself.
attributing a property incorrectly to it. I never mentioned it until
he did. I am not he. Thereafter, I have provided a large factor of
this number, and can, if properly motivated, provide all its prime
149757228779144917176204260591184175807079292786053093556159199041982349
206415406540332144366189548551670508994053634039049939359298138323011269
238802598321754298938863469321281048841531709492264740073694039201 )
Google, Pubkeybreaker's admitted tool of the trade, wouldn't help here.
Divide 10^281-1 by this number, and you will find what I say is true.
The other factor is relatively small and easy to decompose.
I could not, therefore, have arrived at this 200+ digit number simply by
coming up with two primes and multiplying them! It is, instead, a factor
of the number 10^281-1 produced as some form of challenge by the other
with many AO Lusers, to be a troll. Irrelevant references to the axion
of choice are a way of knowing them by their works.

Post by quasi

Post by barker
For reference, here are all six prime or nearly-prime
113136621886721
61743174809323855441087480850698944226478311618140
3206744221352101186333
69854142224881900093955605694268161454638334297085
131413095647940222173363516839384093
15906159258732342511777147133067716573217266315793
54285924941533406890138660648313890248669058360011
65382255194784215933028413820020114354227
17995691257251674192595206160406625002604393173457
87977520923564818642498503782465461988328080852935
96132153154665017233714517729376660209728956672615
19667
98209677165685617966946301691673463791787856420010
91121947698883162911589290005256072552851310637731
03221026560885703118320809283587891336782742672399
42357743229610071851165137671683769570402913782212
648893179591
Look carefully...

I don't see the pattern (but maybe I didn't look as
closely as I should have).

Let me start you on your voyage of discovery. Please do not assume
this is true except that it is a good point to begin your voyage.
A repunit is a string of "1"s. In decimal notation, the digit-
complement of "1" is "9". "0" has its obvious role within repunit
factor strings.
Look for "9"s in the numbers above, and see how frequently they
are adjacent to "0"s. Look for "1"s, and see how frequently they
are adjacent to "1"s. Then even see how frequently "9"s are
adjacent to "0"s. Assume pseudo-normality, compute what expected
frequencies are, and be startled at how much higher these are.
"90009" - there for sure.
Small sample, I hear? Skewed because I chosed the 227th repunit
(10^227-1)/9? Try it with as many others as you can, at least
partially decomposing them and examining the results of part-
decomposition (warning! consider only prime or near-prime factors,
as defined earlier).
You will soon be a convert.
Just do a frequency expectation chart. It will jump out at you.
Decide whether the patterns found in the prime or nearly-prime
factors of (10^n-1)/9 are stronger (= more frequent) if n is prime.
Should you need assistance with factorizations, there are AO-Lusers
with large computing power and limited brain power (Pubkeybreaker
mathematical intuition is either insignificant or absent.
Working out WHY these factors are far from pseudo-normal, and why
these sequences are so common, now that is another matter altogether.

Post by quasi
But suppose the factors of a repunit have digit patterns
which appear with greater frequency than what would occur
in a random digit string. Now what? Does it cut down the
search space when looking for factors? If so, by how much?

Step by step. Learn first to walk. Consider what would the position
be in a lower notational base. 2 and 3 are no use because the concept
of adjacency breaks down and we are left with having to look for more
complex patterns. In fact, restating all numbers in a much larger base
- for example, base 31 - will illustrate the principle clearer.
There are some deep truths in number theory buried within here.

Post by quasi
trolling

As appeared Galois, Leibnitz etc., no doubt. To the
Confederacy, that is.

Post by quasi
quasi

Thank you,
"barker" (associate of the late falsified Dr Pertti Lounesto)

Damn it barker, why can't you just be a troll -- that would
make it so much easier.

I think it's clear you're not a troll (or at least
you have a non-troll side).

I apologize for calling you a troll.

Bravo for your partial factorization of (10^281 - 1)/9.

I'll try to think about the clues you provided.

You clearly have some cool things to teach us.

quasi

[Pubkeybreaker]

Post by quasi
On Mon, 16 Apr 2012 04:43:12 +0200, barker

Post by barker

Post by quasi

Post by barker
No.
It is the smallest one whose prime factors have not been
published. There is a difference...

These factorizations get published very quickly. I know everyone
capable of factoring R281 and none of them have done it. It
REMAINS unfactored.

Post by quasi

Post by barker

Post by quasi
The problem with that is how do we know that it wasn't
obtained simply by multiplying two large primes?

You have contrived to confuse yourself.
attributing a property incorrectly to it. I never mentioned it until
he did. I am not he. Thereafter, I have provided a large factor of
this number, and can, if properly motivated, provide all its prime
149757228779144917176204260591184175807079292786053093556159199041982349
206415406540332144366189548551670508994053634039049939359298138323011269
238802598321754298938863469321281048841531709492264740073694039201 )

You have provided a COMPOSITE COFACTOR of 10^281-1 after dividing out
some (perhaps all, I did not check) of its KNOWN prime factors.

You are a lying troll.

