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The new Mersenne conjecture. (English) Zbl 0694.10005
Some suggestions are made about the errors and omissions in Mersenne’s statement about Mersenne primes, and the following conjecture is made. If two of the following statements are true then the third is also true: (a) \(p=2^ k\pm 1\) or \(p=4^ k\pm 3\), (b) \(M_ p\) is prime, (c) \((2^ p+1)/3\) is prime. The conjecture has been verified for \(p<100 000\) and for some larger values of p, and it is also supported by an heuristic argument.
Reviewer: H.J.Godwin

11A41 Primes
11B39 Fibonacci and Lucas numbers and polynomials and generalizations
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