## idea for finding great mersenne primes

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• One year ago i had a found that 2^p-1 is prime when (x^(2^p-2)/p)=2^z mod 2^p-1. For all x, spezial x 2^k Example.p=17 2^17-1 is prime, because 19^7710=2^12
Message 1 of 1 , Dec 31, 2001
One year ago i had a found that 2^p-1
is prime when (x^(2^p-2)/p)=2^z mod 2^p-1.
For all x, spezial x<>2^k
Example.p=17 2^17-1 is prime, because 19^7710=2^12
mod 2^17-1. The result is ever a power of 2,when 2^p-1
a prime.

When we find a number x und small exponent y
and ABS(x^y-(2^p-1))=2^m Then can we easy check
x^((2^p-2)/p)=2^m mod 2^p-1

The smallest example is.
prime 2^7-1.
We take x=5 and y=3 , we get ABS(5^3-(2^7-1))=2
-> 5^18=2^m mod (2^7-1), 5^3=-2 mod 2^7-1
-> (-2)^6 is a power of 2 mod 2^7-1.
(
The smallest example is 2^5-1
We test 3^6=14 mod 31. 3^3=-4 mod 31. (-4)^2=16 mod 31
)

This examples very rare, but when we find easy another
example x^y-(2^p-1)=2^k then we have found a new
mersenne prime 2^p-1

best

Norman

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