NODE a0f3bd9eRe: (n!+1)^(1/2)
collins@newton.apple.com (Scott Collins)Mon, 11 Apr 94 12:21:30 PDT
>For any number n, if the square root of (n!)+1 is an integer, it is also
>prime. (This is interesting, but rather useless in practice)
For any number a, 1<a<=n, n! mod a == 0; therefore, n!+1 mod a == 1. n!+1
is prime. Prime numbers don't have integral square roots.
Scott Collins | "That's not fair!" -- Sarah
| "You say that so often. I wonder what your basis
408.862.0540 | for comparison is." -- Goblin King
................|....................................................
BUSINESS. fax:974.6094 R254(IL5-2N) collins@newton.apple.com
Apple Computer, Inc. 5 Infinite Loop, MS 305-2D Cupertino, CA 95014
.....................................................................
PERSONAL. 408.257.1746 1024:669687 catalyst@netcom.com
NODE 811ee15aRe: (n!+1)^(1/2)
kafka@desert.hacktic.nl (-=[ Patrick Oonk ]=-)Fri, 15 Apr 94 16:19:49 PDT
collins@newton.apple.com (Scott Collins) once said:
CO> >For any number n, if the square root of (n!)+1 is an integer, it is also
CO> >prime. (This is interesting, but rather useless in practice)
CO>
CO> For any number a, 1<a<=n, n! mod a == 0; therefore, n!+1 mod a == 1. n!+1
CO> is prime. Prime numbers don't have integral square roots.
CO>
CO>
CO> Scott Collins | "That's not fair!" -- Sarah
CO> | "You say that so often. I wonder what your basis
CO> 408.862.0540 | for comparison is." -- Goblin King
CO> ................|....................................................
CO> BUSINESS. fax:974.6094 R254(IL5-2N) collins@newton.apple.com
CO> Apple Computer, Inc. 5 Infinite Loop, MS 305-2D Cupertino, CA 95014
CO> .....................................................................
CO> PERSONAL. 408.257.1746 1024:669687 catalyst@netcom.com
CO>
CO>
---
"In a Time/CNN poll of 1,000 Americans conducted last week by Yankelovich
Partners, two-thirds said it was more important to protect the privacy of
phone calls than to preserve the ability of police to conduct wiretaps.
When informed about the Clipper Chip, 80% said they opposed it."
- Philip Elmer-Dewitt, "Who Should Keep the Keys", TIME, Mar. 4 1994
== To get PGP, FTP /pub/unix/security/crypt/pgp23A.zip from ftp.funet.fi ==
NODE d906c7c0Re: (n!+1)^(1/2)
Matthew J Ghio <mg5n+@andrew.cmu.edu>Mon, 11 Apr 94 13:16:59 PDT
collins@newton.apple.com (Scott Collins):
> >For any number n, if the square root of (n!)+1 is an integer, it is also
> >prime. (This is interesting, but rather useless in practice)
>
>For any number a, 1<a<=n, n! mod a == 0; therefore, n!+1 mod a == 1.
>n!+1 is prime. Prime numbers don't have integral square roots.
Well, it was quoted from memory, so it's possible that I made an error,
but it seems to work as stated...
For example :
(4!+1)^(1/2)=5
(5!+1)^(1/2)=11
(7!+1)^(1/2)=71
I can't find a value which produces a result that is a non-prime
integer. (Of course that doesn't prove that there isn't one.)