 Dickson 1919) that the numbers formula_1 were prime for "n" = 2, 3, 5, 7, 13, 17, 19, 31, 67, 127 and 257, and were composite for all other positive integers "n" ≤ 257.Due to the size of these numbers, Mersenne did not and could not test all of them, nor could his peers in the 17th century.It was eventually determined, after three centuries and the availability of new techniques such as the Lucas–Lehmer test, that Mersenne's conjecture contained five errors, namely two are composite ("n" = 67, 257) and three omitted primes ("n" = 61, 89, 107).