Post by quasi

Post by barker
Divide 10^281-1 by this number, and you will find what I say is true.
The other factor is relatively small and easy to decompose.
I could not, therefore, have arrived at this 200+ digit number simply by
coming up with two primes and multiplying them!

No. You took 10^281-1 and divided out some (perhaps all, I did not
check)
of the known and published prime factors. The remaining cofactor is
composite.

Post by quasi
Damn it barker, why can't you just be a troll -- that would
make it so much easier.
I think it's clear you're not a troll (or at least
you have a non-troll side).
I apologize for calling you a troll.
Bravo for your partial factorization of (10^281 - 1)/9.

Damn it! There are already 4 known and published factors of
10^281-1. The remaining COFACTOR is unfactored. It is within
reach of NFS, but we just haven't gotten to it yet. The
community working on the Cunninghan project is busy with other
numbers. It will be finished.

Before anyone accepts what this troll has been saying about
factoring, you should first check out:

http://homes.cerias.purdue.edu/~ssw/cun/

[Pubkeybreaker]

Post by quasi
On Mon, 16 Apr 2012 04:43:12 +0200, barker

Post by barker

Post by quasi

Post by barker
No.
It is the smallest one whose prime factors have not been
published. There is a difference...

These factorizations get published very quickly.  I know everyone
capable of factoring R281 and none of them have done it. It
REMAINS unfactored.

Post by quasi

Post by barker

Post by quasi
The problem with that is how do we know that it wasn't
obtained simply by multiplying two large primes?

You have contrived to confuse yourself.
attributing a property incorrectly to it. I never mentioned it until
he did. I am not he. Thereafter, I have provided a large factor of
this number, and can, if properly motivated, provide all its prime
149757228779144917176204260591184175807079292786053093556159199041982349
206415406540332144366189548551670508994053634039049939359298138323011269
238802598321754298938863469321281048841531709492264740073694039201 )

You have provided a COMPOSITE COFACTOR of 10^281-1 after dividing out
some (perhaps all, I did not check) of its KNOWN prime factors.
You are a lying troll.

Post by quasi

Post by barker
Divide 10^281-1 by this number, and you will find what I say is true.
The other factor is relatively small and easy to decompose.
I could not, therefore, have arrived at this 200+ digit number simply by
coming up with two primes and multiplying them!

No.  You took 10^281-1 and divided out some (perhaps all, I did not
check)
of the known and published prime factors.  The remaining cofactor is
composite.

Post by quasi
Damn it barker, why can't you just be a troll -- that would
make it so much easier.
I think it's clear you're not a troll (or at least
you have a non-troll side).
I apologize for calling you a troll.
Bravo for your partial factorization of (10^281 - 1)/9.

Damn it!   There are already 4 known and published factors of
10^281-1.  The remaining COFACTOR is unfactored. It is within
reach of NFS, but we just haven't gotten to it yet.  The
community working on the Cunninghan project is busy with other
numbers.  It will be finished.
Before anyone accepts what this troll has been saying about
http://homes.cerias.purdue.edu/~ssw/cun/

Let me add: The known PARTIAL factorization of 10^281-1 is:

281 (1)
563.2597610354323.380431988961690791.133355295524380732608674846305692470329.C210

The notation (1) indicates the index of an algebraic prime factor;
i.e. 10^281-1 is divisible by 10^1 - 1.

All this troll did was divide out some (or all) of these known PRIME
factors to produce
a composite cofactor.

[quasi]

Post by Pubkeybreaker

Post by quasi

Post by barker

Post by quasi

Post by barker
No.
It is the smallest one whose prime factors have not been
published. There is a difference...

These factorizations get published very quickly.  I know everyone
capable of factoring R281 and none of them have done it. It
REMAINS unfactored.

Post by quasi

Post by barker

Post by quasi
The problem with that is how do we know that it wasn't
obtained simply by multiplying two large primes?

You have contrived to confuse yourself.
repunit 10^281-1, attributing a property incorrectly to
it. I never mentioned it until he did. I am not he.
Thereafter, I have provided a large factor of this
number, and can, if properly motivated, provide all

Post by quasi

Post by barker
14975722877914491717620426059118417580707929278605\
30935561591990419823492064154065403321443661895485\
51670508994053634039049939359298138323011269238802\
59832175429893886346932128104884153170949226474007\
3694039201

You have provided a COMPOSITE COFACTOR of 10^281-1
after dividing out some (perhaps all, I did not check) of
its KNOWN prime factors.
You are a lying troll.

Post by quasi

Post by barker

Post by quasi
Divide 10^281-1 by this number, and you will find
what I say is true. The other factor is relatively
small and easy to decompose.

I could not, therefore, have arrived at this 200+
digit number simply by coming up with two primes and
multiplying them!

No.  You took 10^281-1 and divided out some (perhaps all,
I did not check) of the known and published prime factors.
The remaining cofactor is composite.

Post by quasi
Damn it barker, why can't you just be a troll -- that would
make it so much easier.
I think it's clear you're not a troll (or at least
you have a non-troll side).
I apologize for calling you a troll.
Bravo for your partial factorization of (10^281 - 1)/9.

