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	2^136279841 – 1 ^[2]	12 October 2024	41,024,320
2	2^82589933 – 1 ^[3]	7 December 2018	24,862,048
3	2^77232917 – 1 ^[4]	26 December 2017	23,249,425
4	2^74207281 – 1 ^[5]	7 January 2016	22,338,618
5	2^57885161 – 1 ^[6]	25 January 2013	17,425,170
6	2^43112609 – 1 ^[7]	23 August 2008	12,978,189
7	2^42643801 – 1 ^[8]	4 June 2009	12,837,064
8	$\Phi _{3}(-516693^{1048576})$ ^[9]	2 October 2023	11,981,518
9	$\Phi _{3}(-465859^{1048576})$ ^[10]	31 May 2023	11,887,192
10	2^37156667 – 1 ^[7]	6 September 2008	11,185,272
11	2^32582657 – 1 ^[11]	4 September 2006	9,808,358
12	10223×2^31172165 + 1 ^[12]	31 October 2016	9,383,761
13	2^30402457 – 1 ^[13]	15 December 2005	9,152,052
14	4×5^11786358 + 1	1 October 2024	8,238,312
15	2^25964951 – 1 ^[14]	18 February 2005	7,816,230
16	69×2^24612729 – 1	13 August 2024	7,409,172
17	2^24036583 – 1 ^[15]	15 May 2004	7,235,733
18	107347×2^23427517 – 1	4 August 2024	7,052,391
19	3×2^22103376 − 1 ^[16]	30 September 2024	6,653,780
20	1963736^1048576 + 1 ^[17]	24 September 2022	6,598,776
21	1951734^1048576 + 1 ^[18]	9 August 2022	6,595,985
22	202705×2^21320516 + 1 ^[19]	25 November 2021	6,418,121
23	2^20996011 – 1 ^[20]	17 November 2003	6,320,430
24	1059094^1048576 + 1 ^[21]	31 October 2018	6,317,602
25	3×2^20928756 − 1 ^[22]	5 July 2023	6,300,184
26	919444^1048576 + 1 ^[23]	29 August 2017	6,253,210
27	81×2^20498148 + 1	13 June 2023	6,170,560
28	7×2^20267500 + 1	21 July 2022	6,101,127
29	4×5^8431178 + 1	2 January 2024	5,893,142
30	168451×2^19375200 + 1 ^[24]	17 September 2017	5,832,522
31	69×2^19374980 − 1	3 July 2022	5,832,452
32	3×2^18924888 − 1 ^[25]	24 March 2022	5,696,990
33	69×2^18831865 − 1	16 December 2021	5,668,959
34	2×3^11879700 + 1	22 June 2024	5,668,058
35	97139×2^18397548 − 1	23 April 2023	5,538,219
36	7×2^18233956 + 1	1 October 2020	5,488,969
37	3×2^18196595 − 1 ^[26]	8 January 2022	5,477,722
38	4×3^11279466 + 1	10 September 2024	5,381,674
39	3×2^17748034 − 1 ^[27]	6 September 2021	5,342,692
40	$\Phi _{3}(-123447^{524288})$	23 February 2017	5,338,805
41	3622×5^7558139 − 1	18 February 2022	5,282,917
42	7×6^6772401 + 1	9 September 2019	5,269,954
43	2×3^10852677 + 1	8 January 2023	5,178,044
44	8508301×2^17016603 – 1 ^[28]	21 March 2018	5,122,515
45	8×10^5112848 – 1	30 January 2024	5,112,848
46	13×2^16828072 + 1	11 October 2023	5,065,756
47	3×2^16819291 – 1 ^[29]	20 January 2021	5,063,112
48	5287180×3^10574360 – 1	3 November 2024	5,045,259
49	3×2^16408818 + 1 ^[30]	25 October 2020	4,939,547
50	2329989×2^16309923 – 1	13 February 2024	4,909,783
51	69×2^15866556 + 1	20 August 2021	4,776,312
52	2036×3^10009192 + 1	15 February 2024	4,775,602
53	2525332×73^2525332 + 1 ^[31]	28 August 2021	4,705,888
54	1419499×2^15614489 + 1	9 February 2024	4,700,436
55	11×2^15502315 + 1	8 January 2023	4,666,663
56	(10^2332974 + 1)²-2	20 February 2024	4,665,949
57	37×2^15474010 + 1	8 November 2022	4,658,143
58	93839×2^15337656 – 1	28 November 2022	4,617,100
59	2^15317227+2^7658614 + 1	31 July 2020	4,610,945
