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 ${\displaystyle \Phi _{3}(x)}$ is the third cyclotomic polynomial, defined as ${\displaystyle x^{2}+x+1}$.

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	2524190^2097152 + 1 [8]	12 October 2025	13,426,224
7	2^43112609 − 1 [9]	23 August 2008	12,978,189
8	2^42643801 − 1 [10]	4 June 2009	12,837,064
9	${\displaystyle \Phi _{3}(-516693^{1048576})}$ [11]	2 October 2023	11,981,518
10	${\displaystyle \Phi _{3}(-465859^{1048576})}$ [12]	31 May 2023	11,887,192
11	2^37156667 − 1 [9]	6 September 2008	11,185,272
12	2^32582657 − 1 [13]	4 September 2006	9,808,358
13	10223×2^31172165 + 1 [14]	31 October 2016	9,383,761
14	2^30402457 − 1 [15]	15 December 2005	9,152,052
15	4×5^11786358 + 1	1 October 2024	8,238,312
16	2^25964951 − 1 [16]	18 February 2005	7,816,230
17	4052186×69^4052186 + 1 [17]	16 April 2025	7,451,366
18	69×2^24612729 − 1	13 August 2024	7,409,172
19	2^24036583 − 1 [18]	15 May 2004	7,235,733
20	5336284^1048576 + 1 [19]	31 October 2025	7,054,022
21	107347×2^23427517 − 1	4 August 2024	7,052,391
22	3×2^23157875 − 1 [20]	25 June 2025	6,971,216
23	3843236^1048576 + 1 [21]	17 December 2024	6,904,556
24	3×2^22103376 − 1 [22]	30 September 2024	6,653,780
25	1963736^1048576 + 1 [23]	24 September 2022	6,598,776
26	1951734^1048576 + 1 [24]	9 August 2022	6,595,985
27	202705×2^21320516 + 1 [25]	25 November 2021	6,418,121
28	2^20996011 − 1 [26]	17 November 2003	6,320,430
29	1059094^1048576 + 1 [27]	31 October 2018	6,317,602
30	3×2^20928756 − 1 [28]	5 July 2023	6,300,184
31	919444^1048576 + 1 [29]	29 August 2017	6,253,210
32	81×2^20498148 + 1	13 June 2023	6,170,560
33	7×2^20267500 + 1	21 July 2022	6,101,127
34	4×5^8431178 + 1	2 January 2024	5,893,142
35	168451×2^19375200 + 1 [30]	17 September 2017	5,832,522
36	69×2^19374980 − 1	3 July 2022	5,832,452
37	3×2^18924888 − 1 [31]	24 March 2022	5,696,990
38	69×2^18831865 − 1	16 December 2021	5,668,959
39	2×3^11879700 + 1	22 June 2024	5,668,058
40	97139×2^18397548 − 1	23 April 2023	5,538,219
41	7×2^18233956 + 1	1 October 2020	5,488,969
42	3×2^18196595 − 1 [32]	8 January 2022	5,477,722
43	4×3^11279466 + 1	10 September 2024	5,381,674
44	3×2^17748034 − 1 [33]	6 September 2021	5,342,692
45	${\displaystyle \Phi _{3}(-123447^{524288})}$	23 February 2017	5,338,805
46	3622×5^7558139 − 1	18 February 2022	5,282,917
47	7×6^6772401 + 1	9 September 2019	5,269,954
48	2×3^10852677 + 1	8 January 2023	5,178,044
49	8508301×2^17016603 − 1 [34]	21 March 2018	5,122,515
50	8×10^5112848 − 1	30 January 2024	5,112,848
51	13×2^16828072 + 1	11 October 2023	5,065,756
52	3×2^16819291 − 1 [35]	20 January 2021	5,063,112
53	5287180×3^10574360 − 1	3 November 2024	5,045,259
54	3×2^16408818 + 1 [36]	25 October 2020	4,939,547
55	2329989×2^16309923 − 1	13 February 2024	4,909,783
56	69×2^15866556 + 1	20 August 2021	4,776,312
57	2036×3^10009192 + 1	15 February 2024	4,775,602
58	2525332×73^2525332 + 1 [37]	28 August 2021	4,705,888
59	1419499×2^15614489 + 1	9 February 2024	4,700,436
60	11×2^15502315 + 1	8 January 2023	4,666,663
61	(10^2332974 + 1)^2 − 2	20 February 2024	4,665,949
