Cylindrical harmonics
A megaprime is a prime number with at least one million decimal digits[1] (whereas titanic prime is a prime number with at least 1000 digits, and gigantic prime has at least 10000 digits).
Template:As of, 63 megaprimes are known.[2] 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.[3][4]
The term bevaprime has been proposed as a term for a prime with at least 1,000,000,000 digits.[4]
Known megaprimes and mega PRPs
Entries labelled "Prime" have been proved prime; those labelled "PRP" have not. See the article Probable prime.
| Number | Discovery date | Decimal digits | Prime / PRP |
|---|---|---|---|
| 257885161 – 1 | 2013-01-25 | 17,425,170 | Prime |
| 243112609 – 1 | 2008-08-23 | 12,978,189 | Prime |
| 242643801 – 1 | 2009-04-12 | 12,837,064 | Prime |
| 237156667 – 1 | 2008-09-06 | 11,185,272 | Prime |
| 232582657 – 1 | 2006 | 9,808,358 | Prime |
| 230402457 – 1 | 2005-12-15 | 9,152,052 | Prime |
| 225964951 – 1 | 2005-02-18 | 7,816,230 | Prime |
| 224036583 – 1 | 2004-05-15 | 7,235,733 | Prime |
| 220996011 – 1 | 2003-11-17 | 6,320,430 | Prime |
| 213466917 – 1 | 2001-11-14 | 4,053,946 | Prime |
| 19249×213018586 + 1Template:Align | 2007-03-26 | 3,918,990 | Prime |
| 475856524288 + 1Template:Align | 2012-08-08 | 2,976,633 | Prime |
| 356926524288 + 1Template:Align | 2012-06-20 | 2,911,151 | Prime |
| 341112524288 + 1Template:Align | 2012-06-15 | 2,900,832 | Prime |
| 27653×29167433 + 1Template:Align | 2005 | 2,759,677 | Prime |
| 90527 × 29162167 + 1 | 2010 | 2,758,093 | Prime |
| 29092392 + 40291Template:Align | 2011-02 | 2,737,083 | PRP |
| 75898524288 + 1Template:Align | 2011-11-19 | 2,558,647 | Prime |
| 28433×27830457 + 1Template:Align | 2004 | 2,357,207 | Prime |
| 3×27033641 + 1Template:Align | 2011-02-21 | 2,117,338 | Prime |
| 33661×27031232 + 1Template:Align | 2007 | 2,116,617 | Prime |
| 26972593 – 1 | 1999-06-01 | 2,098,960 | Prime |
| 6679881×26679881 + 1Template:Align | 2009-07-25 | 2,010,852 | Prime |
| 6328548×26328548 + 1Template:Align | 2009-04-20 | 1,905,090 | Prime |
| 3×26090515 – 1Template:Align | 2010-04-24 | 1,833,429 | Prime |
| 7×25775996 + 1Template:Align | 2012-11-02 | 1,738,749 | Prime |
| 252191×25497878 – 1Template:Align | 2012-06-23 | 1,655,032 | Prime |
| 258317 × 25450519+1 | 2008 | 1,640,776 | Prime |
| 25146295 + 41693Template:Align | 2009-11 | 1,549,190 | PRP |
| 773620262144 + 1Template:Align | 2012-04-19 | 1,543,643 | Prime |
| 3×25082306 + 1Template:Align | 2009-04-03 | 1,529,928 | Prime |
| 676754262144+1 | 2012 | 1,528,413 | Prime |
| 5359 × 25054502+1 | 2003 | 1,521,561 | Prime |
| 525094262144+1 | 2012 | 1,499,526 | Prime |
| 265711 × 24858008+1 | 2008 | 1,462,412 | Prime |
| 1271 × 24850526-1 | 2012 | 1,460,157 | Prime |
| 361658262144+1 | 2011 | 1,457,075 | Prime |
| 9 × 24683555-1 | 2012 | 1,409,892 | Prime |
| 24583176 + 2131Template:Align | 2009-09 | 1,379,674 | PRP |
| 121×24553899 – 1Template:Align | 2012-02-25 | 1,370,863 | Prime |
| 145310262144+1 | 2011 | 1,353,265 | Prime |
| 353159×24331116 – 1Template:Align | 2011-05-31 | 1,303,802 | Prime |
| 141941×24299438 – 1Template:Align | 2011-05-26 | 1,294,265 | Prime |
| 15 × 24246384+1 | 2013 | 1,278,291 | Prime |
| 3×24235414 – 1Template:Align | 2008-03-23 | 1,274,988 | Prime |
| 191 × 24203426-1 | 2012 | 1,265,360 | Prime |
| Template:Align | 2010-02 | 1,213,572 | PRP |
| 40734262144+1 | 2011 | 1,208,473 | Prime |
| 9 × 24005979-1 | 2012 | 1,205,921 | Prime |
| 27×23855094 – 1Template:Align | 2012-02-28 | 1,160,501 | Prime |
| 24518262144+1 | 2008 | 1,150,678 | Prime |
| 123547×23804809 – 1Template:Align | 2011-05-08 | 1,145,367 | Prime |
| 415267×23771929 – 1Template:Align | 2011-05-08 | 1,135,470 | Prime |
| 11 × 23771821+1 | 2013 | 1,135,433 | Prime |
| 938237 × 23752950-1 | 2007 | 1,129,757 | Prime |
| 65531 × 23629342-1 | 2011 | 1,092,546 | Prime |
| 485767 × 23609357-1 | 2008 | 1,086,531 | Prime |
| 5 × 23569154-1 | 2009 | 1,074,424 | Prime |
| 1019 × 23536312-1 | 2012 | 1,064,539 | Prime |
| 7 × 23511774+1 | 2008 | 1,057,151 | Prime |
| 428639 × 23506452-1 | 2011 | 1,055,553 | Prime |
| 9×23497442 + 1Template:Align | 2012-10-23 | 1,052,836 | Prime |
| 1273 × 23448551-1 | 2012 | 1,038,121 | Prime |
| 191249 × 23417696-1 | 2010 | 1,028,835 | Prime |
| 59 × 23408416-1 | 2010 | 1,026,038 | Prime |
| 81×23352924 + 1Template:Align | 2012-01-17 | 1,009,333 | Prime |
| 1087 × 23336385-1 | 2012 | 1,004,355 | Prime |
| 464253×23321908 – 1Template:Align | 2013 | 1,000,000 | Prime |
| 10999999 + 593499Template:Align | 2012-12-24 | 1,000,000 | PRP |
See also
References
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External links
- Chris Caldwell, The Largest Known Primes Database at The Prime Pages.
- PrimeGrid’s 321 Prime Search, about the discovery of 3×26090515−1.
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fr:Nombre premier#Jalons symboliques
- ↑ Chris Caldwell, The Prime Glossary: megaprime at The Prime Pages. Retrieved on 2008-01-04.
- ↑ Chris Caldwell, The Largest Known Primes at The Prime Pages. Retrieved on 2013-02-24.
- ↑ GIMPS press release, GIMPS Finds First Million-Digit Prime. Retrieved on 2008-01-04.
- ↑ 4.0 4.1 Chris Caldwell, The Largest Known Prime by Year: A Brief History at The Prime Pages. Retrieved on 2008-09-28.