A077586 - OEIS (original) (raw)

First four terms are primes. Fifth (1.61585...*10^616), sixth (5.45374...*10^2465), seventh (2.007...*10^39456) and eighth (1.298...*10^157826) are not primes.

Note that a(n) divides 2^a(n)-2 for every n, so if a(n) is composite then a(n) is a Fermat pseudoprime to base 2; cf. A007013. - Thomas Ordowski, Apr 08 2016

A number MM(p) is prime iff M(p) = A000225(p) = 2^p-1 is a Mersenne prime exponent (A000043), which isn't possible unless p itself is also in A000043. Primes of this form are called double Mersenne primes MM(p). For all Mersenne exponents between 7 and 61, factors of MM(p) are known. The next candidate MM(61) is far too large to be merely stored on any existing hard drive (it would require 3*10^17 bytes), but a distributed search for factors of this and other MM(p) is ongoing, see the doublemersenne.org web site. - M. F. Hasler, Mar 05 2020