62	37×2^15474010 + 1	8 November 2022	4,658,143
63	93839×2^15337656 − 1	28 November 2022	4,617,100
64	2^15317227+2^7658614 + 1	31 July 2020	4,610,945
65	13×2^15294536 + 1	30 September 2023	4,604,116
66	6×5^6546983 + 1	13 June 2020	4,576,146
67	4788920×3^9577840 − 1	14 February 2024	4,569,798
68	31×2^15145093 − 1	9 February 2025	4,559,129
69	69×2^14977631 − 1	3 December 2021	4,508,719
70	192971×2^14773498 − 1	7 March 2021	4,447,272
71	4×3^9214845 + 1	10 September 2024	4,396,600
72	9145334×3^9145334 + 1	25 December 2023	4,363,441
73	4×5^6181673 − 1	15 July 2022	4,320,805
74	396101×2^14259638 − 1	3 February 2024	4,292,585
75	6962×31^2863120 − 1	29 February 2020	4,269,952
76	37×2^14166940 + 1	24 June 2022	4,264,676
77	99739×2^14019102 + 1 [38]	24 December 2019	4,220,176
78	69×2^13832885 − 1	17 January 2022	4,164,116
79	9562633# + 1	25 June 2025	4,151,498
80	404849×2^13764867 + 1	10 March 2021	4,143,644
81	25×2^13719266 + 1	20 September 2022	4,129,912
82	81×2^13708272 + 1	11 October 2022	4,126,603
83	2740879×2^13704395 − 1	26 October 2019	4,125,441
84	479216×3^8625889 − 1	16 November 2019	4,115,601
85	13×2^13584543 − 1	30 May 2025	4,089,357
86	31×2^13514933 − 1	9 February 2025	4,068,402
87	${\displaystyle \Phi _{3}(-143332^{393216})}$	30 January 2017	4,055,114
88	81×2^13470584 + 1	9 October 2022	4,055,052
89	2^13466917 − 1 [39]	14 November 2001	4,053,946
90	5778486×5^5778486 + 1	15 August 2024	4,038,996
91	9×2^13334487 + 1	31 March 2020	4,014,082
92	206039×2^13104952 − 1	26 April 2021	3,944,989
93	2805222×5^5610444 + 1 [40]	2 September 2019	3,921,539
94	5128×22^2919993 + 1	5 December 2024	3,919,869
95	19249×2^13018586 + 1 [41]	26 March 2007	3,918,990
96	2293×2^12918431 − 1	13 February 2021	3,888,839
97	81×2^12804541 + 1	19 September 2022	3,854,553
98	67612×5^5501582 + 1 [42]	8 April 2025	3,845,446
99	18099898^524288 + 1	1 September 2025	3,805,113
100	17544674^524288 + 1 [43]	26 October 2025	3,798,019
101	17502532^524288 + 1 [44]	24 October 2025	3,797,471
102	17445908^524288 + 1 [45]	19 October 2025	3,796,734
103	17177670^524288 + 1 [46]	5 October 2025	3,793,205
104	16211276^524288 + 1 [47]	9 August 2025	3,780,021
105	15958750^524288 + 1 [48]	15 July 2025	3,776,446
106	15852200^524288 + 1 [49]	8 July 2025	3,774,921
107	4×5^5380542 + 1	22 February 2023	3,760,839
108	13520762^524288 + 1 [50]	25 February 2025	3,738,699
109	13427472^524288 + 1 [51]	3 March 2025	3,737,122
110	9×2^12406887 + 1	29 March 2020	3,734,847
111	12900356^524288 + 1 [52]	22 January 2025	3,728,004
112	12693488^524288 + 1 [53]	6 January 2025	3,724,323
113	11937916^524288 + 1 [54]	5 October 2024	3,710,349
114	7×2^12286041 − 1	10 June 2023	3,698,468
115	10913140^524288 + 1 [55]	19 June 2024	3,689,913
116	69×2^12231580 − 1	27 July 2021	3,682,075
117	27×2^12184319 + 1	6 February 2021	3,667,847
118	9332124^524288 + 1 [56]	22 June 2024	3,654,278
119	8630170^524288 + 1 [57]	13 April 2024	3,636,472
120	863282×5^5179692 − 1	17 October 2024	3,620,456
121	670490×12^3352450 − 1	17 October 2024	3,617,907
122	4×3^7578378 + 1	9 September 2024	3,615,806