Damn it!   There are already 4 known and published factors
of 10^281-1.  The remaining COFACTOR is unfactored. It is
within reach of NFS, but we just haven't gotten to it yet.  
The community working on the Cunninghan project is busy
with other numbers.  It will be finished.
Before anyone accepts what this troll has been saying about
http://homes.cerias.purdue.edu/~ssw/cun/

281 (1)
563
.2597610354323
.380431988961690791
.133355295524380732608674846305692470329
.C210
The notation (1) indicates the index of an algebraic prime
factor; i.e. 10^281-1 is divisible by 10^1 - 1.
All this troll did was divide out some (or all) of these
known PRIME factors to produce a composite cofactor.

So barker fooled me again! Barker 3, quasi 0.

He has some ideas about digit patterns, possibly valid,
perhaps interesting, but so far he hasn't shown any
actually new factorizations.

As far as trolls go, he's a pretty sneaky one.

quasi

[Pubkeybreaker]

Post by quasi

Post by Pubkeybreaker

Post by quasi

Post by barker

Post by quasi

Post by barker
No.
It is the smallest one whose prime factors have not been
published. There is a difference...

These factorizations get published very quickly.  I know everyone
capable of factoring R281 and none of them have done it. It
REMAINS unfactored.

Post by quasi

Post by barker

Post by quasi
The problem with that is how do we know that it wasn't
obtained simply by multiplying two large primes?

You have contrived to confuse yourself.
repunit 10^281-1, attributing a property incorrectly to
it. I never mentioned it until he did. I am not he.
Thereafter, I have provided a large factor of this
number, and can, if properly motivated, provide all

Post by quasi

Post by barker
14975722877914491717620426059118417580707929278605\
30935561591990419823492064154065403321443661895485\
51670508994053634039049939359298138323011269238802\
59832175429893886346932128104884153170949226474007\
3694039201

You have provided a COMPOSITE COFACTOR of 10^281-1
after dividing out some (perhaps all, I did not check) of
its KNOWN prime factors.
You are a lying troll.

Post by quasi

Post by barker

Post by quasi
Divide 10^281-1 by this number, and you will find
what I say is true. The other factor is relatively
small and easy to decompose.

I could not, therefore, have arrived at this 200+
digit number simply by coming up with two primes and
multiplying them!

No.  You took 10^281-1 and divided out some (perhaps all,
I did not check) of the known and published prime factors.
The remaining cofactor is composite.

Post by quasi
Damn it barker, why can't you just be a troll -- that would
make it so much easier.
I think it's clear you're not a troll (or at least
you have a non-troll side).
I apologize for calling you a troll.
Bravo for your partial factorization of (10^281 - 1)/9.

Damn it!   There are already 4 known and published factors
of 10^281-1.  The remaining COFACTOR is unfactored. It is
within reach of NFS, but we just haven't gotten to it yet.
The community working on the Cunninghan project is busy
with other numbers.  It will be finished.
Before anyone accepts what this troll has been saying about
http://homes.cerias.purdue.edu/~ssw/cun/

281 (1)
563
.2597610354323
.380431988961690791
.133355295524380732608674846305692470329
.C210
The notation (1) indicates the index of an algebraic prime
factor; i.e. 10^281-1 is divisible by 10^1 - 1.
All this troll did was divide out some (or all) of these
known PRIME factors to produce a composite cofactor.

So barker fooled me again! Barker 3, quasi 0.
He has some ideas about digit patterns, possibly valid,
perhaps interesting, but so far he hasn't shown any
actually new factorizations.
As far as trolls go, he's a pretty sneaky one.
quasi- Hide quoted text -
- Show quoted text -

This business about "digit patterns" has some very limited legitimacy.
If one tries to put together a factoring algorithm based on "reversing
the
multiplication process" (which is what looking at digit patterns
amounts to),
one gets a legitimate way of factoring. The difficulty is that it
leads to
a set of simultaneous diophantine equations (in O(log N)) variables.
Solving
this problem is known (see Garey & Johnson) to be NP-Complete.

[quasi]

Post by Pubkeybreaker

Post by quasi

Post by Pubkeybreaker
All this troll did was divide out some (or all) of these
known PRIME factors to produce a composite cofactor.

So barker fooled me again! Barker 3, quasi 0.
He has some ideas about digit patterns, possibly valid,
perhaps interesting, but so far he hasn't shown any
actually new factorizations.
As far as trolls go, he's a pretty sneaky one.

This business about "digit patterns" has some very limited
legitimacy. If one tries to put together a factoring
algorithm based on "reversing the multiplication process"
(which is what looking at digit patterns amounts to), one
gets a legitimate way of factoring. The difficulty is that
it leads to a set of simultaneous diophantine equations
(in O(log N)) variables. Solving this problem is known (see
Garey & Johnson) to be NP-Complete.

Challenge to barker:

Produce a partial factorization of some composite repunit
(in a base of your choice) for which the factorization is
unpublished and for which it would be infeasible to obtain
that factorization current factoring algorithms.

Short of that, post a simple example (with much smaller
numbers) to illustrate how the anomalous digit patterns for
repunits (definitely an interesting phenomenon) can be used
to algorithmically factor some repunit.

quasi

[Pubkeybreaker]

Post by quasi

Post by Pubkeybreaker

Post by quasi

Post by Pubkeybreaker
All this troll did was divide out some (or all) of these
known PRIME factors to produce a composite cofactor.

