Megaprimtal

Ett megaprimtal är ett primtal med minst en miljon siffror.^[1]

I 6 november 2023 var 2322 megaprimtal kända.^[2] Det första som hittades var Mersenneprimtalet 2^6972593−1 med 2 098 960 siffror. Det hittades 1999 av Nayan Hajratwala.

Begreppet bevaprimtal har föreslagits för att beteckna primtal med mer än en miljard siffror.^{[källa behövs]}

Kända megaprimtal och misstänkta

Står det “primtal” har talet bevisats vara primtal. Står det ”PRP” (probable prime) finns bara misstanke och än så länge inga bevis.

Tal	Datum för upptäckt	Antal siffror	Primtal / PRP
2^82589933 – 1	2018-12-07	24 862 048	Primtal
2^77232917 – 1	2017-12-26	23 249 425	Primtal
2^74207281 – 1	2016-01-07	22 338 618	Primtal
2^57885161 – 1 ^[3]^[4]	2013-01-25	17 425 170	Primtal
2^43112609 – 1	2008-08-23	12 978 189	Primtal
2^42643801 – 1	2009-04-12	12 837 064	Primtal
2^37156667 – 1	2008-09-06	11 185 272	Primtal
2^32582657 – 1	2006-09-04	9 808 358	Primtal
10223*2^31172165 + 1	2016-10-31	9 383 761	Primtal
2^30402457 – 1	2005-12-15	9 152 052	Primtal
${\tfrac {10^{8177207}-1}{9}}$ ^[5]	2021-05-08	8 177 207	PRP
2^25964951 – 1	2005-02-18	7 816 230	Primtal
2^24036583 – 1	2004-05-15	7 235 733	Primtal
202705×2^21320516 – 1	2021-11-25	6 418 121	Primtal
2^20996011 – 1	2003-11-17	6 320 430	Primtal
2^13466917 – 1	2001-11-14	4 053 946	Primtal
19249×2^13018586 + 1 ^[3]	2007-03-26	3 918 990	Primtal
475856⁵²⁴²⁸⁸ + 1 ^[6]	2012-08-08	2 976 633	Primtal
356926⁵²⁴²⁸⁸ + 1 ^[7]	2012-06-20	2 911 151	Primtal
341112⁵²⁴²⁸⁸ + 1 ^[8]	2012-06-15	2 900 832	Primtal
27653×2^9167433 + 1 ^[3]	2005	2 759 677	Primtal
90527 × 2^9162167 + 1	2010	2 758 093	Primtal
2^9092392 + 40291 ^[5]	2011-02	2 737 083	PRP
75898⁵²⁴²⁸⁸ + 1 ^[9]	2011-11-19	2 558 647	Primtal
28433×2^7830457 + 1 ^[3]	2004	2 357 207	Primtal
3×2^7033641 + 1 ^[10]	2011-02-21	2 117 338	Primtal
33661×2^7031232 + 1 ^[3]	2007	2 116 617	Primtal
2^6972593 – 1	1999-06-01	2 098 960	Primtal
6679881×2^6679881 + 1 ^[11]	2009-07-25	2 010 852	Primtal
6328548×2^6328548 + 1 ^[12]	2009-04-20	1 905 090	Primtal
3×2^6090515 – 1 ^[13]	2010-04-24	1 833 429	Primtal
7×2^5775996 + 1 ^[14]	2012-11-02	1 738 749	Primtal
252191×2^5497878 – 1 ^[15]	2012-06-23	1 655 032	Primtal
258317 × 2^5450519+1	2008	1 640 776	Primtal
2^5146295 + 41693 ^[5]	2009-11	1 549 190	PRP
773620²⁶²¹⁴⁴ + 1 ^[16]	2012-04-19	1 543 643	Primtal
3×2^5082306 + 1 ^[17]	2009-04-03	1 529 928	Primtal
676754²⁶²¹⁴⁴+1	2012	1 528 413	Primtal
5359 × 2^5054502+1	2003	1 521 561	Primtal
525094²⁶²¹⁴⁴+1	2012	1 499 526	Primtal
265711 × 2^4858008+1	2008	1 462 412	Primtal
1271 × 2^4850526-1	2012	1 460 157	Primtal
361658²⁶²¹⁴⁴+1	2011	1 457 075	Primtal
9 × 2^4683555-1	2012	1 409 892	Primtal
2^4583176 + 2131 ^[5]	2009-09	1 379 674	PRP
121×2^4553899 – 1 ^[18]	2012-02-25	1 370 863	Primtal
145310²⁶²¹⁴⁴+1	2011	1 353 265	Primtal
353159×2^4331116 – 1 ^[19]	2011-05-31	1 303 802	Primtal
141941×2^4299438 – 1 ^[20]	2011-05-26	1 294 265	Primtal
15 × 2^4246384+1	2013	1 278 291	Primtal
3×2^4235414 – 1 ^[21]	2008-03-23	1 274 988	Primtal
191 × 2^4203426-1	2012	1 265 360	Primtal
${\tfrac {2^{4031399}+1}{3}}$ ^[5]	2010-02	1 213 572	PRP
40734²⁶²¹⁴⁴+1	2011	1 208 473	Primtal
9 × 2^4005979-1	2012	1 205 921	Primtal
27×2^3855094 – 1 ^[22]	2012-02-28	1 160 501	Primtal
24518²⁶²¹⁴⁴+1	2008	1 150 678	Primtal
123547×2^3804809 – 1 ^[23]	2011-05-08	1 145 367	Primtal
415267×2^3771929 – 1 ^[24]	2011-05-08	1 135 470	Primtal
11 × 2^3771821+1	2013	1 135 433	Primtal
938237 × 2^3752950-1	2007	1 129 757	Primtal
65531 × 2^3629342-1	2011	1 092 546	Primtal
485767 × 2^3609357-1	2008	1 086 531	Primtal
5 × 2^3569154-1	2009	1 074 424	Primtal
1019 × 2^3536312-1	2012	1 064 539	Primtal
7 × 2^3511774+1	2008	1 057 151	Primtal
428639 × 2^3506452-1	2011	1 055 553	Primtal
9×2^3497442 + 1 ^[25]	2012-10-23	1 052 836	Primtal
1273 × 2^3448551-1	2012	1 038 121	Primtal
191249 × 2^3417696-1	2010	1 028 835	Primtal
59 × 2^3408416-1	2010	1 026 038	Primtal
81×2^3352924 + 1 ^[26]	2012-01-17	1 009 333	Primtal
1087 × 2^3336385-1	2012	1 004 355	Primtal
464253×2^3321908 – 1 ^[3]	2013	1 000 000	Primtal
10⁹⁹⁹⁹⁹⁹ + 593499 ^[27]	2012-12-24	1 000 000	PRP

