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	51208×5^4857576 +1	6 June 2024	3,395,305
109	2985036⁵²⁴²⁸⁸ +1 ^[43]	18 September 2019	3,394,739
110	6929×2^11255424 -1	7 July 2022	3,388,225
111	2877652⁵²⁴²⁸⁸ +1 ^[44]	29 June 2019	3,386,397
112	2788032⁵²⁴²⁸⁸ +1 ^[45]	17 April 2019	3,379,193
113	2733014⁵²⁴²⁸⁸ +1 ^[46]	18 March 2019	3,374,655
114	9×2^11158963 +1	13 March 2020	3,359,184
115	9271×2^11134335 -1	17 January 2021	3,351,773
116	136804×5^4777253 -1	1 March 2024	3,339,162
117	2312092⁵²⁴²⁸⁸+1 ^[47]	4 August 2018	3,336,572
118	2061748⁵²⁴²⁸⁸+1 ^[48]	20 March 2018	3,310,478
119	1880370⁵²⁴²⁸⁸ + 1 ^[49]	15 January 2018	3,289,511
120	27×2^10902757 - 1	7 March 2022	3,282,059
121	3×2^10829346 + 1 ^[50]	14 January 2014	3,259,959
122	11×2^10803449 + 1	29 May 2022	3,252,164
123	11×2^10797109 + 1	29 May 2022	3,250,255
124	7×2^10612737 - 1	19 May 2022	3,194,154
125	37×2^10599476 + 1	17 June 2022	3,190,762
126	5×2^10495620 - 1	26 September 2021	3,159,498
127	${\tfrac {\Phi _{3}(-3^{3304302}+1)}{3}}$	30 June 2023	3,153,105
128	5×2^10349000 - 1	26 September 2021	3,115,361
129	$\Phi _{3}(-844833^{262144})$	17 January 2017	3,107,335
130	52922×5^4399812-1	3 August 2023	3,075,342
131	$\Phi _{3}(-712012^{262144})$	14 January 2017	3,068,389
132	177742×5^4386703-1	24 July 2023	3,066,180
133	874208×54^1748416-1	26 September 2019	3,028,951
134	475856⁵²⁴²⁸⁸ + 1 ^[51]	8 August 2012	2,976,633
135	2×3^6236772+1	20 December 2022	2,975,697
136	15×3^9830108+1	19 August 2023	2,959,159
137	9×2^9778263+1	5 August 2020	2,943,552
138	1806676×41^1806676+1	11 March 2018	2,913,785
139	356926⁵²⁴²⁸⁸ + 1 ^[52]	20 June 2012	2,911,151
140	341112⁵²⁴²⁸⁸ + 1 ^[53]	15 June 2012	2,900,832
141	213988×5^4138363-1	29 November 2022	2,892,597
142	43×2^9596983-1	28 February 2022	2,888,982
143	121×2^9584444+1 ^[54]	18 November 2020	2,885,208
144	11×2^9381365+1	7 March 2020	2,824,074
145	15×2^9312889+1	7 August 2023	2,803,461
146	49×2^9187790+1	11 September 2022	2,765,803
147	27653×2^9167433 + 1 ^[31]	8 June 2005	2,759,677
148	90527×2^9162167 + 1	30 June 2010	2,758,093
149	6795×2^9144320 - 1	31 March 2021	2,752,719
150	75×2^9079482+1	25 July 2023	2,733,199
151	1323365×116^1323365+1 ^[55]	18 January 2018	2,732,038
152	57×2^9075622-1	7 August 2022	2,732,037
153	63838×5^3887851-1 ^[56]	19 June 2022	2,717,497
154	13×2^8989858 + 1	10 March 2020	2,706,219
155	4159×2^8938471 - 1	19 April 2022	2,690,752
156	273809×2^8932416 − 1 ^[57]	13 December 2017	2,688,931
157	93×2^8898285 + 1	4 March 2024	2,678,653
158	2×3^5570081 + 1	14 February 2020	2,657,605
159	25×2^8788628 + 1 ^[58]	1 March 2021	2,645,643
160	2038×366^1028507 − 1 ^[59]	4 April 2016	2,636,562
161	64598×5^3769854 - 1	14 June 2022	2,635,020
162	63×2^8741225 + 1	6 May 2024	2,631,373
163	8×785⁹⁰⁰³²⁵ + 1	4 June 2022	2,606,325
164	17×2^8636199 + 1 ^[60]	17 February 2021	2,599,757
