Megaprime

A megaprime is a prime number with at least one million decimal digits^[1] (whereas titanic prime is a prime number with at least 1,000 digits, and gigantic prime has at least 10,000 digits).

The number of megaprimes found by year.

As of September 2016, 208 (probable) megaprimes are known, including 192 definitely primes^[2] and 16 probable primes.^[3] 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.^[4]^[5]

The term bevaprime has been proposed as a term for a prime with at least 1,000,000,000 digits.^[5]

In fact, "almost all" primes are megaprimes, as the amount of primes with more than a million digits is infinite. However, the vast majority of known primes are not megaprimes.

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
2^74207281 – 1	2016-01-07	22,338,618	Prime
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	2006-09-04	9,808,358	Prime
10223×2^31172165 + 1	2016-11	9,383,761	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
${\tfrac {2^{{13372531}}+1}{3}}$ ^[3]	2013-09	4,025,533	PRP
${\tfrac {2^{{13347311}}+1}{3}}$ ^[3]	2013-09	4,017,941	PRP
19249×2^13018586 + 1 ^[2]	2007-03-26	3,918,990	Prime
3×2^11895718 − 1 ^[2]	2015-06	3,580,969	Prime
3×2^11731850 − 1 ^[6]	2015-03-13	3,531,640	Prime
3×2^11484018 − 1 ^[7]	2014-11-22	3,457,035	Prime
3×2^10829346 + 1 ^[8]	2014-01-14	3,259,959	Prime
475856⁵²⁴²⁸⁸ + 1 ^[9]	2012-08-08	2,976,633	Prime
356926⁵²⁴²⁸⁸ + 1 ^[10]	2012-06-20	2,911,151	Prime
341112⁵²⁴²⁸⁸ + 1 ^[11]	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 ^[3]	2011-02	2,737,083	PRP
2038×366^1028507 − 1 ^[12]	2016	2,636,562	Prime
29×2^8727880 − 1 ^[12]	2016	2,627,356	PRP^[13]
75898⁵²⁴²⁸⁸ + 1 ^[14]	2011-11-19	2,558,647	Prime
28433×2^7830457 + 1 ^[2]	2004	2,357,207	Prime
502573×2^7181987 − 1 ^[15]	2014-10-04	2,162,000	Prime
402539×2^7173024 − 1 ^[16]	2014-10-02	2,159,301	Prime
3343×2^7166019 - 1	2016	2,157,191	Prime
161041×2^7107964 + 1	2015-01	2,139,716	Prime
3×2^7033641 + 1 ^[17]	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
4×72^1119849 − 1 ^[12]	2016	2,079,933	Prime
40597×2^6808509 – 1 ^[18]	2013-12-25	2,049,571	Prime
6679881×2^6679881 + 1 ^[19]	2009-07-25	2,010,852	Prime
37×2^6660841 − 1	2014	2,005,115	Prime
304207×2^6643565 – 1 ^[20]	2013-10-10	1,999,918	Prime
398023×2^6418059 – 1 ^[21]	2013-10-05	1,932,034	Prime
6328548×2^6328548 + 1 ^[22]	2009-04-20	1,905,090	Prime
3×2^6090515 – 1 ^[23]	2010-04-24	1,833,429	Prime
1583×2^5989282 − 1	2015	1,802,957	Prime
7×2^5775996 + 1 ^[24]	2012-11-02	1,738,749	Prime
1243×2^5686715 - 1	2016	1,711,875	Prime
9×2^5642513 + 1	2013	1,698,567	Prime
2622×11^1621920 – 1 ^[12]	2015	1,689,060	Prime
252191×2^5497878 – 1 ^[25]	2012-06-23	1,655,032	Prime
1828858²⁶²¹⁴⁴+1	2016	1,641,593	Prime
258317 × 2^5450519+1	2008	1,640,776	Prime
1615588²⁶²¹⁴⁴ + 1	2016	1,627,477	Prime
1488256²⁶²¹⁴⁴ + 1	2016	1,618,131	Prime
1415198²⁶²¹⁴⁴ + 1	2016	1,612,400	Prime
${\tfrac {2^{5240707}-1}{75392810903}}$ ^[3]	2016-07	1,577,600	PRP
180062×5^2249192 − 1	2016	1,572,123	Prime
27×2^5213635 + 1	2015	1,569,462	Prime
53546×5^2216664-1	2016	1,549,387	Prime
2^5146295 + 41693 ^[3]	2009-11	1,549,190	PRP
773620²⁶²¹⁴⁴ + 1 ^[26]	2012-04-19	1,543,643	Prime
51×2^5085142 - 1	2014	1,530,782	Prime
3×2^5082306 + 1 ^[27]	2009-04-03	1,529,928	Prime
676754²⁶²¹⁴⁴+1	2012	1,528,413	Prime
296024 × 5^2185270 − 1	2016	1,527,444	Prime
5359 × 2^5054502+1	2003	1,521,561	Prime
13×2^4998362 + 1	2014	1,504,659	Prime
525094²⁶²¹⁴⁴+1	2012	1,499,526	Prime
92158×5^2145024 + 1	2016	1,499,313	Prime
77072×5^2139921 + 1	2016	1,495,746	Prime
