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

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	4×5^11786358 + 1	1 October 2024	8,238,312
14	2^25964951 – 1 ^[11]	18 February 2005	7,816,230
15	69×2^24612729 – 1	13 August 2024	7,409,172
16	2^24036583 – 1 ^[12]	15 May 2004	7,235,733
17	107347×2^23427517 – 1	4 August 2024	7,052,391
18	1963736^1048576 + 1 ^[13]	24 September 2022	6,598,776
19	1951734^1048576 + 1 ^[14]	9 August 2022	6,595,985
20	202705×2^21320516 + 1 ^[15]	25 November 2021	6,418,121
21	2^20996011 – 1 ^[16]	17 November 2003	6,320,430
22	1059094^1048576 + 1 ^[17]	31 October 2018	6,317,602
23	3×2^20928756 − 1 ^[18]	5 July 2023	6,300,184
24	919444^1048576 + 1 ^[19]	29 August 2017	6,253,210
25	81×2^20498148 + 1	13 June 2023	6,170,560
26	7×2^20267500 + 1	21 July 2022	6,101,127
27	4×5^8431178 + 1	2 January 2024	5,893,142
28	168451×2^19375200 + 1 ^[20]	17 September 2017	5,832,522
29	69×2^19374980 − 1	3 July 2022	5,832,452
30	3×2^18924888 − 1 ^[21]	24 March 2022	5,696,990
31	69×2^18831865 − 1	16 December 2021	5,668,959
32	2×3^11879700 + 1	22 June 2024	5,668,058
33	97139×2^18397548 − 1	23 April 2023	5,538,219
34	7×2^18233956 + 1	1 October 2020	5,488,969
35	3×2^18196595 − 1 ^[22]	8 January 2022	5,477,722
36	4×3^11279466 + 1	10 September 2024	5,381,674
37	3×2^17748034 − 1 ^[23]	6 September 2021	5,342,692
38	$\Phi _{3}(-123447^{524288})$	23 February 2017	5,338,805
39	3622×5^7558139 − 1	18 February 2022	5,282,917
40	7×6^6772401 + 1	9 September 2019	5,269,954
41	2×3^10852677 + 1	8 January 2023	5,178,044
42	8508301×2^17016603-1 ^[24]	21 March 2018	5,122,515
43	8×10^5112848-1	30 January 2024	5,112,848
44	13×2^16828072 + 1	11 October 2023	5,065,756
45	3×2^16819291-1 ^[25]	20 January 2021	5,063,112
46	3×2^16408818+1 ^[26]	25 October 2020	4,939,547
47	2329989×2^16309923-1	13 February 2024	4,909,783
48	69×2^15866556+1	20 August 2021	4,776,312
49	2036×3^10009192+1	15 February 2024	4,775,602
50	2525332×73^2525332+1 ^[27]	28 August 2021	4,705,888
51	1419499×2^15614489+1	9 February 2024	4,700,436
52	11×2^15502315+1	8 January 2023	4,666,663
53	(10^2332974+1)²-2	20 February 2024	4,665,949
54	37×2^15474010+1	8 November 2022	4,658,143
55	93839×2^15337656-1	28 November 2022	4,617,100
56	2^15317227+2^7658614+1	31 July 2020	4,610,945
57	13×2^15294536+1	30 September 2023	4,604,116
58	6×5^6546983+1	13 June 2020	4,576,146
59	4788920×3^9577840-1	14 February 2024	4,569,798
60	69×2^14977631-1	3 December 2021	4,508,719
61	192971×2^14773498-1	7 March 2021	4,447,272
62	4×3^9214845+1	10 September 2024	4,396,600
63	9145334×3^9145334+1	25 December 2023	4,363,441
64	4×5^6181673-1	15 July 2022	4,320,805
65	396101×2^14259638-1	3 February 2024	4,292,585
66	6962×31^2863120-1	29 February 2020	4,269,952
67	37×2^14166940+1	24 June 2022	4,264,676
68	99739×2^14019102-1 ^[28]	24 December 2019	4,220,176
69	69×2^13832885-1	17 January 2022	4,164,116
70	404849×2^13764867+1	10 March 2021	4,143,644
