What always fascinated me about this sequence was the huge (multiplicative) gap between the exponents: 2^127 - 1 and 2^521 - 1.
If that property continued after 2^20,996,011 - 1 the next one would be around 2^86,133,241-1 which is bigger than the (provisional) 51st Mersenne prime, so we'd be stuck at "40th verified Mersenne prime found in 2003".
Which really makes you wonder about the density of these primes in exponent terms ...
If that property continued after 2^20,996,011 - 1 the next one would be around 2^86,133,241-1 which is bigger than the (provisional) 51st Mersenne prime, so we'd be stuck at "40th verified Mersenne prime found in 2003".
Which really makes you wonder about the density of these primes in exponent terms ...