123	11×2^11993994 − 1	15 August 2024	3,610,554
124	3761×2^11978874 − 1	6 July 2022	3,606,004
125	95×2^11954552 − 1	28 May 2024	3,598,681
126	259072×5^5136295 − 1	28 October 2024	3,590,122
127	3×2^11895718 − 1 [58]	23 June 2015	3,580,969
128	37×2^11855148 + 1	30 May 2022	3,568,757
129	6339004^524288 + 1 [59]	8 June 2023	3,566,218
130	763795×6^4582771 + 1	11 December 2023	3,566,095
131	5897794^524288 + 1 [41]	18 December 2022	3,549,792
132	3×2^11731850 − 1 [60]	13 March 2015	3,531,640
133	69×2^11718455 − 1 [41]	4 December 2020	3,527,609
134	8629×2^11708579 − 1	19 September 2024	3,524,638
135	41×2^11676439 + 1 [41]	20 June 2022	3,514,960
136	4896418^524288 + 1 [61]	15 May 2022	3,507,424
137	81×2^11616017 + 1 [41]	30 August 2022	3,496,772
138	69×2^11604348 − 1 [41]	4 December 2020	3,493,259
139	4450871×6^4450871 + 1 [41]	17 September 2023	3,463,458
140	9×2^11500843 + 1 [41]	13 March 2020	3,462,100
141	3×2^11484018 − 1 [62]	22 November 2014	3,457,035
142	193997×2^11452891 + 1 [63]	3 April 2018	3,447,670
143	29914×5^4930904 + 1	27 September 2024	3,446,559
144	3638450^524288 + 1 [64]	29 May 2020	3,439,810
145	9221×2^11392194 − 1 [65]	7 February 2021	3,429,397
146	9×2^11366286 + 1	26 March 2020	3,421,594
147	5×2^11355764 − 1	2 October 2021	3,418,427
148	732050×6^4392301 + 1	9 September 2023	3,417,881
149	3214654^524288 + 1 [66]	24 December 2019	3,411,613
150	632760! − 1	20 October 2024	3,395,992
151	146561×2^11280802 − 1 [67]	16 November 2020	3,395,865
152	51208×5^4857576 + 1	6 June 2024	3,395,305
153	2985036^524288 + 1 [68]	18 September 2019	3,394,739
154	4591×2^11270837 − 1	2 January 2025	3,392,864
155	6929×2^11255424 − 1	7 July 2022	3,388,225
156	2877652^524288 + 1 [69]	29 June 2019	3,386,397
157	2788032^524288 + 1 [70]	17 April 2019	3,379,193
158	2733014^524288 + 1 [71]	18 March 2019	3,374,655
159	9×2^11158963 + 1	13 March 2020	3,359,184
160	9271×2^11134335 − 1	17 January 2021	3,351,773
161	136804×5^4777253 − 1	1 March 2024	3,339,162
162	2312092^524288 + 1 [72]	4 August 2018	3,336,572
163	987324×48^1974648 − 1	12 October 2024	3,319,866
164	2061748^524288 + 1 [73]	20 March 2018	3,310,478
165	1880370^524288 + 1 [74]	15 January 2018	3,289,511
166	27×2^10902757 − 1	7 March 2022	3,282,059
167	3×2^10829346 + 1 [75]	14 January 2014	3,259,959
168	11×2^10803449 + 1	29 May 2022	3,252,164
169	11×2^10797109 + 1	29 May 2022	3,250,255
170	7×2^10612737 − 1	19 May 2022	3,194,154
171	7351117# + 1	14 September 2024	3,191,401
172	37×2^10599476 + 1	17 June 2022	3,190,762
173	5×2^10495620 − 1	26 September 2021	3,159,498
174	${\displaystyle {\tfrac {\Phi _{3}(-3^{3304302}+1)}{3}}}$	30 June 2023	3,153,105
175	5×2^10349000 − 1	26 September 2021	3,115,361
176	${\displaystyle \Phi _{3}(-844833^{262144})}$	17 January 2017	3,107,335
177	17×2^10248660 − 1	8 August 2025	3,085,156
178	52922×5^4399812 − 1	3 August 2023	3,075,342
179	${\displaystyle \Phi _{3}(-712012^{262144})}$	14 January 2017	3,068,389
180	177742×5^4386703 − 1	24 July 2023	3,066,180
181	4×3^6402015 + 1	9 September 2024	3,054,539
182	874208×54^1748416 − 1	26 September 2019	3,028,951