71	25×2^13719266+1	20 September 2022	4,129,912
72	81×2^13708272 + 1	11 October 2022	4,126,603
73	2740879×2^13704395-1	26 October 2019	4,125,441
74	479216×3^8625889-1	16 November 2019	4,115,601
75	$\Phi _{3}(-143332^{393216})$	30 January 2017	4,055,114
76	81×2^13470584 + 1	9 October 2022	4,055,052
77	2^13466917 – 1 ^[29]	14 November 2001	4,053,946
78	5778486×5^5778486 + 1	15 August 2024	4,038,996
79	9×2^13334487 + 1	31 March 2020	4,014,082
80	206039×2^13104952 − 1	26 April 2021	3,944,989
81	2805222×5^5610444 + 1 ^[30]	2 September 2019	3,921,539
82	19249×2^13018586 + 1 ^[31]	26 March 2007	3,918,990
83	2293×2^12918431 − 1	13 February 2021	3,888,839
84	81×2^12804541 + 1	19 September 2022	3,854,553
85	4×5^5380542 + 1	22 February 2023	3,760,839
86	9×2^12406887 + 1	29 March 2020	3,734,847
87	7×2^12286041 − 1	10 June 2023	3,698,468
88	10913140⁵²⁴²⁸⁸ + 1 ^[32]	19 June 2024	3,689,913
89	69×2^12231580 − 1	27 July 2021	3,682,075
90	27×2^12184319 + 1	6 February 2021	3,667,847
91	9332124⁵²⁴²⁸⁸ + 1 ^[33]	22 June 2024	3,654,278
92	8630170⁵²⁴²⁸⁸ + 1 ^[34]	13 April 2024	3,636,472
93	4×3^7578378 + 1	9 September 2024	3,615,806
94	11×2^11993994 − 1	15 August 2024	3,610,554
95	3761×2^11978874 − 1	6 July 2022	3,606,004
96	95×2^11954552 − 1	28 May 2024	3,598,681
97	3×2^11895718 − 1 ^[35]	23 June 2015	3,580,969
98	37×2^11855148 + 1	30 May 2022	3,568,757
99	6339004⁵²⁴²⁸⁸ + 1 ^[36]	8 June 2023	3,566,218
100	763795×6^4582771 + 1	11 December 2023	3,566,095
101	5897794⁵²⁴²⁸⁸ + 1 ^[31]	18 December 2022	3,549,792
102	3×2^11731850 − 1 ^[37]	13 March 2015	3,531,640
103	69×2^11718455 − 1 ^[31]	4 December 2020	3,527,609
104	8629×2^11708579 - 1	19 September 2024	3,524,638
105	41×2^11676439 + 1 ^[31]	20 June 2022	3,514,960
106	4896418⁵²⁴²⁸⁸ + 1 ^[38]	15 May 2022	3,507,424
107	81×2^11616017 + 1 ^[31]	30 August 2022	3,496,772
108	69×2^11604348 − 1 ^[31]	4 December 2020	3,493,259
109	4450871×6^4450871 + 1 ^[31]	17 September 2023	3,463,458
110	9×2^11500843 + 1 ^[31]	13 March 2020	3,462,100
111	3×2^11484018 − 1 ^[39]	22 November 2014	3,457,035
112	193997×2^11452891 +1 ^[40]	3 April 2018	3,447,670
113	29914×5^4930904 +1	27 September 2024	3,446,559
114	3638450⁵²⁴²⁸⁸ +1 ^[41]	29 May 2020	3,439,810
115	9221×2^11392194 -1 ^[42]	7 February 2021	3,429,397
116	9×2^11366286 +1	26 March 2020	3,421,594
117	5×2^11355764 -1	2 October 2021	3,418,427
118	732050×6^4392301 +1	9 September 2023	3,417,881
119	3214654⁵²⁴²⁸⁸ +1 ^[43]	24 December 2019	3,411,613
120	146561×2^11280802 -1 ^[44]	16 November 2020	3,395,865
121	51208×5^4857576 +1	6 June 2024	3,395,305
122	2985036⁵²⁴²⁸⁸ +1 ^[45]	18 September 2019	3,394,739
123	6929×2^11255424 -1	7 July 2022	3,388,225
124	2877652⁵²⁴²⁸⁸ +1 ^[46]	29 June 2019	3,386,397
125	2788032⁵²⁴²⁸⁸ +1 ^[47]	17 April 2019	3,379,193
126	2733014⁵²⁴²⁸⁸ +1 ^[48]	18 March 2019	3,374,655
127	9×2^11158963 +1	13 March 2020	3,359,184
128	9271×2^11134335 -1	17 January 2021	3,351,773
