A megaprime is a prime number with at least one million decimal digits.[1]

A titanic prime, a term coined by Samuel Yates in the 1980s, is a prime number with at least 1,000 digits; and a gigantic prime has at least 10,000 digits.

The number of megaprimes found by year.
The number of megaprimes found by year.

As of 11 January 2022, 1268 (probable) megaprimes are known, including 1194 definite primes[2] and 74 probable primes.[3] 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,[4][5] and was subject to a cooperative computing award.

The term bevaprime has been proposed as a term for a prime with at least 1,000,000,000 digits.[6]

In fact, 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 10999999 + 593499, a strong PRP, is actually the smallest megaprime.[7]

The last prime that is not a megaprime is almost certainly 10999999 - 172473.[3]

Known megaprimes and mega PRPs

This is a dynamic list and may never be able to satisfy particular standards for completeness. You can help by adding missing items with reliable sources.

Entries labelled "Prime" have been proved prime; those labelled "PRP" have not and primes that hasn't been fully verified by Prime Pages will be ranked, but be listed as a PRP. See the article Probable prime. Only primes with more than 2,000,000 digits are included in this list.

Rank (only for proven primes)[8] Number Discovery date Decimal digits Prime / PRP
1 282589933 – 1 7 December 2018 24,862,048 Prime
2 277232917 – 1 26 December 2017 23,249,425 Prime
3 274207281 – 1 7 January 2016 22,338,618 Prime
4 257885161 – 1 25 January 2013 17,425,170 Prime
5 243112609 – 1 23 August 2008 12,978,189 Prime
6 242643801 – 1 4 June 2009 12,837,064 Prime
7 237156667 – 1 6 September 2008 11,185,272 Prime
8 232582657 – 1 4 September 2006 9,808,358 Prime
9 10223×231172165 + 1 31 October 2016 9,383,761 Prime
10 230402457 – 1 15 December 2005 9,152,052 Prime
- 8 May 2021 8,177,207 PRP
11 225964951 – 1 18 February 2005 7,816,230 Prime
12 224036583 – 1 15 May 2004 7,235,733 Prime
13 202705×221320516 + 1 1 December 2021 6,418,121 Prime
14 220996011 – 1 17 November 2005 6,320,430 Prime
15 10590941048576 + 1 4 November 2018 6,317,602 Prime
16 9194441048576 + 1 2 September 2017 6,253,210 Prime
17 168451×219375200 + 1 26 September 2017 5,832,522 Prime
- 20 April 2021 5,794,777 PRP
18 69×218831865 - 1 16 December 2021 5,668,959 Prime
19 7×218233956 + 1 1 October 2020 5,488,969 Prime
20 3×217748034 - 1 6 September 2021 5,342,692 Prime
21 23 February 2017 5,338,805 Prime
22 7×66772401 + 1 9 September 2019 5,269,954 Prime
23 8508301×217016603-1 22 March 2018 5,122,515 Prime
24 3×216819291-1 20 January 2021 5,063,112 Prime
25 3×216408818+1 28 October 2020 4,939,547 Prime
26 69×215866556+1 20 August 2021 4,776,312 Prime
27 2525332×732525332+1 28 August 2021 4,705,888 Prime
28 215317227+27658614+1 31 July 2020 4,610,945 Prime
29 6×56546983+1 13 June 2020 4,576,146 Prime
- June 2021 4,556,209 PRP
30 69×214977631-1 3 December 2021 4,508,719 Prime
31 192971×214773498-1 7 March 2021 4,447,272 Prime
32 6962×312863120-1 29 February 2020 4,269,952 Prime
33 99739×214019102-1 25 December 2019 4,220,176 Prime
34 404849×213764867+1 10 March 2021 4,143,644 Prime
35 2740879×213704395-1 26 October 2019 4,125,441 Prime
36 479216×38625889-1 16 November 2019 4,115,601 Prime
37 30 January 2017 4,055,114 Prime
38 213466917 – 1 14 November 2001 4,053,946 Prime
