# The PrimePages: prime number research & records

##### What are the PrimePages?

Webster's New Collegiate Dictionary defines prime as follows.

prime \'prīm\ 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 : PRINCIPALb : having the highest quality or value <~ television time>

Each of Webster's definitions apply, but the most operative is 2a: An integer greater than one is prime if its only positive divisors are itself and one.  For example 15 is not prime because it has other divisors, namely the primes 3 and 5.  These pages presents lists of large primes and key research about them.

##### Largest Known Primes Database

Our central database acts as a “Guinness book” of prime number records!   This list includes the 5000 largest known primes and smaller ones of selected forms updated hourly.

##### Other Lists of Primes Here

The first 1,000 primes and first 50,000,000 primes.  Lists of top 20 records (e.g., twin primes, Mersenne primes...).  Small random primes up to 300 digits.  The smallest titanics with special forms and many more.

### Finding/proving

The theory behind how these record primes are found and proven.

### Questions?

We answer common questions: Is one a prime?   Longest list of primes?   Why?

### Prime Glossary

The Prime Glossary is a collection of definitions related to prime numbers.

The Largest Known Prime by Year discusses how big have the largest known primes been historically.

Over 2000 years ago Euclid proved that there are infinity many.

A short note about 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.

A simple routine to check most small numbers for primality (and a link to a more sophisticated test).