129	136804×5^4777253 -1	1 March 2024	3,339,162
130	2312092⁵²⁴²⁸⁸+1 ^[49]	4 August 2018	3,336,572
131	2061748⁵²⁴²⁸⁸+1 ^[50]	20 March 2018	3,310,478
132	1880370⁵²⁴²⁸⁸ + 1 ^[51]	15 January 2018	3,289,511
133	27×2^10902757 − 1	7 March 2022	3,282,059
134	3×2^10829346 + 1 ^[52]	14 January 2014	3,259,959
135	11×2^10803449 + 1	29 May 2022	3,252,164
136	11×2^10797109 + 1	29 May 2022	3,250,255
137	7×2^10612737 − 1	19 May 2022	3,194,154
138	37×2^10599476 + 1	17 June 2022	3,190,762
139	5×2^10495620 − 1	26 September 2021	3,159,498
140	${\tfrac {\Phi _{3}(-3^{3304302}+1)}{3}}$	30 June 2023	3,153,105
141	5×2^10349000 − 1	26 September 2021	3,115,361
142	$\Phi _{3}(-844833^{262144})$	17 January 2017	3,107,335
143	52922×5^4399812-1	3 August 2023	3,075,342
144	$\Phi _{3}(-712012^{262144})$	14 January 2017	3,068,389
145	177742×5^4386703-1	24 July 2023	3,066,180
146	4×3^6402015+1	9 September 2024	3,054,539
147	874208×54^1748416-1	26 September 2019	3,028,951
148	475856⁵²⁴²⁸⁸ + 1 ^[53]	8 August 2012	2,976,633
149	2×3^6236772+1	20 December 2022	2,975,697
150	15×3^9830108+1	19 August 2023	2,959,159
151	9×2^9778263+1	5 August 2020	2,943,552
152	198×558^1061348+1	30 August 2024	2,915,138
153	1806676×41^1806676+1	11 March 2018	2,913,785
154	356926⁵²⁴²⁸⁸ + 1 ^[54]	20 June 2012	2,911,151
155	341112⁵²⁴²⁸⁸ + 1 ^[55]	15 June 2012	2,900,832
156	213988×5^4138363-1	29 November 2022	2,892,597
157	43×2^9596983-1	28 February 2022	2,888,982
158	121×2^9584444+1 ^[56]	18 November 2020	2,885,208
159	15×2^9482269-1	14 August 2024	2,854,449
160	11×2^9381365+1	7 March 2020	2,824,074
161	15×2^9312889+1	7 August 2023	2,803,461
162	49×2^9187790+1	11 September 2022	2,765,803
163	6369619#+1	12 August 2024	2,765,105
164	27653×2^9167433 + 1 ^[31]	8 June 2005	2,759,677
165	6354977# − 1	12 August 2024	2,758,832
166	90527×2^9162167 + 1	30 June 2010	2,758,093
167	6795×2^9144320 − 1	31 March 2021	2,752,719
168	31×2^9088085 − 1	27 August 2024	2,735,788
169	75×2^9079482+1	25 July 2023	2,733,199
170	1323365×116^1323365+1 ^[57]	18 January 2018	2,732,038
171	57×2^9075622-1	7 August 2022	2,732,037
172	10^2718281-5×10^1631138-5×10^1087142-1	6 August 2024	2,718,281
173	63838×5^3887851-1 ^[58]	19 June 2022	2,717,497
174	13×2^8989858 + 1	10 March 2020	2,706,219
175	4159×2^8938471 − 1	19 April 2022	2,690,752
176	273809×2^8932416 − 1 ^[59]	13 December 2017	2,688,931
177	93×2^8898285 + 1	4 March 2024	2,678,653
178	2×3^5570081 + 1	14 February 2020	2,657,605
179	25×2^8788628 + 1 ^[60]	1 March 2021	2,645,643
180	2038×366^1028507 − 1 ^[61]	4 April 2016	2,636,562
181	64598×5^3769854 − 1	14 June 2022	2,635,020
182	63×2^8741225 + 1	6 May 2024	2,631,373
183	8×785⁹⁰⁰³²⁵ + 1	4 June 2022	2,606,325
184	17×2^8636199 + 1 ^[62]	17 February 2021	2,599,757
185	75898⁵²⁴²⁸⁸ + 1 ^[63]	19 November 2011	2,558,647
186	25×2^8456828 + 1 ^[64]	27 January 2021	2,545,761
187	39×2^8413422 + 1 ^[65]	23 January 2021	2,532,694
