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).

The number of megaprimes found by year.

As of September 2016, 208 (probable) megaprimes are known, including 192 definitely primes^[2] and 16 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
10223×2^31172165 + 1	2016-11	9,383,761	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
475856^524288 + 1 [9]	2012-08-08	2,976,633	Prime
356926^524288 + 1 [10]	2012-06-20	2,911,151	Prime
341112^524288 + 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
29×2^8727880 − 1 [12]	2016	2,627,356	PRP[13]
75898^524288 + 1 [14]	2011-11-19	2,558,647	Prime
28433×2^7830457 + 1 [2]	2004	2,357,207	Prime
502573×2^7181987 − 1 [15]	2014-10-04	2,162,000	Prime
402539×2^7173024 − 1 [16]	2014-10-02	2,159,301	Prime
3343×2^7166019 - 1	2016	2,157,191	Prime
161041×2^7107964 + 1	2015-01	2,139,716	Prime
3×2^7033641 + 1 [17]	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
4×72^1119849 − 1 [12]	2016	2,079,933	Prime
40597×2^6808509 – 1 [18]	2013-12-25	2,049,571	Prime
6679881×2^6679881 + 1 [19]	2009-07-25	2,010,852	Prime
37×2^6660841 − 1	2014	2,005,115	Prime
304207×2^6643565 – 1 [20]	2013-10-10	1,999,918	Prime
398023×2^6418059 – 1 [21]	2013-10-05	1,932,034	Prime
6328548×2^6328548 + 1 [22]	2009-04-20	1,905,090	Prime
3×2^6090515 – 1 [23]	2010-04-24	1,833,429	Prime
1583×2^5989282 − 1	2015	1,802,957	Prime
7×2^5775996 + 1 [24]	2012-11-02	1,738,749	Prime
1243×2^5686715 - 1	2016	1,711,875	Prime
9×2^5642513 + 1	2013	1,698,567	Prime
2622×11^1621920 – 1 [12]	2015	1,689,060	Prime
252191×2^5497878 – 1 [25]	2012-06-23	1,655,032	Prime
1828858^262144+1	2016	1,641,593	Prime
258317 × 2^5450519+1	2008	1,640,776	Prime
1615588^262144 + 1	2016	1,627,477	Prime
1488256^262144 + 1	2016	1,618,131	Prime
1415198^262144 + 1	2016	1,612,400	Prime
${\displaystyle {\tfrac {2^{5240707}-1}{75392810903}}}$ [3]	2016-07	1,577,600	PRP
180062×5^2249192 − 1	2016	1,572,123	Prime
27×2^5213635 + 1	2015	1,569,462	Prime
53546×5^2216664-1	2016	1,549,387	Prime
2^5146295 + 41693 [3]	2009-11	1,549,190	PRP
773620^262144 + 1 [26]	2012-04-19	1,543,643	Prime
51×2^5085142 - 1	2014	1,530,782	Prime
3×2^5082306 + 1 [27]	2009-04-03	1,529,928	Prime
676754^262144+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
525094^262144+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
362978^262144 − 362978^131072 + 1	2015	1,457,490	Prime
361658^262144+1	2011	1,457,075	Prime
100186 × 5^2079747 − 1	2015	1,453,686	Prime
2^4792057 − 2^2396029 + 1	2014	1,442,553	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
192098^262144 − 192098^131072 + 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 [28]	2012-02-25	1,370,863	Prime
27× 2^4542344 − 1	2014	1,367,384	Prime
${\displaystyle {\tfrac {2^{4533073}+2^{2266537}+1}{5}}}$ [3]	2014-03	1,364,591	PRP
145310^262144+1	2011	1,353,265	Prime
36772 × 6^1723287 − 1	2014	1,340,983	Prime
${\displaystyle {\tfrac {13^{1199467}+1}{14}}}$ [3]	2015-12	1,336,138	PRP
151×2^4424321 − 1	2016	1,331,856	Prime
353159×2^4331116 – 1 [29]	2011-05-31	1,303,802	Prime
682156×79^682156 + 1	2016	1,294,484	Prime
141941×2^4299438 – 1 [30]	2011-05-26	1,294,265	Prime
15 × 2^4246384+1	2013	1,278,291	Prime
3×2^4235414 – 1 [31]	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
1259 × 2^4196028-1	2016	1,263,134	Prime
${\displaystyle {\tfrac {2^{4187251}-1}{72234342371519}}}$ [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
39653×430^460397-1 [12]	2016	1,212,446	Prime
40734^262144+1	2011	1,208,473	Prime
9 × 2^4005979 - 1	2012	1,205,921	Prime
12 × 68^656921 + 1 [12]	2016	1,203,815	Prime
1993191 × 4^1993191 − 1	2015	1,200,027	Prime
27×2^3855094 – 1 [32]	2012-02-28	1,160,501	Prime
24518^262144+1	2008	1,150,678	Prime
123547×2^3804809 – 1 [33]	2011-05-08	1,145,367	Prime
415267×2^3771929 – 1 [34]	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 [35]	2014-03-21	1,107,453	Prime
15×2^3668194 – 1	2013	1,104,238	Prime
33300×430^417849-1 [12]	2016	1,100,397	Prime
65531 × 2^3629342-1	2011	1,092,546	Prime
${\displaystyle {\tfrac {106\cdot 23^{800873}-7}{11}}}$ [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 × 492^399095 − 1 [12]		1,074,352	Prime
22934×5^1536762 – 1 [36]	2014-02-06	1,074,155	Prime
${\tfrac {7^{{1264699}}-1}{6}}$ [3]	2014-01	1,068,794	PRP
178658×5^1525224 – 1 [37]	2014-01-31	1,066,092	Prime
465×2^3536871 – 1 [38]	2016-09-30	1,064,707	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 [39]	2012-10-23	1,052,836	Prime
51×2^3490971 + 1	2014	1,050,889	Prime
59912×5^1500861 + 1 [40]	2014-01-17	1,049,062	Prime
$\tfrac{2^{3464473}-1}{604874508299177}$ [3]	2014-10	1,042,896	PRP
37292×5^1487989 + 1 [41]	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 × 414^391179 + 1 [12]		1,023,717	Prime
67×2^3391385 – 1	2014	1,020,911	Prime
173198×5^1457792 – 1 [42]	2013-12-04	1,018,959	Prime
81×2^3352924 + 1 [43]	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
10^999999 + 593499 [44]	2012-12-24	1,000,000	PRP

