A megaprime is a prime number with at least one million decimal digits.Chris Caldwell, The Prime Glossary: megaprime at The PrimePages. Retrieved on 2008-01-04.
Other terms for large primes include "titanic prime", coined by Samuel Yates in the 1980s for a prime with at least 1000 digits (of which the smallest is 10999+7), and "gigantic prime" for a prime with at least 10,000 digitsChris Caldwell, The Prime Glossary: gigantic prime at The PrimePages. Retrieved on 2022-06-21. (of which the smallest is 109999+33603).
, there are 3,797 known megaprimesChris Caldwell, The Largest Known Primes at The PrimePages. which have more than 1,000,000 digits. The first to be found was the Mersenne prime 26972593−1 with 2,098,960 digits, discovered in 1999 by Nayan Hajratwala, a participant in the distributed computing project GIMPS.Chris Caldwell, The Largest Known Prime by Year: A Brief History at The PrimePages. Retrieved on 2008-09-28. Nayan was awarded a Cooperative Computing Award from the Electronic Frontier Foundation for this achievement.
Almost all primes are megaprimes, as the number of primes with fewer than one million digits is finite. However, the vast majority of known primes are not megaprimes.
All numbers from 10999999 through 10999999 + 593498 are known to be composite, and there is a very high probability that 10999999 + 593499, a strong probable prime for each of 8 different bases, is the smallest megaprime.Patrick De Geest, 10^999999 + y, World!Of Numbers , the smallest number known to be a megaprime is 10999999 + 308267×10292000 + 1.
The last prime that is not a megaprime is currently unknown. , the largest prime number known to not be a megaprime is 10999999 − 1022306×10287000 − 1. There is a very high probability that 10999999 − 172473 is the biggest non-mega prime.
See also List of largest known primes and probable primes, a list that includes the largest known megaprimes and probable megaprimes Largest known prime number
References