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

2^{p</sub> − 1,}

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

<math>e^\gamma \log_2(x)<math>,

where γ is the Euler-Mascheroni constant.

See also: New Mersenne conjecture.