Megaprime

A megaprime is a prime number with at least one million decimal digits.[1]

A titanic prime, a term coined by Samuel Yates in the 1980s, is a prime number with at least 1,000 digits; and a gigantic prime has at least 10,000 digits.

The number of megaprimes found by year.

As of 16 December 2021, 1250 (probable) megaprimes are known, including 1178 definite primes[2] and 72 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] and was subject to a cooperative computing award.

The term bevaprime has been proposed as a term for a prime with at least 1,000,000,000 digits.[6]

In fact, 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 10⁹⁹⁹⁹⁹⁹ + 593499, a strong PRP, is actually the smallest megaprime.[7]

The last prime that is not a megaprime is almost certainly 10⁹⁹⁹⁹⁹⁹ - 172473.[3]

Known megaprimes and mega PRPs

Entries labelled "Prime" have been proved prime; those labelled "PRP" have not and primes that hasn't been fully verified by Prime Pages will be ranked, but be listed as a PRP. See the article Probable prime.

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	1 December 2021	6,418,121	Prime
14	2^20996011 – 1 [20]	17 November 2005	6,320,430	Prime
15	1059094^1048576 + 1 [21]	4 November 2018	6,317,602	Prime
16	919444^1048576 + 1 [22]	2 September 2017	6,253,210	Prime
17	168451×2^19375200 + 1 [23]	26 September 2017	5,832,522	Prime
-	${\tfrac {10^{5794777}-1}{9}}$	20 April 2021	5,794,777	PRP
18	7×2^18233956 + 1	1 October 2020	5,488,969	Prime
19	3×2^17748034 - 1 [24]	6 September 2021	5,342,692	Prime
20	$\Phi _{3}(-123447^{524288})$	23 February 2017	5,338,805	Prime
21	7×6^6772401 + 1	9 September 2019	5,269,954	Prime
22	8508301×2^17016603-1 [25]	22 March 2018	5,122,515	Prime
23	3×2^16819291-1 [26]	20 January 2021	5,063,112	Prime
24	3×2^16408818+1 [27]	28 October 2020	4,939,547	Prime
25	69×2^15866556+1	20 August 2021	4,776,312	Prime
26	2525332×73^2525332+1	28 August 2021	4,705,888	Prime
27	2^15317227+2^7658614+1	31 July 2020	4,610,945	Prime
28	6×5^6546983+1	13 June 2020	4,576,146	Prime
-	${\tfrac {2^{15135397}+1}{3}}$ [3]	June 2021	4,556,209	PRP
29	69×2^14977631-1	3 December 2021	4,508,719	Prime
30	192971×2^14773498-1	7 March 2021	4,447,272	Prime
31	6962×31^2863120-1	29 February 2020	4,269,952	Prime
32	99739×2^14019102-1 [28]	25 December 2019	4,220,176	Prime
33	404849×2^13764867+1	10 March 2021	4,143,644	Prime
34	2740879×2^13704395-1	26 October 2019	4,125,441	Prime
35	479216×3^8625889-1	16 November 2019	4,115,601	Prime
36	$\Phi _{3}(-143332^{393216})$	30 January 2017	4,055,114	Prime
37	2^13466917 – 1 [29]	14 November 2001	4,053,946	Prime
-	2^13380298 – 27	March 2021	4,027,872	PRP
-	${\tfrac {2^{13372531}+1}{3}}$ [3]	September 2013	4,025,533	PRP
-	${\tfrac {2^{13347311}+1}{3}}$ [3]	September 2013	4,017,941	PRP
38	9×2^13334487 + 1	31 March 2020	4,014,082	Prime
39	206039×2^13104952 - 1	26 April 2021	3,944,989	Prime
40	2805222×5^5610444 + 1 [30]	3 September 2019	3,921,539	Prime
41	19249×2^13018586 + 1 [2]	26 March 2007	3,918,990	Prime
42	2293×2^12918431 - 1	13 February 2021	3,888,839	Prime
-	${\tfrac {2^{12503723}-2^{6251862}+1}{5}}$ [3]	July 2020	3,763,995	PRP
43	9×2^12406887 + 1	29 March 2020	3,734,847	Prime
44	69×2^12231580 - 1	27 July 2021	3,682,075	Prime