188	31×2^8348000 + 1 ^[66]	19 January 2021	2,513,000
189	27×2^8342438 − 1 ^[67]	1 February 2021	2,511,326
190	3867×2^8261084 − 1	14 April 2021	2,486,838
191	101×2^8152967 + 1	2 December 2023	2,454,290
192	273662×5^3493296 − 1 ^[68]	7 December 2021	2,441,715
193	81×2^8109236 + 1	9 September 2022	2,441,126
194	11×2^8103463 + 1	6 March 2020	2,439,387
195	102818×5^3440382 − 1 ^[69]	8 October 2021	2,404,729
196	11×2^7971110 − 1	25 November 2019	2,399,545
197	27×2^7963247 + 1 ^[70]	14 January 2021	2,397,178
198	3177×2^7954621 − 1	13 June 2021	2,394,584
199	39×2^7946769 + 1 ^[71]	14 January 2021	2,392,218
200	7×6^3072198 + 1	4 August 2019	2,390,636
201	3765×2^7904593 − 1	10 January 2021	2,379,524
202	29×2^7899985 + 1 ^[72]	14 January 2021	2,378,134
203	5113×2^7895471 − 1	27 November 2022	2,376,778
204	861×2^7895451 − 1	21 February 2021	2,376,771
205	75×2^7886683 + 1	4 September 2023	2,374,131
206	99×2^7830910 + 1	24 April 2024	2,357,341
207	28433×2^7830457 + 1 ^[31]	31 December 2004	2,357,207
208	2589×2^7803339 − 1	21 August 2022	2,349,043
209	59×2^7792307 + 1	24 April 2024	2,345,720
210	101×2^7784453 + 1	24 April 2024	2,343,356
211	95×2^7778585 + 1	24 April 2024	2,341,590
212	8401×2^7767655 − 1	24 April 2023	2,338,302
213	9693×2^7767343 − 1	17 November 2023	2,338,208
214	5×2^7755002 − 1	23 September 2021	2,334,489
215	2945×2^7753232 − 1	27 November 2022	2,333,959
216	2×836⁷⁹⁸⁴³¹ + 1	10 September 2024	2,333,181
217	63×2^7743186 + 1	24 April 2024	2,330,934
218	2545×2^7732265 − 1	13 January 2021	2,327,648
219	5539×2^7730709 − 1	15 January 2021	2,327,180
220	4817×2^7719584 − 1	13 June 2021	2,323,831
221	183×558⁸⁴²⁷⁵² + 1	23 August 2024	2,314,734
222	1341174×53^1341174 + 1 ^[73]	21 August 2017	2,312,561
223	9467×2^7680034 − 1	20 February 2022	2,311,925
224	45×2^7661004 + 1 ^[74]	13 December 2020	2,306,194
225	15×2^7619838 + 1 ^[75]	6 December 2020	2,293,801
226	3597×2^7580693 − 1	10 January 2021	2,282,020
227	5256037# + 1	6 August 2024	2,281,955
228	3129×2^7545557 − 1	14 March 2023	2,271,443
229	7401×2^7523295 − 1	21 February 2021	2,264,742
230	45×2^7513661 + 1 ^[76]	12 November 2020	2,261,839
231	$\Phi _{3}(-558640^{196608})$	11 January 2017	2,259,865
232	9×2^7479919 − 1	3 June 2023	2,251,681
233	1875×2^7474308 − 1	21 August 2022	2,249,995
234	69×2^7452023 + 1	23 March 2023	2,243,285
235	1281879×2^7447178 + 1	27 December 2023	2,241,831
236	4×5^3189669 − 1	12 July 2022	2,229,484
237	29×2^7374577 + 1 ^[77]	27 October 2020	2,219,971
238	2653×2^7368343 − 1	18 September 2024	2,218,096
239	21555×2^7364128 − 1	4 September 2024	2,216,828
240	3197×2^7359542 − 1	27 November 2022	2,215,447
241	109838×5^3168862 − 1 ^[78]	13 August 2020	2,214,945
242	95×2^7354869 + 1	25 September 2023	2,214,039
243	101×2^7345194 − 1	5 October 2019	2,211,126
244	85×2^7333444 + 1	25 September 2023	2,207,589
245	15×2^7300254 + 1 ^[79]	25 October 2020	2,197,597
