prime-onlyseries

Prime-only Series

Series of only primes:

2, 3, 7, 127, M127, MM127, MMM127, ... are all prime.

Proof:

1) Show inf. no. of primes, p [Euclid]

2) Show inf. no. mersenne primes, Mp [Infinitude of Even Perfect Numbers - NB typo line 5 '<' should read '<=']

3) Induce to show inf. no. multiple-mersenne primes, .....MMp

4) Apply probabilistic argument to deduce p=2

5) Use Mp prime => p prime to show ALL .....MMM2 prime