60	13×2^15294536 + 1	30 September 2023	4,604,116
61	6×5^6546983 + 1	13 June 2020	4,576,146
62	4788920×3^9577840 – 1	14 February 2024	4,569,798
63	69×2^14977631 – 1	3 December 2021	4,508,719
64	192971×2^14773498 – 1	7 March 2021	4,447,272
65	4×3^9214845 + 1	10 September 2024	4,396,600
66	9145334×3^9145334 + 1	25 December 2023	4,363,441
67	4×5^6181673 – 1	15 July 2022	4,320,805
68	396101×2^14259638 – 1	3 February 2024	4,292,585
69	6962×31^2863120 – 1	29 February 2020	4,269,952
70	37×2^14166940 + 1	24 June 2022	4,264,676
71	99739×2^14019102 – 1 ^[32]	24 December 2019	4,220,176
72	69×2^13832885 – 1	17 January 2022	4,164,116
73	404849×2^13764867 + 1	10 March 2021	4,143,644
74	25×2^13719266 + 1	20 September 2022	4,129,912
75	81×2^13708272 + 1	11 October 2022	4,126,603
76	2740879×2^13704395 – 1	26 October 2019	4,125,441
77	479216×3^8625889 – 1	16 November 2019	4,115,601
78	$\Phi _{3}(-143332^{393216})$	30 January 2017	4,055,114
79	81×2^13470584 + 1	9 October 2022	4,055,052
80	2^13466917 – 1 ^[33]	14 November 2001	4,053,946
81	5778486×5^5778486 + 1	15 August 2024	4,038,996
82	9×2^13334487 + 1	31 March 2020	4,014,082
83	206039×2^13104952 − 1	26 April 2021	3,944,989
84	2805222×5^5610444 + 1 ^[34]	2 September 2019	3,921,539
85	19249×2^13018586 + 1 ^[35]	26 March 2007	3,918,990
86	2293×2^12918431 − 1	13 February 2021	3,888,839
87	81×2^12804541 + 1	19 September 2022	3,854,553
88	4×5^5380542 + 1	22 February 2023	3,760,839
89	9×2^12406887 + 1	29 March 2020	3,734,847
90	11937916⁵²⁴²⁸⁸ + 1 ^[36]	5 October 2024	3,710,349
91	7×2^12286041 − 1	10 June 2023	3,698,468
92	10913140⁵²⁴²⁸⁸ + 1 ^[37]	19 June 2024	3,689,913
93	69×2^12231580 − 1	27 July 2021	3,682,075
94	27×2^12184319 + 1	6 February 2021	3,667,847
95	9332124⁵²⁴²⁸⁸ + 1 ^[38]	22 June 2024	3,654,278
96	8630170⁵²⁴²⁸⁸ + 1 ^[39]	13 April 2024	3,636,472
97	863282×5^5179692 - 1	17 October 2024	3,620,456
98	670490×12^3352450 - 1	17 October 2024	3,617,907
99	4×3^7578378 + 1	9 September 2024	3,615,806
100	11×2^11993994 − 1	15 August 2024	3,610,554
101	3761×2^11978874 − 1	6 July 2022	3,606,004
102	95×2^11954552 − 1	28 May 2024	3,598,681
103	259072×5^5136295 − 1	28 October 2024	3,590,122
104	3×2^11895718 − 1 ^[40]	23 June 2015	3,580,969
105	37×2^11855148 + 1	30 May 2022	3,568,757
106	6339004⁵²⁴²⁸⁸ + 1 ^[41]	8 June 2023	3,566,218
107	763795×6^4582771 + 1	11 December 2023	3,566,095
108	5897794⁵²⁴²⁸⁸ + 1 ^[35]	18 December 2022	3,549,792
109	3×2^11731850 − 1 ^[42]	13 March 2015	3,531,640
110	69×2^11718455 − 1 ^[35]	4 December 2020	3,527,609
111	8629×2^11708579 – 1	19 September 2024	3,524,638
112	41×2^11676439 + 1 ^[35]	20 June 2022	3,514,960
113	4896418⁵²⁴²⁸⁸ + 1 ^[43]	15 May 2022	3,507,424
114	81×2^11616017 + 1 ^[35]	30 August 2022	3,496,772
115	69×2^11604348 − 1 ^[35]	4 December 2020	3,493,259
116	4450871×6^4450871 + 1 ^[35]	17 September 2023	3,463,458
117	9×2^11500843 + 1 ^[35]	13 March 2020	3,462,100
118	3×2^11484018 − 1 ^[44]	22 November 2014	3,457,035
119	193997×2^11452891 +1 ^[45]	3 April 2018	3,447,670
120	29914×5^4930904 +1	27 September 2024	3,446,559
