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[redigera | redigera wikitext]

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[redigera | redigera wikitext]

Titaniska primtal

Gigantiska primtal

Referenser[redigera | redigera wikitext]

^ ”The Prime Glossary: megaprime”. The Prime Pages. http://primes.utm.edu/glossary/page.php?sort=Megaprime. Läst 6 november 2013.
^ Chris Caldwell. ”The Largest Known Primes”. The Prime Pages. http://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. http://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. http://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. http://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. http://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. http://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. http://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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