I was bored at my lunch hour today and was wondering 
whether anyone had investigated the extent of Mersenne 
primes also being the exponents to other Mersenne 
primes.  Sitting down and looking at it, it looks as 
though the 3rd Mersenne prime is M(5) which in expanded 
form is 31 which happens to be the 8th Mersenne prime.  
M(31) is also the first Mersenne prime not to be tested 
as an exponent in a Mersenne prime as it is 10 digits 
or over 2 billion, well beyond the current 16mil or 
even 33mil exponents being tested.

Just thought it was interesting that M(5) is also the 
exponent to M(31).



Cheers,

Thomas A. Mullen
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