183	475856^524288 + 1 [76]	8 August 2012	2,976,633
184	2×3^6236772 + 1	20 December 2022	2,975,697
185	15×3^9830108 + 1	19 August 2023	2,959,159
186	9×2^9778263 + 1	5 August 2020	2,943,552
187	198×558^1061348 + 1	30 August 2024	2,915,138
188	1806676×41^1806676 + 1	11 March 2018	2,913,785
189	356926^524288 + 1 [77]	20 June 2012	2,911,151
190	341112^524288 + 1 [78]	15 June 2012	2,900,832
191	213988×5^4138363 − 1	29 November 2022	2,892,597
192	43×2^9596983 − 1	28 February 2022	2,888,982
193	121×2^9584444 + 1 [79]	18 November 2020	2,885,208
194	15×2^9482269 − 1	14 August 2024	2,854,449
195	6533299# − 1	18 August 2024	2,835,864
196	11×2^9381365 + 1	7 March 2020	2,824,074
197	15×2^9312889 + 1	7 August 2023	2,803,461
198	97×2^9305542 + 1	10 May 2025	2,801,250
199	93×2^9235048 + 1	7 May 2025	2,780,029
200	49×2^9187790 + 1	11 September 2022	2,765,803
201	6369619# + 1	12 August 2024	2,765,105
202	27653×2^9167433 + 1 [41]	8 June 2005	2,759,677
203	6354977# − 1	12 August 2024	2,758,832
204	90527×2^9162167 + 1	30 June 2010	2,758,093
205	6795×2^9144320 − 1	31 March 2021	2,752,719
206	31×2^9088085 − 1	27 August 2024	2,735,788
207	75×2^9079482 + 1	25 July 2023	2,733,199
208	1323365×116^1323365 + 1 [80]	18 January 2018	2,732,038
209	57×2^9075622 − 1	7 August 2022	2,732,037
210	10^2718281 − 5×10^1631138 − 5×10^1087142 − 1	6 August 2024	2,718,281
211	63838×5^3887851 − 1 [81]	19 June 2022	2,717,497
212	13×2^8989858 + 1	10 March 2020	2,706,219
213	271357×2^8943013 − 1	13 October 2025	2,692,121
214	4159×2^8938471 − 1	19 April 2022	2,690,752
215	273809×2^8932416 − 1 [82]	13 December 2017	2,688,931
216	93×2^8898285 + 1	4 March 2024	2,678,653
217	2×3^5570081 + 1	14 February 2020	2,657,605
218	25×2^8788628 + 1 [83]	1 March 2021	2,645,643
219	2038×366^1028507 − 1 [84]	4 April 2016	2,636,562
220	64598×5^3769854 − 1	14 June 2022	2,635,020
221	63×2^8741225 + 1	6 May 2024	2,631,373
222	8×785^900325 + 1	4 June 2022	2,606,325
223	17×2^8636199 + 1 [85]	17 February 2021	2,599,757
224	75898^524288 + 1 [86]	19 November 2011	2,558,647
225	25×2^8456828 + 1 [87]	27 January 2021	2,545,761
226	39×2^8413422 + 1 [88]	23 January 2021	2,532,694
227	31×2^8348000 + 1 [89]	19 January 2021	2,513,000
228	27×2^8342438 − 1 [90]	1 February 2021	2,511,326
229	17×2^8330892 − 1	16 July 2025	2,507,850
230	3867×2^8261084 − 1	14 April 2021	2,486,838
231	101×2^8152967 + 1	2 December 2023	2,454,290
232	9×2^8128075 − 1	8 July 2025	2,446,796
233	273662×5^3493296 − 1 [91]	7 December 2021	2,441,715
234	81×2^8109236 + 1	9 September 2022	2,441,126
235	11×2^8103463 + 1	6 March 2020	2,439,387
236	102818×5^3440382 − 1 [92]	8 October 2021	2,404,729
237	9×2^7979119 − 1	8 July 2025	2,401,956
238	11×2^7971110 − 1	25 November 2019	2,399,545
239	27×2^7963247 + 1 [93]	14 January 2021	2,397,178
240	3177×2^7954621 − 1	13 June 2021	2,394,584
241	39×2^7946769 + 1 [94]	14 January 2021	2,392,218
242	7×6^3072198 + 1	4 August 2019	2,390,636
243	3765×2^7904593 − 1	10 January 2021	2,379,524
244	29×2^7899985 + 1 [95]	14 January 2021	2,378,134
