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. “!” is the factorial, “#” is the primorial, and $\Phi _{3}(x)$ is the third cyclotomic polynomial, defined as $x^{2}+x+1$ .

Rank^[1]^[2]	Number	Discovery date	Decimal digits
1	2^136279841 – 1 ^[3]	12 October 2024	41,024,320
2	2^82589933 – 1 ^[4]	7 December 2018	24,862,048
3	2^77232917 – 1 ^[5]	26 December 2017	23,249,425
4	2^74207281 – 1 ^[6]	7 January 2016	22,338,618
5	2^57885161 – 1 ^[7]	25 January 2013	17,425,170
6	2^43112609 – 1 ^[8]	23 August 2008	12,978,189
7	2^42643801 – 1 ^[9]	4 June 2009	12,837,064
8	$\Phi _{3}(-516693^{1048576})$ ^[10]	2 October 2023	11,981,518
9	$\Phi _{3}(-465859^{1048576})$ ^[11]	31 May 2023	11,887,192
10	2^37156667 – 1 ^[8]	6 September 2008	11,185,272
11	2^32582657 – 1 ^[12]	4 September 2006	9,808,358
12	10223×2^31172165 + 1 ^[13]	31 October 2016	9,383,761
13	2^30402457 – 1 ^[14]	15 December 2005	9,152,052
14	4×5^11786358 + 1	1 October 2024	8,238,312
15	2^25964951 – 1 ^[15]	18 February 2005	7,816,230
16	69×2^24612729 – 1	13 August 2024	7,409,172
17	2^24036583 – 1 ^[16]	15 May 2004	7,235,733
18	107347×2^23427517 – 1	4 August 2024	7,052,391
19	3×2^22103376 − 1 ^[17]	30 September 2024	6,653,780
20	1963736^1048576 + 1 ^[18]	24 September 2022	6,598,776
21	1951734^1048576 + 1 ^[19]	9 August 2022	6,595,985
22	202705×2^21320516 + 1 ^[20]	25 November 2021	6,418,121
23	2^20996011 – 1 ^[21]	17 November 2003	6,320,430
24	1059094^1048576 + 1 ^[22]	31 October 2018	6,317,602
25	3×2^20928756 − 1 ^[23]	5 July 2023	6,300,184
26	919444^1048576 + 1 ^[24]	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 ^[25]	17 September 2017	5,832,522
31	69×2^19374980 − 1	3 July 2022	5,832,452
32	3×2^18924888 − 1 ^[26]	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 ^[27]	8 January 2022	5,477,722
38	4×3^11279466 + 1	10 September 2024	5,381,674
39	3×2^17748034 − 1 ^[28]	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 ^[29]	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 ^[30]	20 January 2021	5,063,112
48	5287180×3^10574360 – 1	3 November 2024	5,045,259
49	3×2^16408818 + 1 ^[31]	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 ^[32]	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 ^[33]	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 ^[34]	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 ^[35]	2 September 2019	3,921,539
85	5128×22^2919993 + 1	5 December 2024	3,919,869
86	19249×2^13018586 + 1 ^[36]	26 March 2007	3,918,990
87	2293×2^12918431 − 1	13 February 2021	3,888,839
88	81×2^12804541 + 1	19 September 2022	3,854,553
89	4×5^5380542 + 1	22 February 2023	3,760,839
90	9×2^12406887 + 1	29 March 2020	3,734,847
91	11937916⁵²⁴²⁸⁸ + 1 ^[37]	5 October 2024	3,710,349
92	7×2^12286041 − 1	10 June 2023	3,698,468
93	10913140⁵²⁴²⁸⁸ + 1 ^[38]	19 June 2024	3,689,913
94	69×2^12231580 − 1	27 July 2021	3,682,075
95	27×2^12184319 + 1	6 February 2021	3,667,847
96	9332124⁵²⁴²⁸⁸ + 1 ^[39]	22 June 2024	3,654,278
97	8630170⁵²⁴²⁸⁸ + 1 ^[40]	13 April 2024	3,636,472
98	863282×5^5179692 - 1	17 October 2024	3,620,456
99	670490×12^3352450 - 1	17 October 2024	3,617,907
100	4×3^7578378 + 1	9 September 2024	3,615,806
101	11×2^11993994 − 1	15 August 2024	3,610,554
102	3761×2^11978874 − 1	6 July 2022	3,606,004
103	95×2^11954552 − 1	28 May 2024	3,598,681
104	259072×5^5136295 − 1	28 October 2024	3,590,122
105	3×2^11895718 − 1 ^[41]	23 June 2015	3,580,969
106	37×2^11855148 + 1	30 May 2022	3,568,757
107	6339004⁵²⁴²⁸⁸ + 1 ^[42]	8 June 2023	3,566,218
108	763795×6^4582771 + 1	11 December 2023	3,566,095