45	27*2^12184319 + 1	6 February 2021	3,667,847	Prime
46	3×2^11895718 − 1 [2]	26 June 2015	3,580,969	Prime
47	3×2^11731850 − 1 [31]	13 March 2015	3,531,640	Prime
48	69×2^11718455 − 1 [2]	4 December 2020	3,527,609	Prime
49	69×2^11604348 − 1 [2]	4 December 2020	3,493,259	Prime
50	9×2^11500843 + 1 [2]	13 March 2020	3,462,100	Prime
51	3×2^11484018 − 1 [32]	22 November 2014	3,457,035	Prime
52	193997*2^11452891 +1	3 April 2018	3,447,670	Prime
53	3638450⁵²⁴²⁸⁸ +1	31 May 2020	3,439,810	Prime
54	9221*2^11392194 -1	7 February 2021	3,429,397	Prime
55	9*2^11366286 +1	26 March 2020	3,421,594	Prime
56	5*2^11355764 -1	2 October 2021	3,418,427	Prime
57	3214654⁵²⁴²⁸⁸ +1	25 December 2019	3,411,613	Prime
58	146561*2^11280802 -1	17 November 2020	3,395,865	Prime
59	2985036⁵²⁴²⁸⁸ +1	19 September 2019	3,394,739	Prime
60	2877652⁵²⁴²⁸⁸ +1	29 June 2019	3,386,397	Prime
61	2788032⁵²⁴²⁸⁸ +1	18 April 2019	3,379,193	Prime
62	2733014⁵²⁴²⁸⁸ +1	19 March 2019	3,374,655	Prime
63	9*2^11158963 +1	13 March 2020	3,359,184	Prime
64	9271*2^11134335 -1	17 January 2021	3,351,773	Prime
65	2312092⁵²⁴²⁸⁸+1	5 August 2018	3,336,572	Prime
66	2061748⁵²⁴²⁸⁸+1	21 March 2018	3,310,478	Prime
67	1880370⁵²⁴²⁸⁸ + 1	15 January 2018	3,289,511	Prime
68	3×2^10829346 + 1 [33]	14 January 2014	3,259,959	Prime
69	5×2^10495620 - 1	26 September 2021	3,159,498	Prime
-	${\tfrac {2^{10443557}-1}{37289325994807}}$ [3]	July 2020	3,143,811	PRP
70	5×2^10349000 - 1	26 September 2021	3,115,361	Prime
71	$\Phi _{3}(-844833^{262144})$	17 January 2017	3,107,335	Prime
72	$\Phi _{3}(-712012^{262144})$	14 January 2017	3,068,389	Prime
73	874208*54^1748416-1	26 September 2019	3,028,951	Prime
74	475856⁵²⁴²⁸⁸ + 1 [34]	8 August 2012	2,976,633	Prime
75	9*2^9778263+1	5 August 2020	2,943,552	Prime
76	1806676*41^1806676+1	12 March 2018	2,913,785	Prime
77	356926⁵²⁴²⁸⁸ + 1 [35]	25 July 2012	2,911,151	Prime
78	341112⁵²⁴²⁸⁸ + 1 [36]	25 June 2012	2,900,832	Prime
79	121*2^9584444+1	20 November 2020	2,885,208	Prime
80	11*41^9381365+1	7 March 2020	2,824,074	Prime
81	27653×2^9167433 + 1 [2]	8 June 2005	2,759,677	Prime
82	90527×2^9162167 + 1	30 June 2010	2,758,093	Prime
-	2^9092392 + 40291 [3]	February 2011	2,737,083	PRP
83	6795×2^9144320 - 1	31 March 2021	2,752,719	Prime
84	1323365*116^1323365+1	18 January 2018	2,732,038	Prime
85	13×2^8989858 + 1	10 March 2020	2,706,219	Prime
86	273809×2^8932416 − 1 [37]	13 December 2017	2,688,931	Prime
87	2×3^5570081 + 1	14 February 2020	2,657,605	Prime
88	25×2^8788628 + 1	1 March 2021	2,645,643	Prime
89	2038×366^1028507 − 1 [37]	4 April 2016	2,636,562	Prime
90	17×2^8636199 + 1	17 February 2021	2,599,757	Prime
91	75898⁵²⁴²⁸⁸ + 1 [38]	19 November 2021	2,558,647	Prime
92	25×2^8456828 + 1	28 January 2021	2,545,761	Prime
93	39×2^8413422 + 1	23 January 2021	2,532,694	Prime
94	31×2^8348000 + 1	19 January 2021	2,513,000	Prime
95	27×2^8342438 - 1	1 February 2021	2,511,326	Prime
96	3867×2^8261084 - 1	14 April 2021	2,486,838	Prime
-	${\tfrac {17^{1990523}-1}{16}}$ [3]	August 2020	2,449,236	PRP
97	273662×5^3493296 - 1	7 December 2021	2,441,715	Prime
98	11×2^8103463 + 1	6 March 2020	2,439,387	Prime
99	102818×5^3440382 - 1	10 October 2021	2,404,729	Prime
100	11×2^7971110 - 1	25 November 2019	2,399,545	Prime
101	27×2^7963247 + 1	16 January 2021	2,397,178	Prime