245	5113×2^7895471 − 1	27 November 2022	2,376,778
246	861×2^7895451 − 1	21 February 2021	2,376,771
247	75×2^7886683 + 1	4 September 2023	2,374,131
248	2661×2^7861390 − 1	28 December 2024	2,366,518
249	21×2^7838882 − 1	15 August 2025	2,359,740
250	30397×2^7838120 + 1	17 August 2025	2,359,514
251	99×2^7830910 + 1	24 April 2024	2,357,341
252	28433×2^7830457 + 1 [41]	31 December 2004	2,357,207
253	2589×2^7803339 − 1	21 August 2022	2,349,043
254	59×2^7792307 + 1	24 April 2024	2,345,720
255	101×2^7784453 + 1	24 April 2024	2,343,356
256	95×2^7778585 + 1	24 April 2024	2,341,590
257	8401×2^7767655 − 1	24 April 2023	2,338,302
258	9693×2^7767343 − 1	17 November 2023	2,338,208
259	5×2^7755002 − 1	23 September 2021	2,334,489
260	2945×2^7753232 − 1	27 November 2022	2,333,959
261	2×836^798431 + 1	10 September 2024	2,333,181
262	63×2^7743186 + 1	24 April 2024	2,330,934
263	2545×2^7732265 − 1	13 January 2021	2,327,648
264	5539×2^7730709 − 1	15 January 2021	2,327,180
265	4817×2^7719584 − 1	13 June 2021	2,323,831
266	183×558^842752 + 1	23 August 2024	2,314,734
267	1341174×53^1341174 + 1 [96]	21 August 2017	2,312,561
268	9467×2^7680034 − 1	20 February 2022	2,311,925
269	45×2^7661004 + 1 [97]	13 December 2020	2,306,194
270	15×2^7619838 + 1 [98]	6 December 2020	2,293,801
271	3645×2^7610003 − 1	28 August 2025	2,290,843
272	3597×2^7580693 − 1	10 January 2021	2,282,020
273	5256037# + 1	6 August 2024	2,281,955
274	38118498221×2^7552807 + 1	7 October 2025	2,273,633
275	3129×2^7545557 − 1	14 March 2023	2,271,443
276	7401×2^7523295 − 1	21 February 2021	2,264,742
277	45×2^7513661 + 1 [99]	12 November 2020	2,261,839
278	${\displaystyle \Phi _{3}(-558640^{196608})}$	11 January 2017	2,259,865
279	2739×2^7483537 − 1	1 May 2025	2,252,773
280	9×2^7479919 − 1	3 June 2023	2,251,681
281	1875×2^7474308 − 1	21 August 2022	2,249,995
282	69×2^7452023 + 1	23 March 2023	2,243,285
283	1281879×2^7447178 + 1	27 December 2023	2,241,831
284	9107×2^7417464 − 1	3 May 2025	2,232,884
285	4×5^3189669 − 1	12 July 2022	2,229,484
286	19×2^7383785 − 1	11 July 2025	2,222,743
287	29×2^7374577 + 1 [100]	27 October 2020	2,219,971
288	2653×2^7368343 − 1	18 September 2024	2,218,096
289	21555×2^7364128 − 1	4 September 2024	2,216,828
290	3197×2^7359542 − 1	27 November 2022	2,215,447
291	109838×5^3168862 − 1 [101]	13 August 2020	2,214,945
292	95×2^7354869 + 1	25 September 2023	2,214,039
293	101×2^7345194 − 1	5 October 2019	2,211,126
294	85×2^7333444 + 1	25 September 2023	2,207,589
295	15×2^7300254 + 1 [102]	25 October 2020	2,197,597
296	6733×2^7285527 − 1	26 October 2025	2,193,166
297	422429! + 1	21 February 2022	2,193,027
298	1759×2^7284439 − 1	28 August 2021	2,192,838
299	1909683×14^1909683 + 1	27 May 2023	2,188,748
300	737×2^7269322 − 1	10 August 2017	2,188,287
301	6909×2^7258896 − 1	18 September 2024	2,185,150
302	93×2^7241494 + 1	25 September 2023	2,179,909
303	118568×5^3112069 + 1 [103]	1 May 2020	2,175,248
304	4215×2^7221386 − 1	27 December 2024	2,173,858
305	40×257^901632 + 1	11 September 2024	2,172,875
306	1685×2^7213108 − 1	13 April 2025	2,171,366
307	580633×2^7208783 − 1	15 February 2024	2,170,066
