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] and gigantic prime for a prime with at least 10,000 digits.[3] Bevaprime has been proposed for a prime with at least 1,000,000,000 digits.[4]

Number of megaprimes found by year through 2017.
Number of megaprimes found by year through 2017.

As of 2022, there are more than 1000 known megaprimes[5] and 78 further probable primes (PRPs) which have more than 1,000,000 digits.[6] 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.[7][8] 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, is the smallest megaprime.[9] As of 2022, 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.[6]

See also

References

  1. ^ Chris Caldwell, The Prime Glossary: megaprime at The PrimePages. Retrieved on 2008-01-04.
  2. ^ Chris Caldwell, The Prime Glossary: titanic prime at The PrimePages. Retrieved on 2022-06-21.
  3. ^ Chris Caldwell, The Prime Glossary: gigantic prime at The PrimePages. Retrieved on 2022-06-21.
  4. ^ "Chris Caldwell, The Largest Known Prime by Year: A Brief History". Archived from the original on 2016-01-01. Retrieved 2008-01-04.((cite web)): CS1 maint: bot: original URL status unknown (link)
  5. ^ Chris Caldwell, The Largest Known Primes at The PrimePages.
  6. ^ a b Henri Lifchitz & Renaud Lifchitz, Probable Primes Top 10000, primenumbers.net
  7. ^ GIMPS press release, GIMPS Finds First Million-Digit Prime. Retrieved on 2008-01-04.
  8. ^ Chris Caldwell, The Largest Known Prime by Year: A Brief History at The PrimePages. Retrieved on 2008-09-28.
  9. ^ Patrick De Geest, 10^999999 + y, World!Of Numbers