See also

• Largest known prime number
• Electronic Frontier Foundation—Awards

References

1. Chris Caldwell, The Prime Glossary: megaprime at The Prime Pages. Retrieved on 2008-01-04.
2. Chris Caldwell, The Largest Known Primes at The Prime Pages.
3. 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.
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
12. Generalized Sierpinski/Riesel primes
13. This number is a 3-PRP, but not prime (it is proven composite)
14. Official announcement of discovery of 75898⁵²⁴²⁸⁸ + 1, PrimeGrid
15. Official announcement of discovery of 502573×2^7181987 − 1, PrimeGrid
16. Official announcement of discovery of 402539×2^7173024 − 1, PrimeGrid
17. Official announcement of discovery of 3×2^7033641 + 1, PrimeGrid
18. Official announcement of discovery of 40597×2^6808509 – 1, PrimeGrid
19. Official announcement of discovery of 6679881×2^6679881 + 1, PrimeGrid
20. Official announcement of discovery of 304207×2^6643565 – 1, PrimeGrid
21. Official announcement of discovery of 398023×2^6418059 – 1, PrimeGrid
22. Official announcement of discovery of 6328548×2^6328548 + 1, PrimeGrid
23. Official announcement of discovery of 3×2^6090515 – 1, PrimeGrid
24. Official announcement of discovery of 7×2^5775996 + 1, PrimeGrid
25. Official announcement of discovery of 252191×2^5497878 – 1, PrimeGrid
26. Official announcement of discovery of 773620²⁶²¹⁴⁴ + 1, PrimeGrid
27. Official announcement of discovery of 3×2^5082306 + 1, PrimeGrid
28. Official announcement of discovery of 121×2^4553899 – 1, PrimeGrid
29. Official announcement of discovery of 353159×2^4331116 – 1, PrimeGrid
30. Official announcement of discovery of 141941×2^4299438 – 1, PrimeGrid
31. Official announcement of discovery of 3×2^4235414 – 1, PrimeGrid
32. Official announcement of discovery of 27×2^3855094 – 1, PrimeGrid
33. Official announcement of discovery of 123547×2^3804809 – 1, PrimeGrid
34. Official announcement of discovery of 415267×2^3771929 – 1, PrimeGrid
35. Official announcement of discovery of 330286×5^1584399 – 1, PrimeGrid
36. Official announcement of discovery of 22934×5^1536762 – 1, PrimeGrid
37. Official announcement of discovery of 178658×5^1525224 – 1, PrimeGrid
38. Official announcement of discovery of 465×2^3536871 – 1, PrimeGrid
39. Official announcement of discovery of 9×2^3497442 + 1, PrimeGrid
40. Official announcement of discovery of 59912×5^1500861 + 1, PrimeGrid
41. Official announcement of discovery of 37292×5^1487989 + 1, PrimeGrid
42. Official announcement of discovery of 173198×5^1457792 – 1, PrimeGrid
43. Official announcement of discovery of 81×2^3352924 + 1, PrimeGrid
44. 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