165	75898⁵²⁴²⁸⁸ + 1 ^[61]	19 November 2011	2,558,647
166	25×2^8456828 + 1 ^[62]	27 January 2021	2,545,761
167	39×2^8413422 + 1 ^[63]	23 January 2021	2,532,694
168	31×2^8348000 + 1 ^[64]	19 January 2021	2,513,000
169	27×2^8342438 - 1 ^[65]	1 February 2021	2,511,326
170	3867×2^8261084 - 1	14 April 2021	2,486,838
171	101×2^8152967 + 1	2 December 2023	2,454,290
172	273662×5^3493296 - 1 ^[66]	7 December 2021	2,441,715
173	81×2^8109236 + 1	9 September 2022	2,441,126
174	11×2^8103463 + 1	6 March 2020	2,439,387
175	102818×5^3440382 - 1 ^[67]	8 October 2021	2,404,729
176	11×2^7971110 - 1	25 November 2019	2,399,545
177	27×2^7963247 + 1 ^[68]	14 January 2021	2,397,178
178	3177×2^7954621 - 1	13 June 2021	2,394,584
179	39×2^7946769 + 1 ^[69]	14 January 2021	2,392,218
180	7×6^3072198 + 1	4 August 2019	2,390,636
181	3765×2^7904593 - 1	10 January 2021	2,379,524
182	29×2^7899985 + 1 ^[70]	14 January 2021	2,378,134
183	5113×2^7895471 - 1	27 November 2022	2,376,778
184	861×2^7895451 - 1	21 February 2021	2,376,771
185	75×2^7886683 + 1	4 September 2023	2,374,131
186	99×2^7830910 + 1	24 April 2024	2,357,341
187	28433×2^7830457 + 1 ^[31]	31 December 2004	2,357,207
188	2589×2^7803339 - 1	21 August 2022	2,349,043
189	59×2^7792307 + 1	24 April 2024	2,345,720
190	101×2^7784453 + 1	24 April 2024	2,343,356
191	95×2^7778585 + 1	24 April 2024	2,341,590
192	8401×2^7767655 - 1	24 April 2023	2,338,302
193	9693×2^7767343 - 1	17 November 2023	2,338,208
194	5×2^7755002 - 1	23 September 2021	2,334,489
195	2945×2^7753232 - 1	27 November 2022	2,333,959
196	63×2^7743186 + 1	24 April 2024	2,330,934
197	2545×2^7732265 - 1	13 January 2021	2,327,648
198	5539×2^7730709 - 1	15 January 2021	2,327,180
199	4817×2^7719584 - 1	13 June 2021	2,323,831
200	1341174×53^1341174 + 1 ^[71]	21 August 2017	2,312,561
201	9467×2^7680034 - 1	20 February 2022	2,311,925
202	45×2^7661004 + 1 ^[72]	13 December 2020	2,306,194
203	15×2^7619838 + 1 ^[73]	6 December 2020	2,293,801
204	3597×2^7580693 - 1	10 January 2021	2,282,020
205	3129×2^7545557 - 1	14 March 2023	2,271,443
206	7401×2^7523295 - 1	21 February 2021	2,264,742
207	45×2^7513661 + 1 ^[74]	12 November 2020	2,261,839
208	$\Phi _{3}(-558640^{196608})$	11 January 2017	2,259,865
209	9×2^7479919 - 1	3 June 2023	2,251,681
210	1875×2^7474308 - 1	21 August 2022	2,249,995
211	69×2^7452023 + 1	23 March 2023	2,243,285
212	1281879×2^7447178 + 1	27 December 2023	2,241,831
213	4×5^3189669 - 1	12 July 2022	2,229,484
214	29×2^7374577 + 1 ^[75]	27 October 2020	2,219,971
215	3197×2^7359542 - 1	27 November 2022	2,215,447
216	109838×5^3168862 - 1 ^[76]	13 August 2020	2,214,945
217	95×2^7354869 + 1	25 September 2023	2,214,039
218	101×2^7345194 - 1	5 October 2019	2,211,126
219	85×2^7333444 + 1	25 September 2023	2,207,589
220	15×2^7300254 + 1 ^[77]	25 October 2020	2,197,597
221	422429! + 1	21 February 2022	2,193,027
