Megaprime

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).

Megaprimes found by year.

As of 17 March 2013 (2013-03-17)^[update], 63 megaprimes are known.^[2] The first to be found was the Mersenne prime 2^6972593−1 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 [edit]

Number	Discovery date	Decimal digits	Prime / PRP
2^57885161 – 1	2013-01-25	17,425,170	Prime
2^43112609 – 1	2008-08-23	12,978,189	Prime
2^42643801 – 1	2009-04-12	12,837,064	Prime
2^37156667 – 1	2008-09-06	11,185,272	Prime
2^32582657 – 1	2006	9,808,358	Prime
2^30402457 – 1	2005-12-15	9,152,052	Prime
2^25964951 – 1	2005-02-18	7,816,230	Prime
2^24036583 – 1	2004-05-15	7,235,733	Prime
2^20996011 – 1	2003-11-17	6,320,430	Prime
2^13466917 – 1	2001-11-14	4,053,946	Prime
19249×2^13018586 + 1 ^[2]	2007-03-26	3,918,990	Prime
475856⁵²⁴²⁸⁸ + 1 ^[5]	2012-08-08	2,976,633	Prime
356926⁵²⁴²⁸⁸ + 1 ^[6]	2012-06-20	2,911,151	Prime
341112⁵²⁴²⁸⁸ + 1 ^[7]	2012-06-15	2,900,832	Prime
27653×2^9167433 + 1 ^[2]	2005	2,759,677	Prime
90527 × 2^9162167 + 1	2010	2,758,093	Prime
2^9092392 + 40291 ^[8]	2011-02	2,737,083	PRP
75898⁵²⁴²⁸⁸ + 1 ^[9]	2011-11-19	2,558,647	Prime
28433×2^7830457 + 1 ^[2]	2004	2,357,207	Prime
3×2^7033641 + 1 ^[10]	2011-02-21	2,117,338	Prime
33661×2^7031232 + 1 ^[2]	2007	2,116,617	Prime
2^6972593 – 1	1999-06-01	2,098,960	Prime
6679881×2^6679881 + 1 ^[11]	2009-07-25	2,010,852	Prime
6328548×2^6328548 + 1 ^[12]	2009-04-20	1,905,090	Prime
3×2^6090515 – 1 ^[13]	2010-04-24	1,833,429	Prime
7×2^5775996 + 1 ^[14]	2012-11-02	1,738,749	Prime
252191×2^5497878 – 1 ^[15]	2012-06-23	1,655,032	Prime
258317 × 2^5450519+1	2008	1,640,776	Prime
2^5146295 + 41693 ^[8]	2009-11	1,549,190	PRP
773620²⁶²¹⁴⁴ + 1 ^[16]	2012-04-19	1,543,643	Prime
3×2^5082306 + 1 ^[17]	2009-04-03	1,529,928	Prime
676754²⁶²¹⁴⁴+1	2012	1,528,413	Prime
5359 × 2^5054502+1	2003	1,521,561	Prime
525094²⁶²¹⁴⁴+1	2012	1,499,526	Prime
265711 × 2^4858008+1	2008	1,462,412	Prime
1271 × 2^4850526-1	2012	1,460,157	Prime
361658²⁶²¹⁴⁴+1	2011	1,457,075	Prime
9 × 2^4683555-1	2012	1,409,892	Prime
2^4583176 + 2131 ^[8]	2009-09	1,379,674	PRP
121×2^4553899 – 1 ^[18]	2012-02-25	1,370,863	Prime
145310²⁶²¹⁴⁴+1	2011	1,353,265	Prime
353159×2^4331116 – 1 ^[19]	2011-05-31	1,303,802	Prime
141941×2^4299438 – 1 ^[20]	2011-05-26	1,294,265	Prime
15 × 2^4246384+1	2013	1,278,291	Prime
3×2^4235414 – 1 ^[21]	2008-03-23	1,274,988	Prime
191 × 2^4203426-1	2012	1,265,360	Prime
$\tfrac{2^{4031399}+1}{3}$ ^[8]	2010-02	1,213,572	PRP
40734²⁶²¹⁴⁴+1	2011	1,208,473	Prime
9 × 2^4005979-1	2012	1,205,921	Prime
27×2^3855094 – 1 ^[22]	2012-02-28	1,160,501	Prime
24518²⁶²¹⁴⁴+1	2008	1,150,678	Prime
123547×2^3804809 – 1 ^[23]	2011-05-08	1,145,367	Prime
415267×2^3771929 – 1 ^[24]	2011-05-08	1,135,470	Prime
11 × 2^3771821+1	2013	1,135,433	Prime
938237 × 2^3752950-1	2007	1,129,757	Prime
65531 × 2^3629342-1	2011	1,092,546	Prime
485767 × 2^3609357-1	2008	1,086,531	Prime
5 × 2^3569154-1	2009	1,074,424	Prime
1019 × 2^3536312-1	2012	1,064,539	Prime
7 × 2^3511774+1	2008	1,057,151	Prime
428639 × 2^3506452-1	2011	1,055,553	Prime
9×2^3497442 + 1 ^[25]	2012-10-23	1,052,836	Prime
1273 × 2^3448551-1	2012	1,038,121	Prime
191249 × 2^3417696-1	2010	1,028,835	Prime
59 × 2^3408416-1	2010	1,026,038	Prime
81×2^3352924 + 1 ^[26]	2012-01-17	1,009,333	Prime
1087 × 2^3336385-1	2012	1,004,355	Prime
464253×2^3321908 – 1 ^[2]	2013	1,000,000	Prime
10⁹⁹⁹⁹⁹⁹ + 593499 ^[27]	2012-12-24	1,000,000	PRP

