Megaprime
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]
As of 16 November 2024[update], there are 2,890 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] As of 2022[update], the smallest number known to be a megaprime is 10999999 + 308267×10292000 + 1.
The last prime that is not a megaprime is almost certainly 10999999 − 172473.[11][12][13]
See also
[edit]- List of largest known primes and probable primes, a list that includes the largest known megaprimes and probable megaprimes
- Largest known prime number
- Electronic Frontier Foundation § Awards
References
[edit]- ^ 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.
- ^ "factordb.com". factordb.com.
- ^ Chris Caldwell, The Prime Glossary: gigantic prime at The PrimePages. Retrieved on 2022-06-21.
- ^ "factordb.com". factordb.com.
- ^ 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
- ^ Sloane, N. J. A. (ed.). "Sequence A340902 (Distance from the largest prime with less than 10^n decimal digits to 10^(10^n-1))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.