Megaprime

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. 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 2^6972593−1 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

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	2^82589933 – 1 [9]	7 December 2018	24,862,048	Prime
2	2^77232917 – 1 [10]	26 December 2017	23,249,425	Prime
3	2^74207281 – 1 [11]	7 January 2016	22,338,618	Prime
4	2^57885161 – 1 [12]	25 January 2013	17,425,170	Prime
5	2^43112609 – 1 [13]	23 August 2008	12,978,189	Prime
6	2^42643801 – 1 [14]	4 June 2009	12,837,064	Prime
7	2^37156667 – 1 [13]	6 September 2008	11,185,272	Prime
8	2^32582657 – 1 [15]	4 September 2006	9,808,358	Prime
9	10223×2^31172165 + 1 [16]	31 October 2016	9,383,761	Prime
10	2^30402457 – 1 [17]	15 December 2005	9,152,052	Prime
-	${\tfrac {10^{8177207}-1}{9}}$	8 May 2021	8,177,207	PRP
11	2^25964951 – 1 [18]	18 February 2005	7,816,230	Prime
12	2^24036583 – 1 [19]	15 May 2004	7,235,733	Prime
13	202705×2^21320516 + 1 [20]	25 November 2021	6,418,121	Prime
14	2^20996011 – 1 [21]	17 November 2005	6,320,430	Prime
15	1059094^1048576 + 1 [22]	4 November 2018	6,317,602	Prime
16	919444^1048576 + 1 [23]	2 September 2017	6,253,210	Prime
17	168451×2^19375200 + 1 [24]	26 September 2017	5,832,522	Prime
-	${\tfrac {10^{5794777}-1}{9}}$	20 April 2021	5,794,777	PRP
18	3×2^18924888 - 1	25 March 2022	5,696,990	Prime
19	69×2^18831865 - 1	16 December 2021	5,668,959	Prime
20	7×2^18233956 + 1	1 October 2020	5,488,969	Prime
21	3×2^18196595 - 1	18 January 2022	5,477,722	Prime
22	3×2^17748034 - 1 [25]	6 September 2021	5,342,692	Prime
23	$\Phi _{3}(-123447^{524288})$	23 February 2017	5,338,805	Prime
24	3622×5^7558139 - 1	18 February 2022	5,282,917	Prime
25	7×6^6772401 + 1	9 September 2019	5,269,954	Prime
26	8508301×2^17016603-1 [26]	22 March 2018	5,122,515	Prime
27	3×2^16819291-1 [27]	20 January 2021	5,063,112	Prime
28	3×2^16408818+1 [28]	28 October 2020	4,939,547	Prime
29	69×2^15866556+1	20 August 2021	4,776,312	Prime
30	2525332×73^2525332+1	28 August 2021	4,705,888	Prime
31	2^15317227+2^7658614+1	31 July 2020	4,610,945	Prime
32	6×5^6546983+1	13 June 2020	4,576,146	Prime
-	${\tfrac {2^{15135397}+1}{3}}$ [4]	June 2021	4,556,209	PRP
33	69×2^14977631-1	3 December 2021	4,508,719	Prime
34	192971×2^14773498-1	7 March 2021	4,447,272	Prime
35	6962×31^2863120-1	29 February 2020	4,269,952	Prime
36	99739×2^14019102-1 [29]	25 December 2019	4,220,176	Prime
37	69×2^13832885-1	17 January 2022	4,164,116	Prime
38	404849×2^13764867+1	10 March 2021	4,143,644	Prime
39	2740879×2^13704395-1	26 October 2019	4,125,441	Prime
40	479216×3^8625889-1	16 November 2019	4,115,601	Prime
41	$\Phi _{3}(-143332^{393216})$	30 January 2017	4,055,114	Prime
42	2^13466917 – 1 [30]	14 November 2001	4,053,946	Prime
-	2^13380298 – 27	March 2021	4,027,872	PRP
-	${\tfrac {2^{13372531}+1}{3}}$ [4]	September 2013	4,025,533	PRP
-	${\tfrac {2^{13347311}+1}{3}}$ [4]	September 2013	4,017,941	PRP
43	9×2^13334487 + 1	31 March 2020	4,014,082	Prime
44	206039×2^13104952 - 1	26 April 2021	3,944,989	Prime
45	2805222×5^5610444 + 1 [31]	3 September 2019	3,921,539	Prime
46	19249×2^13018586 + 1 [3]	26 March 2007	3,918,990	Prime
47	2293×2^12918431 - 1	13 February 2021	3,888,839	Prime
-	${\tfrac {2^{12503723}-2^{6251862}+1}{5}}$ [4]	July 2020	3,763,995	PRP
48	9×2^12406887 + 1	29 March 2020	3,734,847	Prime
49	69×2^12231580 - 1	27 July 2021	3,682,075	Prime
50	27*2^12184319 + 1	6 February 2021	3,667,847	Prime
