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 [InfinitudeofEvenPerfectNumbers]
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