109	5897794⁵²⁴²⁸⁸ + 1 ^[36]	18 December 2022	3,549,792
110	3×2^11731850 − 1 ^[43]	13 March 2015	3,531,640
111	69×2^11718455 − 1 ^[36]	4 December 2020	3,527,609
112	8629×2^11708579 – 1	19 September 2024	3,524,638
113	41×2^11676439 + 1 ^[36]	20 June 2022	3,514,960
114	4896418⁵²⁴²⁸⁸ + 1 ^[44]	15 May 2022	3,507,424
115	81×2^11616017 + 1 ^[36]	30 August 2022	3,496,772
116	69×2^11604348 − 1 ^[36]	4 December 2020	3,493,259
117	4450871×6^4450871 + 1 ^[36]	17 September 2023	3,463,458
118	9×2^11500843 + 1 ^[36]	13 March 2020	3,462,100
119	3×2^11484018 − 1 ^[45]	22 November 2014	3,457,035
120	193997×2^11452891 +1 ^[46]	3 April 2018	3,447,670
121	29914×5^4930904 +1	27 September 2024	3,446,559
122	3638450⁵²⁴²⁸⁸ +1 ^[47]	29 May 2020	3,439,810
123	9221×2^11392194 -1 ^[48]	7 February 2021	3,429,397
124	9×2^11366286 +1	26 March 2020	3,421,594
125	5×2^11355764 -1	2 October 2021	3,418,427
126	732050×6^4392301 +1	9 September 2023	3,417,881
127	3214654⁵²⁴²⁸⁸ +1 ^[49]	24 December 2019	3,411,613
128	632760! - 1	20 October 2024	3,395,992
129	146561×2^11280802 -1 ^[50]	16 November 2020	3,395,865
130	51208×5^4857576 +1	6 June 2024	3,395,305
131	2985036⁵²⁴²⁸⁸ +1 ^[51]	18 September 2019	3,394,739
132	6929×2^11255424 -1	7 July 2022	3,388,225
133	2877652⁵²⁴²⁸⁸ +1 ^[52]	29 June 2019	3,386,397
134	2788032⁵²⁴²⁸⁸ +1 ^[53]	17 April 2019	3,379,193
135	2733014⁵²⁴²⁸⁸ +1 ^[54]	18 March 2019	3,374,655
136	9×2^11158963 +1	13 March 2020	3,359,184
137	9271×2^11134335 -1	17 January 2021	3,351,773
138	136804×5^4777253 -1	1 March 2024	3,339,162
139	2312092⁵²⁴²⁸⁸ + 1 ^[55]	4 August 2018	3,336,572
140	987324×48^1974648 - 1	12 October 2024	3,319,866
141	2061748⁵²⁴²⁸⁸ + 1 ^[56]	20 March 2018	3,310,478
142	1880370⁵²⁴²⁸⁸ + 1 ^[57]	15 January 2018	3,289,511
143	27×2^10902757 − 1	7 March 2022	3,282,059
144	3×2^10829346 + 1 ^[58]	14 January 2014	3,259,959
145	11×2^10803449 + 1	29 May 2022	3,252,164
146	11×2^10797109 + 1	29 May 2022	3,250,255
147	7×2^10612737 − 1	19 May 2022	3,194,154
148	7351117# + 1	14 September 2024	3,191,401
149	37×2^10599476 + 1	17 June 2022	3,190,762
150	5×2^10495620 − 1	26 September 2021	3,159,498
151	${\tfrac {\Phi _{3}(-3^{3304302}+1)}{3}}$	30 June 2023	3,153,105
152	5×2^10349000 − 1	26 September 2021	3,115,361
153	$\Phi _{3}(-844833^{262144})$	17 January 2017	3,107,335
154	52922×5^4399812 – 1	3 August 2023	3,075,342
155	$\Phi _{3}(-712012^{262144})$	14 January 2017	3,068,389
156	177742×5^4386703 – 1	24 July 2023	3,066,180
157	4×3^6402015 + 1	9 September 2024	3,054,539
158	874208×54^1748416 – 1	26 September 2019	3,028,951
159	475856⁵²⁴²⁸⁸ + 1 ^[59]	8 August 2012	2,976,633
160	2×3^6236772 + 1	20 December 2022	2,975,697
161	15×3^9830108 + 1	19 August 2023	2,959,159
162	9×2^9778263 + 1	5 August 2020	2,943,552
163	198×558^1061348 + 1	30 August 2024	2,915,138
164	1806676×41^1806676 + 1	11 March 2018	2,913,785
165	356926⁵²⁴²⁸⁸ + 1 ^[60]	20 June 2012	2,911,151
166	341112⁵²⁴²⁸⁸ + 1 ^[61]	15 June 2012	2,900,832
167	213988×5^4138363 – 1	29 November 2022	2,892,597
168	43×2^9596983 – 1	28 February 2022	2,888,982
169	121×2^9584444 + 1 ^[62]	18 November 2020	2,885,208
170	15×2^9482269 – 1	14 August 2024	2,854,449
171	6533299# - 1	18 August 2024	2,835,864
172	11×2^9381365 + 1	7 March 2020	2,824,074
173	15×2^9312889 + 1	7 August 2023	2,803,461
174	49×2^9187790 + 1	11 September 2022	2,765,803
175	6369619# + 1	12 August 2024	2,765,105
176	27653×2^9167433 + 1 ^[36]	8 June 2005	2,759,677
177	6354977# − 1	12 August 2024	2,758,832
178	90527×2^9162167 + 1	30 June 2010	2,758,093
