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Old 2019-06-25, 20:13   #1
sweety439
 
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Nov 2016
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Default Double Wagstaff prime?

If M(p) = 2^p-1, then M(M(p)) is called double Mersenne number, and if this number is prime, then it is called double Mersenne prime, M(M(p)) is prime for p = 2, 3, 5 and 7, but not for all 11<=p<=59, and the status is unknown for p=61. Now, we consider the Wagstaff number W(p) = (2^p+1)/3 for odd prime p, then W(W(p)) is called double Wagstaff number , and if this number is prime, then it is called double Wagstaff prime, it is known that W(W(p)) is prime for p = 3, 5 and 7, but not for all 11<=p<=29 (the p=23 case is divisible by 129469791307, see factordb), but how about p=31 or above? Are there any double Wagstaff primes > W(W(7))? (related to the conjecture that there are no double Mersenne primes > M(M(7)))
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