Megaprime

From Wikipedia, the free encyclopedia

A megaprime is a prime number with at least one million decimal digits^[1] (whereas titanic prime is a prime number with at least 1000 digits, and gigantic prime has at least 10000 digits).

The number of megaprimes found by year.

As of 17 March 2013 (2013-03-17), 63 megaprimes are known.^[2] 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.^[3]^[4]

The term bevaprime has been proposed as a term for a prime with at least 1,000,000,000 digits.^[4]

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
2^57885161 – 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	9,808,358	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
19249×2^13018586 + 1 ^[2]	2007-03-26	3,918,990	Prime
475856⁵²⁴²⁸⁸ + 1 ^[5]	2012-08-08	2,976,633	Prime
356926⁵²⁴²⁸⁸ + 1 ^[6]	2012-06-20	2,911,151	Prime
341112⁵²⁴²⁸⁸ + 1 ^[7]	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 ^[8]	2011-02	2,737,083	PRP
75898⁵²⁴²⁸⁸ + 1 ^[9]	2011-11-19	2,558,647	Prime
28433×2^7830457 + 1 ^[2]	2004	2,357,207	Prime
3×2^7033641 + 1 ^[10]	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
6679881×2^6679881 + 1 ^[11]	2009-07-25	2,010,852	Prime
6328548×2^6328548 + 1 ^[12]	2009-04-20	1,905,090	Prime
3×2^6090515 – 1 ^[13]	2010-04-24	1,833,429	Prime
7×2^5775996 + 1 ^[14]	2012-11-02	1,738,749	Prime
252191×2^5497878 – 1 ^[15]	2012-06-23	1,655,032	Prime
258317 × 2^5450519+1	2008	1,640,776	Prime
2^5146295 + 41693 ^[8]	2009-11	1,549,190	PRP
773620²⁶²¹⁴⁴ + 1 ^[16]	2012-04-19	1,543,643	Prime
3×2^5082306 + 1 ^[17]	2009-04-03	1,529,928	Prime
676754²⁶²¹⁴⁴+1	2012	1,528,413	Prime
5359 × 2^5054502+1	2003	1,521,561	Prime
525094²⁶²¹⁴⁴+1	2012	1,499,526	Prime
265711 × 2^4858008+1	2008	1,462,412	Prime
1271 × 2^4850526-1	2012	1,460,157	Prime
361658²⁶²¹⁴⁴+1	2011	1,457,075	Prime
9 × 2^4683555-1	2012	1,409,892	Prime
2^4583176 + 2131 ^[8]	2009-09	1,379,674	PRP
121×2^4553899 – 1 ^[18]	2012-02-25	1,370,863	Prime
145310²⁶²¹⁴⁴+1	2011	1,353,265	Prime
353159×2^4331116 – 1 ^[19]	2011-05-31	1,303,802	Prime
141941×2^4299438 – 1 ^[20]	2011-05-26	1,294,265	Prime
15 × 2^4246384+1	2013	1,278,291	Prime
3×2^4235414 – 1 ^[21]	2008-03-23	1,274,988	Prime
191 × 2^4203426-1	2012	1,265,360	Prime
$\tfrac{2^{4031399}+1}{3}$ ^[8]	2010-02	1,213,572	PRP
40734²⁶²¹⁴⁴+1	2011	1,208,473	Prime
9 × 2^4005979-1	2012	1,205,921	Prime
27×2^3855094 – 1 ^[22]	2012-02-28	1,160,501	Prime
24518²⁶²¹⁴⁴+1	2008	1,150,678	Prime
123547×2^3804809 – 1 ^[23]	2011-05-08	1,145,367	Prime
415267×2^3771929 – 1 ^[24]	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
65531 × 2^3629342-1	2011	1,092,546	Prime
485767 × 2^3609357-1	2008	1,086,531	Prime
5 × 2^3569154-1	2009	1,074,424	Prime
1019 × 2^3536312-1	2012	1,064,539	Prime
7 × 2^3511774+1	2008	1,057,151	Prime
428639 × 2^3506452-1	2011	1,055,553	Prime
9×2^3497442 + 1 ^[25]	2012-10-23	1,052,836	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
81×2^3352924 + 1 ^[26]	2012-01-17	1,009,333	Prime
1087 × 2^3336385-1	2012	1,004,355	Prime
464253×2^3321908 – 1 ^[2]	2013	1,000,000	Prime
10⁹⁹⁹⁹⁹⁹ + 593499 ^[27]	2012-12-24	1,000,000	PRP