179	6795×2^9144320 − 1	31 March 2021	2,752,719
180	31×2^9088085 − 1	27 August 2024	2,735,788
181	75×2^9079482 + 1	25 July 2023	2,733,199
182	1323365×116^1323365 + 1 ^[63]	18 January 2018	2,732,038
183	57×2^9075622 – 1	7 August 2022	2,732,037
184	10^2718281-5×10^1631138-5×10^1087142 – 1	6 August 2024	2,718,281
185	63838×5^3887851 – 1 ^[64]	19 June 2022	2,717,497
186	13×2^8989858 + 1	10 March 2020	2,706,219
187	4159×2^8938471 − 1	19 April 2022	2,690,752
188	273809×2^8932416 − 1 ^[65]	13 December 2017	2,688,931
189	93×2^8898285 + 1	4 March 2024	2,678,653
190	2×3^5570081 + 1	14 February 2020	2,657,605
191	25×2^8788628 + 1 ^[66]	1 March 2021	2,645,643
192	2038×366^1028507 − 1 ^[67]	4 April 2016	2,636,562
193	64598×5^3769854 − 1	14 June 2022	2,635,020
194	63×2^8741225 + 1	6 May 2024	2,631,373
195	8×785⁹⁰⁰³²⁵ + 1	4 June 2022	2,606,325
196	17×2^8636199 + 1 ^[68]	17 February 2021	2,599,757
197	75898⁵²⁴²⁸⁸ + 1 ^[69]	19 November 2011	2,558,647
198	25×2^8456828 + 1 ^[70]	27 January 2021	2,545,761
199	39×2^8413422 + 1 ^[71]	23 January 2021	2,532,694
200	31×2^8348000 + 1 ^[72]	19 January 2021	2,513,000
201	27×2^8342438 − 1 ^[73]	1 February 2021	2,511,326
202	3867×2^8261084 − 1	14 April 2021	2,486,838
203	101×2^8152967 + 1	2 December 2023	2,454,290
204	273662×5^3493296 − 1 ^[74]	7 December 2021	2,441,715
205	81×2^8109236 + 1	9 September 2022	2,441,126
206	11×2^8103463 + 1	6 March 2020	2,439,387
207	102818×5^3440382 − 1 ^[75]	8 October 2021	2,404,729
208	11×2^7971110 − 1	25 November 2019	2,399,545
209	27×2^7963247 + 1 ^[76]	14 January 2021	2,397,178
210	3177×2^7954621 − 1	13 June 2021	2,394,584
211	39×2^7946769 + 1 ^[77]	14 January 2021	2,392,218
212	7×6^3072198 + 1	4 August 2019	2,390,636
213	3765×2^7904593 − 1	10 January 2021	2,379,524
214	29×2^7899985 + 1 ^[78]	14 January 2021	2,378,134
215	5113×2^7895471 − 1	27 November 2022	2,376,778
216	861×2^7895451 − 1	21 February 2021	2,376,771
217	75×2^7886683 + 1	4 September 2023	2,374,131
218	99×2^7830910 + 1	24 April 2024	2,357,341
219	28433×2^7830457 + 1 ^[36]	31 December 2004	2,357,207
220	2589×2^7803339 − 1	21 August 2022	2,349,043
221	59×2^7792307 + 1	24 April 2024	2,345,720
222	101×2^7784453 + 1	24 April 2024	2,343,356
223	95×2^7778585 + 1	24 April 2024	2,341,590
224	8401×2^7767655 − 1	24 April 2023	2,338,302
225	9693×2^7767343 − 1	17 November 2023	2,338,208
226	5×2^7755002 − 1	23 September 2021	2,334,489
227	2945×2^7753232 − 1	27 November 2022	2,333,959
228	2×836⁷⁹⁸⁴³¹ + 1	10 September 2024	2,333,181
229	63×2^7743186 + 1	24 April 2024	2,330,934
230	2545×2^7732265 − 1	13 January 2021	2,327,648
231	5539×2^7730709 − 1	15 January 2021	2,327,180
232	4817×2^7719584 − 1	13 June 2021	2,323,831
233	183×558⁸⁴²⁷⁵² + 1	23 August 2024	2,314,734
234	1341174×53^1341174 + 1 ^[79]	21 August 2017	2,312,561
235	9467×2^7680034 − 1	20 February 2022	2,311,925
236	45×2^7661004 + 1 ^[80]	13 December 2020	2,306,194
237	15×2^7619838 + 1 ^[81]	6 December 2020	2,293,801
238	3597×2^7580693 − 1	10 January 2021	2,282,020
239	5256037# + 1	6 August 2024	2,281,955
240	3129×2^7545557 − 1	14 March 2023	2,271,443
241	7401×2^7523295 − 1	21 February 2021	2,264,742
242	45×2^7513661 + 1 ^[82]	12 November 2020	2,261,839
243	$\Phi _{3}(-558640^{196608})$	11 January 2017	2,259,865
244	9×2^7479919 − 1	3 June 2023	2,251,681
245	1875×2^7474308 − 1	21 August 2022	2,249,995
246	69×2^7452023 + 1	23 March 2023	2,243,285
247	1281879×2^7447178 + 1	27 December 2023	2,241,831
248	4×5^3189669 − 1	12 July 2022	2,229,484
249	29×2^7374577 + 1 ^[83]	27 October 2020	2,219,971