121	3638450⁵²⁴²⁸⁸ +1 ^[46]	29 May 2020	3,439,810
122	9221×2^11392194 -1 ^[47]	7 February 2021	3,429,397
123	9×2^11366286 +1	26 March 2020	3,421,594
124	5×2^11355764 -1	2 October 2021	3,418,427
125	732050×6^4392301 +1	9 September 2023	3,417,881
126	3214654⁵²⁴²⁸⁸ +1 ^[48]	24 December 2019	3,411,613
127	146561×2^11280802 -1 ^[49]	16 November 2020	3,395,865
128	51208×5^4857576 +1	6 June 2024	3,395,305
129	2985036⁵²⁴²⁸⁸ +1 ^[50]	18 September 2019	3,394,739
130	6929×2^11255424 -1	7 July 2022	3,388,225
131	2877652⁵²⁴²⁸⁸ +1 ^[51]	29 June 2019	3,386,397
132	2788032⁵²⁴²⁸⁸ +1 ^[52]	17 April 2019	3,379,193
133	2733014⁵²⁴²⁸⁸ +1 ^[53]	18 March 2019	3,374,655
134	9×2^11158963 +1	13 March 2020	3,359,184
135	9271×2^11134335 -1	17 January 2021	3,351,773
136	136804×5^4777253 -1	1 March 2024	3,339,162
137	2312092⁵²⁴²⁸⁸ + 1 ^[54]	4 August 2018	3,336,572
138	987324×48^1974648 - 1	12 October 2024	3,319,866
139	2061748⁵²⁴²⁸⁸ + 1 ^[55]	20 March 2018	3,310,478
140	1880370⁵²⁴²⁸⁸ + 1 ^[56]	15 January 2018	3,289,511
141	27×2^10902757 − 1	7 March 2022	3,282,059
142	3×2^10829346 + 1 ^[57]	14 January 2014	3,259,959
143	11×2^10803449 + 1	29 May 2022	3,252,164
144	11×2^10797109 + 1	29 May 2022	3,250,255
145	7×2^10612737 − 1	19 May 2022	3,194,154
146	7351117# + 1	14 September 2024	3,191,401
147	37×2^10599476 + 1	17 June 2022	3,190,762
148	5×2^10495620 − 1	26 September 2021	3,159,498
149	${\tfrac {\Phi _{3}(-3^{3304302}+1)}{3}}$	30 June 2023	3,153,105
150	5×2^10349000 − 1	26 September 2021	3,115,361
151	$\Phi _{3}(-844833^{262144})$	17 January 2017	3,107,335
152	52922×5^4399812 – 1	3 August 2023	3,075,342
153	$\Phi _{3}(-712012^{262144})$	14 January 2017	3,068,389
154	177742×5^4386703 – 1	24 July 2023	3,066,180
155	4×3^6402015 + 1	9 September 2024	3,054,539
156	874208×54^1748416 – 1	26 September 2019	3,028,951
157	475856⁵²⁴²⁸⁸ + 1 ^[58]	8 August 2012	2,976,633
158	2×3^6236772 + 1	20 December 2022	2,975,697
159	15×3^9830108 + 1	19 August 2023	2,959,159
160	9×2^9778263 + 1	5 August 2020	2,943,552
161	198×558^1061348 + 1	30 August 2024	2,915,138
162	1806676×41^1806676 + 1	11 March 2018	2,913,785
163	356926⁵²⁴²⁸⁸ + 1 ^[59]	20 June 2012	2,911,151
164	341112⁵²⁴²⁸⁸ + 1 ^[60]	15 June 2012	2,900,832
165	213988×5^4138363 – 1	29 November 2022	2,892,597
166	43×2^9596983 – 1	28 February 2022	2,888,982
167	121×2^9584444 + 1 ^[61]	18 November 2020	2,885,208
168	15×2^9482269 – 1	14 August 2024	2,854,449
169	11×2^9381365 + 1	7 March 2020	2,824,074
170	15×2^9312889 + 1	7 August 2023	2,803,461
171	49×2^9187790 + 1	11 September 2022	2,765,803
172	6369619#+1	12 August 2024	2,765,105
173	27653×2^9167433 + 1 ^[35]	8 June 2005	2,759,677
174	6354977# − 1	12 August 2024	2,758,832
175	90527×2^9162167 + 1	30 June 2010	2,758,093
176	6795×2^9144320 − 1	31 March 2021	2,752,719
177	31×2^9088085 − 1	27 August 2024	2,735,788
178	75×2^9079482 + 1	25 July 2023	2,733,199
179	1323365×116^1323365 + 1 ^[62]	18 January 2018	2,732,038
180	57×2^9075622 – 1	7 August 2022	2,732,037
181	10^2718281-5×10^1631138-5×10^1087142 – 1	6 August 2024	2,718,281