51	3×2^11895718 − 1 [3]	26 June 2015	3,580,969	Prime
52	3×2^11731850 − 1 [32]	13 March 2015	3,531,640	Prime
53	69×2^11718455 − 1 [3]	4 December 2020	3,527,609	Prime
54	69×2^11604348 − 1 [3]	4 December 2020	3,493,259	Prime
55	9×2^11500843 + 1 [3]	13 March 2020	3,462,100	Prime
56	3×2^11484018 − 1 [33]	22 November 2014	3,457,035	Prime
57	193997*2^11452891 +1	3 April 2018	3,447,670	Prime
58	3638450⁵²⁴²⁸⁸ +1	31 May 2020	3,439,810	Prime
59	9221*2^11392194 -1	7 February 2021	3,429,397	Prime
60	9*2^11366286 +1	26 March 2020	3,421,594	Prime
61	5*2^11355764 -1	2 October 2021	3,418,427	Prime
62	3214654⁵²⁴²⁸⁸ +1	25 December 2019	3,411,613	Prime
63	146561*2^11280802 -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*2^11158963 +1	13 March 2020	3,359,184	Prime
69	9271*2^11134335 -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	27×2^10902757 - 1	7 March 2022	3,282,059	Prime
74	3×2^10829346 + 1 [34]	14 January 2014	3,259,959	Prime
75	5×2^10495620 - 1	26 September 2021	3,159,498	Prime
-	${\tfrac {2^{10443557}-1}{37289325994807}}$ [4]	9 July 2020	3,143,811	PRP
76	5×2^10349000 - 1	26 September 2021	3,115,361	Prime
77	$\Phi _{3}(-844833^{262144})$	17 January 2017	3,107,335	Prime
78	$\Phi _{3}(-712012^{262144})$	14 January 2017	3,068,389	Prime
79	874208*54^1748416-1	26 September 2019	3,028,951	Prime
80	475856⁵²⁴²⁸⁸ + 1 [35]	8 August 2012	2,976,633	Prime
81	9*2^9778263+1	5 August 2020	2,943,552	Prime
82	1806676*41^1806676+1	12 March 2018	2,913,785	Prime
83	356926⁵²⁴²⁸⁸ + 1 [36]	25 July 2012	2,911,151	Prime
84	341112⁵²⁴²⁸⁸ + 1 [37]	25 June 2012	2,900,832	Prime
85	43*2^9596983-1	28 February 2022	2,888,982	Prime
86	121*2^9584444+1	20 November 2020	2,885,208	Prime
87	11*2^9381365+1	7 March 2020	2,824,074	Prime
88	27653×2^9167433 + 1 [3]	8 June 2005	2,759,677	Prime
89	90527×2^9162167 + 1	30 June 2010	2,758,093	Prime
-	2^9092392 + 40291 [4]	February 2011	2,737,083	PRP
90	6795×2^9144320 - 1	31 March 2021	2,752,719	Prime
91	1323365*116^1323365+1	18 January 2018	2,732,038	Prime
92	13×2^8989858 + 1	10 March 2020	2,706,219	Prime
93	4159×2^8938471 - 1	19 April 2022	2,690,752	Prime
94	273809×2^8932416 − 1 [38]	13 December 2017	2,688,931	Prime
95	2×3^5570081 + 1	14 February 2020	2,657,605	Prime
96	25×2^8788628 + 1	1 March 2021	2,645,643	Prime
97	2038×366^1028507 − 1 [38]	4 April 2016	2,636,562	Prime
98	17×2^8636199 + 1	17 February 2021	2,599,757	Prime
99	75898⁵²⁴²⁸⁸ + 1 [39]	19 November 2021	2,558,647	Prime
100	25×2^8456828 + 1	28 January 2021	2,545,761	Prime
101	39×2^8413422 + 1	23 January 2021	2,532,694	Prime
102	31×2^8348000 + 1	19 January 2021	2,513,000	Prime
103	27×2^8342438 - 1	1 February 2021	2,511,326	Prime
104	3867×2^8261084 - 1	14 April 2021	2,486,838	Prime
-	${\tfrac {17^{1990523}-1}{16}}$ [4]	August 2020	2,449,236	PRP
105	273662×5^3493296 - 1 [40]	7 December 2021	2,441,715	Prime
106	11×2^8103463 + 1	6 March 2020	2,439,387	Prime
107	102818×5^3440382 - 1 [41]	8 October 2021	2,404,729	Prime
108	11×2^7971110 - 1	25 November 2019	2,399,545	Prime
109	27×2^7963247 + 1	16 January 2021	2,397,178	Prime
110	3177×2^7954621 - 1	13 June 2021	2,394,584	Prime
111	39×2^7946769 + 1	15 January 2021	2,392,218	Prime
112	7×6^3072198 + 1	4 August 2019	2,390,636	Prime
113	3765×2^7904593 - 1	10 January 2021	2,379,524	Prime
114	29×2^7899985 + 1	15 January 2021	2,378,134	Prime
115	861×2^7895451 - 1	21 February 2021	2,376,771	Prime
-	${\tfrac {11^{2264611}+1}{12}}$ [4]	July 2021	2,358,349	PRP
