TITLE: Are all prime numbers up to Mersenne Prime 48 known?
QUESTION [6 upvotes]: In January this year the biggest prime number so far has been found and it is a Mersenne Prime. $$2^{57885161}-1$$.
My question:
Are all prime numbers from 0 up to $2^{57885161}-1$ found, or not?
If you only look for prime numbers which are Mersenne Primes, you skip quite a few.

REPLY [6 votes]: As you may know, GIMPS is conducting a search.  They give each user a different prime number to test.  Then they give that number to a different user to check.
They only test numbers of the form $2^p-1$, where $p$ is also prime.  So they have only checked a few million possible values of $p$, that is a few million possible values of $2^p-1$.
The link www.mersenne.org/report_milestones/ shows that they have checked all primes
$2^p-1$ if $p$ is below  44,576,437, and have double-checked primes $2^p-1$ for values of $p$ up to $p=26,187,517$.  
There are around $(2^{57885161})/57885161$, or around $2^{57885135}$ unknown primes below the current record.