308	6039×2^7207973 − 1	24 March 2021	2,169,820
309	1871×2^7207954 − 1	26 September 2025	2,169,814
310	502573×2^7181987 − 1 [104]	4 October 2014	2,162,000
311	402539×2^7173024 − 1 [105]	2 October 2014	2,159,301
312	3343×2^7166019 − 1	29 September 2016	2,157,191
313	4137×2^7132569 − 1	11 April 2025	2,147,121
314	161041×2^7107964 + 1 [106]	6 January 2015	2,139,716
315	294×213^918952 − 1	19 September 2023	2,139,672
316	17×2^7101254 − 1	11 July 2025	2,137,692
317	27×2^7046834 + 1 [107]	11 October 2018	2,121,310
318	1759×2^7046791 − 1	28 August 2021	2,121,299
319	327×2^7044001 − 1	13 January 2021	2,120,459
320	5×2^7037188 − 1	22 September 2021	2,118,406
321	3×2^7033641 + 1 [108]	21 February 2011	2,117,338
322	625783×2^7031319 − 1	10 February 2024	2,116,644
323	33661×2^7031232 + 1 [41]	30 October 2007	2,116,617
324	${\displaystyle \Phi _{3}(-237804^{196608})}$	6 January 2017	2,114,016
325	207494×5^3017502 − 1	16 March 2020	2,109,149
326	15×2^6993631 − 1	25 August 2021	2,105,294
327	8943501×2^6972593 − 1	8 January 2022	2,098,967
328	6020095×2^6972593 − 1	4 September 2022	2,098,967
329	2^6972593 − 1 [109]	1 June 1999	2,098,960
330	273×2^6963847 − 1	16 November 2022	2,096,330
331	6219×2^6958945 − 1	7 January 2021	2,094,855
332	51×2^6945567 + 1	26 May 2020	2,090,826
333	8×10^2084563 − 1	1 June 2025	2,084,564
334	3323×2^6921196 − 1	18 September 2024	2,083,492
335	238694×5^2979422 − 1 [110]	12 March 2020	2,082,532
336	4×72^1119849 − 1 [84]	7 September 2016	2,079,933
337	129×2^6900230 + 1	5 June 2025	2,077,179
338	33×2^6894190 − 1	27 July 2021	2,075,360
339	4778027# − 1	31 July 2024	2,073,926
340	105×2^6884697 + 1	2 June 2025	2,072,503
341	2345×2^6882320 − 1	13 April 2022	2,071,789
342	57×2^6857990 + 1	17 August 2023	2,064,463
343	146264×5^2953282 − 1 [111]	9 March 2020	2,064,261
344	72752758^262144 + 1	4 November 2025	2,060,937
345	72718062^262144 + 1	4 November 2025	2,060,883
346	72071732^262144 + 1	22 October 2025	2,059,866
347	71737620^262144 + 1	18 October 2025	2,059,337
348	71380700^262144 + 1	13 October 2025	2,058,770
349	69×2^6838971 − 1	1 March 2020	2,058,738
350	35816×5^2945294 − 1 [112]	5 March 2020	2,058,677
351	71107798^262144 + 1	11 October 2025	2,058,333
352	127×2^6836153 − 1	25 June 2018	2,057,890
353	105×2^6835099 + 1	26 May 2025	2,057,572
354	70520422^262144 + 1	29 September 2025	2,057,389
355	70349734^262144 + 1	27 September 2025	2,057,113
356	19×2^6833086 + 1 [113]	24 October 2020	2,056,966
357	69844790^262144 + 1	22 September 2025	2,056,293
358	69810332^262144 + 1	22 September 2025	2,056,237
359	69290228^262144 + 1	20 September 2025	2,055,386
360	69170386^262144 + 1	13 September 2025	2,055,189
361	68717884^262144 + 1	30 August 2025	2,054,441
362	68000464^262144 + 1	10 August 2025	2,053,246
363	67886950^262144 + 1	9 August 2025	2,053,056
364	67673558^262144 + 1	5 August 2025	2,052,698
365	67535128^262144 + 1	2 August 2025	2,052,465
366	67433562^262144 + 1	2 August 2025	2,052,293
367	67167678^262144 + 1	24 July 2025	2,051,844
368	67141518^262144 + 1	24 July 2025	2,051,799
