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-   -   New conjecture about Mersenne primes (https://www.mersenneforum.org/showthread.php?t=24018)

tetramur 2019-01-20 15:47

New conjecture about Mersenne primes
 
William Bouris claimed in his mad proofs, that:
"if p= 4*k+1, and q= 2*p+3 are both prime, then if [(M_r)^p-p] mod q == N, and q mod N == +/-1, then (M_r), the base, is prime. also, if (M_r) mod p = 1, then choose a different 'p' or if N is a square, then (M_r) is prime."
The source site has been broken about four months ago. How could this claim be proven/disproven?

tetramur 2019-01-20 17:12

[QUOTE=tetramur;506481]William Bouris claimed in his mad proofs, that:
"if p= 4*k+1, and q= 2*p+3 are both prime, then if [(M_r)^p-p] mod q == N, and q mod N == +/-1, then (M_r), the base, is prime. also, if (M_r) mod p = 1, then choose a different 'p' or if N is a square, then (M_r) is prime."
The source site has been broken about four months ago. How could this claim be proven/disproven?[/QUOTE]
Easy - disproven.
Counterexample:
Take r = 1279 (prime), p = 557, q = 1117.
((M_1279)^557-557) mod 1117 = 713
1117 mod 713 = 404, not +/-1
713 is not square
M_1279 mod 557 = 269


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