How do you start finding large primes? That depends on you, on
what you know and on what you want. For example, you can download a program and then either join an existing
project or take off on your own; or you might write your own
program. We briefly explain each of these options further below.
When seeking primes, you must first decide what type of prime you
want. The primes found to set size records are usual prime for
which the classical primality tests work wellthat means primes with
forms like N = a^{.}b^{n}±1
(the classical tests require one of N±1 to factor
substantially). But you can also seek to prove smaller, but more
difficult numbers primenumbers N for which N±1 do
not factor easily. These records are much smaller, and much harder
to find.
Downloading a Program
If you want to set a record for the largest known prime, and are
looking for a long shot and a big monetary prize, then the best starting
place might be to join George Woltman's Great Internet Mersenne Prime
Search (GIMPS). The chance of finding the next record is minute, but
could be rewarding (e.g., there is a $100,000 prize)! The GIMPS site provides all you need to
get started.
If you just want to get your name "in the books" by finding a prime
that makes the list of the 5000 largest known primes, then consider Yves Gallot's
Proth.exe. This program has proven thousands of primes and at
times has accounted for the majority of the primes on the list.
Another important player is Chris Nash's OpenPFGW.
This one requires a little more thought to get started, but also allows
much more freedom in the choice of project. The OpenPFGW project
includes an email list that might help you get started.
Others are emerging as key players, for example Jean Penné's LLR. It is a
good idea to watch the list of top 20 programs
to see what folks are using and always talk with others involved in the
searches.
If you have a prime in mind, one that is not ammeniable to the
classical tests, Marcel Martin's
Primo (formerly Titanix) is one of the best implementations of ECPP
around, it is easy to install and use on Windows machines.
But this is just the tip of the iceberg. See our Prime Links++
for more programs. Talk to others who are involved in searching for
primes... The approach to take is as individual as you are!
Writing your Own Program
This approach offers freedom, but freedom can be expensive. You
will need to understand both the mathematics of primality proving and
the secrets of fast arithemtic on large numbers. Prime Links++ lists
some useful libraries. Be sure to talk to others. If you are
a coder, you might also take the middle ground and join the group working
on OpenPFGW.
