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 1,000 digits, and gigantic prime has at least 10,000 digits).

As of January 2016^[update], 164 (probable) megaprimes are known, including 150 definitely primes^[2] and 14 probable primes.^[3] 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.^[4]^[5]

The term bevaprime has been proposed as a term for a prime with at least 1,000,000,000 digits.^[5]

In fact, "almost all" primes are megaprimes, as the amount of primes with more than a million digits is infinite. However, the vast majority of known primes are not megaprimes.

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
2^74207281 – 1	2016-01-07	22,338,618	Prime
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	2006-09-04	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
${\tfrac {2^{13372531}+1}{3}}$ ^[3]	2013-09	4,025,533	PRP
${\tfrac {2^{13347311}+1}{3}}$ ^[3]	2013-09	4,017,941	PRP
19249×2^13018586 + 1 ^[2]	2007-03-26	3,918,990	Prime
3×2^11895718 − 1 ^[2]	2015-06	3,580,969	Prime
3×2^11731850 − 1 ^[6]	2015-03-13	3,531,640	Prime
3×2^11484018 − 1 ^[7]	2014-11-22	3,457,035	Prime
3×2^10829346 + 1 ^[8]	2014-01-14	3,259,959	Prime
475856⁵²⁴²⁸⁸ + 1 ^[9]	2012-08-08	2,976,633	Prime
356926⁵²⁴²⁸⁸ + 1 ^[10]	2012-06-20	2,911,151	Prime
341112⁵²⁴²⁸⁸ + 1 ^[11]	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 ^[3]	2011-02	2,737,083	PRP
2038×366^1028507 − 1 ^[12]	2016	2,636,562	Prime
75898⁵²⁴²⁸⁸ + 1 ^[13]	2011-11-19	2,558,647	Prime
28433×2^7830457 + 1 ^[2]	2004	2,357,207	Prime
502573×2^7181987 − 1 ^[14]	2014-10-04	2,162,000	Prime
402539×2^7173024 − 1 ^[15]	2014-10-02	2,159,301	Prime
161041×2^7107964 + 1	2015-01	2,139,716	Prime
3×2^7033641 + 1 ^[16]	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
40597×2^6808509 – 1 ^[17]	2013-12-25	2,049,571	Prime
6679881×2^6679881 + 1 ^[18]	2009-07-25	2,010,852	Prime
37×2^6660841 − 1	2014	2,005,115	Prime
304207×2^6643565 – 1 ^[19]	2013-10-10	1,999,918	Prime
398023×2^6418059 – 1 ^[20]	2013-10-05	1,932,034	Prime
6328548×2^6328548 + 1 ^[21]	2009-04-20	1,905,090	Prime
3×2^6090515 – 1 ^[22]	2010-04-24	1,833,429	Prime
1583×2^5989282 − 1	2015	1,802,957	Prime
7×2^5775996 + 1 ^[23]	2012-11-02	1,738,749	Prime
9×2^5642513 + 1	2013	1,698,567	Prime
2622×11^1621920 – 1 ^[12]	2015	1,689,060	Prime
252191×2^5497878 – 1 ^[24]	2012-06-23	1,655,032	Prime
258317 × 2^5450519+1	2008	1,640,776	Prime
1615588²⁶²¹⁴⁴ + 1	2016	1,627,477	Prime
1488256²⁶²¹⁴⁴ + 1	2016	1,618,131	Prime
1415198²⁶²¹⁴⁴ + 1	2016	1,612,400	Prime
27×2^5213635 + 1	2015	1,569,462	Prime
2^5146295 + 41693 ^[3]	2009-11	1,549,190	PRP
773620²⁶²¹⁴⁴ + 1 ^[25]	2012-04-19	1,543,643	Prime
51×2^5085142 - 1	2014	1,530,782	Prime
3×2^5082306 + 1 ^[26]	2009-04-03	1,529,928	Prime
676754²⁶²¹⁴⁴+1	2012	1,528,413	Prime
296024 × 5^2185270 − 1	2016	1,527,444	Prime
5359 × 2^5054502+1	2003	1,521,561	Prime
13×2^4998362 + 1	2014	1,504,659	Prime
525094²⁶²¹⁴⁴+1	2012	1,499,526	Prime
92158×5^2145024 + 1	2016	1,499,313	Prime
77072×5^2139921 + 1	2016	1,495,746	Prime
306398 × 5^2112410 − 1	2016	1,476,517	Prime
265711 × 2^4858008+1	2008	1,462,412	Prime
154222 × 5^2091432 + 1	2015	1,461,854	Prime