So barker fooled me again! Barker 3, quasi 0.
He has some ideas about digit patterns, possibly valid,
perhaps interesting, but so far he hasn't shown any
actually new factorizations.
As far as trolls go, he's a pretty sneaky one.

This business about "digit patterns" has some very limited
legitimacy. If one tries to put together a factoring
algorithm based on "reversing the multiplication process"
(which is what looking at digit patterns amounts to), one
gets a legitimate way of factoring.  The difficulty is that
it leads to a set of simultaneous diophantine equations
(in O(log N)) variables. Solving this problem is known (see
Garey & Johnson) to be NP-Complete.

Produce a partial factorization of some composite repunit
(in a base of your choice) for which the factorization is
unpublished and for which it would be infeasible to obtain
that factorization current factoring algorithms.
Short of that, post a simple example (with much smaller
numbers) to illustrate how the anomalous digit patterns for
repunits (definitely an interesting phenomenon) can be used
to algorithmically factor some repunit.

I predict: He can't and won't. He is a fraud.

[Pubkeybreaker]

Post by Pubkeybreaker

Post by quasi

Post by Pubkeybreaker

Post by quasi

Post by Pubkeybreaker
All this troll did was divide out some (or all) of these
known PRIME factors to produce a composite cofactor.

So barker fooled me again! Barker 3, quasi 0.
He has some ideas about digit patterns, possibly valid,
perhaps interesting, but so far he hasn't shown any
actually new factorizations.
As far as trolls go, he's a pretty sneaky one.

This business about "digit patterns" has some very limited
legitimacy. If one tries to put together a factoring
algorithm based on "reversing the multiplication process"
(which is what looking at digit patterns amounts to), one
gets a legitimate way of factoring. The difficulty is that
it leads to a set of simultaneous diophantine equations
(in O(log N)) variables. Solving this problem is known (see
Garey & Johnson) to be NP-Complete.

Produce a partial factorization of some composite repunit
(in a base of your choice) for which the factorization is
unpublished and for which it would be infeasible to obtain
that factorization current factoring algorithms.
Short of that, post a simple example (with much smaller
numbers) to illustrate how the anomalous digit patterns for
repunits (definitely an interesting phenomenon) can be used
to algorithmically factor some repunit.

I predict: He can't and won't. He is a fraud.

Having written all that, I take it all back. I've had email
from barker, and he provided enough of one of the 107 digit
long factors of R281 for me to know he is legit. Judging by
where he sent the email from, he could work for the NSA, and
this explains a lot. When they factorize something, they
don't usually publish it.

While I can't be certain of this, he also seems to have found
a new result about digit patterns in prime factors of repunits.
Don't know about the near-prime factors, though.

Damnit: sorry. Just because I'm posting from Podunk, Mass., it
doesn't mean I have no manners or voted Hussein.

[quasi]

On Thu, 19 Apr 2012 04:43:01 +0200, Pubkeybreaker

Post by Pubkeybreaker

Post by Pubkeybreaker

Post by quasi

Post by Pubkeybreaker

Post by quasi

Post by Pubkeybreaker
All this troll did was divide out some (or all) of these
known PRIME factors to produce a composite cofactor.

So barker fooled me again! Barker 3, quasi 0.
He has some ideas about digit patterns, possibly valid,
perhaps interesting, but so far he hasn't shown any
actually new factorizations.
As far as trolls go, he's a pretty sneaky one.

This business about "digit patterns" has some very limited
legitimacy. If one tries to put together a factoring
algorithm based on "reversing the multiplication process"
(which is what looking at digit patterns amounts to), one
gets a legitimate way of factoring. The difficulty is that
it leads to a set of simultaneous diophantine equations
(in O(log N)) variables. Solving this problem is known (see
Garey & Johnson) to be NP-Complete.

Produce a partial factorization of some composite repunit
(in a base of your choice) for which the factorization is
unpublished and for which it would be infeasible to obtain
that factorization current factoring algorithms.
Short of that, post a simple example (with much smaller
numbers) to illustrate how the anomalous digit patterns for
repunits (definitely an interesting phenomenon) can be used
to algorithmically factor some repunit.

I predict: He can't and won't. He is a fraud.

Having written all that, I take it all back. I've had email
from barker, and he provided enough of one of the 107 digit
long factors of R281 for me to know he is legit. Judging by
where he sent the email from, he could work for the NSA, and
this explains a lot. When they factorize something, they
don't usually publish it.
While I can't be certain of this, he also seems to have found
a new result about digit patterns in prime factors of repunits.
Don't know about the near-prime factors, though.
Damnit: sorry. Just because I'm posting from Podunk, Mass., it
doesn't mean I have no manners or voted Hussein.

Of course, he did enter sci.math in full troll-mode with his
"nontrivial factorization" of a prime p as 1*p,

Also, when he posted a supposedly new factor of R281, it was
just R281 divided by previously published factors.

And he did ridicule many of his respondents, notably you.

So even if he's not a troll, he's at least part-troll.

