Mersenne numbers

Downloadable files related to Mersenne numbers

Wagstaff numbers

Downloadable files related to Wagstaff numbers

Repunits (base 10)

Downloadable files related to repunits

Other

The “new Mersenne conjecture”

Fun fact

For the 50 odd exponents p of the 51 known Mersenne primes, there is a marked prevalence of p=1 (mod 4) versus p=3 (mod 4).

More specifically, a two-to-one prevalence of p=1 (mod 8) over each of the other three values.

p (mod 4) = 13
3119
p (mod 8) = 1357
19 91210

But for the exponents p of the 43 known Wagstaff primes, there is a marked prevalence of p=3 (mod 4) versus p=1 (mod 4).

More specifically, a two-to-one prevalence of p=7 (mod 8) over each of the other three values.

p (mod 4) = 13
1528
p (mod 8) = 1357
 810 718

Hmmm.