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Old 2018-12-16, 20:12   #53
GP2
 
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Sep 2003

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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"
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