Double Mersenne primes have the format: 2^(2^prime(n) - 1) - 1. MM61 means 2^(2^61-1)-1 or 22305843009213693951 - 1. This number has approximately 694127911065419641 digits. It is unknown whether this number is prime or composite.
This is the smallest double Mersenne prime for which it is unknown whether it is composite or prime. Yet people are obsessed with proving that it is prime. Or not.
"A number of people (including the author of this page) have tried finding divisors of MM61, MM89, MM107, MM127, MM521, MM607 and others, but so far without success"
--http://sites.google.com/site/anthonydforbes/mm61.htm
It has been proven that MM61 is not divisible by any number up to 1167025860000000.
That is some dedication. I wonder if we will ever know the answer.
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