102	3177×2^7954621 - 1	13 June 2021	2,394,584	Prime
103	39×2^7946769 + 1	15 January 2021	2,392,218	Prime
104	7×6^3072198 + 1	4 August 2019	2,390,636	Prime
105	3765×2^7904593 - 1	10 January 2021	2,379,524	Prime
106	29×2^7899985 + 1	15 January 2021	2,378,134	Prime
107	861×2^7895451 - 1	21 February 2021	2,376,771	Prime
-	${\tfrac {11^{2264611}+1}{12}}$ [3]	July 2021	2,358,349	PRP
108	28433×2^7830457 + 1 [2]	31 December 2004	2,357,207	Prime
109	5×2^7755002 - 1	23 September 2021	2,334,489	Prime
110	2545×2^7732265 - 1	13 January 2021	2,327,648	Prime
111	5539×2^7730709 - 1	15 January 2021	2,327,180	Prime
112	4817×2^7719584 - 1	13 June 2021	2,323,831	Prime
113	1341174×53^1341174 + 1	22 August 2017	2,312,561	Prime
114	45×2^7661004 + 1	13 December 2020	2,306,194	Prime
115	15×2^7619838 + 1	24 December 2020	2,293,801	Prime
116	3597×2^7580693 - 1	10 January 2021	2,282,020	Prime
117	7401×2^7523295 - 1	21 February 2021	2,264,742	Prime
118	45×2^7513661 + 1	12 November 2020	2,261,839	Prime
119	$\Phi _{3}(-558640^{196608})$	11 January 2017	2,259,865	Prime
120	29×2^7374577 + 1	28 October 2020	2,219,971	Prime
121	109838×5^3168862 - 1	13 August 2020	2,219,971	Prime
122	101×2^7345194 - 1	5 October 2019	2,219,971	Prime
-	${\tfrac {2^{7313983}-1}{305492080276193}}$ [3]	March 2018	2,201,714	PRP
123	15×2^7300254 + 1	25 October 2020	2,219,971	Prime
124	1759×2^7284439 - 1	28 August 2021	2,219,971	Prime
125	737×2^7269322 − 1	10 August 2017	2,188,287	Prime
126	118568×5^3112069 + 1	2 May 2020	2,175,248	Prime
127	6039×2^7207973 − 1	24 March 2021	2,169,820	Prime
128	502573×2^7181987 − 1 [39]	4 October 2014	2,162,000	Prime
129	402539×2^7173024 − 1 [40]	2 October 2014	2,159,301	Prime
130	3343×2^7166019 - 1	29 September 2016	2,157,191	Prime
131	161041×2^7107964 + 1	8 January 2015	2,139,716	Prime
-	${\tfrac {2^{7080247}-1}{17045259548603283727480473638587228614426296913631}}$	October 2017	2,131,318	PRP
132	27*2^7046834+1	16 October 2018	2,121,310	Prime
133	1759×2^7046791 - 1	28 August 2021	2,121,299	Prime
134	327×2^7044001 - 1	13 January 2021	2,120,459	Prime
135	5×2^7037188 - 1	22 September 2021	2,118,406	Prime
136	3×2^7033641 + 1 [41]	21 February 2011	2,117,338	Prime
137	33661×2^7031232 + 1 [2]	30 October 2007	2,116,617	Prime
138	$\Phi _{3}(-237804^{196608})$	6 January 2017	2,114,016	Prime
139	207494*5^3017502-1	19 March 2020	2,109,149	Prime
140	15*2^6993631-1	25 August 2021	2,105,294	Prime
141	2^6972593 – 1 [4]	1 June 1999	2,098,960	Prime
142	6219*2^6958945-1	7 January 2021	2,094,855	Prime
143	51*2^6945567+1	26 May 2020	2,090,826	Prime
144	238694*5^2979422-1	13 March 2020	2,082,532	Prime
145	4×72^1119849 − 1 [37]	7 September 2016	2,079,933	Prime
146	33*2^6894190-1	27 July 2021	2,075,360	Prime
147	146264*5^2953282-1	10 March 2020	2,064,261	Prime
148	69*2^6838971-1	1 March 2020	2,058,738	Prime
149	35816*5^2945294-1	5 March 2020	2,058,677	Prime
150	127*2^6836153-1	25 June 2018	2,057,890	Prime
151	19*2^6833086+1	25 October 2020	2,056,966	Prime
152	40597×2^6808509 – 1 [42]	27 November 2013	2,049,571	Prime
153	283*2^6804701-1	19 January 2020	2,048,431	Prime
154	1861209*2^6789999+1	2 December 2020	2,044,000	Prime
155	5817*2^6789459-1	9 January 2021	2,043,835	Prime
156	8435*2^6786180-1	7 January 2021	2,042,848	Prime