116	28433×2^7830457 + 1 [3]	31 December 2004	2,357,207	Prime
117	5×2^7755002 - 1	23 September 2021	2,334,489	Prime
118	2545×2^7732265 - 1	13 January 2021	2,327,648	Prime
119	5539×2^7730709 - 1	15 January 2021	2,327,180	Prime
120	4817×2^7719584 - 1	13 June 2021	2,323,831	Prime
121	1341174×53^1341174 + 1	22 August 2017	2,312,561	Prime
122	9467×2^7680034 - 1	20 February 2022	2,311,925	Prime
-	${\tfrac {5^{3300593}-1}{4}}$ [4]	February 2022	2,307,015	PRP
123	45×2^7661004 + 1	13 December 2020	2,306,194	Prime
124	15×2^7619838 + 1	24 December 2020	2,293,801	Prime
125	3597×2^7580693 - 1	10 January 2021	2,282,020	Prime
126	7401×2^7523295 - 1	21 February 2021	2,264,742	Prime
127	45×2^7513661 + 1	12 November 2020	2,261,839	Prime
128	$\Phi _{3}(-558640^{196608})$	11 January 2017	2,259,865	Prime
129	29×2^7374577 + 1	28 October 2020	2,219,971	Prime
130	109838×5^3168862 - 1	13 August 2020	2,219,971	Prime
131	101×2^7345194 - 1	5 October 2019	2,219,971	Prime
-	${\tfrac {2^{7313983}-1}{305492080276193}}$ [4]	March 2018	2,201,714	PRP
132	15×2^7300254 + 1	25 October 2020	2,219,971	Prime
133	422429! + 1	21 February 2022	2,193,027	Prime
134	1759×2^7284439 - 1	28 August 2021	2,192,838	Prime
135	737×2^7269322 − 1	10 August 2017	2,188,287	Prime
136	118568×5^3112069 + 1	2 May 2020	2,175,248	Prime
137	6039×2^7207973 − 1	24 March 2021	2,169,820	Prime
138	502573×2^7181987 − 1 [42]	4 October 2014	2,162,000	Prime
139	402539×2^7173024 − 1 [43]	2 October 2014	2,159,301	Prime
140	3343×2^7166019 - 1	29 September 2016	2,157,191	Prime
141	161041×2^7107964 + 1	8 January 2015	2,139,716	Prime
-	${\tfrac {2^{7080247}-1}{17045259548603283727480473638587228614426296913631}}$	October 2017	2,131,318	PRP
142	27*2^7046834+1	16 October 2018	2,121,310	Prime
143	1759×2^7046791 - 1	28 August 2021	2,121,299	Prime
144	327×2^7044001 - 1	13 January 2021	2,120,459	Prime
145	5×2^7037188 - 1	22 September 2021	2,118,406	Prime
146	3×2^7033641 + 1 [44]	21 February 2011	2,117,338	Prime
147	33661×2^7031232 + 1 [3]	30 October 2007	2,116,617	Prime
148	$\Phi _{3}(-237804^{196608})$	6 January 2017	2,114,016	Prime
149	207494*5^3017502-1	19 March 2020	2,109,149	Prime
150	15*2^6993631-1	25 August 2021	2,105,294	Prime
151	8943501*2^6972593-1	8 January 2022	2,098,967	Prime
152	2^6972593 – 1 [5]	1 June 1999	2,098,960	Prime
153	6219*2^6958945-1	7 January 2021	2,094,855	Prime
154	51*2^6945567+1	26 May 2020	2,090,826	Prime
155	238694*5^2979422-1	13 March 2020	2,082,532	Prime
156	4×72^1119849 − 1 [38]	7 September 2016	2,079,933	Prime
157	33*2^6894190-1	27 July 2021	2,075,360	Prime
158	2345*2^6882320-1	13 April 2022	2,071,789	Prime
159	146264*5^2953282-1	10 March 2020	2,064,261	Prime
160	69*2^6838971-1	1 March 2020	2,058,738	Prime
161	35816*5^2945294-1	5 March 2020	2,058,677	Prime
162	127*2^6836153-1	25 June 2018	2,057,890	Prime
163	19*2^6833086+1	25 October 2020	2,056,966	Prime
164	40597×2^6808509 – 1 [45]	27 November 2013	2,049,571	Prime
165	283*2^6804701-1	19 January 2020	2,048,431	Prime
166	1861209*2^6789999+1	2 December 2020	2,044,000	Prime
167	5817*2^6789459-1	9 January 2021	2,043,835	Prime
168	8435*2^6786180-1	7 January 2021	2,042,848	Prime
169	51*2^6753404+1	26 May 2020	2,032,979	Prime
170	9995*2^6711008-1	31 December 2020	2,020,219	Prime
171	39*2^6684941+1	20 October 2020	2,012,370	Prime
172	6679881×2^6679881 + 1 [46]	25 July 2009	2,010,852	Prime
173	37×2^6660841 − 1 [38]	30 July 2014	2,005,115	Prime
174	39*2^6648997+1	20 October 2020	2,001,550	Prime