References

↑ Chris Caldwell, The Prime Glossary: megaprime at The Prime Pages. Retrieved on 2008-01-04.
↑ 2.0 2.1 2.2 2.3 2.4 2.5 Chris Caldwell, The Largest Known Primes at The Prime Pages. Retrieved on 2013-02-24.
↑ GIMPS press release, GIMPS Finds First Million-Digit Prime. Retrieved on 2008-01-04.
↑ 4.0 4.1 Chris Caldwell, The Largest Known Prime by Year: A Brief History at The Prime Pages. Retrieved on 2008-09-28.
↑ Official announcement of discovery of 475856⁵²⁴²⁸⁸ + 1, PrimeGrid
↑ Official announcement of discovery of 356926⁵²⁴²⁸⁸ + 1, PrimeGrid
↑ Official announcement of discovery of 341112⁵²⁴²⁸⁸ + 1, PrimeGrid
↑ 8.0 8.1 8.2 8.3 Probable Primes Top 10000, primenumbers.net
↑ 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

External links

Chris Caldwell, The Largest Known Primes Database at The Prime Pages.
PrimeGrid’s 321 Prime Search, about the discovery of 3×2^6090515−1.

v t e Prime number classes

By formula	Fermat (2^2ⁿ + 1) Mersenne (2^p − 1) Double Mersenne (2^{2^p−1} − 1) Wagstaff (2^p + 1)/3 Proth (k·2ⁿ + 1) Factorial (n! ± 1) Primorial (p_n# ± 1) Euclid (p_n# + 1) Pythagorean (4n + 1) Pierpont (2^u·3^v + 1) Solinas (2^a ± 2^b ± 1) Cullen (n·2ⁿ + 1) Woodall (n·2ⁿ − 1) Cuban (x³ − y³)/(x − y) Carol (2ⁿ − 1)² − 2 Kynea (2ⁿ + 1)² − 2 Leyland (x^y + y^x) Thabit (3·2ⁿ − 1) Mills (floor(A^3ⁿ))

By integer sequence	Fibonacci Lucas Motzkin Bell Partitions Pell Perrin Newman–Shanks–Williams

By property	Lucky Wall–Sun–Sun Wilson Wieferich Wieferich pair Fortunate Ramanujan Pillai Regular Strong Stern Supersingular (elliptic curve) Supersingular (moonshine theory) Wolstenholme Good Super Higgs Highly cototient Illegal

Base-dependent	Happy Dihedral Palindromic Emirp Repunit (10ⁿ − 1)/9 Permutable Circular Truncatable Strobogrammatic Minimal Full reptend Unique Primeval Self Smarandache–Wellin

Patterns	Twin (p, p + 2) Bi-twin chain (p − 1, p + 1, 2p − 1, 2p + 1, …) Triplet (p, p + 2 or p + 4, p + 6) Quadruplet (p, p + 2, p + 6, p + 8) Tuple Cousin (p, p + 4) Sexy (p, p + 6) Chen Sophie Germain (p, 2p + 1) Cunningham chain (p, 2p ± 1, …) Safe (p, (p − 1)/2) Arithmetic progression (p + a·n, n = 0, 1, …) Balanced (consecutive p − n, p, p + n)

By size	Titanic (1,000+ digits) Gigantic (10,000+) Mega (1,000,000+) Largest known

Complex numbers	Eisenstein prime Gaussian prime

Composite numbers	Pseudoprime Almost prime Semiprime Interprime

Related topics	Probable prime Industrial-grade prime Formula for primes Prime gap

List of prime numbers

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Megaprime

Known megaprimes and mega PRPs

See also

References

External links