Megaprime

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

Other terms for large primes include titanic prime, coined by Samuel Yates in the 1980s for a prime with at least 1,000 digits, and gigantic prime for a prime with at least 10,000 digits.[citation needed] Bevaprime has been proposed for a prime with at least 1,000,000,000 digits.[2]

Number of megaprimes found by year through 2017.

As of 2022, there are more than 1000 known definite megaprimes[3] and 78 probable primes (PRPs) which have more than 1,000,000 digits.[4] 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.[5][6] Nayan was awarded a Cooperative Computing Award from the Electronic Frontier Foundation for this achievement.

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 that 10999999 + 593499, a strong probable prime, is the smallest megaprime.[7] As of 2022, the smallest number to be known as a megaprime is 10999999 + 308267*10292000 + 1.

The last prime that is not a megaprime is almost certainly 10999999 - 172473.[4]

Known megaprimes and mega PRPs[edit]

Entries labelled "Prime" have been proved prime; those labelled "PRP" have not, and primes that have not been fully verified by PrimePages 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 25 November 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 3×218924888 - 1 25 March 2022 5,696,990 Prime
19 69×218831865 - 1 16 December 2021 5,668,959 Prime
20 7×218233956 + 1 1 October 2020 5,488,969 Prime
21 3×218196595 - 1 18 January 2022 5,477,722 Prime
22 3×217748034 - 1 6 September 2021 5,342,692 Prime
23 23 February 2017 5,338,805 Prime
24 3622×57558139 - 1 18 February 2022 5,282,917 Prime
25 7×66772401 + 1 9 September 2019 5,269,954 Prime
26 8508301×217016603-1 22 March 2018 5,122,515 Prime
27 3×216819291-1 20 January 2021 5,063,112 Prime
28 3×216408818+1 28 October 2020 4,939,547 Prime
29 69×215866556+1 20 August 2021 4,776,312 Prime
30 2525332×732525332+1 28 August 2021 4,705,888 Prime
31 215317227+27658614+1 31 July 2020 4,610,945 Prime
32 6×56546983+1 13 June 2020 4,576,146 Prime
- June 2021 4,556,209 PRP
33 69×214977631-1 3 December 2021 4,508,719 Prime
34 192971×214773498-1 7 March 2021 4,447,272 Prime
35 6962×312863120-1 29 February 2020 4,269,952 Prime
36 99739×214019102-1 25 December 2019 4,220,176 Prime
37 69×213832885-1 17 January 2022 4,164,116 Prime
38 404849×213764867+1 10 March 2021 4,143,644 Prime
39 2740879×213704395-1 26 October 2019 4,125,441 Prime
40 479216×38625889-1 16 November 2019 4,115,601 Prime
41 30 January 2017 4,055,114 Prime
42 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
43 9×213334487 + 1 31 March 2020 4,014,082 Prime
44 206039×213104952 - 1 26 April 2021 3,944,989 Prime
45 2805222×55610444 + 1 3 September 2019 3,921,539 Prime
46 19249×213018586 + 1 26 March 2007 3,918,990 Prime
47 2293×212918431 - 1 13 February 2021 3,888,839 Prime
- July 2020 3,763,995 PRP
48 9×212406887 + 1 29 March 2020 3,734,847 Prime
49 69×212231580 - 1 27 July 2021 3,682,075 Prime
50 27*212184319 + 1 6 February 2021 3,667,847 Prime
51 3×211895718 − 1 26 June 2015 3,580,969 Prime
52 3×211731850 − 1 13 March 2015 3,531,640 Prime
53 69×211718455 − 1 4 December 2020 3,527,609 Prime
54 69×211604348 − 1 4 December 2020 3,493,259 Prime
55 9×211500843 + 1 13 March 2020 3,462,100 Prime
56 3×211484018 − 1 22 November 2014 3,457,035 Prime
57 193997*211452891 +1 3 April 2018 3,447,670 Prime
58 3638450524288 +1 31 May 2020 3,439,810 Prime
59 9221*211392194 -1 7 February 2021 3,429,397 Prime
60 9*211366286 +1 26 March 2020 3,421,594 Prime
61 5*211355764 -1 2 October 2021 3,418,427 Prime
62 3214654524288 +1 25 December 2019 3,411,613 Prime
63 146561*211280802 -1 17 November 2020 3,395,865 Prime
64 2985036524288 +1 19 September 2019 3,394,739 Prime
65 2877652524288 +1 29 June 2019 3,386,397 Prime
66 2788032524288 +1 18 April 2019 3,379,193 Prime
67 2733014524288 +1 19 March 2019 3,374,655 Prime
68 9*211158963 +1 13 March 2020 3,359,184 Prime
69 9271*211134335 -1 17 January 2021 3,351,773 Prime
70 2312092524288+1 5 August 2018 3,336,572 Prime
71 2061748524288+1 21 March 2018 3,310,478 Prime
72 1880370524288 + 1 15 January 2018 3,289,511 Prime
73 27×210902757 - 1 7 March 2022 3,282,059 Prime
74 3×210829346 + 1 14 January 2014 3,259,959 Prime
75 5×210495620 - 1 26 September 2021 3,159,498 Prime
- 9 July 2020 3,143,811 PRP
76 5×210349000 - 1 26 September 2021 3,115,361 Prime
77 17 January 2017 3,107,335 Prime
78 14 January 2017 3,068,389 Prime
79 874208*541748416-1 26 September 2019 3,028,951 Prime
80 475856524288 + 1 8 August 2012 2,976,633 Prime
81 9*29778263+1 5 August 2020 2,943,552 Prime
82 1806676*411806676+1 12 March 2018 2,913,785 Prime
83 356926524288 + 1 25 July 2012 2,911,151 Prime
84 341112524288 + 1 25 June 2012 2,900,832 Prime
85 43*29596983-1 28 February 2022 2,888,982 Prime