222	1759×2^7284439 - 1	28 August 2021	2,192,838
223	1909683×14^1909683 + 1	27 May 2023	2,188,748
224	737×2^7269322 − 1	10 August 2017	2,188,287
225	93×2^7241494 + 1	25 September 2023	2,179,909
226	118568×5^3112069 + 1 ^[78]	1 May 2020	2,175,248
227	580633×2^7208783 − 1	15 February 2024	2,170,066
228	6039×2^7207973 − 1	24 March 2021	2,169,820
229	502573×2^7181987 − 1 ^[79]	4 October 2014	2,162,000
230	402539×2^7173024 − 1 ^[80]	2 October 2014	2,159,301
231	3343×2^7166019 - 1	29 September 2016	2,157,191
232	161041×2^7107964 + 1 ^[81]	6 January 2015	2,139,716
233	294×213⁹¹⁸⁹⁵²-1	19 September 2023	2,139,672
234	27×2^7046834+1 ^[82]	11 October 2018	2,121,310
235	1759×2^7046791 - 1	28 August 2021	2,121,299
236	327×2^7044001 - 1	13 January 2021	2,120,459
237	5×2^7037188 - 1	22 September 2021	2,118,406
238	3×2^7033641 + 1 ^[83]	21 February 2011	2,117,338
239	625783×2^7031319 - 1	10 February 2024	2,116,644
240	33661×2^7031232 + 1 ^[31]	30 October 2007	2,116,617
241	$\Phi _{3}(-237804^{196608})$	6 January 2017	2,114,016
242	207494×5^3017502-1	16 March 2020	2,109,149
243	15×2^6993631-1	25 August 2021	2,105,294
244	8943501×2^6972593-1	8 January 2022	2,098,967
245	6020095×2^6972593-1	4 September 2022	2,098,967
246	2^6972593 – 1 ^[84]	1 June 1999	2,098,960
247	273×2^6963847-1	16 November 2022	2,096,330
248	6219×2^6958945-1	7 January 2021	2,094,855
249	51×2^6945567+1	26 May 2020	2,090,826
250	238694×5^2979422-1 ^[85]	12 March 2020	2,082,532
251	4×72^1119849 − 1 ^[59]	7 September 2016	2,079,933
252	33×2^6894190-1	27 July 2021	2,075,360
253	2345×2^6882320-1	13 April 2022	2,071,789
254	57×2^6857990+1	17 August 2023	2,064,463
255	146264×5^2953282-1 ^[86]	9 March 2020	2,064,261
256	69×2^6838971-1	1 March 2020	2,058,738
257	35816×5^2945294-1 ^[87]	5 March 2020	2,058,677
258	127×2^6836153-1	25 June 2018	2,057,890
259	19×2^6833086+1 ^[88]	24 October 2020	2,056,966
260	65×2^6810465 + 1	22 September 2023	2,050,157
261	40597×2^6808509 – 1 ^[89]	25 December 2013	2,049,571
262	283×2^6804701-1	19 January 2020	2,048,431
263	1861209×2^6789999+1	2 December 2020	2,044,000
264	5817×2^6789459-1	9 January 2021	2,043,835
265	8435×2^6786180-1	7 January 2021	2,042,848
266	51×2^6753404+1	26 May 2020	2,032,979
267	93×2^6750726+1	18 September 2023	2,032,173
268	69×2^6745775+1	21 March 2023	2,030,683
269	9995×2^6711008-1	31 December 2020	2,020,219
270	39×2^6684941+1 ^[90]	20 October 2020	2,012,370
271	6679881×2^6679881 + 1 ^[91]	25 July 2009	2,010,852
272	37×2^6660841 − 1 ^[59]	30 July 2014	2,005,115
273	39×2^6648997+1 ^[92]	20 October 2020	2,001,550
274	10^2000007-10^1127194-10⁸⁷²⁸¹²-1	12 January 2024	2,000,007
275	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

Largest known primes[edit]

Largest known probable primes (PRPs)[edit]

See also[edit]

References[edit]

External links[edit]