List of largest known primes and probable primes

The table below lists the largest currently known prime numbers and probable primes (PRPs) as tracked by the PrimePages and by Henri & Renaud Lifchitz's PRP Records. Numbers with more than 2,000,000 digits are shown.

Largest known primes[edit]

These numbers have been proved prime by computer with a primality test for their form, for example the Lucas–Lehmer primality test for Mersenne numbers. $\Phi _{3}(x)$ is the third cyclotomic polynomial, defined as $x^{2}+x+1$ .

Rank^[1]	Number	Discovery date	Decimal digits
1	2^82589933 – 1 ^[2]	7 December 2018	24,862,048
2	2^77232917 – 1 ^[3]	26 December 2017	23,249,425
3	2^74207281 – 1 ^[4]	7 January 2016	22,338,618
4	2^57885161 – 1 ^[5]	25 January 2013	17,425,170
5	2^43112609 – 1 ^[6]	23 August 2008	12,978,189
6	2^42643801 – 1 ^[7]	4 June 2009	12,837,064
7	$\Phi _{3}(-516693^{1048576})$	2 October 2023	11,981,518
8	$\Phi _{3}(-465859^{1048576})$	31 May 2023	11,887,192
9	2^37156667 – 1 ^[6]	6 September 2008	11,185,272
10	2^32582657 – 1 ^[8]	4 September 2006	9,808,358
11	10223×2^31172165 + 1 ^[9]	31 October 2016	9,383,761
12	2^30402457 – 1 ^[10]	15 December 2005	9,152,052
13	2^25964951 – 1 ^[11]	18 February 2005	7,816,230
14	2^24036583 – 1 ^[12]	15 May 2004	7,235,733
15	1963736^1048576 + 1 ^[13]	24 September 2022	6,598,776
16	1951734^1048576 + 1 ^[14]	9 August 2022	6,595,985
17	202705×2^21320516 + 1 ^[15]	25 November 2021	6,418,121
18	2^20996011 – 1 ^[16]	17 November 2003	6,320,430
19	1059094^1048576 + 1 ^[17]	31 October 2018	6,317,602
20	3×2^20928756 - 1 ^[18]	5 July 2023	6,300,184
21	919444^1048576 + 1 ^[19]	29 August 2017	6,253,210
22	81×2^20498148 + 1	13 June 2023	6,170,560
23	7×2^20267500 + 1	21 July 2022	6,101,127
24	4×5^8431178 + 1	2 January 2024	5,893,142
25	168451×2^19375200 + 1 ^[20]	17 September 2017	5,832,522
26	69×2^19374980 - 1	3 July 2022	5,832,452
27	3×2^18924888 - 1 ^[21]	24 March 2022	5,696,990
28	69×2^18831865 - 1	16 December 2021	5,668,959
29	97139×2^18397548 - 1	23 April 2023	5,538,219
30	7×2^18233956 + 1	1 October 2020	5,488,969
31	3×2^18196595 - 1 ^[22]	8 January 2022	5,477,722
32	3×2^17748034 - 1 ^[23]	6 September 2021	5,342,692
33	$\Phi _{3}(-123447^{524288})$	23 February 2017	5,338,805
34	3622×5^7558139 - 1	18 February 2022	5,282,917
35	7×6^6772401 + 1	9 September 2019	5,269,954
36	2×3^10852677 + 1	8 January 2023	5,178,044
37	8508301×2^17016603-1 ^[24]	21 March 2018	5,122,515
38	8×10^5112848-1	30 January 2024	5,112,848
39	13×2^16828072 + 1	11 October 2023	5,065,756
40	3×2^16819291-1 ^[25]	20 January 2021	5,063,112
41	3×2^16408818+1 ^[26]	25 October 2020	4,939,547
42	2329989×2^16309923-1	13 February 2024	4,909,783
43	69×2^15866556+1	20 August 2021	4,776,312
44	2036×3^10009192+1	15 February 2024	4,775,602
45	2525332×73^2525332+1 ^[27]	28 August 2021	4,705,888
46	1419499×2^15614489+1	9 February 2024	4,700,436
47	11×2^15502315+1	8 January 2023	4,666,663
48	(10^2332974+1)²-2	20 February 2024	4,665,949
49	37×2^15474010+1	8 November 2022	4,658,143
50	93839×2^15337656-1	28 November 2022	4,617,100
51	2^15317227+2^7658614+1	31 July 2020	4,610,945
52	13×2^15294536+1	30 September 2023	4,604,116
53	6×5^6546983+1	13 June 2020	4,576,146
54	4788920×3^9577840-1	14 February 2024	4,569,798
55	69×2^14977631-1	3 December 2021	4,508,719
56	192971×2^14773498-1	7 March 2021	4,447,272
57	9145334×3^9145334+1	25 December 2023	4,363,441
58	4×5^6181673-1	15 July 2022	4,320,805
59	396101×2^14259638-1	3 February 2024	4,292,585
60	6962×31^2863120-1	29 February 2020	4,269,952
