barker
2012-04-12 07:24:50 UTC
Following the miserable failure of the regulars of SCI.MATH and junior
groups
to solve my first problem, I provide a new one. This time, there is no
trick,
no reliance on your poor reading powers, only on your poor math powers.
ALL numbers referred to here must be positive integers, expressed in
base-10.
Consider the two primes:
113136621886721
and
617431748093238554410874808506989442264783116181403206744221352101186333
Multiply these together to give Y. I will even give Y to you explicitly:
698541422248819000939556056942681614546383342970851314130956479402221733
63516839384093
Examine it closely.
Now comes the problem.
-------------------
Find X, a prime, such that a "simple" function of X and Y equals a very
"beautifully patterned" number Z.
-------------------
Of course, after the failure of SCI.MATH (exception: Perrti's Ghost)
to solve my first problem, you can be wary of what I mean by "simple"
and by "beautifully patterned".
A "simple" function of X and Y is one that can be written, using
exactly one of the 5 ordinary mathematical symbols +,-,*,/,^, as
as well as X and Y, and nothing else.
So X^Y is a "simple function" of X and Y.
But
X-Y is a "simple function" of X and Y if and only if X>Y, as its value
must be a positive integer (see the note at the start of the problem).
X+2 is not, as there is no dependence on Y, and there is a "2".
So I think "simple" function is well-defined here. There are only 10
of them as specified, and 2 are duplicates due to commutativity.
"Beautifully patterned" must remain subjective. But there is no trick.
For Z to be beautifully patterned it must display some pattern, form or
symmetry that would make the non-mathematician observer very confident
that a number of that magnitude was not arrived at just by chance. So
13271409540204145128 is not "beautifully patterned", as written in base
10 as it is, there is nothing which distinguishes it to the layperson
but
34567890122109876543 probably is
and
3005003005003005003005003 definitely is
but
0 is not because 0 is not a positive integer
but
just 1 might be.
Of course, no "simple" function of X and Y can give 1; remember that
X must be prime, so setting X=Y+1 and the function as X-Y would not work.
Do not be concerned this is tricky, "my" Z is very beautifully patterned
and large and it will take your breath away. It is much more striking
than any of the examples given above or below.
Note if X did not have itself to be prime, this would be trivial. For
example, we could just take the beautifully patterned:
770077007700770077007700770077007700770077007700770077007700770077007700
77007700770077
(that is going to serve as Z) and subtract from it Y i.e.
698541422248819000939556056942681614546383342970851314130956479402221733
63516839384093
to give X, so then the simple function X+Y would give the beautifully
patterned number. But X is non-prime here, so it is not the solution.
Again, here is the problem:
Y= 698541422248819000939556056942681614546383342970851314130956479402221
73363516839384093
-------------------
Find X, a prime, such that a "simple" function of X and Y gives a very
"beautifully patterned" number Z.
-------------------
The trick is examining the two original primes which were multiplied to
give Y, and to see their structural pattern, and use induction and your
intuition. Fools with or without powerful programs will make no progress
here. Of course, examining Y as well is necessary.
I will provide a solution (no suggestion it is unique) in due course. I
do already have it, and it illustrates a subtle number theory principle.
Thank you,
"barker" (associate of the late falsified Dr Pertti Lounesto)
groups
to solve my first problem, I provide a new one. This time, there is no
trick,
no reliance on your poor reading powers, only on your poor math powers.
ALL numbers referred to here must be positive integers, expressed in
base-10.
Consider the two primes:
113136621886721
and
617431748093238554410874808506989442264783116181403206744221352101186333
Multiply these together to give Y. I will even give Y to you explicitly:
698541422248819000939556056942681614546383342970851314130956479402221733
63516839384093
Examine it closely.
Now comes the problem.
-------------------
Find X, a prime, such that a "simple" function of X and Y equals a very
"beautifully patterned" number Z.
-------------------
Of course, after the failure of SCI.MATH (exception: Perrti's Ghost)
to solve my first problem, you can be wary of what I mean by "simple"
and by "beautifully patterned".
A "simple" function of X and Y is one that can be written, using
exactly one of the 5 ordinary mathematical symbols +,-,*,/,^, as
as well as X and Y, and nothing else.
So X^Y is a "simple function" of X and Y.
But
X-Y is a "simple function" of X and Y if and only if X>Y, as its value
must be a positive integer (see the note at the start of the problem).
X+2 is not, as there is no dependence on Y, and there is a "2".
So I think "simple" function is well-defined here. There are only 10
of them as specified, and 2 are duplicates due to commutativity.
"Beautifully patterned" must remain subjective. But there is no trick.
For Z to be beautifully patterned it must display some pattern, form or
symmetry that would make the non-mathematician observer very confident
that a number of that magnitude was not arrived at just by chance. So
13271409540204145128 is not "beautifully patterned", as written in base
10 as it is, there is nothing which distinguishes it to the layperson
but
34567890122109876543 probably is
and
3005003005003005003005003 definitely is
but
0 is not because 0 is not a positive integer
but
just 1 might be.
Of course, no "simple" function of X and Y can give 1; remember that
X must be prime, so setting X=Y+1 and the function as X-Y would not work.
Do not be concerned this is tricky, "my" Z is very beautifully patterned
and large and it will take your breath away. It is much more striking
than any of the examples given above or below.
Note if X did not have itself to be prime, this would be trivial. For
example, we could just take the beautifully patterned:
770077007700770077007700770077007700770077007700770077007700770077007700
77007700770077
(that is going to serve as Z) and subtract from it Y i.e.
698541422248819000939556056942681614546383342970851314130956479402221733
63516839384093
to give X, so then the simple function X+Y would give the beautifully
patterned number. But X is non-prime here, so it is not the solution.
Again, here is the problem:
Y= 698541422248819000939556056942681614546383342970851314130956479402221
73363516839384093
-------------------
Find X, a prime, such that a "simple" function of X and Y gives a very
"beautifully patterned" number Z.
-------------------
The trick is examining the two original primes which were multiplied to
give Y, and to see their structural pattern, and use induction and your
intuition. Fools with or without powerful programs will make no progress
here. Of course, examining Y as well is necessary.
I will provide a solution (no suggestion it is unique) in due course. I
do already have it, and it illustrates a subtle number theory principle.
Thank you,
"barker" (associate of the late falsified Dr Pertti Lounesto)