182	63838×5^3887851 – 1 ^[63]	19 June 2022	2,717,497
183	13×2^8989858 + 1	10 March 2020	2,706,219
184	4159×2^8938471 − 1	19 April 2022	2,690,752
185	273809×2^8932416 − 1 ^[64]	13 December 2017	2,688,931
186	93×2^8898285 + 1	4 March 2024	2,678,653
187	2×3^5570081 + 1	14 February 2020	2,657,605
188	25×2^8788628 + 1 ^[65]	1 March 2021	2,645,643
189	2038×366^1028507 − 1 ^[66]	4 April 2016	2,636,562
190	64598×5^3769854 − 1	14 June 2022	2,635,020
191	63×2^8741225 + 1	6 May 2024	2,631,373
192	8×785⁹⁰⁰³²⁵ + 1	4 June 2022	2,606,325
193	17×2^8636199 + 1 ^[67]	17 February 2021	2,599,757
194	75898⁵²⁴²⁸⁸ + 1 ^[68]	19 November 2011	2,558,647
195	25×2^8456828 + 1 ^[69]	27 January 2021	2,545,761
196	39×2^8413422 + 1 ^[70]	23 January 2021	2,532,694
197	31×2^8348000 + 1 ^[71]	19 January 2021	2,513,000
198	27×2^8342438 − 1 ^[72]	1 February 2021	2,511,326
199	3867×2^8261084 − 1	14 April 2021	2,486,838
200	101×2^8152967 + 1	2 December 2023	2,454,290
201	273662×5^3493296 − 1 ^[73]	7 December 2021	2,441,715
202	81×2^8109236 + 1	9 September 2022	2,441,126
203	11×2^8103463 + 1	6 March 2020	2,439,387
204	102818×5^3440382 − 1 ^[74]	8 October 2021	2,404,729
205	11×2^7971110 − 1	25 November 2019	2,399,545
206	27×2^7963247 + 1 ^[75]	14 January 2021	2,397,178
207	3177×2^7954621 − 1	13 June 2021	2,394,584
208	39×2^7946769 + 1 ^[76]	14 January 2021	2,392,218
209	7×6^3072198 + 1	4 August 2019	2,390,636
210	3765×2^7904593 − 1	10 January 2021	2,379,524
211	29×2^7899985 + 1 ^[77]	14 January 2021	2,378,134
212	5113×2^7895471 − 1	27 November 2022	2,376,778
213	861×2^7895451 − 1	21 February 2021	2,376,771
214	75×2^7886683 + 1	4 September 2023	2,374,131
215	99×2^7830910 + 1	24 April 2024	2,357,341
216	28433×2^7830457 + 1 ^[35]	31 December 2004	2,357,207
217	2589×2^7803339 − 1	21 August 2022	2,349,043
218	59×2^7792307 + 1	24 April 2024	2,345,720
219	101×2^7784453 + 1	24 April 2024	2,343,356
220	95×2^7778585 + 1	24 April 2024	2,341,590
221	8401×2^7767655 − 1	24 April 2023	2,338,302
222	9693×2^7767343 − 1	17 November 2023	2,338,208
223	5×2^7755002 − 1	23 September 2021	2,334,489
224	2945×2^7753232 − 1	27 November 2022	2,333,959
225	2×836⁷⁹⁸⁴³¹ + 1	10 September 2024	2,333,181
226	63×2^7743186 + 1	24 April 2024	2,330,934
227	2545×2^7732265 − 1	13 January 2021	2,327,648
228	5539×2^7730709 − 1	15 January 2021	2,327,180
229	4817×2^7719584 − 1	13 June 2021	2,323,831
230	183×558⁸⁴²⁷⁵² + 1	23 August 2024	2,314,734
231	1341174×53^1341174 + 1 ^[78]	21 August 2017	2,312,561
232	9467×2^7680034 − 1	20 February 2022	2,311,925
233	45×2^7661004 + 1 ^[79]	13 December 2020	2,306,194
234	15×2^7619838 + 1 ^[80]	6 December 2020	2,293,801
235	3597×2^7580693 − 1	10 January 2021	2,282,020
236	5256037# + 1	6 August 2024	2,281,955
237	3129×2^7545557 − 1	14 March 2023	2,271,443
238	7401×2^7523295 − 1	21 February 2021	2,264,742
239	45×2^7513661 + 1 ^[81]	12 November 2020	2,261,839
240	$\Phi _{3}(-558640^{196608})$	11 January 2017	2,259,865
241	9×2^7479919 − 1	3 June 2023	2,251,681
242	1875×2^7474308 − 1	21 August 2022	2,249,995
