20190120, 15:47  #1 
"unknown"
Jan 2019
anywhere
17_{10} Posts 
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)^pp] 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? 
20190120, 17:12  #2  
"unknown"
Jan 2019
anywhere
17 Posts 
Quote:
Counterexample: Take r = 1279 (prime), p = 557, q = 1117. ((M_1279)^557557) mod 1117 = 713 1117 mod 713 = 404, not +/1 713 is not square M_1279 mod 557 = 269 Last fiddled with by tetramur on 20190120 at 17:13 

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