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Lenstra-Pomerance-Wagstaff conjecture

In number theory, Lenstra , Pomerance , and Wagstaff have conjectured that not only are there an infinite number of Mersenne primes, meaning prime numbers of the form

2p − 1,

but that the number of Mersenne primes with exponent p less than x is asymptotically approximated by

eγlog2(x),

where γ is the Euler-Mascheroni constant.

See also: New Mersenne conjecture.

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03-10-2013 05:06:04
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