250	2653×2^7368343 − 1	18 September 2024	2,218,096
251	21555×2^7364128 − 1	4 September 2024	2,216,828
252	3197×2^7359542 − 1	27 November 2022	2,215,447
253	109838×5^3168862 − 1 ^[84]	13 August 2020	2,214,945
254	95×2^7354869 + 1	25 September 2023	2,214,039
255	101×2^7345194 − 1	5 October 2019	2,211,126
256	85×2^7333444 + 1	25 September 2023	2,207,589
257	15×2^7300254 + 1 ^[85]	25 October 2020	2,197,597
258	422429! + 1	21 February 2022	2,193,027
259	1759×2^7284439 − 1	28 August 2021	2,192,838
260	1909683×14^1909683 + 1	27 May 2023	2,188,748
261	737×2^7269322 − 1	10 August 2017	2,188,287
262	6909×2^7258896 − 1	18 September 2024	2,185,150
263	93×2^7241494 + 1	25 September 2023	2,179,909
264	118568×5^3112069 + 1 ^[86]	1 May 2020	2,175,248
265	40×257⁹⁰¹⁶³² + 1	11 September 2024	2,172,875
266	580633×2^7208783 − 1	15 February 2024	2,170,066
267	6039×2^7207973 − 1	24 March 2021	2,169,820
268	502573×2^7181987 − 1 ^[87]	4 October 2014	2,162,000
269	402539×2^7173024 − 1 ^[88]	2 October 2014	2,159,301
270	3343×2^7166019 − 1	29 September 2016	2,157,191
271	161041×2^7107964 + 1 ^[89]	6 January 2015	2,139,716
272	294×213⁹¹⁸⁹⁵² – 1	19 September 2023	2,139,672
273	27×2^7046834 + 1 ^[90]	11 October 2018	2,121,310
274	1759×2^7046791 − 1	28 August 2021	2,121,299
275	327×2^7044001 − 1	13 January 2021	2,120,459
276	5×2^7037188 − 1	22 September 2021	2,118,406
277	3×2^7033641 + 1 ^[91]	21 February 2011	2,117,338
278	625783×2^7031319 − 1	10 February 2024	2,116,644
279	33661×2^7031232 + 1 ^[36]	30 October 2007	2,116,617
280	$\Phi _{3}(-237804^{196608})$	6 January 2017	2,114,016
281	207494×5^3017502 – 1	16 March 2020	2,109,149
282	15×2^6993631 – 1	25 August 2021	2,105,294
283	8943501×2^6972593 – 1	8 January 2022	2,098,967
284	6020095×2^6972593 – 1	4 September 2022	2,098,967
285	2^6972593 – 1 ^[92]	1 June 1999	2,098,960
286	273×2^6963847 – 1	16 November 2022	2,096,330
287	6219×2^6958945 – 1	7 January 2021	2,094,855
288	51×2^6945567 + 1	26 May 2020	2,090,826
289	3323×2^6921196 – 1	18 September 2024	2,083,492
290	238694×5^2979422 – 1 ^[93]	12 March 2020	2,082,532
291	4×72^1119849 − 1 ^[67]	7 September 2016	2,079,933
292	33×2^6894190 – 1	27 July 2021	2,075,360
293	4778027# − 1	31 July 2024	2,073,926
294	2345×2^6882320 – 1	13 April 2022	2,071,789
295	57×2^6857990 + 1	17 August 2023	2,064,463
296	146264×5^2953282 – 1 ^[94]	9 March 2020	2,064,261
297	69×2^6838971 – 1	1 March 2020	2,058,738
298	35816×5^2945294 – 1 ^[95]	5 March 2020	2,058,677
299	127×2^6836153 – 1	25 June 2018	2,057,890
300	19×2^6833086 + 1 ^[96]	24 October 2020	2,056,966
301	65×2^6810465 + 1	22 September 2023	2,050,157
302	40597×2^6808509 – 1 ^[97]	25 December 2013	2,049,571
303	283×2^6804701 – 1	19 January 2020	2,048,431
304	1861209×2^6789999 + 1	2 December 2020	2,044,000
305	5817×2^6789459 – 1	9 January 2021	2,043,835
306	8435×2^6786180 – 1	7 January 2021	2,042,848
307	51×2^6753404 + 1	26 May 2020	2,032,979
308	93×2^6750726 + 1	18 September 2023	2,032,173
309	69×2^6745775 + 1	21 March 2023	2,030,683
310	9995×2^6711008 – 1	31 December 2020	2,020,219
311	39×2^6684941 + 1 ^[98]	20 October 2020	2,012,370
312	6679881×2^6679881 + 1 ^[99]	25 July 2009	2,010,852
313	37×2^6660841 − 1 ^[67]	30 July 2014	2,005,115
314	43330794²⁶²¹⁴⁴ + 1	3 December 2024	2,001,941
315	39×2^6648997 + 1 ^[100]	20 October 2020	2,001,550
316	42781592²⁶²¹⁴⁴ + 1	18 November 2024	2,000,489
317	10^2000007 – 10^1127194 – 10⁸⁷²⁸¹² – 1	12 January 2024	2,000,007
318	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. F(n) is the nth Fibonacci number.