I'll admit that the digit pattern anomalies he described are
intriguing, but he dodged my question as to how such patterns
could be used to factor numbers which out of range of other
known factorization methods.

If it's a search space speedup, then a speedup by what factor?
Perhaps the patterns are used in some other way, but then what
way? I asked for an example with small numbers to illustrate
the method, but so far, no response.

Also, if as you say, he works for NSA, then he has access to
immense computing power, so for all we know, his latest
R281 result was obtained by standard factoring algorithms
multiprocessed on a huge network of powerful computers.

And why did he respond privately to you rather than publicly
in sci.math? That effectively limits the pool of his critics.
What's up with that?

He's done enough sneaky things up to this point that I think,
to redeem himself, a private email to you followed by your
revision of judgement is not sufficient. He needs to come
clean publicly in sci.math. Let's see something concrete and
nontrivial -- not just vague hints showing the potential for
new results.

quasi

[Pubkeybreaker]

Post by quasi

Post by Pubkeybreaker

Post by quasi

Post by Pubkeybreaker
All this troll did was divide out some (or all) of these
known PRIME factors to produce a composite cofactor.

So barker fooled me again! Barker 3, quasi 0.
He has some ideas about digit patterns, possibly valid,
perhaps interesting, but so far he hasn't shown any
actually new factorizations.
As far as trolls go, he's a pretty sneaky one.

This business about "digit patterns" has some very limited
legitimacy. If one tries to put together a factoring
algorithm based on "reversing the multiplication process"
(which is what looking at digit patterns amounts to), one
gets a legitimate way of factoring. The difficulty is that
it leads to a set of simultaneous diophantine equations
(in O(log N)) variables. Solving this problem is known (see
Garey & Johnson) to be NP-Complete.

Produce a partial factorization of some composite repunit
(in a base of your choice) for which the factorization is
unpublished and for which it would be infeasible to obtain
that factorization current factoring algorithms.
Short of that, post a simple example (with much smaller
numbers) to illustrate how the anomalous digit patterns for
repunits (definitely an interesting phenomenon) can be used
to algorithmically factor some repunit.

I predict:   He can't and won't.  He is a fraud.

Having written all that, I take it all back.  I've had email
from barker, and he provided enough of one of the 107 digit
long factors of R281 for me to know he is legit. Judging by
where he sent the email from, he could work for the NSA, and
this explains a lot. When they factorize something, they
don't usually publish it.
While I can't be certain of this, he also seems to have found
a new result about digit patterns in prime factors of repunits.
Don't know about the near-prime factors, though.
Damnit:  sorry. Just because I'm posting from Podunk, Mass., it
doesn't mean I have no manners or voted Hussein.- Hide quoted text -
- Show quoted text -

The above post is a forgery. I did not write it.

[Pubkeybreaker]

Post by quasi

Post by Pubkeybreaker

Post by quasi

Post by Pubkeybreaker
All this troll did was divide out some (or all) of these
known PRIME factors to produce a composite cofactor.

So barker fooled me again! Barker 3, quasi 0.
He has some ideas about digit patterns, possibly valid,
perhaps interesting, but so far he hasn't shown any
actually new factorizations.
As far as trolls go, he's a pretty sneaky one.

This business about "digit patterns" has some very limited
legitimacy. If one tries to put together a factoring
algorithm based on "reversing the multiplication process"
(which is what looking at digit patterns amounts to), one
gets a legitimate way of factoring. The difficulty is that
it leads to a set of simultaneous diophantine equations
(in O(log N)) variables. Solving this problem is known (see
Garey & Johnson) to be NP-Complete.

Produce a partial factorization of some composite repunit
(in a base of your choice) for which the factorization is
unpublished and for which it would be infeasible to obtain
that factorization current factoring algorithms.
Short of that, post a simple example (with much smaller
numbers) to illustrate how the anomalous digit patterns for
repunits (definitely an interesting phenomenon) can be used
to algorithmically factor some repunit.

I predict:   He can't and won't.  He is a fraud.

Having written all that, I take it all back.  I've had email
from barker, and he provided enough of one of the 107 digit
long factors of R281 for me to know he is legit. Judging by
where he sent the email from, he could work for the NSA, and
this explains a lot. When they factorize something, they
don't usually publish it.
While I can't be certain of this, he also seems to have found
a new result about digit patterns in prime factors of repunits.
Don't know about the near-prime factors, though.
Damnit:  sorry. Just because I'm posting from Podunk, Mass., it
doesn't mean I have no manners or voted Hussein.- Hide quoted text -
- Show quoted text -

The above post is a forgery.  I did not write it.- Hide quoted text -
- Show quoted text -

Please note. Anyone who has read my posts over the years should
realize
that I do not write in the same style as the forgery.

I would never speculate in public about an employee of the NSA.
Indeed. Anyone who know how the NSA really operates should know
that they would not let an employee post spam the way Barker did,
nor would an NSA employee risk his/her career by posting spam under
a non-de-plume.

Furthermore, if barker had sent me a factorization, I would certainly
NOT keep the factors private.

And the last sentence in the forgery is totally out of character for
me.

