The Prime
Pages: Prime Number Research, Records and Results

E-mail list
New record prime (GIMPS): 282,589,933-1 with 24,862,048 digits by P. Laroche, G. Woltman, A. Blosser, et al. (7 Dec 2018).
The Largest Known Primes Database The "Guinness book" of prime number records!  Includes the 5000 largest known primes and smaller ones of selected forms  (one-page summary)  updated daily!
What are the Prime pages?

Prime Curios! (The speed limit is 31 in downtown Trenton Tennessee)Webster's New Collegiate Dictionary defines prime as follows.

prime \'prim\ n [ME, fr. MF, fem. of prin first, L primus; akin to L prior] 1 : first in time : ORIGINAL 2 a : having no factor except itself and one <3 is a ~ number> b : having no common factor except one <12 and 25 are relatively ~> 3 a : first in rank, authority or significance : PRINCIPAL b : having the highest quality or value <~ television time>

Each of Webster's definitions may be applied to this page, but the most operative is 2a: An integer greater than one is prime if its only positive divisors are itself and one (otherwise it is composite).  For example: 15 is composite because it has the two prime divisors 3 and 5. 

Lists of Primes The first 1,000 primes.  The first 50,000,000 primes.  Top 20 records (e.g., twin primes, Mersenne primes...)  Lists of 300 digit primes.  And much more!
Finding primes, proving primality Explains the mathematical theory behind how these record primes are found.
How many are there? Infinity, but How Big of an Infinity?
The Largest Known Prime by Year: A Brief History Discusses how big have the largest known primes been historically (and uses that to predict how big they will be)!

More prime resources

Conjectures and Open Problems
A short list of conjectures and open problems relating to primes.
The Riemann Hypothesis
One of the most important conjectures in prime number theory. When (and if) it is proven, many of the bounds on prime estimates can be improved and primality proving can be simplified.
Prime Curios!
"Prime Curios!" is an exciting collection of curiosities, wonders and trivia related to prime numbers.
Prime Glossary
Definition of terms related to prime numbers and primality.
Check a Number's Primality
A simple routine to check most small numbers for primality.
Important Discovery: "Primes in P"
Primality can be tested in deterministic polynomial time--this is of great theoretical value; but of questionable practical value.
The Prime Pages © 1994-2018    Professor Chris Caldwell   (e-mail)