157	51*2^6753404+1	26 May 2020	2,032,979	Prime
158	9995*2^6711008-1	31 December 2020	2,020,219	Prime
160	6679881×2^6679881 + 1 [43]	2009-07-25	2,010,852	Prime
161	37×2^6660841 − 1 [37]	2014	2,005,115	Prime
163	304207×2^6643565 – 1 [44]	2013-10-10	1,999,918	Prime
173	398023×2^6418059 – 1 [45]	2013-10-05	1,932,034	Prime
176	1582137x2^6328550 + 1 [46]	2009-04-20	1,905,090	Prime
194	194368*5^2638045-1	2018	1,843,920	Prime
198	66916*5^2628609-1	2018	1,837,324	Prime
199	3×2^6090515 – 1 [47]	2010-04-24	1,833,429	Prime
210	1583×2^5989282 − 1	2015	1,802,957	Prime
213	327926*5^2542838-1	2018	1,777,374	Prime
214	81556*5^2539960+1	2018	1,775,361	Prime
215	5828034²⁶²¹⁴⁴+1	2018	1,773,542	Prime
218	5205422²⁶²¹⁴⁴+1	2018	1,760,679	Prime
219	5152128²⁶²¹⁴⁴+1	2018	1,759,508	Prime
220	4489246²⁶²¹⁴⁴+1	2018	1,743,828	Prime
221	7×2^5775996 + 1 [48]	2012-11-02	1,738,749	Prime
223	4246258²⁶²¹⁴⁴+1	2018	1,737,493	Prime
224	3933508²⁶²¹⁴⁴+1	2018	1,728,783	Prime
225	3853792²⁶²¹⁴⁴+1	2018	1,726,452	Prime
226	3673932²⁶²¹⁴⁴ + 1	2017	1,721,010	Prime
227	3596074²⁶²¹⁴⁴ + 1	2017	1,718,572	Prime
228	3547726²⁶²¹⁴⁴ + 1	2017	1,717,031	Prime
230	1243×2^5686715 - 1	2016	1,711,875	Prime
233	3060772²⁶²¹⁴⁴ + 1	2017	1,700,222	Prime
234	9×2^5642513 + 1	2013	1,698,567	Prime
236	2622×11^1621920 – 1 [37]	2015	1,689,060	Prime
237	2676404²⁶²¹⁴⁴ + 1	2017	1,684,945	Prime
238	301562×5^2408646 - 1	2017	1,683,577	Prime
239	2611294²⁶²¹⁴⁴ + 1	2017	1,682,141	Prime
240	171362×5^2400996 − 1	2017	1,678,230	Prime
241	2514168²⁶²¹⁴⁴ + 1	2017	1,677,825	Prime
244	252191×2^5497878 – 1 [49]	2012-06-23	1,655,032	Prime
245	2042774²⁶²¹⁴⁴ + 1	2016	1,654,187	Prime
246	1828858²⁶²¹⁴⁴+1	2016	1,641,593	Prime
247	258317 × 2^5450519+1	2008	1,640,776	Prime
249	5*2^5429494-1	2017	1,634,442	Prime
250	43*2^5408183-1	2018	1,628,027	Prime
251	1615588²⁶²¹⁴⁴ + 1	2016	1,627,477	Prime
252	1349×2^5385004 − 1	2017	1,621,051	Prime
253	1488256²⁶²¹⁴⁴ + 1	2016	1,618,131	Prime
254	1415198²⁶²¹⁴⁴ + 1	2016	1,612,400	Prime
256	$\Phi _{3}(-1082083^{131072})$	2017	1,581,846	Prime
-	${\tfrac {2^{5240707}-1}{75392810903}}$ [3]	2016-07	1,577,600	PRP
258	180062×5^2249192 − 1	2016	1,572,123	Prime
260	27×2^5213635 + 1	2015	1,569,462	Prime
262	$\Phi _{3}(-843575^{131072})$	2017	1,553,498	Prime
264	53546×5^2216664-1	2016	1,549,387	Prime
-	2^5146295 + 41693 [3]	2009-11	1,549,190	PRP
265	773620²⁶²¹⁴⁴ + 1 [50]	2012-04-19	1,543,643	Prime
271	51×2^5085142 - 1	2014	1,530,782	Prime
272	3×2^5082306 + 1 [51]	2009-04-03	1,529,928	Prime
273	676754²⁶²¹⁴⁴+1	2012	1,528,413	Prime
274	296024 × 5^2185270 − 1	2016	1,527,444	Prime
275	5359 × 2^5054502+1	2003	1,521,561	Prime
276	13×2^4998362 + 1	2014	1,504,659	Prime
277	525094²⁶²¹⁴⁴+1	2012	1,499,526	Prime
278	92158×5^2145024 + 1	2016	1,499,313	Prime
279	77072×5^2139921 + 1	2016	1,495,746	Prime
282	306398 × 5^2112410 − 1	2016	1,476,517	Prime
283	265711 × 2^4858008+1	2008	1,462,412	Prime
284	154222 × 5^2091432 + 1	2015	1,461,854	Prime
285	1271 × 2^4850526-1	2012	1,460,157	Prime
286	$\Phi _{3}(-362978^{131072})$	2015	1,457,490	Prime
287	361658²⁶²¹⁴⁴+1	2011	1,457,075	Prime
-	${\tfrac {2^{4834891}-1}{120254426180274428677241}}$ [3]	2017-01	1,455,425	PRP
288	100186 × 5^2079747 − 1	2015	1,453,686	Prime
290	$\Phi _{19168228L}(2)$ [nb 1]	2014	1,442,553	Prime
292	653 × 10^1435026 − 1 [37]	2014	1,435,029	Prime
