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PrimePages 5000 Largest 5000 Largest Top 20 Primes Prover Bios Search Primes FAQ Curios! Glossary Home Home PageThe 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 : PRINCIPAL b : 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. List Summary SEARCH PRIMES PRINT LISTS VERIFICATION STATUS Minimum Sizes 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 . See also the various database searches . Finding/proving The theory behind how these record primes are found and proven. Proving Questions? We answer common questions: Is one a prime? Longest list of primes? Why? FAQ Prime Glossary The Prime Glossary is a collection of definitions related to prime numbers. Prime Glossary Largest Known Prime by Year ↓ The Largest Known Prime by Year discusses how big have the largest known primes been historically. How many primes are there? ↓ Over 2000 years ago Euclid proved that there are infinity many. How Big of an Infinity? The Riemann Hypothesis ↓ 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. Check a Number’s Primality ↓ A simple routine to check most small numbers for primality (and a link to a more sophisticated test). Check Primality Eve’s Dad showed her a really big prime! Visit the Prime Curios! Printed from the PrimePages t5k.org © Reginald McLean. Collections Prime Glossary Prime Curios! Proving Primality Frequently Asked Questions Proofs Prime Lists Largest Known Primes Top 5000 List Lists of Small Primes Records for Different Types Mersenne Primes Pages How many primes? Largest Known by Year Prover Bios Top 20 Provers Contact Us Copyright © 2022 PrimePages . ( Privacy notice...