Megaprime
Template:Short description A megaprime is a prime number with at least one million decimal digits.[1]
Other terms for large primes include "titanic prime", coined by Samuel Yates in the 1980s for a prime with at least 1000 digits[2] (of which the smallest is 10999+7),[3] and "gigantic prime" for a prime with at least 10,000 digits[4] (of which the smallest is 109999+33603).[5]
since 17 May 2025[update]Template:Dated maintenance category (articles)Script error: No such module "Check for unknown parameters"., there are 3,354 known megaprimes[6] which have more than 1,000,000 digits.[7] 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.[8][9] 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.[10] since 2024[update]Template:Dated maintenance category (articles)Script error: No such module "Check for unknown parameters"., the smallest number known to be a megaprime is 10999999 + 308267×10292000 + 1.
The last prime that is not a megaprime is currently unknown. since 2024[update]Template:Dated maintenance category (articles)Script error: No such module "Check for unknown parameters"., 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.[11][12][13]
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
- Template:Section link
References
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- ↑ Chris Caldwell, The Prime Glossary: megaprime at The PrimePages. Retrieved on 2008-01-04.
- ↑ Chris Caldwell, The Prime Glossary: titanic prime at The PrimePages. Retrieved on 2022-06-21.
- ↑ Script error: No such module "citation/CS1".
- ↑ Chris Caldwell, The Prime Glossary: gigantic prime at The PrimePages. Retrieved on 2022-06-21.
- ↑ Script error: No such module "citation/CS1".
- ↑ Chris Caldwell, The Largest Known Primes at The PrimePages.
- ↑ Henri Lifchitz & Renaud Lifchitz, Probable Primes Top 10000, primenumbers.net
- ↑ GIMPS press release, GIMPS Finds First Million-Digit Prime. Retrieved on 2008-01-04.
- ↑ Chris Caldwell, The Largest Known Prime by Year: A Brief History at The PrimePages. Retrieved on 2008-09-28.
- ↑ Patrick De Geest, 10^999999 + y, World!Of Numbers
- ↑ Henri Lifchitz & Renaud Lifchitz, Probable Primes search for 10^999999-a, primenumbers.net
- ↑ Patrick De Geest, Border Probable Primes around 'Powers of Ten', worldofnumbers.com
- ↑ Script error: No such module "citation/CS1".Script error: No such module "Check for unknown parameters".
Script error: No such module "Check for unknown parameters".