306398 × 5^2112410 − 1	2016	1,476,517	Prime
265711 × 2^4858008+1	2008	1,462,412	Prime
154222 × 5^2091432 + 1	2015	1,461,854	Prime
1271 × 2^4850526-1	2012	1,460,157	Prime
362978²⁶²¹⁴⁴ − 362978¹³¹⁰⁷² + 1	2015	1,457,490	Prime
361658²⁶²¹⁴⁴+1	2011	1,457,075	Prime
100186 × 5^2079747 − 1	2015	1,453,686	Prime
2^4792057 − 2^2396029 + 1	2014	1,442,553	Prime
653 × 10^1435026 − 1 ^[12]	2014	1,435,029	Prime
144052× 5^2018290 + 1	2015	1,410,730	Prime
9 × 2^4683555 − 1	2012	1,409,892	Prime
11 × 2^4643238 − 1	2014	1,397,755	Prime
192098²⁶²¹⁴⁴ − 192098¹³¹⁰⁷² + 1	2015	1,385,044	Prime
27 × 2^4583717 − 1	2014	1,379,838	Prime
2^4583176 + 2131 ^[3]	2009-09	1,379,674	PRP
121×2^4553899 – 1 ^[28]	2012-02-25	1,370,863	Prime
27× 2^4542344 − 1	2014	1,367,384	Prime
${\tfrac {2^{4533073}+2^{2266537}+1}{5}}$ ^[3]	2014-03	1,364,591	PRP
145310²⁶²¹⁴⁴+1	2011	1,353,265	Prime
36772 × 6^1723287 − 1	2014	1,340,983	Prime
${\tfrac {13^{1199467}+1}{14}}$ ^[3]	2015-12	1,336,138	PRP
151×2^4424321 − 1	2016	1,331,856	Prime
353159×2^4331116 – 1 ^[29]	2011-05-31	1,303,802	Prime
682156×79⁶⁸²¹⁵⁶ + 1	2016	1,294,484	Prime
141941×2^4299438 – 1 ^[30]	2011-05-26	1,294,265	Prime
15 × 2^4246384+1	2013	1,278,291	Prime
3×2^4235414 – 1 ^[31]	2008-03-23	1,274,988	Prime
109208 × 5^1816285 + 1	2014	1,269,534	Prime
191 × 2^4203426-1	2012	1,265,360	Prime
1259 × 2^4196028-1	2016	1,263,134	Prime
${\tfrac {2^{4187251}-1}{72234342371519}}$ ^[3]	2016-05	1,260,475	PRP
${\tfrac {14^{{1091401}}+1}{15}}$ ^[3]	2014-03	1,250,885	PRP
$\tfrac{16^{1025393}+1}{17}$ ^[3]	2014-08	1,234,695	PRP
${\tfrac {2^{{4031399}}+1}{3}}$ ^[3]	2010-02	1,213,572	PRP
39653×430⁴⁶⁰³⁹⁷-1 ^[12]	2016	1,212,446	Prime
40734²⁶²¹⁴⁴+1	2011	1,208,473	Prime
9 × 2^4005979 - 1	2012	1,205,921	Prime
12 × 68⁶⁵⁶⁹²¹ + 1 ^[12]	2016	1,203,815	Prime
1993191 × 4^1993191 − 1	2015	1,200,027	Prime
27×2^3855094 – 1 ^[32]	2012-02-28	1,160,501	Prime
24518²⁶²¹⁴⁴+1	2008	1,150,678	Prime
123547×2^3804809 – 1 ^[33]	2011-05-08	1,145,367	Prime
415267×2^3771929 – 1 ^[34]	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
23451 × 2^3739388 + 1 ^[12]	2015	1,125,673	Prime
2^3704053 + 2^1852027 + 1	2014	1,115,032	Prime
330286×5^1584399 – 1 ^[35]	2014-03-21	1,107,453	Prime
15×2^3668194 – 1	2013	1,104,238	Prime
33300×430⁴¹⁷⁸⁴⁹-1 ^[12]	2016	1,100,397	Prime
65531 × 2^3629342-1	2011	1,092,546	Prime
${\tfrac {106\cdot 23^{800873}-7}{11}}$ ^[3]	2015-05	1,090,573	PRP
485767 × 2^3609357-1	2008	1,086,531	Prime
5 × 2^3569154-1	2009	1,074,424	Prime
81 × 492³⁹⁹⁰⁹⁵ − 1 ^[12]		1,074,352	Prime
22934×5^1536762 – 1 ^[36]	2014-02-06	1,074,155	Prime
${\tfrac {7^{{1264699}}-1}{6}}$ ^[3]	2014-01	1,068,794	PRP
178658×5^1525224 – 1 ^[37]	2014-01-31	1,066,092	Prime
465×2^3536871 – 1 ^[38]	2016-09-30	1,064,707	Prime
1019 × 2^3536312-1	2012	1,064,539	Prime
2×10^1059002 – 1	2013	1,059,003	Prime
7 × 2^3511774+1	2008	1,057,151	Prime
428639 × 2^3506452-1	2011	1,055,553	Prime
9×2^3497442 + 1 ^[39]	2012-10-23	1,052,836	Prime
51×2^3490971 + 1	2014	1,050,889	Prime
59912×5^1500861 + 1 ^[40]	2014-01-17	1,049,062	Prime
$\tfrac{2^{3464473}-1}{604874508299177}$ ^[3]	2014-10	1,042,896	PRP
37292×5^1487989 + 1 ^[41]	2013-12-29	1,040,065	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
24 × 414³⁹¹¹⁷⁹ + 1 ^[12]		1,023,717	Prime
67×2^3391385 – 1	2014	1,020,911	Prime
173198×5^1457792 – 1 ^[42]	2013-12-04	1,018,959	Prime
81×2^3352924 + 1 ^[43]	2012-01-17	1,009,333	Prime
1087 × 2^3336385-1	2012	1,004,355	Prime
464253×2^3321908 – 1	2013	1,000,000	Prime
191273×2^3321908 – 1 ^[2]	2013	1,000,000	Prime
10⁹⁹⁹⁹⁹⁹ + 593499 ^[44]	2012-12-24	1,000,000	PRP