61	37×2^14166940+1	24 June 2022	4,264,676
62	99739×2^14019102-1 ^[28]	24 December 2019	4,220,176
63	69×2^13832885-1	17 January 2022	4,164,116
64	404849×2^13764867+1	10 March 2021	4,143,644
65	25×2^13719266+1	20 September 2022	4,129,912
66	81×2^13708272 + 1	11 October 2022	4,126,603
67	2740879×2^13704395-1	26 October 2019	4,125,441
68	479216×3^8625889-1	16 November 2019	4,115,601
69	$\Phi _{3}(-143332^{393216})$	30 January 2017	4,055,114
70	81×2^13470584 + 1	9 October 2022	4,055,052
71	2^13466917 – 1 ^[29]	14 November 2001	4,053,946
72	9×2^13334487 + 1	31 March 2020	4,014,082
73	206039×2^13104952 - 1	26 April 2021	3,944,989
74	2805222×5^5610444 + 1 ^[30]	2 September 2019	3,921,539
75	19249×2^13018586 + 1 ^[31]	26 March 2007	3,918,990
76	2293×2^12918431 - 1	13 February 2021	3,888,839
77	81×2^12804541 + 1	19 September 2022	3,854,553
78	4×5^5380542 + 1	22 February 2023	3,760,839
79	9×2^12406887 + 1	29 March 2020	3,734,847
80	7×2^12286041 - 1	10 June 2023	3,698,468
81	69×2^12231580 - 1	27 July 2021	3,682,075
82	27×2^12184319 + 1	6 February 2021	3,667,847
83	8630170⁵²⁴²⁸⁸ + 1 ^[32]	13 April 2024	3,636,472
84	3761×2^11978874 − 1	6 July 2022	3,606,004
85	95×2^11954552 − 1	28 May 2024	3,598,681
86	3×2^11895718 − 1 ^[33]	23 June 2015	3,580,969
87	37×2^11855148 + 1	30 May 2022	3,568,757
88	6339004⁵²⁴²⁸⁸ + 1 ^[34]	8 June 2023	3,566,218
89	763795×6^4582771 + 1	11 December 2023	3,566,095
90	5897794⁵²⁴²⁸⁸ + 1 ^[31]	18 December 2022	3,549,792
91	3×2^11731850 − 1 ^[35]	13 March 2015	3,531,640
92	69×2^11718455 − 1 ^[31]	4 December 2020	3,527,609
93	41×2^11676439 + 1 ^[31]	20 June 2022	3,514,960
94	4896418⁵²⁴²⁸⁸ + 1 ^[36]	15 May 2022	3,507,424
95	81×2^11616017 + 1 ^[31]	30 August 2022	3,496,772
96	69×2^11604348 − 1 ^[31]	4 December 2020	3,493,259
97	4450871×6^4450871 + 1 ^[31]	17 September 2023	3,463,458
98	9×2^11500843 + 1 ^[31]	13 March 2020	3,462,100
99	3×2^11484018 − 1 ^[37]	22 November 2014	3,457,035
100	193997×2^11452891 +1 ^[38]	3 April 2018	3,447,670
101	3638450⁵²⁴²⁸⁸ +1 ^[39]	29 May 2020	3,439,810
102	9221×2^11392194 -1 ^[40]	7 February 2021	3,429,397
103	9×2^11366286 +1	26 March 2020	3,421,594
104	5×2^11355764 -1	2 October 2021	3,418,427
105	732050×6^4392301 +1	9 September 2023	3,417,881
106	3214654⁵²⁴²⁸⁸ +1 ^[41]	24 December 2019	3,411,613
107	146561×2^11280802 -1 ^[42]	16 November 2020	3,395,865
108	2985036⁵²⁴²⁸⁸ +1 ^[43]	18 September 2019	3,394,739
109	6929×2^11255424 -1	7 July 2022	3,388,225
110	2877652⁵²⁴²⁸⁸ +1 ^[44]	29 June 2019	3,386,397
111	2788032⁵²⁴²⁸⁸ +1 ^[45]	17 April 2019	3,379,193
112	2733014⁵²⁴²⁸⁸ +1 ^[46]	18 March 2019	3,374,655
113	9×2^11158963 +1	13 March 2020	3,359,184
114	9271×2^11134335 -1	17 January 2021	3,351,773
115	136804×5^4777253 -1	1 March 2024	3,339,162
116	2312092⁵²⁴²⁸⁸+1 ^[47]	4 August 2018	3,336,572
117	2061748⁵²⁴²⁸⁸+1 ^[48]	20 March 2018	3,310,478
118	1880370⁵²⁴²⁸⁸ + 1 ^[49]	15 January 2018	3,289,511
119	27×2^10902757 - 1	7 March 2022	3,282,059
120	3×2^10829346 + 1 ^[50]	14 January 2014	3,259,959
121	11×2^10803449 + 1	29 May 2022	3,252,164
122	11×2^10797109 + 1	29 May 2022	3,250,255
123	7×2^10612737 - 1	19 May 2022	3,194,154
124	37×2^10599476 + 1	17 June 2022	3,190,762
125	5×2^10495620 - 1	26 September 2021	3,159,498
126	${\tfrac {\Phi _{3}(-3^{3304302}+1)}{3}}$	30 June 2023	3,153,105
127	5×2^10349000 - 1	26 September 2021	3,115,361
128	$\Phi _{3}(-844833^{262144})$	17 January 2017	3,107,335
129	52922×5^4399812-1	3 August 2023	3,075,342
130	$\Phi _{3}(-712012^{262144})$	14 January 2017	3,068,389
131	177742×5^4386703-1	24 July 2023	3,066,180