246	422429! + 1	21 February 2022	2,193,027
247	1759×2^7284439 − 1	28 August 2021	2,192,838
248	1909683×14^1909683 + 1	27 May 2023	2,188,748
249	737×2^7269322 − 1	10 August 2017	2,188,287
250	6909×2^7258896 − 1	18 September 2024	2,185,150
251	93×2^7241494 + 1	25 September 2023	2,179,909
252	118568×5^3112069 + 1 ^[80]	1 May 2020	2,175,248
253	40×257⁹⁰¹⁶³² + 1	11 September 2024	2,172,875
254	580633×2^7208783 − 1	15 February 2024	2,170,066
255	6039×2^7207973 − 1	24 March 2021	2,169,820
256	502573×2^7181987 − 1 ^[81]	4 October 2014	2,162,000
257	402539×2^7173024 − 1 ^[82]	2 October 2014	2,159,301
258	3343×2^7166019 − 1	29 September 2016	2,157,191
259	161041×2^7107964 + 1 ^[83]	6 January 2015	2,139,716
260	294×213⁹¹⁸⁹⁵²-1	19 September 2023	2,139,672
261	27×2^7046834+1 ^[84]	11 October 2018	2,121,310
262	1759×2^7046791 − 1	28 August 2021	2,121,299
263	327×2^7044001 − 1	13 January 2021	2,120,459
264	5×2^7037188 − 1	22 September 2021	2,118,406
265	3×2^7033641 + 1 ^[85]	21 February 2011	2,117,338
266	625783×2^7031319 − 1	10 February 2024	2,116,644
267	33661×2^7031232 + 1 ^[31]	30 October 2007	2,116,617
268	$\Phi _{3}(-237804^{196608})$	6 January 2017	2,114,016
269	207494×5^3017502-1	16 March 2020	2,109,149
270	15×2^6993631-1	25 August 2021	2,105,294
271	8943501×2^6972593-1	8 January 2022	2,098,967
272	6020095×2^6972593-1	4 September 2022	2,098,967
273	2^6972593 – 1 ^[86]	1 June 1999	2,098,960
274	273×2^6963847-1	16 November 2022	2,096,330
275	6219×2^6958945-1	7 January 2021	2,094,855
276	51×2^6945567+1	26 May 2020	2,090,826
277	3323×2^6921196-1	18 September 2024	2,083,492
278	238694×5^2979422-1 ^[87]	12 March 2020	2,082,532
279	4×72^1119849 − 1 ^[61]	7 September 2016	2,079,933
280	33×2^6894190-1	27 July 2021	2,075,360
281	4778027# − 1	31 July 2024	2,073,926
282	2345×2^6882320-1	13 April 2022	2,071,789
283	57×2^6857990+1	17 August 2023	2,064,463
284	146264×5^2953282-1 ^[88]	9 March 2020	2,064,261
285	69×2^6838971-1	1 March 2020	2,058,738
286	35816×5^2945294-1 ^[89]	5 March 2020	2,058,677
287	127×2^6836153-1	25 June 2018	2,057,890
288	19×2^6833086+1 ^[90]	24 October 2020	2,056,966
289	65×2^6810465 + 1	22 September 2023	2,050,157
290	40597×2^6808509 – 1 ^[91]	25 December 2013	2,049,571
291	283×2^6804701-1	19 January 2020	2,048,431
292	1861209×2^6789999+1	2 December 2020	2,044,000
293	5817×2^6789459-1	9 January 2021	2,043,835
294	8435×2^6786180-1	7 January 2021	2,042,848
295	51×2^6753404+1	26 May 2020	2,032,979
296	93×2^6750726+1	18 September 2023	2,032,173
297	69×2^6745775+1	21 March 2023	2,030,683
298	9995×2^6711008-1	31 December 2020	2,020,219
299	39×2^6684941+1 ^[92]	20 October 2020	2,012,370
300	6679881×2^6679881 + 1 ^[93]	25 July 2009	2,010,852
301	37×2^6660841 − 1 ^[61]	30 July 2014	2,005,115
302	39×2^6648997+1 ^[94]	20 October 2020	2,001,550
303	10^2000007-10^1127194-10⁸⁷²⁸¹²-1	12 January 2024	2,000,007
304	10^2000005-10^1051046-10⁹⁴⁸⁹⁵⁸-1	6 January 2024	2,000,005