- 213380298 – 27 March 2021 4,027,872 PRP
- September 2013 4,025,533 PRP
- September 2013 4,017,941 PRP
39 9×213334487 + 1 31 March 2020 4,014,082 Prime
40 206039×213104952 - 1 26 April 2021 3,944,989 Prime
41 2805222×55610444 + 1 3 September 2019 3,921,539 Prime
42 19249×213018586 + 1 26 March 2007 3,918,990 Prime
43 2293×212918431 - 1 13 February 2021 3,888,839 Prime
- July 2020 3,763,995 PRP
44 9×212406887 + 1 29 March 2020 3,734,847 Prime
45 69×212231580 - 1 27 July 2021 3,682,075 Prime
46 27*212184319 + 1 6 February 2021 3,667,847 Prime
47 3×211895718 − 1 26 June 2015 3,580,969 Prime
48 3×211731850 − 1 13 March 2015 3,531,640 Prime
49 69×211718455 − 1 4 December 2020 3,527,609 Prime
50 69×211604348 − 1 4 December 2020 3,493,259 Prime
51 9×211500843 + 1 13 March 2020 3,462,100 Prime
52 3×211484018 − 1 22 November 2014 3,457,035 Prime
53 193997*211452891 +1 3 April 2018 3,447,670 Prime
54 3638450524288 +1 31 May 2020 3,439,810 Prime
55 9221*211392194 -1 7 February 2021 3,429,397 Prime
56 9*211366286 +1 26 March 2020 3,421,594 Prime
57 5*211355764 -1 2 October 2021 3,418,427 Prime
58 3214654524288 +1 25 December 2019 3,411,613 Prime
59 146561*211280802 -1 17 November 2020 3,395,865 Prime
60 2985036524288 +1 19 September 2019 3,394,739 Prime
61 2877652524288 +1 29 June 2019 3,386,397 Prime
62 2788032524288 +1 18 April 2019 3,379,193 Prime
63 2733014524288 +1 19 March 2019 3,374,655 Prime
64 9*211158963 +1 13 March 2020 3,359,184 Prime
65 9271*211134335 -1 17 January 2021 3,351,773 Prime
66 2312092524288+1 5 August 2018 3,336,572 Prime
67 2061748524288+1 21 March 2018 3,310,478 Prime
68 1880370524288 + 1 15 January 2018 3,289,511 Prime
69 3×210829346 + 1 14 January 2014 3,259,959 Prime
70 5×210495620 - 1 26 September 2021 3,159,498 Prime
- 9 July 2020 3,143,811 PRP
71 5×210349000 - 1 26 September 2021 3,115,361 Prime
72 17 January 2017 3,107,335 Prime
73 14 January 2017 3,068,389 Prime
74 874208*541748416-1 26 September 2019 3,028,951 Prime
75 475856524288 + 1 8 August 2012 2,976,633 Prime
76 9*29778263+1 5 August 2020 2,943,552 Prime
77 1806676*411806676+1 12 March 2018 2,913,785 Prime
78 356926524288 + 1 25 July 2012 2,911,151 Prime
79 341112524288 + 1 25 June 2012 2,900,832 Prime
80 121*29584444+1 20 November 2020 2,885,208 Prime
81 11*29381365+1 7 March 2020 2,824,074 Prime
82 27653×29167433 + 1 8 June 2005 2,759,677 Prime
83 90527×29162167 + 1 30 June 2010 2,758,093 Prime
- 29092392 + 40291 February 2011 2,737,083 PRP
84 6795×29144320 - 1 31 March 2021 2,752,719 Prime
86 1323365*1161323365+1 18 January 2018 2,732,038 Prime
86 13×28989858 + 1 10 March 2020 2,706,219 Prime
87 273809×28932416 − 1 13 December 2017 2,688,931 Prime
88 2×35570081 + 1 14 February 2020 2,657,605 Prime
89 25×28788628 + 1 1 March 2021 2,645,643 Prime
90 2038×3661028507 − 1 4 April 2016 2,636,562 Prime
91 17×28636199 + 1 17 February 2021 2,599,757 Prime
92 75898524288 + 1 19 November 2021 2,558,647 Prime
93 25×28456828 + 1 28 January 2021 2,545,761 Prime
94 39×28413422 + 1 23 January 2021 2,532,694 Prime
95 31×28348000 + 1 19 January 2021 2,513,000 Prime
96 27×28342438 - 1 1 February 2021 2,511,326 Prime
97 3867×28261084 - 1 14 April 2021 2,486,838 Prime
- August 2020 2,449,236 PRP
98 273662×53493296 - 1 7 December 2021 2,441,715 Prime
99 11×28103463 + 1 6 March 2020 2,439,387 Prime
100 102818×53440382 - 1 10 October 2021 2,404,729 Prime