86 121*29584444+1 20 November 2020 2,885,208 Prime
87 11*29381365+1 7 March 2020 2,824,074 Prime
88 27653×29167433 + 1 8 June 2005 2,759,677 Prime
89 90527×29162167 + 1 30 June 2010 2,758,093 Prime
- 29092392 + 40291 February 2011 2,737,083 PRP
90 6795×29144320 - 1 31 March 2021 2,752,719 Prime
91 1323365*1161323365+1 18 January 2018 2,732,038 Prime
92 13×28989858 + 1 10 March 2020 2,706,219 Prime
93 4159×28938471 - 1 19 April 2022 2,690,752 Prime
94 273809×28932416 − 1 13 December 2017 2,688,931 Prime
95 2×35570081 + 1 14 February 2020 2,657,605 Prime
96 25×28788628 + 1 1 March 2021 2,645,643 Prime
97 2038×3661028507 − 1 4 April 2016 2,636,562 Prime
98 17×28636199 + 1 17 February 2021 2,599,757 Prime
99 75898524288 + 1 19 November 2021 2,558,647 Prime
100 25×28456828 + 1 28 January 2021 2,545,761 Prime
101 39×28413422 + 1 23 January 2021 2,532,694 Prime
102 31×28348000 + 1 19 January 2021 2,513,000 Prime
103 27×28342438 - 1 1 February 2021 2,511,326 Prime
104 3867×28261084 - 1 14 April 2021 2,486,838 Prime
- August 2020 2,449,236 PRP
105 273662×53493296 - 1 7 December 2021 2,441,715 Prime
106 11×28103463 + 1 6 March 2020 2,439,387 Prime
107 102818×53440382 - 1 8 October 2021 2,404,729 Prime
108 11×27971110 - 1 25 November 2019 2,399,545 Prime
109 27×27963247 + 1 16 January 2021 2,397,178 Prime
110 3177×27954621 - 1 13 June 2021 2,394,584 Prime
111 39×27946769 + 1 15 January 2021 2,392,218 Prime
112 7×63072198 + 1 4 August 2019 2,390,636 Prime
113 3765×27904593 - 1 10 January 2021 2,379,524 Prime
114 29×27899985 + 1 15 January 2021 2,378,134 Prime
115 861×27895451 - 1 21 February 2021 2,376,771 Prime
- July 2021 2,358,349 PRP
116 28433×27830457 + 1 31 December 2004 2,357,207 Prime
117 5×27755002 - 1 23 September 2021 2,334,489 Prime
118 2545×27732265 - 1 13 January 2021 2,327,648 Prime
119 5539×27730709 - 1 15 January 2021 2,327,180 Prime
120 4817×27719584 - 1 13 June 2021 2,323,831 Prime
121 1341174×531341174 + 1 22 August 2017 2,312,561 Prime
122 9467×27680034 - 1 20 February 2022 2,311,925 Prime
- February 2022 2,307,015 PRP
123 45×27661004 + 1 13 December 2020 2,306,194 Prime
124 15×27619838 + 1 24 December 2020 2,293,801 Prime
125 3597×27580693 - 1 10 January 2021 2,282,020 Prime
126 7401×27523295 - 1 21 February 2021 2,264,742 Prime
127 45×27513661 + 1 12 November 2020 2,261,839 Prime
128 11 January 2017 2,259,865 Prime
129 29×27374577 + 1 28 October 2020 2,219,971 Prime
130 109838×53168862 - 1 13 August 2020 2,219,971 Prime
131 101×27345194 - 1 5 October 2019 2,219,971 Prime
- March 2018 2,201,714 PRP
132 15×27300254 + 1 25 October 2020 2,219,971 Prime
133 422429! + 1 21 February 2022 2,193,027 Prime
134 1759×27284439 - 1 28 August 2021 2,192,838 Prime
135 737×27269322 − 1 10 August 2017 2,188,287 Prime
136 118568×53112069 + 1 2 May 2020 2,175,248 Prime
137 6039×27207973 − 1 24 March 2021 2,169,820 Prime
138 502573×27181987 − 1 4 October 2014 2,162,000 Prime
139 402539×27173024 − 1 2 October 2014 2,159,301 Prime
140 3343×27166019 - 1 29 September 2016 2,157,191 Prime
141 161041×27107964 + 1 8 January 2015 2,139,716 Prime
- October 2017 2,131,318 PRP
142 27*27046834+1 16 October 2018 2,121,310 Prime
143 1759×27046791 - 1 28 August 2021 2,121,299 Prime
144 327×27044001 - 1 13 January 2021 2,120,459 Prime
145 5×27037188 - 1 22 September 2021 2,118,406 Prime
146 3×27033641 + 1 21 February 2011 2,117,338 Prime
147 33661×27031232 + 1 30 October 2007 2,116,617 Prime
148 6 January 2017 2,114,016 Prime
149 207494*53017502-1 19 March 2020 2,109,149 Prime
150 15*26993631-1 25 August 2021 2,105,294 Prime
151 8943501*26972593-1 8 January 2022 2,098,967 Prime
152 26972593 – 1 1 June 1999 2,098,960 Prime
153 6219*26958945-1 7 January 2021 2,094,855 Prime
154 51*26945567+1 26 May 2020 2,090,826 Prime
155 238694*52979422-1 13 March 2020 2,082,532 Prime
156 4×721119849 − 1 7 September 2016 2,079,933 Prime
157 33*26894190-1 27 July 2021 2,075,360 Prime
158 2345*26882320-1 13 April 2022 2,071,789 Prime
159 146264*52953282-1 10 March 2020 2,064,261 Prime
160 69*26838971-1 1 March 2020 2,058,738 Prime
161 35816*52945294-1 5 March 2020 2,058,677 Prime
162 127*26836153-1 25 June 2018 2,057,890 Prime
163 19*26833086+1 25 October 2020 2,056,966 Prime
164 40597×26808509 – 1 27 November 2013 2,049,571 Prime
165 283*26804701-1 19 January 2020 2,048,431 Prime
166 1861209*26789999+1 2 December 2020 2,044,000 Prime
167 5817*26789459-1 9 January 2021 2,043,835 Prime
168 8435*26786180-1 7 January 2021 2,042,848 Prime
169 51*26753404+1 26 May 2020 2,032,979 Prime
170 9995*26711008-1 31 December 2020 2,020,219 Prime
171 39*26684941+1 20 October 2020 2,012,370 Prime
172 6679881×26679881 + 1 25 July 2009 2,010,852 Prime
173 37×26660841 − 1 30 July 2014 2,005,115 Prime
174 39*26648997+1 20 October 2020 2,001,550 Prime