132	874208×54^1748416-1	26 September 2019	3,028,951
133	475856⁵²⁴²⁸⁸ + 1 ^[51]	8 August 2012	2,976,633
134	2×3^6236772+1	20 December 2022	2,975,697
135	15×3^9830108+1	19 August 2023	2,959,159
136	9×2^9778263+1	5 August 2020	2,943,552
137	1806676×41^1806676+1	11 March 2018	2,913,785
138	356926⁵²⁴²⁸⁸ + 1 ^[52]	20 June 2012	2,911,151
139	341112⁵²⁴²⁸⁸ + 1 ^[53]	15 June 2012	2,900,832
140	213988×5^4138363-1	29 November 2022	2,892,597
141	43×2^9596983-1	28 February 2022	2,888,982
142	121×2^9584444+1 ^[54]	18 November 2020	2,885,208
143	11×2^9381365+1	7 March 2020	2,824,074
144	15×2^9312889+1	7 August 2023	2,803,461
145	49×2^9187790+1	11 September 2022	2,765,803
146	27653×2^9167433 + 1 ^[31]	8 June 2005	2,759,677
147	90527×2^9162167 + 1	30 June 2010	2,758,093
148	6795×2^9144320 - 1	31 March 2021	2,752,719
149	75×2^9079482+1	25 July 2023	2,733,199
150	1323365×116^1323365+1 ^[55]	18 January 2018	2,732,038
151	57×2^9075622-1	7 August 2022	2,732,037
152	63838×5^3887851-1 ^[56]	19 June 2022	2,717,497
153	13×2^8989858 + 1	10 March 2020	2,706,219
154	4159×2^8938471 - 1	19 April 2022	2,690,752
155	273809×2^8932416 − 1 ^[57]	13 December 2017	2,688,931
156	93×2^8898285 + 1	4 March 2024	2,678,653
157	2×3^5570081 + 1	14 February 2020	2,657,605
158	25×2^8788628 + 1 ^[58]	1 March 2021	2,645,643
159	2038×366^1028507 − 1 ^[59]	4 April 2016	2,636,562
160	64598×5^3769854 - 1	14 June 2022	2,635,020
161	63×2^8741225 + 1	6 May 2024	2,631,373
162	8×785⁹⁰⁰³²⁵ + 1	4 June 2022	2,606,325
163	17×2^8636199 + 1 ^[60]	17 February 2021	2,599,757
164	75898⁵²⁴²⁸⁸ + 1 ^[61]	19 November 2011	2,558,647
165	25×2^8456828 + 1 ^[62]	27 January 2021	2,545,761
166	39×2^8413422 + 1 ^[63]	23 January 2021	2,532,694
167	31×2^8348000 + 1 ^[64]	19 January 2021	2,513,000
168	27×2^8342438 - 1 ^[65]	1 February 2021	2,511,326
169	3867×2^8261084 - 1	14 April 2021	2,486,838
170	101×2^8152967 + 1	2 December 2023	2,454,290
171	273662×5^3493296 - 1 ^[66]	7 December 2021	2,441,715
172	81×2^8109236 + 1	9 September 2022	2,441,126
173	11×2^8103463 + 1	6 March 2020	2,439,387
174	102818×5^3440382 - 1 ^[67]	8 October 2021	2,404,729
175	11×2^7971110 - 1	25 November 2019	2,399,545
176	27×2^7963247 + 1 ^[68]	14 January 2021	2,397,178
177	3177×2^7954621 - 1	13 June 2021	2,394,584
178	39×2^7946769 + 1 ^[69]	14 January 2021	2,392,218
179	7×6^3072198 + 1	4 August 2019	2,390,636
180	3765×2^7904593 - 1	10 January 2021	2,379,524
181	29×2^7899985 + 1 ^[70]	14 January 2021	2,378,134
182	5113×2^7895471 - 1	27 November 2022	2,376,778
183	861×2^7895451 - 1	21 February 2021	2,376,771
184	75×2^7886683 + 1	4 September 2023	2,374,131
185	99×2^7830910 + 1	24 April 2024	2,357,341
186	28433×2^7830457 + 1 ^[31]	31 December 2004	2,357,207
187	2589×2^7803339 - 1	21 August 2022	2,349,043
188	59×2^7792307 + 1	24 April 2024	2,345,720
189	101×2^7784453 + 1	24 April 2024	2,343,356
190	95×2^7778585 + 1	24 April 2024	2,341,590
191	8401×2^7767655 - 1	24 April 2023	2,338,302
192	9693×2^7767343 - 1	17 November 2023	2,338,208
193	5×2^7755002 - 1	23 September 2021	2,334,489
194	2945×2^7753232 - 1	27 November 2022	2,333,959
195	63×2^7743186 + 1	24 April 2024	2,330,934
196	2545×2^7732265 - 1	13 January 2021	2,327,648
197	5539×2^7730709 - 1	15 January 2021	2,327,180
198	4817×2^7719584 - 1	13 June 2021	2,323,831
199	1341174×53^1341174 + 1 ^[71]	21 August 2017	2,312,561
200	9467×2^7680034 - 1	20 February 2022	2,311,925
201	45×2^7661004 + 1 ^[72]	13 December 2020	2,306,194
202	15×2^7619838 + 1 ^[73]	6 December 2020	2,293,801
203	3597×2^7580693 - 1	10 January 2021	2,282,020