References

Chris Caldwell, The Prime Glossary: megaprime at The PrimePages. Retrieved on 2008-01-04.
"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)
Chris Caldwell, The Largest Known Primes at The PrimePages.
Henri Lifchitz & Renaud Lifchitz, Probable Primes Top 10000, primenumbers.net
GIMPS press release, GIMPS Finds First Million-Digit Prime. Retrieved on 2008-01-04.
Chris Caldwell, The Largest Known Prime by Year: A Brief History at The PrimePages. Retrieved on 2008-09-28.
Patrick De Geest, 10^999999 + y, World!Of Numbers
Caldwell, Chris K. "THE LARGEST KNOWN PRIMES (The 5,000 largest known primes)". Retrieved 23 November 2018.
"Official press release of 51st Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 7 December 2018.
"Official press release of 50th Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 26 December 2017.
"Official press release of 49th Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 7 January 2016.
"Official press release of 48th Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 25 January 2013.
"Official press release of 45th and 46th Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 10 September 2008.
"Official press release of 47th Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 25 January 2013.
"Official press release of 44th Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 25 January 2013.
Official announcement of discovery of 10223×2^31172165 + 1, PrimeGrid
"Official press release of 43rd Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 25 January 2013.
"Official press release of 42nd Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 25 January 2013.
"Official press release of 41st Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 25 January 2013.
Official announcement of discovery of 202705×2^21320516 + 1, PrimeGrid
"Official press release of 40th Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 25 January 2013.
Official announcement of discovery of 1059094^1048576 + 1, PrimeGrid
Official announcement of discovery of 919444^1048576 + 1, PrimeGrid
Official announcement of discovery of 168451×2^19375200 + 1, PrimeGrid
Official announcement of discovery of 3×2^17748034 - 1, PrimeGrid
Official announcement of discovery of 8508301×2^17016603-1, PrimeGrid
Official announcement of discovery of 3×2^16819291-1, PrimeGrid
Official announcement of discovery of 3×2^16408818+1, PrimeGrid
Official announcement of discovery of 99739×2^14019102-1, PrimeGrid
"Official press release of 39th Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 25 January 2013.
Official announcement of discovery of 2805222×5^5610444 + 1, PrimeGrid
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
Generalized Sierpinski/Riesel primes
Official announcement of discovery of 75898⁵²⁴²⁸⁸ + 1, PrimeGrid
Official announcement of discovery of 273662*5^3493296 + 1, PrimeGrid
102818*5^3440382-1, 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

External links

Chris Caldwell, The Largest Known Primes Database at The PrimePages
Top PRPs
A text file for the top primes
PrimeGrid’s 321 Prime Search, about the discovery of 3×2^6090515−1

This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.

[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)

[The_largest_known_primes-3] Chris Caldwell, The Largest Known Primes at The PrimePages.