1271 × 2^4850526-1	2012	1,460,157	Prime
362978²⁶²¹⁴⁴ − 362978¹³¹⁰⁷² + 1	2015	1,457,490	Prime
361658²⁶²¹⁴⁴+1	2011	1,457,075	Prime
100186 × 5^2079747 − 1	2015	1,453,686	Prime
653 × 10^1435026 − 1 ^[12]	2014	1,435,029	Prime
144052× 5^2018290 + 1	2015	1,410,730	Prime
9 × 2^4683555 − 1	2012	1,409,892	Prime
11 × 2^4643238 − 1	2014	1,397,755	Prime
192098²⁶²¹⁴⁴ − 192098¹³¹⁰⁷² + 1	2015	1,385,044	Prime
27 × 2^4583717 − 1	2014	1,379,838	Prime
2^4583176 + 2131 ^[3]	2009-09	1,379,674	PRP
121×2^4553899 – 1 ^[27]	2012-02-25	1,370,863	Prime
27× 2^4542344 − 1	2014	1,367,384	Prime
${\tfrac {2^{4533073}+2^{2266537}+1}{5}}$ ^[3]	2014-03	1,364,591	PRP
145310²⁶²¹⁴⁴+1	2011	1,353,265	Prime
36772 × 6^1723287 − 1	2014	1,340,983	Prime
${\tfrac {13^{1199467}+1}{14}}$ ^[3]	2015-12	1,336,138	PRP
353159×2^4331116 – 1 ^[28]	2011-05-31	1,303,802	Prime
141941×2^4299438 – 1 ^[29]	2011-05-26	1,294,265	Prime
15 × 2^4246384+1	2013	1,278,291	Prime
3×2^4235414 – 1 ^[30]	2008-03-23	1,274,988	Prime
109208 × 5^1816285 + 1	2014	1,269,534	Prime
191 × 2^4203426-1	2012	1,265,360	Prime
${\tfrac {2^{4187251}-1}{72234342371519}}$ ^[3]	2016-05	1,260,475	PRP
${\tfrac {14^{1091401}+1}{15}}$ ^[3]	2014-03	1,250,885	PRP
${\tfrac {16^{1025393}+1}{17}}$ ^[3]	2014-08	1,234,695	PRP
${\tfrac {2^{4031399}+1}{3}}$ ^[3]	2010-02	1,213,572	PRP
40734²⁶²¹⁴⁴+1	2011	1,208,473	Prime
9 × 2^4005979 - 1	2012	1,205,921	Prime
12 × 68⁶⁵⁶⁹²¹ + 1 ^[12]	2016	1,203,815	Prime
1993191 × 4^1993191 − 1	2015	1,200,027	Prime
27×2^3855094 – 1 ^[31]	2012-02-28	1,160,501	Prime
24518²⁶²¹⁴⁴+1	2008	1,150,678	Prime
123547×2^3804809 – 1 ^[32]	2011-05-08	1,145,367	Prime
415267×2^3771929 – 1 ^[33]	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
23451 × 2^3739388 + 1 ^[12]	2015	1,125,673	Prime
2^3704053 + 2^1852027 + 1	2014	1,115,032	Prime
330286×5^1584399 – 1 ^[34]	2014-03-21	1,107,453	Prime
15×2^3668194 – 1	2013	1,104,238	Prime
65531 × 2^3629342-1	2011	1,092,546	Prime
${\tfrac {106\cdot 23^{800873}-7}{11}}$ ^[3]	2015-05	1,090,573	PRP
485767 × 2^3609357-1	2008	1,086,531	Prime
5 × 2^3569154-1	2009	1,074,424	Prime
81 × 492³⁹⁹⁰⁹⁵ − 1 ^[12]		1,074,352	Prime
22934×5^1536762 – 1 ^[35]	2014-02-06	1,074,155	Prime
${\tfrac {7^{1264699}-1}{6}}$ ^[3]	2014-01	1,068,794	PRP
178658×5^1525224 – 1 ^[36]	2014-01-31	1,066,092	Prime
1019 × 2^3536312-1	2012	1,064,539	Prime
2×10^1059002 – 1	2013	1,059,003	Prime
7 × 2^3511774+1	2008	1,057,151	Prime
428639 × 2^3506452-1	2011	1,055,553	Prime
9×2^3497442 + 1 ^[37]	2012-10-23	1,052,836	Prime
51×2^3490971 + 1	2014	1,050,889	Prime
59912×5^1500861 + 1 ^[38]	2014-01-17	1,049,062	Prime
${\tfrac {2^{3464473}-1}{604874508299177}}$ ^[3]	2014-10	1,042,896	PRP
37292×5^1487989 + 1 ^[39]	2013-12-29	1,040,065	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
24 × 414³⁹¹¹⁷⁹ + 1 ^[12]		1,023,717	Prime
67×2^3391385 – 1	2014	1,020,911	Prime
173198×5^1457792 – 1 ^[40]	2013-12-04	1,018,959	Prime
81×2^3352924 + 1 ^[41]	2012-01-17	1,009,333	Prime
1087 × 2^3336385-1	2012	1,004,355	Prime
464253×2^3321908 – 1	2013	1,000,000	Prime
191273×2^3321908 – 1 ^[2]	2013	1,000,000	Prime
10⁹⁹⁹⁹⁹⁹ + 593499 ^[42]	2012-12-24	1,000,000	PRP