204	3129×2^7545557 - 1	14 March 2023	2,271,443
205	7401×2^7523295 - 1	21 February 2021	2,264,742
206	45×2^7513661 + 1 ^[74]	12 November 2020	2,261,839
207	$\Phi _{3}(-558640^{196608})$	11 January 2017	2,259,865
208	9×2^7479919 - 1	3 June 2023	2,251,681
209	1875×2^7474308 - 1	21 August 2022	2,249,995
210	69×2^7452023 + 1	23 March 2023	2,243,285
211	1281879×2^7447178 + 1	27 December 2023	2,241,831
212	4×5^3189669 - 1	12 July 2022	2,229,484
213	29×2^7374577 + 1 ^[75]	27 October 2020	2,219,971
214	3197×2^7359542 - 1	27 November 2022	2,215,447
215	109838×5^3168862 - 1 ^[76]	13 August 2020	2,214,945
216	95×2^7354869 + 1	25 September 2023	2,214,039
217	101×2^7345194 - 1	5 October 2019	2,211,126
218	85×2^7333444 + 1	25 September 2023	2,207,589
219	15×2^7300254 + 1 ^[77]	25 October 2020	2,197,597
220	422429! + 1	21 February 2022	2,193,027
221	1759×2^7284439 - 1	28 August 2021	2,192,838
222	1909683×14^1909683 + 1	27 May 2023	2,188,748
223	737×2^7269322 − 1	10 August 2017	2,188,287
224	93×2^7241494 + 1	25 September 2023	2,179,909
225	118568×5^3112069 + 1 ^[78]	1 May 2020	2,175,248
226	580633×2^7208783 − 1	15 February 2024	2,170,066
227	6039×2^7207973 − 1	24 March 2021	2,169,820
228	502573×2^7181987 − 1 ^[79]	4 October 2014	2,162,000
229	402539×2^7173024 − 1 ^[80]	2 October 2014	2,159,301
230	3343×2^7166019 - 1	29 September 2016	2,157,191
231	161041×2^7107964 + 1 ^[81]	6 January 2015	2,139,716
232	294×213⁹¹⁸⁹⁵²-1	19 September 2023	2,139,672
233	27×2^7046834+1 ^[82]	11 October 2018	2,121,310
234	1759×2^7046791 - 1	28 August 2021	2,121,299
235	327×2^7044001 - 1	13 January 2021	2,120,459
236	5×2^7037188 - 1	22 September 2021	2,118,406
237	3×2^7033641 + 1 ^[83]	21 February 2011	2,117,338
238	625783×2^7031319 - 1	10 February 2024	2,116,644
239	33661×2^7031232 + 1 ^[31]	30 October 2007	2,116,617
240	$\Phi _{3}(-237804^{196608})$	6 January 2017	2,114,016
241	207494×5^3017502-1	16 March 2020	2,109,149
242	15×2^6993631-1	25 August 2021	2,105,294
243	8943501×2^6972593-1	8 January 2022	2,098,967
244	6020095×2^6972593-1	4 September 2022	2,098,967
245	2^6972593 – 1 ^[84]	1 June 1999	2,098,960
246	273×2^6963847-1	16 November 2022	2,096,330
247	6219×2^6958945-1	7 January 2021	2,094,855
248	51×2^6945567+1	26 May 2020	2,090,826
249	238694×5^2979422-1 ^[85]	12 March 2020	2,082,532
250	4×72^1119849 − 1 ^[59]	7 September 2016	2,079,933
251	33×2^6894190-1	27 July 2021	2,075,360
252	2345×2^6882320-1	13 April 2022	2,071,789
253	57×2^6857990+1	17 August 2023	2,064,463
254	146264×5^2953282-1 ^[86]	9 March 2020	2,064,261
255	69×2^6838971-1	1 March 2020	2,058,738
256	35816×5^2945294-1 ^[87]	5 March 2020	2,058,677
257	127×2^6836153-1	25 June 2018	2,057,890
258	19×2^6833086+1 ^[88]	24 October 2020	2,056,966
259	65×2^6810465 + 1	22 September 2023	2,050,157
260	40597×2^6808509 – 1 ^[89]	25 December 2013	2,049,571
261	283×2^6804701-1	19 January 2020	2,048,431
262	1861209×2^6789999+1	2 December 2020	2,044,000
263	5817×2^6789459-1	9 January 2021	2,043,835
264	8435×2^6786180-1	7 January 2021	2,042,848
265	51×2^6753404+1	26 May 2020	2,032,979
266	93×2^6750726+1	18 September 2023	2,032,173
267	69×2^6745775+1	21 March 2023	2,030,683
268	9995×2^6711008-1	31 December 2020	2,020,219
269	39×2^6684941+1 ^[90]	20 October 2020	2,012,370
270	6679881×2^6679881 + 1 ^[91]	25 July 2009	2,010,852
271	37×2^6660841 − 1 ^[59]	30 July 2014	2,005,115
272	39×2^6648997+1 ^[92]	20 October 2020	2,001,550
273	10^2000007-10^1127194-10⁸⁷²⁸¹²-1	12 January 2024	2,000,007
274	10^2000005-10^1051046-10⁹⁴⁸⁹⁵⁸-1	6 January 2024	2,000,005