369	67062340^262144 + 1	22 July 2025	2,051,665
370	66498472^262144 + 1	8 July 2025	2,050,704
371	66342922^262144 + 1	4 July 2025	2,050,437
372	66266188^262144 + 1	3 July 2025	2,050,305
373	65×2^6810465 + 1	22 September 2023	2,050,157
374	40597×2^6808509 − 1 [114]	25 December 2013	2,049,571
375	283×2^6804701 − 1	19 January 2020	2,048,431
376	65136498^262144 + 1	20 June 2025	2,048,348
377	64989720^262144 + 1	18 June 2025	2,048,091
378	64074894^262144 + 1	30 May 2025	2,046,447
379	64010198^262144 + 1	30 May 2025	2,046,362
380	63833640^262144 + 1	27 May 2025	2,046,047
381	8×10^2045966 − 1	31 May 2025	2,045,967
382	63784742^262144 + 1	26 May 2025	2,045,960
383	63558122^262144 + 1	27 May 2025	2,045,555
384	63448958^262144 + 1	22 May 2025	2,045,359
385	63286690^262144 + 1	19 May 2025	2,045,068
386	62767176^262144 + 1	9 May 2025	2,044,129
387	62747994^262144 + 1	9 May 2025	2,044,095
388	1861209×2^6789999 + 1	2 December 2020	2,044,000
389	5817×2^6789459 − 1	9 January 2021	2,043,835
390	62311952^262144 + 1	3 May 2025	2,043,301
391	62199610^262144 + 1	5 May 2025	2,043,095
392	62152830^262144 + 1	1 May 2025	2,043,010
393	62136706^262144 + 1	2 May 2025	2,042,980
394	8435×2^6786180 − 1	7 January 2021	2,042,848
395	61238184^262144 + 1	21 April 2025	2,041,322
396	119×2^6777781 + 1	18 May 2025	2,040,318
397	59145944^262144 + 1	29 March 2025	2,037,364
398	58936230^262144 + 1	28 March 2025	2,036,960
399	58870004^262144 + 1	28 March 2025	2,036,832
400	58846688^262144 + 1	28 March 2025	2,036,787
401	58333324^262144 + 1	28 March 2025	2,035,789
402	58288282^262144 + 1	28 March 2025	2,035,701
403	57643582^262144 + 1	28 March 2025	2,034,435
404	57594478^262144 + 1	28 March 2025	2,034,338
405	57478518^262144 + 1	28 March 2025	2,034,108
406	57429230^262144 + 1	27 March 2025	2,034,111
407	51×2^6753404 + 1	26 May 2020	2,032,979
408	93×2^6750726 + 1	18 September 2023	2,032,173
409	56303352^262144 + 1	27 March 2025	2,031,757
410	56295176^262144 + 1	26 March 2025	2,031,740
411	55952434^262144 + 1	26 March 2025	2,031,045
412	55892864^262144 + 1	27 March 2025	2,030,920
413	69×2^6745775 + 1	21 March 2023	2,030,683
414	55702322^262144 + 1	27 March 2025	2,030,535
415	55695224^262144 + 1	25 March 2025	2,030,520
416	55169618^262144 + 1	25 March 2025	2,029,441
417	55007338^262144 + 1	25 March 2025	2,029,105
418	54852328^262144 + 1	25 March 2025	2,028,784
419	54528918^262144 + 1	26 March 2025	2,028,111
420	54044092^262144 + 1	24 March 2025	2,027,094
421	53903472^262144 + 1	24 March 2025	2,026,797
422	53750036^262144 + 1	24 March 2025	2,026,473
423	53616962^262144 + 1	28 March 2025	2,026,191
424	53311612^262144 + 1	24 March 2025	2,025,540
425	4681×2^6728157 − 1	25 August 2025	2,025,381
426	53008094^262144 + 1	23 March 2025	2,024,890
427	52648144^262144 + 1	21 March 2025	2,024,115
428	52599274^262144 + 1	20 March 2025	2,024,009
429	52592976^262144 + 1	21 March 2025	2,023,995
430	117×2^6719464 + 1	10 May 2025	2,022,763
431	51992174^262144 + 1	16 March 2025	2,022,687
432	51852794^262144 + 1	14 March 2025	2,022,382
433	51714136^262144 + 1	13 March 2025	2,022,077
