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 2018-12-16, 20:12 #53 GP2     Sep 2003 3×863 Posts Not including M51, here's a histogram of the final hexadecimal digit of the exponents of Mersenne primes: Code:  # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # 2 1 3 5 7 9 B D F We can see that the prevalence of 1 (mod 4) vs. 3 (mod 4) is really a two-to-one prevalence of 1 (mod 8) vs. the other three: (We include M51 here since its exponent has already been revealed to be 5 (mod 8) ) Code: 1 19 3 9 5 11 12 7 10 2 1 Similarly, a histogram of the final hexadecimal digit of the exponents of Wagstaff primes: Code:  # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # 1 3 5 7 9 B D F We can see that the prevalence of 3 (mod 4) vs. 1 (mod 4) is really a two-to-one prevalence of 7 (mod 8) vs. the other three: Code: 1 8 3 10 5 7 7 18 Last fiddled with by GP2 on 2018-12-16 at 20:35 Reason: "prevalence" instead of "preference"