no Pi I'm working on about Mersenne numbers.

[QUOTE=3.14159;234193]I have a challenge for you all;

k * n! + 1 = p[sup]2[/sup], where p is a prime integer, and where k ≤ n!

Ex: 5 * 8! + 1 = 449[sup]2[/sup][/QUOTE]

I find none with 8 < n < 10,000. I don't expect that any exist with larger n; the heuristic probability of finding one is less than 10^-17825.

[QUOTE=CRGreathouse;234282]I find none with 8 < n < 10,000. I don't expect that any exist with larger n; the heuristic probability of finding one is less than 10^-17825.[/QUOTE]

:orly owl: How did you arrive at those figures?

[QUOTE=3.14159;234285]How did you arrive at those figures?[/QUOTE]

For n <= 1e4: direct search; for n > 1e4: numerical integration.

The same technique suggests about 4.9 below 1e4, which is a pretty good estimate (there are 6).

What are the odds of a 210-digit odd number being a p105 * p105?

I'm guessing from 0.001% to 0.1%.

[QUOTE=3.14159;234294]What are the odds of a 210-digit odd number being a p105 * p105?[/QUOTE]

An easy upper bound is 0.00155%. A closer analysis gets 0.00127419%, though my calculations on the latter assume the Riemann hypothesis.

[QUOTE=CRGreathouse;234297]An easy upper bound is 0.00155%. A closer analysis gets 0.00127419%, though my calculations on the latter assume the Riemann hypothesis.[/QUOTE]

There's those unproven conjectures again..

[QUOTE=3.14159;234298]There's those unproven conjectures again..[/QUOTE]

Thus my first answer, which does not assume it. I could have given a better unconditional answer, but that would be too much work.

[URL="http://4.bp.blogspot.com/_rvR3ouziO8g/TMTL4iDv-uI/AAAAAAAAAuA/NPWgKtjtflE/s1600/rep.PNG"]ep[/URL]

the right mathematics can not cheat

[QUOTE=CRGreathouse;234299]Thus my first answer, which does not assume it. I could have given a better unconditional answer, but that would be too much work.[/QUOTE]

Hopefully it would be accurate..

[QUOTE=cmd;234301][URL="http://4.bp.blogspot.com/_rvR3ouziO8g/TMTL4iDv-uI/AAAAAAAAAuA/NPWgKtjtflE/s1600/rep.PNG"]ep[/URL][/QUOTE]

Hey, can you try spamming another thread, bozo?