Largest known probable primes (PRPs)[edit]

These are probable primes. Primality has not been proven because it is too hard for general numbers of this size but they are expected to be primes.

Rank^[93]	Number	Discovery date	Decimal digits
1	${\tfrac {10^{8177207}-1}{9}}$	8 May 2021	8,177,207
2	${\tfrac {10^{5794777}-1}{9}}$	20 April 2021	5,794,777
3	${\tfrac {2^{15135397}+1}{3}}$ ^[93]	June 2021	4,556,209
4	${\tfrac {3^{8530117}-1}{2}}$ ^[93]	November 2023	4,069,900
5	2^13380298 – 27	March 2021	4,027,872
6	${\tfrac {2^{13372531}+1}{3}}$ ^[93]	September 2013	4,025,533
7	${\tfrac {2^{13347311}+1}{3}}$ ^[93]	September 2013	4,017,941
8	${\tfrac {2^{12720787}-1}{1666870069020922905132673131516413926009285199}}$ ^[93]	3 July 2022	3,829,294
9	${\tfrac {3^{7973131}-1}{2}}$ ^[93]	November 2023	3,804,150
10	${\tfrac {2^{12588091}-1}{32075464348897282169539424801}}$ ^[93]	10 April 2023	3,789,365
11	${\tfrac {2^{12503723}-2^{6251862}+1}{5}}$ ^[93]	July 2020	3,763,995
12	${\tfrac {5^{5154509}-1}{4}}$ ^[93]	February 2024	3,602,847
13	${\tfrac {5^{4939471}-1}{4}}$ ^[93]	January 2024	3,452,542
14	${\tfrac {2^{10443557}-1}{37289325994807}}$ ^[93]	9 July 2020	3,143,811
15	2^9092392 + 40291 ^[93]	February 2011	2,737,083
16	${\tfrac {6^{3360347}-1}{5}}$ ^[93]	October 2023	2,614,858
17	${\tfrac {17^{1990523}-1}{16}}$ ^[93]	August 2020	2,449,236
18	${\tfrac {35963^{524288}+1}{2}}$ ^[93]	August 2022	2,388,581
19	${\tfrac {11^{2264611}+1}{12}}$ ^[93]	July 2021	2,358,349
20	${\tfrac {5^{3300593}-1}{4}}$ ^[93]	February 2022	2,307,015
21	${\tfrac {3^{4694803}+2^{4694803}}{5}}$ ^[93]	December 2023	2,239,990
22	${\tfrac {2^{7313983}-1}{305492080276193}}$ ^[93]	1 March 2018	2,201,714
23	${\tfrac {3^{4571447}+2^{4571447}}{5}}$ ^[93]	December 2023	2,181,134
24	3^4532794 + 4532794³	October 2023	2,162,693
25	${\tfrac {2^{7080247}-1}{17045259548603283727480473638587228614426296913631}}$	27 October 2017	2,131,318
26	360834³⁵⁶³⁴⁵ + 356345³⁶⁰⁸³⁴	February 2024	2,003,304
27	360339³⁵⁶⁵⁷² + 356572³⁶⁰³³⁹	May 2024	2,000,656