I'm afraid, quasi, that you've been taken in, AGAIN.

[Jan Andres]

Post by Pubkeybreaker

Post by quasi

Post by Pubkeybreaker

Post by quasi

Post by Pubkeybreaker
All this troll did was divide out some (or all) of these
known PRIME factors to produce a composite cofactor.

So barker fooled me again! Barker 3, quasi 0.
He has some ideas about digit patterns, possibly valid,
perhaps interesting, but so far he hasn't shown any
actually new factorizations.
As far as trolls go, he's a pretty sneaky one.

This business about "digit patterns" has some very limited
legitimacy. If one tries to put together a factoring
algorithm based on "reversing the multiplication process"
(which is what looking at digit patterns amounts to), one
gets a legitimate way of factoring. The difficulty is that
it leads to a set of simultaneous diophantine equations
(in O(log N)) variables. Solving this problem is known (see
Garey & Johnson) to be NP-Complete.

Produce a partial factorization of some composite repunit
(in a base of your choice) for which the factorization is
unpublished and for which it would be infeasible to obtain
that factorization current factoring algorithms.
Short of that, post a simple example (with much smaller
numbers) to illustrate how the anomalous digit patterns for
repunits (definitely an interesting phenomenon) can be used
to algorithmically factor some repunit.

I predict:   He can't and won't.  He is a fraud.

Having written all that, I take it all back.  I've had email
from barker, and he provided enough of one of the 107 digit
long factors of R281 for me to know he is legit. Judging by
where he sent the email from, he could work for the NSA, and
this explains a lot. When they factorize something, they
don't usually publish it.
While I can't be certain of this, he also seems to have found
a new result about digit patterns in prime factors of repunits.
Don't know about the near-prime factors, though.
Damnit:  sorry. Just because I'm posting from Podunk, Mass., it
doesn't mean I have no manners or voted Hussein.- Hide quoted text -
- Show quoted text -

The above post is a forgery.  I did not write it.- Hide quoted text -
- Show quoted text -

Please note. Anyone who has read my posts over the years should
realize
that I do not write in the same style as the forgery.

That, plus the forgery is obvious by inspecting the posting's Path:
header. The forged posting has exactly the same (somewhat unusual) Path:
as barker's postings.

[Pubkeybreaker]

Post by quasi

Post by Pubkeybreaker

Post by quasi

Post by Pubkeybreaker
All this troll did was divide out some (or all) of these
known PRIME factors to produce a composite cofactor.

So barker fooled me again! Barker 3, quasi 0.
He has some ideas about digit patterns, possibly valid,
perhaps interesting, but so far he hasn't shown any
actually new factorizations.
As far as trolls go, he's a pretty sneaky one.

This business about "digit patterns" has some very limited
legitimacy. If one tries to put together a factoring
algorithm based on "reversing the multiplication process"
(which is what looking at digit patterns amounts to), one
gets a legitimate way of factoring. The difficulty is that
it leads to a set of simultaneous diophantine equations
(in O(log N)) variables. Solving this problem is known (see
Garey & Johnson) to be NP-Complete.

Produce a partial factorization of some composite repunit
(in a base of your choice) for which the factorization is
unpublished and for which it would be infeasible to obtain
that factorization current factoring algorithms.
Short of that, post a simple example (with much smaller
numbers) to illustrate how the anomalous digit patterns for
repunits (definitely an interesting phenomenon) can be used
to algorithmically factor some repunit.

I predict:   He can't and won't.  He is a fraud.

Having written all that, I take it all back.  I've had email
from barker, and he provided enough of one of the 107 digit
long factors of R281 for me to know he is legit. Judging by
where he sent the email from, he could work for the NSA, and
this explains a lot. When they factorize something, they
don't usually publish it.
While I can't be certain of this, he also seems to have found
a new result about digit patterns in prime factors of repunits.
Don't know about the near-prime factors, though.
Damnit:  sorry. Just because I'm posting from Podunk, Mass., it
doesn't mean I have no manners or voted Hussein.- Hide quoted text -
- Show quoted text -

The above post is a forgery.  I did not write it.- Hide quoted text -
- Show quoted text -

Please note.  Anyone who has read my posts over the years should
realize
that I do not write in the same style as the forgery.

as barker's postings.- Hide quoted text -
- Show quoted text -

The fact that 'barker' posted such a forgery says a lot about his lack
of character and lack of integrity.

[Tonico]

..................................................................

Post by Pubkeybreaker

Please note.  Anyone who has read my posts over the years should
realize
that I do not write in the same style as the forgery.

as barker's postings.-

The fact that 'barker' posted such a forgery says a lot about his lack
of character and lack of integrity.-

Wasn't this OBVIOUS since his first post, where he used his alter ego
Pertti's Ghost to praise him(self)??

I could write that I told ya, but instead I just will write that I did
tell you.

Tonio

[quasi]

Non-relevant news-groups trimmed.

On Thu, 19 Apr 2012 14:21:51 +0200, Pubkeybreaker

Post by Pubkeybreaker

Post by quasi

Post by Pubkeybreaker

Post by quasi

Post by Pubkeybreaker
All this troll did was divide out some (or all) of these
known PRIME factors to produce a composite cofactor.