101 11×27971110 - 1 25 November 2019 2,399,545 Prime
102 27×27963247 + 1 16 January 2021 2,397,178 Prime
103 3177×27954621 - 1 13 June 2021 2,394,584 Prime
104 39×27946769 + 1 15 January 2021 2,392,218 Prime
105 7×63072198 + 1 4 August 2019 2,390,636 Prime
106 3765×27904593 - 1 10 January 2021 2,379,524 Prime
107 29×27899985 + 1 15 January 2021 2,378,134 Prime
108 861×27895451 - 1 21 February 2021 2,376,771 Prime
- July 2021 2,358,349 PRP
109 28433×27830457 + 1 31 December 2004 2,357,207 Prime
110 5×27755002 - 1 23 September 2021 2,334,489 Prime
111 2545×27732265 - 1 13 January 2021 2,327,648 Prime
112 5539×27730709 - 1 15 January 2021 2,327,180 Prime
113 4817×27719584 - 1 13 June 2021 2,323,831 Prime
114 1341174×531341174 + 1 22 August 2017 2,312,561 Prime
115 45×27661004 + 1 13 December 2020 2,306,194 Prime
116 15×27619838 + 1 24 December 2020 2,293,801 Prime
117 3597×27580693 - 1 10 January 2021 2,282,020 Prime
118 7401×27523295 - 1 21 February 2021 2,264,742 Prime
119 45×27513661 + 1 12 November 2020 2,261,839 Prime
120 11 January 2017 2,259,865 Prime
121 29×27374577 + 1 28 October 2020 2,219,971 Prime
122 109838×53168862 - 1 13 August 2020 2,219,971 Prime
123 101×27345194 - 1 5 October 2019 2,219,971 Prime
- March 2018 2,201,714 PRP
124 15×27300254 + 1 25 October 2020 2,219,971 Prime
125 1759×27284439 - 1 28 August 2021 2,219,971 Prime
126 737×27269322 − 1 10 August 2017 2,188,287 Prime
127 118568×53112069 + 1 2 May 2020 2,175,248 Prime
128 6039×27207973 − 1 24 March 2021 2,169,820 Prime
129 502573×27181987 − 1 4 October 2014 2,162,000 Prime
130 402539×27173024 − 1 2 October 2014 2,159,301 Prime
131 3343×27166019 - 1 29 September 2016 2,157,191 Prime
132 161041×27107964 + 1 8 January 2015 2,139,716 Prime
- October 2017 2,131,318 PRP
133 27*27046834+1 16 October 2018 2,121,310 Prime
134 1759×27046791 - 1 28 August 2021 2,121,299 Prime
135 327×27044001 - 1 13 January 2021 2,120,459 Prime
136 5×27037188 - 1 22 September 2021 2,118,406 Prime
137 3×27033641 + 1 21 February 2011 2,117,338 Prime
138 33661×27031232 + 1 30 October 2007 2,116,617 Prime
139 6 January 2017 2,114,016 Prime
140 207494*53017502-1 19 March 2020 2,109,149 Prime
141 15*26993631-1 25 August 2021 2,105,294 Prime
142 8943501*26972593-1 8 January 2022 2,098,967 Prime
143 26972593 – 1 1 June 1999 2,098,960 Prime
144 6219*26958945-1 7 January 2021 2,094,855 Prime
145 51*26945567+1 26 May 2020 2,090,826 Prime
146 238694*52979422-1 13 March 2020 2,082,532 Prime
147 4×721119849 − 1 7 September 2016 2,079,933 Prime
148 33*26894190-1 27 July 2021 2,075,360 Prime
149 146264*52953282-1 10 March 2020 2,064,261 Prime
150 69*26838971-1 1 March 2020 2,058,738 Prime
151 35816*52945294-1 5 March 2020 2,058,677 Prime
152 127*26836153-1 25 June 2018 2,057,890 Prime
153 19*26833086+1 25 October 2020 2,056,966 Prime
154 40597×26808509 – 1 27 November 2013 2,049,571 Prime
155 283*26804701-1 19 January 2020 2,048,431 Prime
156 1861209*26789999+1 2 December 2020 2,044,000 Prime
157 5817*26789459-1 9 January 2021 2,043,835 Prime
158 8435*26786180-1 7 January 2021 2,042,848 Prime
159 51*26753404+1 26 May 2020 2,032,979 Prime
160 9995*26711008-1 31 December 2020 2,020,219 Prime
161 39*26684941+1 20 October 2020 2,012,370 Prime
162 6679881×26679881 + 1 25 July 2009 2,010,852 Prime
163 37×26660841 − 1 30 July 2014 2,005,115 Prime
164 39*26648997+1 20 October 2020 2,001,550 Prime