295	1229 x 2^4703492-1	2018	1,415,896	Prime
298	144052× 5^2018290 + 1	2015	1,410,730	Prime
300	9 × 2^4683555 − 1	2012	1,409,892	Prime
302	34x993⁴⁶⁹²⁴⁵+1	2018	1,406,305	Prime
303	79x2^4658115-1	2018	1,402,235	Prime
306	11 × 2^4643238 − 1	2014	1,397,755	Prime
307	68×995⁴⁶⁵⁹⁰⁸ − 1 [37]	2017	1,396,712	Prime
309	$\Phi _{3}(-192098^{131072})$	2015	1,385,044	Prime
310	27× 2^4583717 − 1	2014	1,379,838	Prime
-	2^4583176 + 2131 [3]	2009-09	1,379,674	PRP
311	121×2^4553899 – 1 [52]	2012-02-25	1,370,863	Prime
312	27× 2^4542344 − 1	2014	1,367,384	Prime
-	$\Phi _{18132292M}(2)$ ^[*] [3]	2014-03	1,364,591	PRP
314	4×797⁴⁶⁸⁷⁰² + 1 [37]	2017	1,359,920	Prime
315	145310²⁶²¹⁴⁴+1	2011	1,353,265	Prime
317	36772 × 6^1723287 − 1	2014	1,340,983	Prime
-	${\tfrac {13^{1199467}+1}{14}}$ [3]	2015-12	1,336,138	PRP
320	151×2^4424321 − 1	2016	1,331,856	Prime
-	${\tfrac {5^{1888279}-1}{4}}$ [3]	2018	1,319,850	PRP
322	49x2^4365175-1	2017	1,314,051	Prime
323	49x2^4360869-1	2017	1,312,755	Prime
324	13x2^4333087-1	2018	1,304,391	Prime
325	353159×2^4331116 – 1 [53]	2011-05-31	1,303,802	Prime
327	682156×79⁶⁸²¹⁵⁶ + 1	2016	1,294,484	Prime
328	141941×2^4299438 – 1 [54]	2011-05-26	1,294,265	Prime
330	15 × 2^4246384+1	2013	1,278,291	Prime
331	3×2^4235414 – 1 [55]	2008-03-23	1,274,988	Prime
334	109208 × 5^1816285 + 1	2014	1,269,534	Prime
335	1091x2^4215518-1	2018	1,269,001	Prime
336	191 × 2^4203426-1	2012	1,265,360	Prime
337	1259 × 2^4196028-1	2016	1,263,134	Prime
-	${\tfrac {2^{4194304}+1026473}{3}}$ [3]	2017-07	1,262,611	PRP
338	325918x5^1803339-1	2014	1,260,486	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
339	133778x5^1785689+1	2014	1,248,149	Prime
340	17x2^4107544-1	2015	1,236,496	Prime
341	24032x5^1768249+1	2014	1,235,958	Prime
342	172×159⁵⁶¹³¹⁹ − 1 [37]	2017	1,235,689	Prime
-	${\tfrac {16^{1025393}+1}{17}}$ [3]	2014-08	1,234,695	PRP
348	1031×2^4054974−1	2017	1,220,672	Prime
-	${\tfrac {2^{4031399}+1}{3}}$ [3]	2010-02	1,213,572	PRP
350	39653×430⁴⁶⁰³⁹⁷-1 [37]	2016	1,212,446	Prime
351	40734²⁶²¹⁴⁴+1	2011	1,208,473	Prime
352	9 × 2^4005979 - 1	2012	1,205,921	Prime
353	12 × 68⁶⁵⁶⁹²¹ + 1 [37]	2016	1,203,815	Prime
354	67×688⁴²³⁸⁹³ + 1 [37]	2017	1,202,836	Prime
355	1993191 × 4^1993191 − 1	2015	1,200,027	Prime
356	138172x5^1714207-1	2014	1,198,185	Prime
358	$\Phi _{3}(-1202113^{98304})$	2016	1,195,366	Prime
361	$\Phi _{3}(-1110815^{98304})$	2016	1,188,622	Prime
362	22478x5^1675150-1	2014	1,170,884	Prime
363	1199x2^3889576-1	2018	1,170,883	Prime
364	298989x2^3886857+1	2014	1,170,067	Prime
365	27×2^3855094 – 1 [56]	2012-02-28	1,160,501	Prime
367	164x978³⁸⁷⁹²⁰-1	2018	1,160,015	Prime
370	30x514⁴²⁴⁶⁵²-1	2017	1,151,218	Prime
371	24518²⁶²¹⁴⁴+1	2008	1,150,678	Prime
372	$\Phi _{3}(-700219^{98304})$	2016	1,149,220	Prime
374	109x980³⁸³⁶⁶⁹-1	2018	1,147,643	Prime
375	123547×2^3804809 – 1 [57]	2011-05-08	1,145,367	Prime
376	2564x75⁶¹⁰⁷⁵³+1	2014	1,145,203	Prime
377	$\Phi _{3}(-660955^{98304})$	2016	1,144,293	Prime
379	326834x5^1634978-1	2014	1,142,807	Prime
381	415267×2^3771929 – 1 [58]	2011-05-08	1,135,470	Prime
383	11 × 2^3771821+1	2013	1,135,433	Prime
384	938237 × 2^3752950-1	2007	1,129,757	Prime
386	207394x5^1612573-1	2014	1,127,146	Prime
387	684×10^1127118 + 1 [37]	2017	1,127,121	Prime
388	$\Phi _{3}(-535386^{98304})$	2016	1,126,302	Prime