So barker fooled me again! Barker 3, quasi 0.
He has some ideas about digit patterns, possibly valid,
perhaps interesting, but so far he hasn't shown any
actually new factorizations.
As far as trolls go, he's a pretty sneaky one.

This business about "digit patterns" has some very limited
legitimacy. If one tries to put together a factoring
algorithm based on "reversing the multiplication process"
(which is what looking at digit patterns amounts to), one
gets a legitimate way of factoring. The difficulty is that
it leads to a set of simultaneous diophantine equations
(in O(log N)) variables. Solving this problem is known (see
Garey & Johnson) to be NP-Complete.

Produce a partial factorization of some composite repunit
(in a base of your choice) for which the factorization is
unpublished and for which it would be infeasible to obtain
that factorization current factoring algorithms.
Short of that, post a simple example (with much smaller
numbers) to illustrate how the anomalous digit patterns for
repunits (definitely an interesting phenomenon) can be used
to algorithmically factor some repunit.

I predict: He can't and won't. He is a fraud.

Having written all that, I take it all back. I've had email
from barker, and he provided enough of one of the 107 digit
long factors of R281 for me to know he is legit. Judging by
where he sent the email from, he could work for the NSA, and
this explains a lot. When they factorize something, they
don't usually publish it.
While I can't be certain of this, he also seems to have found
a new result about digit patterns in prime factors of repunits.
Don't know about the near-prime factors, though.
Damnit: sorry. Just because I'm posting from Podunk, Mass., it
doesn't mean I have no manners or voted Hussein.- Hide quoted text -
- Show quoted text -

The above post is a forgery. I did not write it.- Hide quoted text -
- Show quoted text -

Please note. Anyone who has read my posts over the years should
realize that I do not write in the same style as the forgery.
I would never speculate in public about an employee of the NSA.
Indeed.

Indeed?

"blablabla!" Don't play innocent, Pubkeybreaker.

Explain then how the IP trackback of the post of yours to which I am
replying gives:
whois 74.104.192.30 >>> Lowell, Mass.
while the IP trackback of the "alleged" forger gives this:
whois 199.46.200.231 >>> Waltham, Mass. which is 20 mins from Lowell?

Much too much of a coincidence. But you _really_ had me fooled.

I think an explanation is in order, Pubkeybreaker. You've made enough
mischief here, I won't let you fool me yet again with your sneakiness.

quasi

[Pubkeybreaker]

Post by quasi
Non-relevant news-groups trimmed.
On Thu, 19 Apr 2012 14:21:51 +0200, Pubkeybreaker

Post by quasi

Post by Pubkeybreaker

Post by quasi

Post by Pubkeybreaker
All this troll did was divide out some (or all) of these
known PRIME factors to produce a composite cofactor.

So barker fooled me again! Barker 3, quasi 0.
He has some ideas about digit patterns, possibly valid,
perhaps interesting, but so far he hasn't shown any
actually new factorizations.
As far as trolls go, he's a pretty sneaky one.

This business about "digit patterns" has some very limited
legitimacy. If one tries to put together a factoring
algorithm based on "reversing the multiplication process"
(which is what looking at digit patterns amounts to), one
gets a legitimate way of factoring. The difficulty is that
it leads to a set of simultaneous diophantine equations
(in O(log N)) variables. Solving this problem is known (see
Garey & Johnson) to be NP-Complete.

Produce a partial factorization of some composite repunit
(in a base of your choice) for which the factorization is
unpublished and for which it would be infeasible to obtain
that factorization current factoring algorithms.
Short of that, post a simple example (with much smaller
numbers) to illustrate how the anomalous digit patterns for
repunits (definitely an interesting phenomenon) can be used
to algorithmically factor some repunit.

I predict: He can't and won't. He is a fraud.

Having written all that, I take it all back. I've had email
from barker, and he provided enough of one of the 107 digit
long factors of R281 for me to know he is legit. Judging by
where he sent the email from, he could work for the NSA, and
this explains a lot. When they factorize something, they
don't usually publish it.
While I can't be certain of this, he also seems to have found
a new result about digit patterns in prime factors of repunits.
Don't know about the near-prime factors, though.
Damnit: sorry. Just because I'm posting from Podunk, Mass., it
doesn't mean I have no manners or voted Hussein.- Hide quoted text -
- Show quoted text -

The above post is a forgery. I did not write it.- Hide quoted text -
- Show quoted text -

Please note.  Anyone who has read my posts over the years should
realize that I do not write in the same style as the forgery.
I would never speculate in public about an employee of the NSA.
Indeed.

Indeed?
"blablabla!" Don't play innocent, Pubkeybreaker.
Explain then how the IP trackback of the post of yours to which I am
    whois 74.104.192.30 >>> Lowell, Mass.
    whois 199.46.200.231 >>> Waltham, Mass. which is 20 mins from Lowell?
Much too much of a coincidence. But you _really_ had me fooled.
I think an explanation is in order, Pubkeybreaker. You've made enough
mischief here, I won't let you fool me yet again with your sneakiness.
quasi- Hide quoted text -
- Show quoted text -

Another forgery.

