[zeep]

not really, it is very hard to test any very large number for primality... this project only test numbers that satisfy the Mersenne prime definition though... 9 of the 10 known largest primes are Mersenne prime numbers probably because there is more people testing these numbers.

http://primes.utm.edu/largest.html#biggest

[schoen]

But the biggest reason that the largest known primes have this form is that they are subject to a much faster special-form primality test.

https://en.wikipedia.org/wiki/Lucas%E2%80%93Lehmer_primality...

There's no known general-form primality test that is nearly as fast for numbers of corresponding sizes.

[ehsankia]

People test these because it's the easiest pattern we know of for constructing large primes. So if you want to maximize your chances of finding a large prime, you'll check for the mersenne form.

[mygo]

people test these because we have the technology to check if a large number of the Mersenne form is prime at a faster speed than numbers that do not conform.