Largest known probable primes (PRPs)

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^[95]	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	${\tfrac {2^{15135397}+1}{3}}$ ^[95]	June 2021	4,556,209
4	${\tfrac {3^{8530117}-1}{2}}$ ^[95]	November 2023	4,069,900
5	2^13380298 – 27	March 2021	4,027,872
6	${\tfrac {2^{13372531}+1}{3}}$ ^[95]	September 2013	4,025,533
7	${\tfrac {2^{13347311}+1}{3}}$ ^[95]	September 2013	4,017,941
8	${\tfrac {2^{12720787}-1}{1666870069020922905132673131516413926009285199}}$ ^[95]	3 July 2022	3,829,294
9	${\tfrac {3^{7973131}-1}{2}}$ ^[95]	November 2023	3,804,150
10	${\tfrac {2^{12588091}-1}{32075464348897282169539424801}}$ ^[95]	10 April 2023	3,789,365
11	${\tfrac {2^{12503723}-2^{6251862}+1}{5}}$ ^[95]	July 2020	3,763,995
12	${\tfrac {5^{5154509}-1}{4}}$ ^[95]	February 2024	3,602,847
13	${\tfrac {5^{4939471}-1}{4}}$ ^[95]	January 2024	3,452,542
14	${\tfrac {2^{10443557}-1}{37289325994807}}$ ^[95]	9 July 2020	3,143,811
15	2^9092392 + 40291 ^[95]	February 2011	2,737,083
16	${\tfrac {6^{3360347}-1}{5}}$ ^[95]	October 2023	2,614,858
17	${\tfrac {2^{8247949}-1}{45487316822291087700751210632267642069671672071}}$ ^[95]	3 June 2024	2,482,834
18	${\tfrac {17^{1990523}-1}{16}}$ ^[95]	August 2020	2,449,236
19	${\tfrac {35963^{524288}+1}{2}}$ ^[95]	August 2022	2,388,581
20	500186⁵⁴⁴⁶⁵ + 54465⁵⁰⁰¹⁸⁶ ^[95]	August 2024	2,368,940
21	${\tfrac {11^{2264611}+1}{12}}$ ^[95]	July 2021	2,358,349
22	${\tfrac {5^{3300593}-1}{4}}$ ^[95]	February 2022	2,307,015
23	${\tfrac {3^{4694803}+2^{4694803}}{5}}$ ^[95]	December 2023	2,239,990
24	${\tfrac {2^{7313983}-1}{305492080276193}}$ ^[95]	1 March 2018	2,201,714
25	${\tfrac {3^{4571447}+2^{4571447}}{5}}$ ^[95]	December 2023	2,181,134
26	${\tfrac {15^{1848811}+1}{16}}$ ^[95]	July 2024	2,174,370
27	F(10367321)	10 August 2024	2,166,642
28	${\tfrac {15^{1841911}+1}{16}}$ ^[95]	July 2024	2,166,255
29	3^4532794 + 4532794³	October 2023	2,162,693
30	F(10317107)	27 July 2024	2,156,148
31	${\tfrac {2^{7080247}-1}{17045259548603283727480473638587228614426296913631}}$	27 October 2017	2,131,318
32	360834³⁵⁶³⁴⁵ + 356345³⁶⁰⁸³⁴	February 2024	2,003,304
33	360339³⁵⁶⁵⁷² + 356572³⁶⁰³³⁹	May 2024	2,000,656