[quasi]

On Sat, 21 Apr 2012 20:54:50 -0700 (PDT), Pubkeybreaker

Post by Pubkeybreaker

Post by quasi
Non-relevant news-groups trimmed.
On Thu, 19 Apr 2012 14:21:51 +0200, Pubkeybreaker

Post by quasi

Post by Pubkeybreaker

Post by quasi

Post by Pubkeybreaker
All this troll did was divide out some (or all) of these
known PRIME factors to produce a composite cofactor.

So barker fooled me again! Barker 3, quasi 0.
He has some ideas about digit patterns, possibly valid,
perhaps interesting, but so far he hasn't shown any
actually new factorizations.
As far as trolls go, he's a pretty sneaky one.

This business about "digit patterns" has some very limited
legitimacy. If one tries to put together a factoring
algorithm based on "reversing the multiplication process"
(which is what looking at digit patterns amounts to), one
gets a legitimate way of factoring. The difficulty is that
it leads to a set of simultaneous diophantine equations
(in O(log N)) variables. Solving this problem is known (see
Garey & Johnson) to be NP-Complete.

Produce a partial factorization of some composite repunit
(in a base of your choice) for which the factorization is
unpublished and for which it would be infeasible to obtain
that factorization current factoring algorithms.
Short of that, post a simple example (with much smaller
numbers) to illustrate how the anomalous digit patterns for
repunits (definitely an interesting phenomenon) can be used
to algorithmically factor some repunit.

I predict: He can't and won't. He is a fraud.

Having written all that, I take it all back. I've had email
from barker, and he provided enough of one of the 107 digit
long factors of R281 for me to know he is legit. Judging by
where he sent the email from, he could work for the NSA, and
this explains a lot. When they factorize something, they
don't usually publish it.
While I can't be certain of this, he also seems to have found
a new result about digit patterns in prime factors of repunits.
Don't know about the near-prime factors, though.
Damnit: sorry. Just because I'm posting from Podunk, Mass., it
doesn't mean I have no manners or voted Hussein.- Hide quoted text -
- Show quoted text -

The above post is a forgery. I did not write it.

Please note.  Anyone who has read my posts over the years should
realize that I do not write in the same style as the forgery.
I would never speculate in public about an employee of the NSA.
Indeed.

Indeed?
"blablabla!" Don't play innocent, Pubkeybreaker.
Explain then how the IP trackback of the post of yours to which I am
    whois 74.104.192.30 >>> Lowell, Mass.
    whois 199.46.200.231 >>> Waltham, Mass. which is 20 mins from Lowell?
Much too much of a coincidence. But you _really_ had me fooled.
I think an explanation is in order, Pubkeybreaker. You've made enough
mischief here, I won't let you fool me yet again with your sneakiness.

Another forgery.

Yep.

quasi

[Nomen Nescio]

Post by quasi
Explain then how the IP trackback of the post of yours to which I am
whois 74.104.192.30 >>> Lowell, Mass.
whois 199.46.200.231 >>> Waltham, Mass. which is 20 mins from Lowell?

Yes, the stubborn fact remains that the forger and the (alleged) victim
are
posting from a few miles apart. The story is all in the email/post
headers.
All cites are from this usenet thread.

This is from the (alleged) forgery:

From: Pubkeybreaker <***@aol.com>
Date: Wed, 18 Apr 2012 21:43:01 -0500 (ET)
NNTP-Posting-Host: 199.46.200.231
Cite: "Having written all that, I take it all back."

This is from the (alleged) protest at the above forgery:

From: Pubkeybreaker <***@aol.com>
Date: Thu, 19 Apr 2012 04:47:49 -0500 (ET)
NNTP-Posting-Host: 74.104.192.30
Cite: "The above post is a forgery. I did not write it."

From further (alleged) proof that the (alleged) forgery was a forgery:

From: Pubkeybreaker <***@aol.com>
Date: Thu, 19 Apr 2012 06:22:31 -0500 (ET)
NNTP-Posting-Host: 199.46.198.232
Cite: "Anyone who has read my posts over the years should realize that I
do not write in the same style as the forgery."

Forgive me for being skeptical, Pubkeybreaker, but since WHOIS informs us
that the IP address of an (alleged) forger and two of "your" IP addresses
lie approximately at the vertices of an isosceles triangle, shorter side
about 10 miles and longer sides about 20 miles, and this (alleged) forger
is located at one end of the shorter side, Occam's Razor tells us either
you have pissed off someone (at the _S_?) who is playing with you, or
you have been hacked, or
you and the forger are connected, maybe at the hip.

Discuss. :/

I am more interested in whether certain patterns within the prime or near
prime factors of repunits are more likely than others, but since that is
not on the agenda, discussing why you may be lying will serve in its
place.

[Pubkeybreaker]

On Apr 15, 10:43 pm, barker

Post by barker
attributing a property incorrectly to it.

You are not only a troll, you are an outright LIAR. I said that
10^281-1 was the smallest number of the form 10^n-1 that had not been
FULLY factored. That was and is a correct statement.

[Frederick Williams]

Post by barker
Rule 1: Always stop at the first error or anomaly.

Go on then.