Factorization in reverse

[barker]

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 four primes or
nearly-primes as to what identifies them as being likely repunit factors.

Guidance 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)

[Pubkeybreaker]

On Apr 14, 4:51 pm, barker

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

Idiot. The only "problem" here is one of table lookup.

Post by barker
113136621886721
and
617431748093238554410874808506989442264783116181403206744221352101186333
which when multiplied yield
698541422248819000939556056942681614546383342970851314130956479402221733
63516839384093
What prime, when multiplied by this last number, will yield a repunit?

if one greps the factor database maintained by the Mersenne forum or
one greps the Cunningham tables, the answer becomes IMMEDIATELY
available.

There is nothing to "solve"

[Pubkeybreaker]

Post by Pubkeybreaker
On Apr 14, 4:51 pm, barker

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

Idiot.  The only "problem" here is one of table lookup.

Post by barker
113136621886721
and
617431748093238554410874808506989442264783116181403206744221352101186333
which when multiplied yield
698541422248819000939556056942681614546383342970851314130956479402221733
63516839384093
What prime, when multiplied by this last number, will yield a repunit?

if one greps the factor database maintained by the Mersenne forum or
one greps the Cunningham tables, the answer becomes IMMEDIATELY
available.
There is nothing to "solve"

In fact, all one needs to do is Google for the second prime.