[PRPTop-4] Henri Lifchitz & Renaud Lifchitz, Probable Primes Top 10000, primenumbers.net

[1stmegaprime-5] GIMPS press release, GIMPS Finds First Million-Digit Prime. Retrieved on 2008-01-04.

[largest-6] Chris Caldwell, The Largest Known Prime by Year: A Brief History at The PrimePages. Retrieved on 2008-09-28.

[worldofnumbers-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.

[4546prime-13] "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 10223×2^31172165 + 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 202705×2^21320516 + 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 1059094^1048576 + 1, PrimeGrid

[23] Official announcement of discovery of 919444^1048576 + 1, PrimeGrid

[24] Official announcement of discovery of 168451×2^19375200 + 1, PrimeGrid

[25] Official announcement of discovery of 3×2^17748034 - 1, PrimeGrid

[26] Official announcement of discovery of 8508301×2^17016603-1, PrimeGrid

[27] Official announcement of discovery of 3×2^16819291-1, PrimeGrid

[28] Official announcement of discovery of 3×2^16408818+1, PrimeGrid

[29] Official announcement of discovery of 99739×2^14019102-1, 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 2805222×5^5610444 + 1, PrimeGrid

[32] Official announcement of discovery of 3×2^11731850 − 1, PrimeGrid

[33] Official announcement of discovery of 3×2^11484018 − 1, PrimeGrid

[34] Official announcement of discovery of 3×2^10829346 + 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

[GSRP-38] Generalized Sierpinski/Riesel primes

[39] Official announcement of discovery of 75898⁵²⁴²⁸⁸ + 1, PrimeGrid

[40] Official announcement of discovery of 273662*5^3493296 + 1, PrimeGrid

[41] 102818*5^3440382-1, PrimeGrid

[42] Official announcement of discovery of 502573×2^7181987 − 1, PrimeGrid

[43] Official announcement of discovery of 402539×2^7173024 − 1, PrimeGrid

[44] Official announcement of discovery of 3×2^7033641 + 1, PrimeGrid

[45] Official announcement of discovery of 40597×2^6808509 – 1, PrimeGrid

[46] Official announcement of discovery of 6679881×2^6679881 + 1, PrimeGrid

Prime number classes
By formula	Fermat ( $2 2 n + 1$ ) Mersenne ( $2 p - 1$ ) Double Mersenne ( $2 2 p -1 - 1$ ) Wagstaff $(2 p + 1)/3$ Proth ( $k \cdot2 n + 1$ ) Factorial ( $n! \pm 1$ ) Primorial ( $p n # \pm 1$ ) Euclid ( $p n # + 1$ ) Pythagorean ( $4 n + 1$ ) Pierpont ( $2 m \cdot3 n + 1$ ) Quartan ( $x 4 + y 4$ ) Solinas ( $2 m \pm 2 n \pm 1$ ) Cullen ( $n \cdot2 n + 1$ ) Woodall ( $n \cdot2 n - 1$ ) Cuban ( $x 3 - y 3)/(x - y$ ) Leyland ( $x y + y x$ ) Thabit ( $3\cdot2 n - 1$ ) Williams ( $(b -1)\cdot b n - 1$ ) Mills ( $⌊ A 3 n ⌋$ )
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	Palindromic Emirp Repunit $(10 n - 1)/9$ Permutable Circular Truncatable Minimal Delicate Primeval Full reptend Unique Happy Self Smarandache–Wellin Strobogrammatic Dihedral Tetradic
Patterns	Twin ( $p, p + 2$ ) Bi-twin chain ( $n \pm 1, 2 n \pm 1, 4 n \pm 1, \dots$ ) 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/Safe ( $p, 2 p + 1$ ) Cunningham ( $p, 2 p \pm 1, 4 p \pm 3, 8 p \pm 7, ...$ ) Arithmetic progression ( $p + a\cdotn, n = 0, 1, 2, 3, ...$ ) Balanced ( $consecutive p - n, p, p + n$ )
By size	Mega (1,000,000+ digits) Largest known
Complex numbers	Eisenstein prime Gaussian prime
Composite numbers	Pseudoprime Catalan Elliptic Euler Euler–Jacobi Fermat Frobenius Lucas Somer–Lucas Strong Carmichael number Almost prime Semiprime Interprime Pernicious
Related topics	Probable prime Industrial-grade prime Illegal prime Formula for primes Prime gap
First 60 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 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281
List of prime numbers

Megaprime

Known megaprimes and mega PRPs

See also

References

External links