389	104944x5^1610735-1	2014	1,125,861	Prime
390	23451 × 2^3739388 + 1 [37]	2015	1,125,673	Prime
394	2^3704053 + 2^1852027 + 1	2014	1,115,032	Prime
397	330286×5^1584399 – 1 [59]	2014-03-21	1,107,453	Prime
400	13x2^3675223-1	2016	1,106,354	Prime
402	15×2^3668194 – 1	2013	1,104,238	Prime
400	13*2^3664703-1	2016	1,103,187	Prime
401	$\Phi _{3}(-406515^{98304})$	2016	1,102,790	Prime
403	33300×430⁴¹⁷⁸⁴⁹-1 [37]	2016	1,100,397	Prime
409	65531 × 2^3629342-1	2011	1,092,546	Prime
412	113x2^3628034-1	2014	1,092,150	Prime
-	${\tfrac {106\cdot 23^{800873}-7}{11}}$ [3]	2015-05	1,090,573	PRP
416	29x920³⁶⁷⁸¹⁰-1	2015	1,090,113	Prime
418	14641x2^3618876+1	2018	1,089,395	Prime
423	485767 × 2^3609357-1	2008	1,086,531	Prime
430	189x2^3596375+1	2016	1,082,620	Prime
433	35x2^3587843+1	2014	1,080,050	Prime
434	275x2^3585539+1	2016	1,079,358	Prime
435	2x59⁶⁰⁸⁶⁸⁵+1	2014	1,077,892	Prime
438	309x2^3577339+1	2016	1,076,889	Prime
440	251x2^3574535+1	2016	1,076,045	Prime
443	35x2^3570777+1	2014	1,074,913	Prime
444	33x2^3570132+1	2014	1,074,719	Prime
445	5 × 2^3569154-1	2009	1,074,424	Prime
446	81 × 492³⁹⁹⁰⁹⁵ − 1 [37]	2015	1,074,352	Prime
447	22934×5^1536762 – 1 [60]	2014-02-06	1,074,155	Prime
449	771x2^3564109+1	2018	1,072,907	Prime
450	381x2^3563676+1	2016	1,072,776	Prime
451	555x2^3563328+1	2018	1,072,672	Prime
452	1183x2^3560584+1	2018	1,071,846	Prime
453	415x2^3559614+1	2016	1,071,554	Prime
454	1103x2^3558176-1	2018	1,071,121	Prime
455	1379x2^3557072-1	2018	1,070,789	Prime
456	681x2^3553141+1	2018	1,069,605	Prime
457	599x2^3551793+1	2018	1,069,200	Prime
458	621x2^3551472+1	2018	1,069,103	Prime
-	${\tfrac {7^{1264699}-1}{6}}$ [3]	2014-01	1,068,794	PRP
459	773x2^3550373+1	2018	1,068,772	Prime
460	1199x2^3548380-1	2018	1,068,172	Prime
461	191x2^3548117+1	2015	1,068,092	Prime
462	867x2^3547711+1	2018	1,067,971	Prime
463	$\Phi _{3}(3^{1118781}+1)/3$	2014	1,067,588	Prime
464	351x2^3545752+1	2016	1,067,381	Prime
465	93x2^3544744+1	2014	1,067,077	Prime
466	1159x2^3543702+1	2018	1,066,764	Prime
467	178658x5^1525224 – 1 [61]	2014-01-31	1,066,092	Prime
468	1085x2^3539671+1	2018	1,065,551	Prime
469	465×2^3536871 – 1 [62]	2016-09-30	1,064,707	Prime
470	1019 × 2^3536312-1	2012	1,064,539	Prime
471	1179x2^3534450+1	2018	1,063,979	Prime
472	447x2^3533656+1	2016	1,063,740	Prime
473	1059x2^3533550+1	2016	1,063,529	Prime
475	553x2^3532758+1	2018	1,063,469	Prime
476	141x2^3529287+1	2015	1,062,424	Prime
477	13x2^3527315-1	2016	1,061,829	Prime
478	1393x2^3525571-1	2017	1,061,306	Prime
479	1071x2^3523944+1	2018	1,060,816	Prime
480	329x2^3518451+1	2016	1,059,162	Prime
481	135x2^3518338+1	2015	1,059,128	Prime
482	2×10^1059002 – 1	2013	1,059,003	Prime
483	64x10^1058794+1	2017	1,058,796	Prime
484	599x2^3515959+1	2018	1,058,412	Prime
485	7 × 2^3511774+1	2008	1,057,151	Prime
486	1135x2^3510890+1	2018	1,056,887	Prime
487	428639 × 2^3506452-1	2011	1,055,553	Prime
489	555x2^3502765+1	2018	1,054,441	Prime
490	643x2^3501974+1	2018	1,054,203	Prime
491	2x23⁷⁷⁴¹⁰⁹+1	2014	1,054,127	Prime
492	1159x2^3501490+1	2018	1,054,057	Prime
495	9×2^3497442 + 1 [63]	2012-10-23	1,052,836	Prime
498	51×2^3490971 + 1	2014	1,050,889	Prime
504	59912×5^1500861 + 1 [64]	2014-01-17	1,049,062	Prime
-	${\tfrac {2^{3464473}-1}{604874508299177}}$ [3]	2014-10	1,042,896	PRP