Rank^[101]	Number	Discovery date	Decimal digits
1	${\tfrac {10^{8177207}-1}{9}}$ ^[101]	8 May 2021	8,177,207
2	${\tfrac {10^{5794777}-1}{9}}$ ^[101]	20 April 2021	5,794,777
3	${\tfrac {2^{15135397}+1}{3}}$ ^[101]	June 2021	4,556,209
4	${\tfrac {3^{8530117}-1}{2}}$ ^[101]	November 2023	4,069,900
5	2^13380298 – 27 ^[101]	March 2021	4,027,872
6	${\tfrac {2^{13372531}+1}{3}}$ ^[101]	September 2013	4,025,533
7	${\tfrac {2^{13347311}+1}{3}}$ ^[101]	September 2013	4,017,941
8	${\tfrac {2^{12720787}-1}{1666870069020922905132673131516413926009285199}}$ ^[101]	3 July 2022	3,829,294
9	${\tfrac {3^{7973131}-1}{2}}$ ^[101]	November 2023	3,804,150
10	${\tfrac {2^{12588091}-1}{32075464348897282169539424801}}$ ^[101]	10 April 2023	3,789,365
11	${\tfrac {2^{12503723}-2^{6251862}+1}{5}}$ ^[101]	July 2020	3,763,995
12	${\tfrac {5^{5154509}-1}{4}}$ ^[101]	February 2024	3,602,847
13	${\tfrac {5^{4939471}-1}{4}}$ ^[101]	January 2024	3,452,542
14	${\tfrac {3^{7034611}+1}{4}}$ ^[101]	December 2024	3,356,362
15	${\tfrac {2^{10443557}-1}{37289325994807}}$ ^[101]	9 July 2020	3,143,811
16	2^9092392 + 40291 ^[101]	February 2011	2,737,083
17	${\tfrac {6^{3360347}-1}{5}}$ ^[101]	October 2023	2,614,858
18	${\tfrac {2^{8247949}-1}{45487316822291087700751210632267642069671672071}}$ ^[101]	3 June 2024	2,482,834
19	${\tfrac {17^{1990523}-1}{16}}$ ^[101]	August 2020	2,449,236
20	${\tfrac {35963^{524288}+1}{2}}$ ^[101]	August 2022	2,388,581
21	500186⁵⁴⁴⁶⁵ + 54465⁵⁰⁰¹⁸⁶ ^[101]	August 2024	2,368,940
22	${\tfrac {11^{2264611}+1}{12}}$ ^[101]	July 2021	2,358,349
23	${\tfrac {5^{3300593}-1}{4}}$ ^[101]	February 2022	2,307,015
24	${\tfrac {3^{4694803}+2^{4694803}}{5}}$ ^[101]	December 2023	2,239,990
25	${\tfrac {2^{7313983}-1}{305492080276193}}$ ^[101]	1 March 2018	2,201,714
26	${\tfrac {3^{4571447}+2^{4571447}}{5}}$ ^[101]	December 2023	2,181,134
27	${\tfrac {15^{1848811}+1}{16}}$ ^[101]	July 2024	2,174,370
28	F(10367321) ^[101]	10 August 2024	2,166,642
29	${\tfrac {15^{1841911}+1}{16}}$ ^[101]	July 2024	2,166,255
30	3^4532794 + 4532794³ ^[101]	October 2023	2,162,693
31	F(10317107) ^[101]	27 July 2024	2,156,148
32	${\tfrac {2^{7080247}-1}{17045259548603283727480473638587228614426296913631}}$ ^[101]	27 October 2017	2,131,318
33	360834³⁵⁶³⁴⁵ + 356345³⁶⁰⁸³⁴ ^[101]	February 2024	2,003,304
34	360339³⁵⁶⁵⁷² + 356572³⁶⁰³³⁹ ^[101]	May 2024	2,000,656

