Fermat Numbers and Elite Primes

Fn+1 = (Fn − 1) + 1, n ≥ 0 and are pairwise coprime. It is conjectured that Fn are always square-free and that, beyond F4, they are never prime. The latter would imply that there are exactly 31 regular polygons with an odd number Gm of sides that can be constructed by straightedge and compass [2]. The values G1, G2, . . ., G31 encompass all divisors of 232−1 except unity [3]. Let G0 = 1. If we scan each row of Pascal’s triangle modulo 2 as a binary integer, then the numbers Gm (listed in ascending order) are naturally extended without bound. The reciprocal sum [4]