560	37292×5^1487989 + 1 [65]	2013-12-29	1,040,065	Prime
575	1273 × 2^3448551-1	2012	1,038,121	Prime
649	191249 × 2^3417696-1	2010	1,028,835	Prime
675	59 × 2^3408416-1	2010	1,026,038	Prime
689	24 × 414³⁹¹¹⁷⁹ + 1 [37]	2016	1,023,717	Prime
703	342924651×2^3394939 – 1	2017	1,021,988	Prime
711	67×2^3391385 – 1	2014	1,020,911	Prime
738	173198×5^1457792 – 1 [66]	2013-12-04	1,018,959	Prime
932	81×2^3352924 + 1 [67]	2012-01-17	1,009,333	Prime
1024	1087 × 2^3336385-1	2012	1,004,355	Prime
1158	464253×2^3321908 – 1	2013	1,000,000	Prime
1160	191273×2^3321908 – 1 [2]	23 May 2013	1,000,000	Prime
1161	1814570322984178⁶⁵⁵³⁶ + 1	12 March 2020	1,000,000	Prime
1162	1814570322977518⁶⁵⁵³⁶ + 1	12 March 2020	1,000,000	Prime
1163	3292665455999520712131951642528³²⁷⁶⁸ + 1	17 July 2020	1,000,000	Prime
1164	3292665455999520712131951625894³²⁷⁶⁸ + 1	17 July 2020	1,000,000	Prime
1165	108416458051325316667867924053113194188466370431999 17731311876¹⁶³⁸⁴ + 1	23 December 2020	1,000,000	Prime
1166	108416458051325316667867924053113194188466370431999 17731150000¹⁶³⁸⁴ + 1	17 December 2020	1,000,000	Prime
1167	117541283763947820803514936063599937165870515987063 348437723855381224452611844232886228245901292532817 349347812678729375350⁸¹⁹² + 1	15 June 2021	1,000,000	Prime
1168	117541283763947820803514936063599937165870515987063 348437723855381224452611844232886228245901292532817 349347812678729240092⁸¹⁹² + 1	10 May 2021	1,000,000	Prime
1169	117541283763947820803514936063599937165870515987063 348437723855381224452611844232886228245901292532817 349347812678729154678⁸¹⁹² + 1	2 May 2021	1,000,000	Prime
1170	117541283763947820803514936063599937165870515987063 348437723855381224452611844232886228245901292532817 349347812678729122666⁸¹⁹² + 1	2 May 2021	1,000,000	Prime
1171	117541283763947820803514936063599937165870515987063 348437723855381224452611844232886228245901292532817 349347812678729023786⁸¹⁹² + 1	6 April 2021	1,000,000	Prime
-	138159533888769035882147458995963805584809676992814 878233984916869972869600503621759663902898091163546 434463090695593184764982641875302546673096047093511 481998019892105889132464543550102310865144502037206 65411679519151409973433052122012098115876⁴⁰⁹⁶ + 1	November 2021	1,000,000	PRP
-	138159533888769035882147458995963805584809676992814 878233984916869972869600503621759663902898091163546 434463090695593184764982641875302546673096047093511 481998019892105889132464543550102310865144502037206 65411679519151409973433052122012098003208⁴⁰⁹⁶ + 1	November 2021	1,000,000	PRP
1172	138159533888769035882147458995963805584809676992814 878233984916869972869600503621759663902898091163546 434463090695593184764982641875302546673096047093511 481998019892105889132464543550102310865144502037206 65411679519151409973433052122012097875144⁴⁰⁹⁶ + 1	15 August 2021	1,000,000	Prime
1173	138159533888769035882147458995963805584809676992814 878233984916869972869600503621759663902898091163546 434463090695593184764982641875302546673096047093511 481998019892105889132464543550102310865144502037206 65411679519151409973433052122012097840702⁴⁰⁹⁶ + 1	3 August 2021	1,000,000	Prime
1174	10⁹⁹⁹⁹⁹⁹ + 308267×10²⁹²⁰⁰⁰ + 1 [2]	19 February 2021	1,000,000	Prime (and PRP)
-	10⁹⁹⁹⁹⁹⁹ + 593499 [3] [7]	24 December 2012	1,000,000	PRP

