New Mersenne Conjecture

1. p = 2^k ± 1 or p = 4^k ± 3 for some k.
2. 2^p − 1 is prime (a Mersenne prime).
3. (2^p + 1) / 3 is prime (a Wagstaff prime).

References

• P. T. Bateman, J. L. Selfridge and Wagstaff, Jr., Samuel S., The new Mersenne conjecture, Amer. Math. Monthly, 96 (1989) 125-128

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