243	69×2^7452023 + 1	23 March 2023	2,243,285
244	1281879×2^7447178 + 1	27 December 2023	2,241,831
245	4×5^3189669 − 1	12 July 2022	2,229,484
246	29×2^7374577 + 1 ^[82]	27 October 2020	2,219,971
247	2653×2^7368343 − 1	18 September 2024	2,218,096
248	21555×2^7364128 − 1	4 September 2024	2,216,828
249	3197×2^7359542 − 1	27 November 2022	2,215,447
250	109838×5^3168862 − 1 ^[83]	13 August 2020	2,214,945
251	95×2^7354869 + 1	25 September 2023	2,214,039
252	101×2^7345194 − 1	5 October 2019	2,211,126
253	85×2^7333444 + 1	25 September 2023	2,207,589
254	15×2^7300254 + 1 ^[84]	25 October 2020	2,197,597
255	422429! + 1	21 February 2022	2,193,027
256	1759×2^7284439 − 1	28 August 2021	2,192,838
257	1909683×14^1909683 + 1	27 May 2023	2,188,748
258	737×2^7269322 − 1	10 August 2017	2,188,287
259	6909×2^7258896 − 1	18 September 2024	2,185,150
260	93×2^7241494 + 1	25 September 2023	2,179,909
261	118568×5^3112069 + 1 ^[85]	1 May 2020	2,175,248
262	40×257⁹⁰¹⁶³² + 1	11 September 2024	2,172,875
263	580633×2^7208783 − 1	15 February 2024	2,170,066
264	6039×2^7207973 − 1	24 March 2021	2,169,820
265	502573×2^7181987 − 1 ^[86]	4 October 2014	2,162,000
266	402539×2^7173024 − 1 ^[87]	2 October 2014	2,159,301
267	3343×2^7166019 − 1	29 September 2016	2,157,191
268	161041×2^7107964 + 1 ^[88]	6 January 2015	2,139,716
269	294×213⁹¹⁸⁹⁵² – 1	19 September 2023	2,139,672
270	27×2^7046834 + 1 ^[89]	11 October 2018	2,121,310
271	1759×2^7046791 − 1	28 August 2021	2,121,299
272	327×2^7044001 − 1	13 January 2021	2,120,459
273	5×2^7037188 − 1	22 September 2021	2,118,406
274	3×2^7033641 + 1 ^[90]	21 February 2011	2,117,338
275	625783×2^7031319 − 1	10 February 2024	2,116,644
276	33661×2^7031232 + 1 ^[35]	30 October 2007	2,116,617
277	$\Phi _{3}(-237804^{196608})$	6 January 2017	2,114,016
278	207494×5^3017502 – 1	16 March 2020	2,109,149
279	15×2^6993631 – 1	25 August 2021	2,105,294
280	8943501×2^6972593 – 1	8 January 2022	2,098,967
281	6020095×2^6972593 – 1	4 September 2022	2,098,967
282	2^6972593 – 1 ^[91]	1 June 1999	2,098,960
283	273×2^6963847 – 1	16 November 2022	2,096,330
284	6219×2^6958945 – 1	7 January 2021	2,094,855
285	51×2^6945567 + 1	26 May 2020	2,090,826
286	3323×2^6921196 – 1	18 September 2024	2,083,492
287	238694×5^2979422 – 1 ^[92]	12 March 2020	2,082,532
288	4×72^1119849 − 1 ^[66]	7 September 2016	2,079,933
289	33×2^6894190 – 1	27 July 2021	2,075,360
290	4778027# − 1	31 July 2024	2,073,926
291	2345×2^6882320 – 1	13 April 2022	2,071,789
292	57×2^6857990 + 1	17 August 2023	2,064,463
293	146264×5^2953282 – 1 ^[93]	9 March 2020	2,064,261
294	69×2^6838971 – 1	1 March 2020	2,058,738
295	35816×5^2945294 – 1 ^[94]	5 March 2020	2,058,677
296	127×2^6836153 – 1	25 June 2018	2,057,890
297	19×2^6833086 + 1 ^[95]	24 October 2020	2,056,966
298	65×2^6810465 + 1	22 September 2023	2,050,157
299	40597×2^6808509 – 1 ^[96]	25 December 2013	2,049,571
300	283×2^6804701 – 1	19 January 2020	2,048,431
301	1861209×2^6789999 + 1	2 December 2020	2,044,000
302	5817×2^6789459 – 1	9 January 2021	2,043,835
303	8435×2^6786180 – 1	7 January 2021	2,042,848