References[edit]

^ 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.
^ ^a ^b "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 1963736^1048576 + 1, PrimeGrid
^ Official announcement of discovery of 1951734^1048576 + 1, PrimeGrid
^ 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 3×2^20928756 - 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 3×2^18924888 - 1, PrimeGrid
^ Official announcement of discovery of 3×2^18196595 - 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 2525332×73^2525332+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
^ ^a ^b ^c ^d ^e ^f ^g ^h ⁱ ^j ^k Chris Caldwell, The Largest Known Primes at The PrimePages.
^ Official announcement of discovery of 8630170⁵²⁴²⁸⁸ + 1, PrimeGrid
^ Official announcement of discovery of 3×2^11895718−1, PrimeGrid
^ Official announcement of discovery of 6339004⁵²⁴²⁸⁸ + 1, PrimeGrid
^ Official announcement of discovery of 3×2^11731850 − 1, PrimeGrid
^ Official announcement of discovery of 4896418⁵²⁴²⁸⁸ + 1, PrimeGrid
^ Official announcement of discovery of 3×2^11484018 − 1, PrimeGrid
^ Official announcement of discovery of 193997×2^11452891 + 1, PrimeGrid
^ Official announcement of discovery of 3638450⁵²⁴²⁸⁸ + 1, PrimeGrid
^ Official announcement of discovery of 9221×2^11392194 -1, PrimeGrid
^ Official announcement of discovery of 3214654⁵²⁴²⁸⁸ + 1, PrimeGrid
^ Official announcement of discovery of 146561×2^11280802 -1, PrimeGrid
^ Official announcement of discovery of 2985036⁵²⁴²⁸⁸ + 1, PrimeGrid
^ Official announcement of discovery of 2877652⁵²⁴²⁸⁸ + 1, PrimeGrid
^ Official announcement of discovery of 2788032⁵²⁴²⁸⁸ + 1, PrimeGrid
^ Official announcement of discovery of 2733014⁵²⁴²⁸⁸ + 1, PrimeGrid
^ Official announcement of discovery of 2312092⁵²⁴²⁸⁸ + 1, PrimeGrid
^ Official announcement of discovery of 2061748⁵²⁴²⁸⁸ + 1, PrimeGrid
^ Official announcement of discovery of 1880370⁵²⁴²⁸⁸ + 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
^ Official announcement of discovery of 121×2^9584444+1, PrimeGrid
^ Official announcement of discovery of 1323365×116^1323365 + 1, PrimeGrid
^ Official announcement of discovery of 63838×5^3887851-1, PrimeGrid
^ Official announcement of discovery of 273809×2^8932416 -1, PrimeGrid
^ Official announcement of discovery of 25×2^8788628 + 1, PrimeGrid
^ ^a ^b ^c "CRUS - Proven Conjectures". www.noprimeleftbehind.net.
^ Official announcement of discovery of 17×2^8636199 + 1, PrimeGrid
^ Official announcement of discovery of 75898⁵²⁴²⁸⁸ + 1, PrimeGrid
^ Official announcement of discovery of 25×2^8456828 + 1, PrimeGrid
^ Official announcement of discovery of 39×2^8413822 + 1, PrimeGrid
^ Official announcement of discovery of 31×2^8348000 + 1, PrimeGrid
^ Official announcement of discovery of 27×2^8342438 - 1, PrimeGrid
^ Official announcement of discovery of 273662×5^3493296 + 1, PrimeGrid
^ 102818×5^3440382-1, PrimeGrid
^ Official announcement of discovery of 27×2^7963247 + 1, PrimeGrid
^ Official announcement of discovery of 39×2^7946769 + 1, PrimeGrid
^ Official announcement of discovery of 29×2^7899985 + 1, PrimeGrid
^ Official announcement of discovery of 1341174×53^1341174 + 1, PrimeGrid
^ Official announcement of discovery of 45×2^7661004 + 1, PrimeGrid
^ Official announcement of discovery of 15×2^7619838 + 1, PrimeGrid
^ Official announcement of discovery of 45×2^7513661 + 1, PrimeGrid
^ Official announcement of discovery of 29×2^7374577 + 1, PrimeGrid
^ 109838×5^3168862-1, PrimeGrid
^ Official announcement of discovery of 29×2^7300254 + 1, PrimeGrid
^ 118568×5^3112069+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 161041×2^7107964 + 1, PrimeGrid
^ Official announcement of discovery of 27×2^7046834 + 1, PrimeGrid
^ Official announcement of discovery of 3×2^7033641 + 1, PrimeGrid
^ GIMPS press release, GIMPS Finds First Million-Digit Prime. Retrieved on 2008-01-04.
^ 238694×5^2979422-1, PrimeGrid
^ 146264×5^2953282-1, PrimeGrid
^ 35816×5^2945294-1, PrimeGrid
^ Official announcement of discovery of 19×2^6833086 + 1, PrimeGrid
^ Official announcement of discovery of 40597×2^6808509 – 1, PrimeGrid
^ Official announcement of discovery of 39×2^6684941 + 1, PrimeGrid
^ Official announcement of discovery of 6679881×2^6679881 + 1, PrimeGrid
^ Official announcement of discovery of 39×2^6648997 + 1, PrimeGrid
^ ^a ^b ^c ^d ^e ^f ^g ^h ⁱ ^j ^k ^l ^m ⁿ ^o ^p ^q ^r ^s ^t ^u Henri Lifchitz & Renaud Lifchitz, Probable Primes Top 10000, primenumbers.net

