It's a very large prime number which has a very convenient representation, which makes it useful. You could use it in a Mersenne Twister RNG, for instance.
I think think when this was written, that number-1 was the largest known mersenne prime (which are the prime numbers that can be written as 2^something - 1). Some more context on this particular prime here: https://primes.utm.edu/notes/756839.html
I'm too busy to check but I'd bet money that it's a Mersenne prime. The series looks exponential (like 2^n) and it's not hard to imagine that fenceposting (±1) led to each member in the series being (2^n)-1 - which is the form for Mersenne primes.
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 ...
I was looking at a list of prime numbers in binary format and I noticed a pattern, where if 2^n - 1, a Mersenne Prime, is in the list, then (2^(n+1) - 2^(n) - 1) is also in the list.
I looked at the list of Mersenne Primes on Wikipedia and checked the primality of (2^43112610 - 2^43112609 - 1) on Wolfram Alpha, but to test for any results larger than that, the results are inconclusive.
The largest discovered prime number is a Mersenne Prime (2^82589933 - 1), so I'm wondering how I can go about testing (2^82589934 - 2^82589933 - 1).
reply