References

^ 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 10913140⁵²⁴²⁸⁸ + 1, PrimeGrid
^ Official announcement of discovery of 9332124⁵²⁴²⁸⁸ + 1, PrimeGrid
^ 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 ^v ^w ^x ^y Henri Lifchitz & Renaud Lifchitz, Probable Primes Top 10000, primenumbers.net

External links

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 10913140⁵²⁴²⁸⁸ + 1, PrimeGrid

[33] Official announcement of discovery of 9332124⁵²⁴²⁸⁸ + 1, PrimeGrid

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[GSRP-61] "CRUS - Proven Conjectures". www.noprimeleftbehind.net.

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

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

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

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

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

[67] Official announcement of discovery of 27×2^8342438 − 1, PrimeGrid

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

[69] 102818×5^3440382-1, PrimeGrid

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

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

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

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

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

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

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

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

[78] 109838×5^3168862-1, PrimeGrid

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

[80] 118568×5^3112069+1, PrimeGrid

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

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

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

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

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

[1stmegaprime-86] GIMPS press release, GIMPS Finds First Million-Digit Prime. Retrieved on 2008-01-04.

[87] 238694×5^2979422-1, PrimeGrid

[88] 146264×5^2953282-1, PrimeGrid

[89] 35816×5^2945294-1, PrimeGrid

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

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

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

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

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

[PRPTop-95] ^ ^a ^b ^c ^d ^e ^f ^g ^h ⁱ ^j ^k ^l ^m ⁿ ^o ^p ^q ^r ^s ^t ^u ^v ^w ^x ^y Henri Lifchitz & Renaud Lifchitz, Probable Primes Top 10000, primenumbers.net

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List of largest known primes and probable primes

Largest known primes

Largest known probable primes (PRPs)

See also

References

External links