External links[edit]

Chris Caldwell, The Largest Known Primes Database at The PrimePages
The 5000 largest known primes at The PrimePages
The 10,000 largest known probable primes at primenumbers.net
PrimeGrid’s 321 Prime Search, about the discovery of 3×2^6090515−1

[1] Caldwell, Chris K. "THE LARGEST KNOWN PRIMES (The 5,000 largest known primes)". Retrieved 23 November 2018.

[2] "Official press release of 51st Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 7 December 2018.

[3] "Official press release of 50th Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 26 December 2017.

[4] "Official press release of 49th Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 7 January 2016.

[5] "Official press release of 48th Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 25 January 2013.

[4546prime-6] "Official press release of 45th and 46th Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 10 September 2008.

[7] "Official press release of 47th Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 25 January 2013.

[8] "Official press release of 44th Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 25 January 2013.

[9] Official announcement of discovery of 10223×2^31172165 + 1, PrimeGrid

[10] "Official press release of 43rd Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 25 January 2013.

[11] "Official press release of 42nd Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 25 January 2013.

[12] "Official press release of 41st Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 25 January 2013.

[13] Official announcement of discovery of 1963736^1048576 + 1, PrimeGrid

[14] Official announcement of discovery of 1951734^1048576 + 1, PrimeGrid

[15] Official announcement of discovery of 202705×2^21320516 + 1, PrimeGrid

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

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

[18] Official announcement of discovery of 3×2^20928756 - 1, PrimeGrid

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

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

[21] Official announcement of discovery of 3×2^18924888 - 1, PrimeGrid

[22] Official announcement of discovery of 3×2^18196595 - 1, PrimeGrid

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

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

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

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

[27] Official announcement of discovery of 2525332×73^2525332+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

[The_largest_known_primes-31] ^ ^a ^b ^c ^d ^e ^f ^g ^h ⁱ ^j ^k Chris Caldwell, The Largest Known Primes at The PrimePages.

