# Is a probable prime known larger than the largest known prime?

According to Wikipedia, the largest known prime is $2^{57,885,161}-1$ with $17,425,170$ digits.

Because a probable prime is usually easier to find than a proven prime (although for the Mersenne-primes, there is an algorithm to prove primilaty as fast as a probable prime test), I wonder if there is a larger known probable prime.

The same for twin primes, the largest known pair is $3,756,801,695,685\times 2^{666,669}\pm1$ with $200,700$ digits. Is there known a larger pair for which both entries are probable primes ?

• Probably known but not published. Note that we are talking about ranges where being satisfied with a highly probable prime is not useful, and someone publishing that they found a probable prime is something I find unlikely. Then again, there may be a community out there where probable primes, being candidates for primeness-provers, are collected. And as you say, for "structured" primes such as Mersenne, a definite proof can be as fast as a probale test. – Hagen von Eitzen Sep 8 '15 at 21:34

The largest PRP there is $(2^{13372531}+1)/3$ which is much smaller than $2^{57 885161}-1$ (about a quarter the number of digits). Generally, PRPs take as much effort to find as Mersenne primes of a similar size, but more effort is put toward Mersenne primes because of interest, convenient software, greater publicity, and the EFF prizes.