304	51×2^6753404 + 1	26 May 2020	2,032,979
305	93×2^6750726 + 1	18 September 2023	2,032,173
306	69×2^6745775 + 1	21 March 2023	2,030,683
307	9995×2^6711008 – 1	31 December 2020	2,020,219
308	39×2^6684941 + 1 ^[97]	20 October 2020	2,012,370
309	6679881×2^6679881 + 1 ^[98]	25 July 2009	2,010,852
310	37×2^6660841 − 1 ^[66]	30 July 2014	2,005,115
311	39×2^6648997 + 1 ^[99]	20 October 2020	2,001,550
312	42781592²⁶²¹⁴⁴ + 1	18 November 2024	2,000,489
313	10^2000007 – 10^1127194 – 10⁸⁷²⁸¹² – 1	12 January 2024	2,000,007
314	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^[100]	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	${\tfrac {2^{15135397}+1}{3}}$ ^[100]	June 2021	4,556,209
4	${\tfrac {3^{8530117}-1}{2}}$ ^[100]	November 2023	4,069,900
5	2^13380298 – 27	March 2021	4,027,872
6	${\tfrac {2^{13372531}+1}{3}}$ ^[100]	September 2013	4,025,533
7	${\tfrac {2^{13347311}+1}{3}}$ ^[100]	September 2013	4,017,941
8	${\tfrac {2^{12720787}-1}{1666870069020922905132673131516413926009285199}}$ ^[100]	3 July 2022	3,829,294
9	${\tfrac {3^{7973131}-1}{2}}$ ^[100]	November 2023	3,804,150
10	${\tfrac {2^{12588091}-1}{32075464348897282169539424801}}$ ^[100]	10 April 2023	3,789,365
11	${\tfrac {2^{12503723}-2^{6251862}+1}{5}}$ ^[100]	July 2020	3,763,995
12	${\tfrac {5^{5154509}-1}{4}}$ ^[100]	February 2024	3,602,847
13	${\tfrac {5^{4939471}-1}{4}}$ ^[100]	January 2024	3,452,542
14	${\tfrac {2^{10443557}-1}{37289325994807}}$ ^[100]	9 July 2020	3,143,811
15	2^9092392 + 40291 ^[100]	February 2011	2,737,083
16	${\tfrac {6^{3360347}-1}{5}}$ ^[100]	October 2023	2,614,858
17	${\tfrac {2^{8247949}-1}{45487316822291087700751210632267642069671672071}}$ ^[100]	3 June 2024	2,482,834
18	${\tfrac {17^{1990523}-1}{16}}$ ^[100]	August 2020	2,449,236
19	${\tfrac {35963^{524288}+1}{2}}$ ^[100]	August 2022	2,388,581
20	500186⁵⁴⁴⁶⁵ + 54465⁵⁰⁰¹⁸⁶ ^[100]	August 2024	2,368,940
21	${\tfrac {11^{2264611}+1}{12}}$ ^[100]	July 2021	2,358,349
22	${\tfrac {5^{3300593}-1}{4}}$ ^[100]	February 2022	2,307,015
23	${\tfrac {3^{4694803}+2^{4694803}}{5}}$ ^[100]	December 2023	2,239,990
24	${\tfrac {2^{7313983}-1}{305492080276193}}$ ^[100]	1 March 2018	2,201,714
25	${\tfrac {3^{4571447}+2^{4571447}}{5}}$ ^[100]	December 2023	2,181,134
26	${\tfrac {15^{1848811}+1}{16}}$ ^[100]	July 2024	2,174,370
27	F(10367321)	10 August 2024	2,166,642
28	${\tfrac {15^{1841911}+1}{16}}$ ^[100]	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 52nd Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 21 October 2024.
^ "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.
^ "PrimePage Primes: Phi(3, - 516693^1048576)". t5k.org. Retrieved 18 October 2024.
^ "PrimePage Primes: Phi(3, - 465859^1048576)". t5k.org. Retrieved 18 October 2024.
^ "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 3×2^22103376 − 1, PrimeGrid
^ 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 11937916⁵²⁴²⁸⁸ + 1, PrimeGrid
^ 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 52nd Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 21 October 2024.