References

^ Caldwell, Chris K. "THE LARGEST KNOWN PRIMES (The 5,000 largest known primes)". Retrieved 23 November 2018.
^ The known primes with 2,000,000 digits or more
^ "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 ^z ^aa ^ab ^ac ^ad ^ae ^af ^ag ^ah ^ai 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] The known primes with 2,000,000 digits or more

[3] "Official press release of 52nd Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 21 October 2024.

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

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

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

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

[4546prime-8] "Official press release of 45th and 46th Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 10 September 2008.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[The_largest_known_primes-36] ^ ^a ^b ^c ^d ^e ^f ^g ^h ⁱ ^j ^k Chris Caldwell, The Largest Known Primes at The PrimePages.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[GSRP-67] "CRUS - Proven Conjectures". www.noprimeleftbehind.net.

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

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

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

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

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

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

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

[75] 102818×5^3440382 – 1, PrimeGrid

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

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

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

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

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

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

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

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

[84] 109838×5^3168862 – 1, PrimeGrid

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

[86] 118568×5^3112069 + 1, PrimeGrid

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

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

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

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

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

[1stmegaprime-92] GIMPS press release, GIMPS Finds First Million-Digit Prime. Retrieved on 2008-01-04.

[93] 238694×5^2979422 – 1, PrimeGrid

[94] 146264×5^2953282 – 1, PrimeGrid

[95] 35816×5^2945294 – 1, PrimeGrid

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

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

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

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

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

[PRPTop-101] ^ ^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 ^z ^aa ^ab ^ac ^ad ^ae ^af ^ag ^ah ^ai 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