20120919, 20:09  #1 
"Åke Tilander"
Apr 2011
Sandviken, Sweden
1000110110_{2} Posts 
Are there infinitely many double Mersenne primes?
If Lenstra–Pomerance–Wagstaffs conjecture that there are infinitely many Mersenne primes is true, does this imply as well that there are infinitely many double Mersenne primes?
If so is it possible to estimate the density of them? 
20120919, 22:24  #2 
Aug 2006
3·5^{2}·79 Posts 
Just the opposite! The LenstraPomeranceWagstaff heuristic suggests that there are only finitely many double Mersenne primes. In particular, it says that with high probability we've discovered them all. (Does anyone want to crunch this number?)

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