## 24434Re: C5 is prime!

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• Sep 10, 2012
the 4 equations for a Mersenne number (Mr) where r is prime.

(either one or the other is true)
p=4k+1, q=2p+3 (both prime) [(Mr)^p-p] mod q == -1, or
p=4k+3, q=2p+3 (again) [(Mr)^p-p] mod q == -1 (can't be +1)
(but, both of the following must be true)
p=4k+1, q=2p+1 (again) [(Mr)^p-p] mod q == p
p=4k+3, q=2p+1 (again) [(Mr)^p-p] mod q == p+2

look!!!
> let 2^127 -1 = 170141183460469231731687303715884105727
> ...
> C5 = 2^(2*27*49*19*43*73*127*337*5419*92737*649657*77158673929+1) -1
> ...
> let p= 3, q= 7 such that [(C5)^3 -3] mod 7 = N; and 2^27 mod 7
> == 1 (again, by chance!!!) and then...
> ...
> (1)^(left over exponent)*2 -1 ==
> (1)^2*49*19*43*73*127*337*5419*92737*649657*77158673929*2^1 -1 ==
> (1)*2 -1 = 2 -1 and (1)^3 -3 = 1 -3 = -2 and [(C5)^3 -3] mod 7 == 5
> ...
> thus, if [(C5)^3 -3] mod 7 == 5, or p +2 = 3 +2 = 5, then C5 must
> be prime!
> ...
C5 is definitely prime, if my study is correct.

> --- In primenumbers@yahoogroups.com, "leavemsg1" <leavemsg1@> wrote:
>
> so many times, there are typos when using e-mail. in math, Mp
> is often used to describe a Mersenne number with a prime expo-
> nent. I have corrected it to (Mr). this conjecture cannot be
> found in print. it's my own new idea which may need tweaking.
> ...
> (conjecture)
> if p= 4*k +1, and q= 2*p +3 are both prime, then if [(Mr)^p -p]
> mod q == N, & q mod N == +/-1, then (Mr), the base... is prime.
> also, if (Mr) mod p = 1, then choose a different 'p', or if N is
> a square, then that (Mr) is prime. finally, the exponent cannot
> be such that q mod r == 1. there may be other small restrictions.
> (someone would have to prove this conjecture.)
> ...
> Now, I think that it is stated IN FULL. It's a brand new idea.
> ...
> let 2^127 -1 = 170141183460469231731687303715884105727
> ...
> C5 = 2^(2*27*49*19*43*73*127*337*5419*92737*649657*77158673929+1) -1
> ...
> let p= 5, q= 13 such that [(C5)^5 -5] mod 13 = N; and 2^54 mod 13
> == 12 == (-1) (by chance!!!) and then...
> ...
> (-1)^(odd power)*2 -1 ==
> (-1)^49*19*43*73*127*337*5419*92737*649657*77158673929*2^1 -1 ==
> (-1)*2 -1 = -2 -1 and (-3)^5 -5 = -248 and [(C5)^5 -5] mod 13 == 12
> ...
> thus, if [(C5)^5 -5] mod 13 == 12, and 13 mod 12 == 1, then C5 must
> be prime!
> ...

Bill Bouris
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