Se även

Titaniska primtal

Gigantiska primtal

Referenser

^ ”The Prime Glossary: megaprime”. The Prime Pages. https://primes.utm.edu/glossary/page.php?sort=Megaprime. Läst 6 november 2013.
^ Chris Caldwell. ”The Largest Known Primes”. The Prime Pages. https://primes.utm.edu/primes/lists/short.txt. Läst 6 november 2013.
^ [a b c d e f] ”The Largest Known Prime by Year: A Brief History”. University of Tennessee at Martin. https://primes.utm.edu/notes/by_year.html. Läst 4 november 2013.
^ Kate Bevan (6 februari 2013). ”The prime number that adds up to 17million digits and would take over a year to write out by hand”. Daily Mail - Mail Online. https://www.dailymail.co.uk/sciencetech/article-2274505/Biggest-prime-number-At-17-MILLION-digits-year-write-hand.html. Läst 6 november 2013.
^ [a b c d e] Probable Primes Top 10000, primenumbers.net
^ Official announcement of discovery of 475856⁵²⁴²⁸⁸ + 1, PrimeGrid
^ Official announcement of discovery of 356926⁵²⁴²⁸⁸ + 1, PrimeGrid
^ Official announcement of discovery of 341112⁵²⁴²⁸⁸ + 1, PrimeGrid
^ 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

[def-1] ”The Prime Glossary: megaprime”. The Prime Pages. https://primes.utm.edu/glossary/page.php?sort=Megaprime. Läst 6 november 2013.

[The_largest_known_primes-2] Chris Caldwell. ”The Largest Known Primes”. The Prime Pages. https://primes.utm.edu/primes/lists/short.txt. Läst 6 november 2013.

[largest-3] [a b c d e f] ”The Largest Known Prime by Year: A Brief History”. University of Tennessee at Martin. https://primes.utm.edu/notes/by_year.html. Läst 4 november 2013.

[News-4] Kate Bevan (6 februari 2013). ”The prime number that adds up to 17million digits and would take over a year to write out by hand”. Daily Mail - Mail Online. https://www.dailymail.co.uk/sciencetech/article-2274505/Biggest-prime-number-At-17-MILLION-digits-year-write-hand.html. Läst 6 november 2013.

[PRPTop-5] [a b c d e] Probable Primes Top 10000, primenumbers.net

[grid-6] Official announcement of discovery of 475856⁵²⁴²⁸⁸ + 1, PrimeGrid

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

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

[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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