References

^ Chris Caldwell, The Prime Glossary: megaprime at The Prime Pages. Retrieved on 2008-01-04.
^ ^a ^b ^c ^d ^e ^f ^g Chris Caldwell, The Largest Known Primes at The Prime Pages.
^ ^a ^b ^c ^d ^e ^f ^g ^h ⁱ ^j ^k ^l ^m ⁿ ^o Henri Lifchitz & Renaud Lifchitz, Probable Primes Top 10000, primenumbers.net
^ 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 3×2^11731850 − 1, PrimeGrid
^ Official announcement of discovery of 3×2^11484018 − 1, PrimeGrid
^ Official announcement of discovery of 3×2^10829346 + 1, PrimeGrid
^ 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 ^e ^f ^g Generalized Sierpinski/Riesel primes
^ Official announcement of discovery of 75898⁵²⁴²⁸⁸ + 1, PrimeGrid
^ Official announcement of discovery of 502573×2^7181987 − 1, PrimeGrid
^ Official announcement of discovery of 402539×2^7173024 − 1, PrimeGrid
^ Official announcement of discovery of 3×2^7033641 + 1, PrimeGrid
^ Official announcement of discovery of 40597×2^6808509 – 1, PrimeGrid
^ Official announcement of discovery of 6679881×2^6679881 + 1, PrimeGrid
^ Official announcement of discovery of 304207×2^6643565 – 1, PrimeGrid
^ Official announcement of discovery of 398023×2^6418059 – 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 330286×5^1584399 – 1, PrimeGrid
^ Official announcement of discovery of 22934×5^1536762 – 1, PrimeGrid
^ Official announcement of discovery of 178658×5^1525224 – 1, PrimeGrid
^ Official announcement of discovery of 9×2^3497442 + 1, PrimeGrid
^ Official announcement of discovery of 59912×5^1500861 + 1, PrimeGrid
^ Official announcement of discovery of 37292×5^1487989 + 1, PrimeGrid
^ Official announcement of discovery of 173198×5^1457792 – 1, PrimeGrid
^ Official announcement of discovery of 81×2^3352924 + 1, PrimeGrid
^ Patrick De Geest, 10^999999 + y, World!Of Numbers

External links

Chris Caldwell, The Largest Known Primes Database at The Prime Pages
Top PRPs
A text file for all top primes
PrimeGrid’s 321 Prime Search, about the discovery of 3×2^6090515−1

[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 ^g Chris Caldwell, The Largest Known Primes at The Prime Pages.

[PRPTop-3] ^ ^a ^b ^c ^d ^e ^f ^g ^h ⁱ ^j ^k ^l ^m ⁿ ^o Henri Lifchitz & Renaud Lifchitz, Probable Primes Top 10000, primenumbers.net

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

[largest-5] Chris Caldwell, The Largest Known Prime by Year: A Brief History at The Prime Pages. Retrieved on 2008-09-28.

[6] Official announcement of discovery of 3×2^11731850 − 1, PrimeGrid

[7] Official announcement of discovery of 3×2^11484018 − 1, PrimeGrid

[8] Official announcement of discovery of 3×2^10829346 + 1, PrimeGrid

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

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

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

[GSRP-12] ^ ^a ^b ^c ^d ^e ^f ^g Generalized Sierpinski/Riesel primes

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

[14] Official announcement of discovery of 502573×2^7181987 − 1, PrimeGrid

[15] Official announcement of discovery of 402539×2^7173024 − 1, PrimeGrid

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

[17] Official announcement of discovery of 40597×2^6808509 – 1, PrimeGrid

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

[19] Official announcement of discovery of 304207×2^6643565 – 1, PrimeGrid

[20] Official announcement of discovery of 398023×2^6418059 – 1, PrimeGrid

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

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

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

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

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

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

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

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

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

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

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

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

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

[34] Official announcement of discovery of 330286×5^1584399 – 1, PrimeGrid

[35] Official announcement of discovery of 22934×5^1536762 – 1, PrimeGrid

[36] Official announcement of discovery of 178658×5^1525224 – 1, PrimeGrid

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

[38] Official announcement of discovery of 59912×5^1500861 + 1, PrimeGrid

[39] Official announcement of discovery of 37292×5^1487989 + 1, PrimeGrid

[40] Official announcement of discovery of 173198×5^1457792 – 1, PrimeGrid

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

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

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Known megaprimes and mega PRPs

See also

References

External links