References [edit]

^ Chris Caldwell, The Prime Glossary: megaprime at The Prime Pages. Retrieved on 2008-01-04.
^ ^a ^b ^c ^d ^e ^f 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.
^ ^a ^b Chris Caldwell, The Largest Known Prime by Year: A Brief History at The Prime Pages. Retrieved on 2008-09-28.
^ Official announcement of discovery of 475856⁵²⁴²⁸⁸ + 1, PrimeGrid
^ Official announcement of discovery of 356926⁵²⁴²⁸⁸ + 1, PrimeGrid
^ Official announcement of discovery of 341112⁵²⁴²⁸⁸ + 1, PrimeGrid
^ ^a ^b ^c ^d Probable Primes Top 10000, primenumbers.net
^ Official announcement of discovery of 75898⁵²⁴²⁸⁸ + 1, PrimeGrid
^ Official announcement of discovery of 3×2^7033641 + 1, PrimeGrid
^ Official announcement of discovery of 6679881×2^6679881 + 1, PrimeGrid
^ Official announcement of discovery of 6328548×2^6328548 + 1, PrimeGrid
^ Official announcement of discovery of 3×2^6090515 – 1, PrimeGrid
^ Official announcement of discovery of 7×2^5775996 + 1, PrimeGrid
^ Official announcement of discovery of 252191×2^5497878 – 1, PrimeGrid
^ Official announcement of discovery of 773620²⁶²¹⁴⁴ + 1, PrimeGrid
^ Official announcement of discovery of 3×2^5082306 + 1, PrimeGrid
^ Official announcement of discovery of 121×2^4553899 – 1, PrimeGrid
^ Official announcement of discovery of 353159×2^4331116 – 1, PrimeGrid
^ Official announcement of discovery of 141941×2^4299438 – 1, PrimeGrid
^ Official announcement of discovery of 3×2^4235414 – 1, PrimeGrid
^ Official announcement of discovery of 27×2^3855094 – 1, PrimeGrid
^ Official announcement of discovery of 123547×2^3804809 – 1, PrimeGrid
^ Official announcement of discovery of 415267×2^3771929 – 1, PrimeGrid
^ Official announcement of discovery of 9×2^3497442 + 1, PrimeGrid
^ Official announcement of discovery of 81×2^3352924 + 1, PrimeGrid
^ Patrick De Geest, 10^999999 + y, World!Of Numbers

External links [edit]

Chris Caldwell, The Largest Known Primes Database at The Prime Pages.
PrimeGrid’s 321 Prime Search, about the discovery of 3×2^6090515−1.

This number article is a stub. You can help Wikipedia by expanding it.

[1] Chris Caldwell, The Prime Glossary: megaprime at The Prime Pages. Retrieved on 2008-01-04.

[The_largest_known_primes-2] ^ ^a ^b ^c ^d ^e ^f Chris Caldwell, The Largest Known Primes at The Prime Pages. Retrieved on 2013-02-24.

[3] GIMPS press release, GIMPS Finds First Million-Digit Prime. Retrieved on 2008-01-04.

[largest-4] Chris Caldwell, The Largest Known Prime by Year: A Brief History at The Prime Pages. Retrieved on 2008-09-28.

[5] Official announcement of discovery of 475856⁵²⁴²⁸⁸ + 1, PrimeGrid

[6] Official announcement of discovery of 356926⁵²⁴²⁸⁸ + 1, PrimeGrid

[7] Official announcement of discovery of 341112⁵²⁴²⁸⁸ + 1, PrimeGrid

[PRPTop-8] Probable Primes Top 10000, primenumbers.net

[9] Official announcement of discovery of 75898⁵²⁴²⁸⁸ + 1, PrimeGrid

[10] Official announcement of discovery of 3×2^7033641 + 1, PrimeGrid

[11] Official announcement of discovery of 6679881×2^6679881 + 1, PrimeGrid

[12] Official announcement of discovery of 6328548×2^6328548 + 1, PrimeGrid

[13] Official announcement of discovery of 3×2^6090515 – 1, PrimeGrid

[14] Official announcement of discovery of 7×2^5775996 + 1, PrimeGrid

[15] Official announcement of discovery of 252191×2^5497878 – 1, PrimeGrid

[16] Official announcement of discovery of 773620²⁶²¹⁴⁴ + 1, PrimeGrid

[17] Official announcement of discovery of 3×2^5082306 + 1, PrimeGrid

[18] Official announcement of discovery of 121×2^4553899 – 1, PrimeGrid

[19] Official announcement of discovery of 353159×2^4331116 – 1, PrimeGrid

[20] Official announcement of discovery of 141941×2^4299438 – 1, PrimeGrid

[21] Official announcement of discovery of 3×2^4235414 – 1, PrimeGrid

[22] Official announcement of discovery of 27×2^3855094 – 1, PrimeGrid

[23] Official announcement of discovery of 123547×2^3804809 – 1, PrimeGrid

[24] Official announcement of discovery of 415267×2^3771929 – 1, PrimeGrid

[25] Official announcement of discovery of 9×2^3497442 + 1, PrimeGrid

[26] Official announcement of discovery of 81×2^3352924 + 1, PrimeGrid

[27] Patrick De Geest, 10^999999 + y, World!Of Numbers

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Megaprime

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Known megaprimes and mega PRPs [edit]

See also [edit]

References [edit]

External links [edit]

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