First, make sure the numbers are proven prime, not a probable
prime (see the pages on finding primes and proving primality if you
have any questions). Also, make sure the primes are either
large enough to be one of the 5000 largest known primes or of a special
type (which we list)
and large enough to be in the top 20 of that form.
Once they are proven primes, submit them using our prime submission page! As
explained on that page, this process will involve three steps (which
sound more daunting than they are):
First you create a prover-account. These
pages have the biographical information on those who found the primes. At
a minimum it would have their names, but could (if they choose) have
their e-mail, a picture, bio-information, link to their web site... You
only do this once!
Second, create a proof code. The proof code is a database entry that
explains how the primes were proven, what software was involved, and
sometimes, what projects this prime was part of. This is done only once
for each combination of software... Most provers do it once,
but a few have a dozen or more proof-codes.