Notes

See also

References

  1. ^ Chris Caldwell, The Prime Glossary: megaprime at The Prime Pages. Retrieved on 2008-01-04.
  2. ^ a b c d e f g h i Chris Caldwell, The Largest Known Primes at The Prime Pages.
  3. ^ a b c d e f g h i j k Henri Lifchitz & Renaud Lifchitz, Probable Primes Top 10000, primenumbers.net
  4. ^ a b 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. ^ "Chris Caldwell, The Largest Known Prime by Year: A Brief History". Archived from the original on 2016-01-01. Retrieved 2008-01-04.CS1 maint: bot: original URL status unknown (link)
  7. ^ Patrick De Geest, 10^999999 + y, World!Of Numbers
  8. ^ Caldwell, Chris K. "THE LARGEST KNOWN PRIMES (The 5,000 largest known primes)". Retrieved 23 November 2018.
  9. ^ "Official press release of 51st Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 7 December 2018.
  10. ^ "Official press release of 50th Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 26 December 2017.
  11. ^ "Official press release of 49th Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 7 January 2016.
  12. ^ "Official press release of 48th Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 25 January 2013.
  13. ^ a b "Official press release of 45th and 46th Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 10 September 2008.
  14. ^ "Official press release of 47th Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 25 January 2013.
  15. ^ "Official press release of 44th Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 25 January 2013.
  16. ^ Official announcement of discovery of 10223×231172165 + 1, PrimeGrid
  17. ^ "Official press release of 43rd Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 25 January 2013.
  18. ^ "Official press release of 42nd Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 25 January 2013.
  19. ^ "Official press release of 41st Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 25 January 2013.
  20. ^ Official announcement of discovery of 202705×221320516 + 1, PrimeGrid
  21. ^ "Official press release of 40th Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 25 January 2013.
  22. ^ Official announcement of discovery of 10590941048576 + 1, PrimeGrid
  23. ^ Official announcement of discovery of 9194441048576 + 1, PrimeGrid
  24. ^ Official announcement of discovery of 168451×219375200 + 1, PrimeGrid
  25. ^ Official announcement of discovery of 3×217748034 - 1, PrimeGrid
  26. ^ Official announcement of discovery of 8508301×217016603-1, PrimeGrid
  27. ^ Official announcement of discovery of 3×216819291-1, PrimeGrid
  28. ^ Official announcement of discovery of 3×216408818+1, PrimeGrid
  29. ^ Official announcement of discovery of 99739×214019102-1, PrimeGrid
  30. ^ "Official press release of 39th Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 25 January 2013.
  31. ^ Official announcement of discovery of 2805222×55610444 + 1, PrimeGrid
  32. ^ Official announcement of discovery of 3×211731850 − 1, PrimeGrid
  33. ^ Official announcement of discovery of 3×211484018 − 1, PrimeGrid
  34. ^ Official announcement of discovery of 3×210829346 + 1, PrimeGrid
  35. ^ Official announcement of discovery of 475856524288 + 1, PrimeGrid
  36. ^ Official announcement of discovery of 356926524288 + 1, PrimeGrid
  37. ^ Official announcement of discovery of 341112524288 + 1, PrimeGrid
  38. ^ a b c d Generalized Sierpinski/Riesel primes
  39. ^ Official announcement of discovery of 75898524288 + 1, PrimeGrid
  40. ^ Official announcement of discovery of 502573×27181987 − 1, PrimeGrid
  41. ^ Official announcement of discovery of 402539×27173024 − 1, PrimeGrid
  42. ^ Official announcement of discovery of 3×27033641 + 1, PrimeGrid
  43. ^ Official announcement of discovery of 40597×26808509 – 1, PrimeGrid
  44. ^ Official announcement of discovery of 6679881×26679881 + 1, PrimeGrid