See also[edit]

References[edit]

  1. ^ Chris Caldwell, The Prime Glossary: megaprime at The PrimePages. Retrieved on 2008-01-04.
  2. ^ "Chris Caldwell, The Largest Known Prime by Year: A Brief History". Archived from the original on 2016-01-01. Retrieved 2008-01-04.{{cite web}}: CS1 maint: bot: original URL status unknown (link)
  3. ^ a b c d e f g h i Chris Caldwell, The Largest Known Primes at The PrimePages.
  4. ^ a b c d e f g h i j k l Henri Lifchitz & Renaud Lifchitz, Probable Primes Top 10000, primenumbers.net
  5. ^ a b GIMPS press release, GIMPS Finds First Million-Digit Prime. Retrieved on 2008-01-04.
  6. ^ Chris Caldwell, The Largest Known Prime by Year: A Brief History at The PrimePages. Retrieved on 2008-09-28.
  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 273662*53493296 + 1, PrimeGrid
  41. ^ 102818*53440382-1, PrimeGrid
  42. ^ Official announcement of discovery of 502573×27181987 − 1, PrimeGrid
  43. ^ Official announcement of discovery of 402539×27173024 − 1, PrimeGrid
  44. ^ Official announcement of discovery of 3×27033641 + 1, PrimeGrid
  45. ^ Official announcement of discovery of 40597×26808509 – 1, PrimeGrid
  46. ^ Official announcement of discovery of 6679881×26679881 + 1, PrimeGrid

External links[edit]