[32] Official announcement of discovery of 8630170⁵²⁴²⁸⁸ + 1, PrimeGrid

[33] Official announcement of discovery of 3×2^11895718−1, PrimeGrid

[34] Official announcement of discovery of 6339004⁵²⁴²⁸⁸ + 1, PrimeGrid

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

[36] Official announcement of discovery of 4896418⁵²⁴²⁸⁸ + 1, PrimeGrid

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

[38] Official announcement of discovery of 193997×2^11452891 + 1, PrimeGrid

[39] Official announcement of discovery of 3638450⁵²⁴²⁸⁸ + 1, PrimeGrid

[40] Official announcement of discovery of 9221×2^11392194 -1, PrimeGrid

[41] Official announcement of discovery of 3214654⁵²⁴²⁸⁸ + 1, PrimeGrid

[42] Official announcement of discovery of 146561×2^11280802 -1, PrimeGrid

[43] Official announcement of discovery of 2985036⁵²⁴²⁸⁸ + 1, PrimeGrid

[44] Official announcement of discovery of 2877652⁵²⁴²⁸⁸ + 1, PrimeGrid

[45] Official announcement of discovery of 2788032⁵²⁴²⁸⁸ + 1, PrimeGrid

[46] Official announcement of discovery of 2733014⁵²⁴²⁸⁸ + 1, PrimeGrid

[47] Official announcement of discovery of 2312092⁵²⁴²⁸⁸ + 1, PrimeGrid

[48] Official announcement of discovery of 2061748⁵²⁴²⁸⁸ + 1, PrimeGrid

[49] Official announcement of discovery of 1880370⁵²⁴²⁸⁸ + 1, PrimeGrid

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

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

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

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

[54] Official announcement of discovery of 121×2^9584444+1, PrimeGrid

[55] Official announcement of discovery of 1323365×116^1323365 + 1, PrimeGrid

[56] Official announcement of discovery of 63838×5^3887851-1, PrimeGrid

[57] Official announcement of discovery of 273809×2^8932416 -1, PrimeGrid

[58] Official announcement of discovery of 25×2^8788628 + 1, PrimeGrid

[GSRP-59] "CRUS - Proven Conjectures". www.noprimeleftbehind.net.

[60] Official announcement of discovery of 17×2^8636199 + 1, PrimeGrid

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

[62] Official announcement of discovery of 25×2^8456828 + 1, PrimeGrid

[63] Official announcement of discovery of 39×2^8413822 + 1, PrimeGrid

[64] Official announcement of discovery of 31×2^8348000 + 1, PrimeGrid

[65] Official announcement of discovery of 27×2^8342438 - 1, PrimeGrid

[66] Official announcement of discovery of 273662×5^3493296 + 1, PrimeGrid

[67] 102818×5^3440382-1, PrimeGrid

[68] Official announcement of discovery of 27×2^7963247 + 1, PrimeGrid

[69] Official announcement of discovery of 39×2^7946769 + 1, PrimeGrid

[70] Official announcement of discovery of 29×2^7899985 + 1, PrimeGrid

[71] Official announcement of discovery of 1341174×53^1341174 + 1, PrimeGrid

[72] Official announcement of discovery of 45×2^7661004 + 1, PrimeGrid

[73] Official announcement of discovery of 15×2^7619838 + 1, PrimeGrid

[74] Official announcement of discovery of 45×2^7513661 + 1, PrimeGrid

[75] Official announcement of discovery of 29×2^7374577 + 1, PrimeGrid

[76] 109838×5^3168862-1, PrimeGrid

[77] Official announcement of discovery of 29×2^7300254 + 1, PrimeGrid

[78] 118568×5^3112069+1, PrimeGrid

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

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

[81] Official announcement of discovery of 161041×2^7107964 + 1, PrimeGrid

[82] Official announcement of discovery of 27×2^7046834 + 1, PrimeGrid

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

[1stmegaprime-84] GIMPS press release, GIMPS Finds First Million-Digit Prime. Retrieved on 2008-01-04.

[85] 238694×5^2979422-1, PrimeGrid

[86] 146264×5^2953282-1, PrimeGrid

[87] 35816×5^2945294-1, PrimeGrid

[88] Official announcement of discovery of 19×2^6833086 + 1, PrimeGrid

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

[90] Official announcement of discovery of 39×2^6684941 + 1, PrimeGrid

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

[92] Official announcement of discovery of 39×2^6648997 + 1, PrimeGrid

[PRPTop-93] ^ ^a ^b ^c ^d ^e ^f ^g ^h ⁱ ^j ^k ^l ^m ⁿ ^o ^p ^q ^r ^s ^t ^u Henri Lifchitz & Renaud Lifchitz, Probable Primes Top 10000, primenumbers.net

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v t e 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
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 Unique
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 list
Complex numbers	Eisenstein prime Gaussian prime
Composite numbers	Pseudoprime Catalan Elliptic Euler Euler–Jacobi Fermat Frobenius Lucas Perrin Somer–Lucas Strong Carmichael number Almost prime Semiprime Sphenic number 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

List of largest known primes and probable primes

Largest known primes[edit]

Largest known probable primes (PRPs)[edit]

See also[edit]

References[edit]

External links[edit]

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