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

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

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

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

[4546prime-7] "Official press release of 45th and 46th Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 10 September 2008.

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

[9] "PrimePage Primes: Phi(3, - 516693^1048576)". t5k.org. Retrieved 18 October 2024.

[10] "PrimePage Primes: Phi(3, - 465859^1048576)". t5k.org. Retrieved 18 October 2024.

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

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

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

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

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

[16] Official announcement of discovery of 3×2^22103376 − 1, PrimeGrid

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

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

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

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

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

[22] Official announcement of discovery of 3×2^20928756 − 1, PrimeGrid

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

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

[25] Official announcement of discovery of 3×2^18924888 − 1, PrimeGrid

[26] Official announcement of discovery of 3×2^18196595 − 1, PrimeGrid

[27] Official announcement of discovery of 3×2^17748034 − 1, PrimeGrid

[28] Official announcement of discovery of 8508301×2^17016603 – 1, PrimeGrid

[29] Official announcement of discovery of 3×2^16819291 – 1, PrimeGrid

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

[31] Official announcement of discovery of 2525332×73^2525332 + 1, PrimeGrid

[32] Official announcement of discovery of 99739×2^14019102 – 1, PrimeGrid

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

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

[The_largest_known_primes-35] ^ ^a ^b ^c ^d ^e ^f ^g ^h ⁱ ^j ^k Chris Caldwell, The Largest Known Primes at The PrimePages.

[36] Official announcement of discovery of 11937916⁵²⁴²⁸⁸ + 1, PrimeGrid

[37] Official announcement of discovery of 10913140⁵²⁴²⁸⁸ + 1, PrimeGrid

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[63] Official announcement of discovery of 63838×5^3887851 – 1, PrimeGrid

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

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

[GSRP-66] "CRUS - Proven Conjectures". www.noprimeleftbehind.net.

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

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

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

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

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

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

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

[74] 102818×5^3440382 – 1, PrimeGrid

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

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

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

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

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

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

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

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

[83] 109838×5^3168862 – 1, PrimeGrid

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

[85] 118568×5^3112069 + 1, PrimeGrid

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

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

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

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

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

[1stmegaprime-91] GIMPS press release, GIMPS Finds First Million-Digit Prime. Retrieved on 2008-01-04.

[92] 238694×5^2979422 – 1, PrimeGrid

[93] 146264×5^2953282 – 1, PrimeGrid

[94] 35816×5^2945294 – 1, PrimeGrid

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

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

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

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

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

[PRPTop-100] ^ ^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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Largest known primes

Largest known probable primes (PRPs)

See also

References

External links