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