Yet, this is still a divisibility sequence, the terms can be prime only if the number of 1 in the sequence is prime, that is, only if the n is prime. The proof is very simple, and similar to the "binary proof" for mersenne numbers: if the number of 1 in the sequence is not prime, then split them in equal strings and you just factored your number. For example, N=(10^151)/9=111 111 111 111 111=111*(1001001001001)=11111 11111 11111=11111*(10000100001), and you have already (at least) two different ways to factor N, without any calculus.
So, for such a number to be prime, n must be prime.
Last fiddled with by LaurV on 20180104 at 03:30
