Summer is over. Can't believe I haven't posted anything on math for three months. So here it is ...
Further to my previous post on Mersenne primes, here is another neat fact about these special prime numbers. All Mersenne primes M, except for the first one, are congruent to 7 modulo 24. In other words, they can be written in the form M = 24N + 7 for some integer N. For example,
M3 = 7 = 24 x 0 + 7
M5 = 31 = 24 x 1 + 7
M7 = 127 = 24 x 5 + 7
M13 = 8191 = 24 x 341 + 7