Notes

$\Phi _{nL}(b)$ = gcd( $\Phi _{n}(b)$ , the aurifeuillean L part of $b^{n}-1$ ), $\Phi _{nM}(b)$ = gcd( $\Phi _{n}(b)$ ,the aurifeuillean M part of $b^{n}-1$ ).

References

Chris Caldwell, The Prime Glossary: megaprime at The Prime Pages. Retrieved on 2008-01-04.
Chris Caldwell, The Largest Known Primes at The Prime Pages.
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 Prime Pages. Retrieved on 2008-09-28.
"Chris Caldwell, The Largest Known Prime by Year: A Brief History". Archived from the original on 2016-01-01. Retrieved 2008-01-04.CS1 maint: bot: original URL status unknown (link)
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 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 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

External links

Chris Caldwell, The Largest Known Primes Database at The Prime Pages
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.

[52] $\Phi _{nL}(b)$ = gcd( $\Phi _{n}(b)$ , the aurifeuillean L part of $b^{n}-1$ ), $\Phi _{nM}(b)$ = gcd( $\Phi _{n}(b)$ ,the aurifeuillean M part of $b^{n}-1$ ).

[1] Chris Caldwell, The Prime Glossary: megaprime at The Prime Pages. Retrieved on 2008-01-04.

[The_largest_known_primes-2] Chris Caldwell, The Largest Known Primes at The Prime Pages.

[PRPTop-3] Henri Lifchitz & Renaud Lifchitz, Probable Primes Top 10000, primenumbers.net

[1stmegaprime-4] GIMPS press release, GIMPS Finds First Million-Digit Prime. Retrieved on 2008-01-04.

[largest-5] Chris Caldwell, The Largest Known Prime by Year: A Brief History at The Prime Pages. Retrieved on 2008-09-28.

[6] "Chris Caldwell, The Largest Known Prime by Year: A Brief History". Archived from the original on 2016-01-01. Retrieved 2008-01-04.CS1 maint: bot: original URL status unknown (link)

[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 press release of 40th Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 25 January 2013.

[21] Official announcement of discovery of 1059094^1048576 + 1, PrimeGrid

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

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

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

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

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

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

[28] Official announcement of discovery of 99739×2^14019102-1, PrimeGrid

[29] "Official press release of 39th Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 25 January 2013.

[30] Official announcement of discovery of 2805222×5^5610444 + 1, PrimeGrid

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

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

[33] Official announcement of discovery of 3×2^10829346 + 1, PrimeGrid

[34] Official announcement of discovery of 475856⁵²⁴²⁸⁸ + 1, PrimeGrid

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

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

[GSRP-37] Generalized Sierpinski/Riesel primes

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

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

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

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

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

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

[44] Official announcement of discovery of 304207×2^6643565 – 1, PrimeGrid

[45] Official announcement of discovery of 398023×2^6418059 – 1, PrimeGrid

[46] Official announcement of discovery of 6328548×2^6328548 + 1, PrimeGrid

[47] Official announcement of discovery of 3×2^6090515 – 1, PrimeGrid

[48] Official announcement of discovery of 7×2^5775996 + 1, PrimeGrid

[49] Official announcement of discovery of 252191×2^5497878 – 1, PrimeGrid

[50] Official announcement of discovery of 773620²⁶²¹⁴⁴ + 1, PrimeGrid

[51] Official announcement of discovery of 3×2^5082306 + 1, PrimeGrid

[53] Official announcement of discovery of 121×2^4553899 – 1, PrimeGrid

[54] Official announcement of discovery of 353159×2^4331116 – 1, PrimeGrid

[55] Official announcement of discovery of 141941×2^4299438 – 1, PrimeGrid

[56] Official announcement of discovery of 3×2^4235414 – 1, PrimeGrid

[57] Official announcement of discovery of 27×2^3855094 – 1, PrimeGrid

[58] Official announcement of discovery of 123547×2^3804809 – 1, PrimeGrid

[59] Official announcement of discovery of 415267×2^3771929 – 1, PrimeGrid

[60] Official announcement of discovery of 330286×5^1584399 – 1, PrimeGrid

[61] Official announcement of discovery of 22934×5^1536762 – 1, PrimeGrid

[62] Official announcement of discovery of 178658×5^1525224 – 1, PrimeGrid

[63] Official announcement of discovery of 465×2^3536871 – 1, PrimeGrid

[64] Official announcement of discovery of 9×2^3497442 + 1, PrimeGrid

[65] Official announcement of discovery of 59912×5^1500861 + 1, PrimeGrid

[66] Official announcement of discovery of 37292×5^1487989 + 1, PrimeGrid

[67] Official announcement of discovery of 173198×5^1457792 – 1, PrimeGrid

[68] Official announcement of discovery of 81×2^3352924 + 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 ( $n - 1, n + 1, 2 n - 1, 2 n + 1, \dots$ ) 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

Notes

See also

References

External links