References

↑ Chris Caldwell, The Prime Glossary: megaprime at The Prime Pages. Retrieved on 2008-01-04.
1 2 3 4 5 6 7 Chris Caldwell, The Largest Known Primes at The Prime Pages.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Henri Lifchitz & Renaud Lifchitz, Probable Primes Top 10000, primenumbers.net
↑ GIMPS press release, GIMPS Finds First Million-Digit Prime. Retrieved on 2008-01-04.
1 2 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 3×2^11731850 − 1, PrimeGrid
↑ Official announcement of discovery of 3×2^11484018 − 1, PrimeGrid
↑ Official announcement of discovery of 3×2^10829346 + 1, PrimeGrid
↑ Official announcement of discovery of 475856⁵²⁴²⁸⁸ + 1, PrimeGrid
↑ Official announcement of discovery of 356926⁵²⁴²⁸⁸ + 1, PrimeGrid
↑ Official announcement of discovery of 341112⁵²⁴²⁸⁸ + 1, PrimeGrid
1 2 3 4 5 6 7 8 9 10 11 Generalized Sierpinski/Riesel primes
↑ This number is a 3-PRP, but not prime (it is proven composite)
↑ Official announcement of discovery of 75898⁵²⁴²⁸⁸ + 1, PrimeGrid
↑ Official announcement of discovery of 502573×2^7181987 − 1, PrimeGrid
↑ Official announcement of discovery of 402539×2^7173024 − 1, PrimeGrid
↑ Official announcement of discovery of 3×2^7033641 + 1, PrimeGrid
↑ Official announcement of discovery of 40597×2^6808509 – 1, PrimeGrid
↑ Official announcement of discovery of 6679881×2^6679881 + 1, PrimeGrid
↑ Official announcement of discovery of 304207×2^6643565 – 1, PrimeGrid
↑ Official announcement of discovery of 398023×2^6418059 – 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 330286×5^1584399 – 1, PrimeGrid
↑ Official announcement of discovery of 22934×5^1536762 – 1, PrimeGrid
↑ Official announcement of discovery of 178658×5^1525224 – 1, PrimeGrid
↑ Official announcement of discovery of 465×2^3536871 – 1, PrimeGrid
↑ Official announcement of discovery of 9×2^3497442 + 1, PrimeGrid
↑ Official announcement of discovery of 59912×5^1500861 + 1, PrimeGrid
↑ Official announcement of discovery of 37292×5^1487989 + 1, PrimeGrid
↑ Official announcement of discovery of 173198×5^1457792 – 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
Top PRPs
A text file for all top primes
PrimeGrid’s 321 Prime Search, about the discovery of 3×2^6090515−1

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) Quartan (x⁴ + y⁴) 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 Pell Newman–Shanks–Williams Perrin Partitions Bell Motzkin

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

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

Patterns	Twin (p, p + 2) Bi-twin chain (n − 1, n + 1, 2n − 1, 2n + 1, …) Triplet (p, p + 2 or p + 4, p + 6) Quadruplet (p, p + 2, p + 6, p + 8) k−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 Illegal prime Formula for primes Prime gap

First 50 primes	2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229

List of prime numbers

Large numbers

Examples in numerical order

Expression methods

Notations	Knuth's up-arrow notation Conway chained arrow notation Steinhaus–Moser notation

Operators	Hyperoperation Tetration Pentation Ackermann function Bowers' operators

This article is issued from Wikipedia - version of the 11/9/2016. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.

Megaprime

Known megaprimes and mega PRPs

See also

References

External links