Lenstra-Pomerance-Wagstaff conjecture

Encyclopedia : L : LE : LEN : Lenstra-Pomerance-Wagstaff conjecture

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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-1],

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

[e^\gamma\cdot\log_2(x)],

where γ is the Euler-Mascheroni constant.

See also

• New Mersenne conjecture

 

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