434	51283286^262144 + 1	9 March 2025	2,021,124
435	51125138^262144 + 1	7 March 2025	2,020,773
436	9995×2^6711008 − 1	31 December 2020	2,020,219
437	50454356^262144 + 1	1 March 2025	2,019,269
438	50449664^262144 + 1	28 February 2025	2,019,259
439	50366208^262144 + 1	28 February 2025	2,019,070
440	50121532^262144 + 1	27 February 2025	2,018,516
441	49536902^262144 + 1	25 February 2025	2,017,180
442	49235348^262144 + 1	23 February 2025	2,016,485
443	49209090^262144 + 1	23 February 2025	2,016,424
444	48055302^262144 + 1	18 February 2025	2,013,723
445	47707672^262144 + 1	16 February 2025	2,012,896
446	39×2^6684941 + 1 [115]	20 October 2020	2,012,370
447	47351862^262144 + 1	15 February 2025	2,012,044
448	47281922^262144 + 1	13 February 2025	2,011,876
449	47255958^262144 + 1	13 February 2025	2,011,813
450	6679881×2^6679881 + 1 [116]	25 July 2009	2,010,852
451	46831458^262144 + 1	11 February 2025	2,010,786
452	46378776^262144 + 1	8 February 2025	2,009,680
453	45073202^262144 + 1	21 January 2025	2,006,469
454	45007104^262144 + 1	19 January 2025	2,006,202
455	44819108^262144 + 1	14 January 2025	2,005,786
456	44666524^262144 + 1	12 January 2025	2,005,397
457	37×2^6660841 − 1 [84]	30 July 2014	2,005,115
458	44144624^262144 + 1	29 December 2024	2,004,059
459	44030166^262144 + 1	30 December 2024	2,003,764
460	43330794^262144 + 1	3 December 2024	2,001,941
461	39×2^6648997 + 1 [117]	20 October 2020	2,001,550
462	42781592^262144 + 1	18 November 2024	2,000,489
463	10^2000007 − 10^1127194 − 10^872812 − 1	12 January 2024	2,000,007
464	10^2000005 − 10^1051046 − 10^948958 − 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[118]	Number	Discovery date	Decimal digits
1	${\displaystyle {\tfrac {10^{8177207}-1}{9}}}$ [118]	8 May 2021	8,177,207
2	${\displaystyle {\tfrac {10^{5794777}-1}{9}}}$ [118]	19 April 2021	5,794,777
3	${\displaystyle {\tfrac {2^{15135397}+1}{3}}}$ [118]	June 2021	4,556,209
4	${\displaystyle {\tfrac {3^{8530117}-1}{2}}}$ [118]	November 2023	4,069,900
5	2^13380298 − 27 [118]	March 2021	4,027,872
6	${\displaystyle {\tfrac {2^{13372531}+1}{3}}}$ [118]	September 2013	4,025,533
7	${\displaystyle {\tfrac {2^{13347311}+1}{3}}}$ [118]	September 2013	4,017,941
8	${\displaystyle {\tfrac {2^{12720787}-1}{1666870069020922905132673131516413926009285199}}}$ [118]	3 July 2022	3,829,294
9	${\displaystyle {\tfrac {3^{7973131}-1}{2}}}$ [118]	November 2023	3,804,150
10	${\displaystyle {\tfrac {2^{12588091}-1}{32075464348897282169539424801}}}$ [118]	10 April 2023	3,789,365
11	${\displaystyle {\tfrac {2^{12503723}-2^{6251862}+1}{5}}}$ [118]	July 2020	3,763,995
12	${\displaystyle {\tfrac {5^{5154509}-1}{4}}}$ [118]	February 2024	3,602,847
13	${\displaystyle {\tfrac {5^{4939471}-1}{4}}}$ [118]	January 2024	3,452,542
14	${\displaystyle {\tfrac {3^{7034611}+1}{4}}}$ [118]	December 2024	3,356,362
15	${\displaystyle {\tfrac {2^{10443557}-1}{37289325994807}}}$ [118]	9 July 2020	3,143,811
16	2^9092392 + 40291 [118]	February 2011	2,737,083
17	${\displaystyle {\tfrac {14^{2307467}+1}{15}}}$ [118]	June 2025	2,644,652
18	${\displaystyle {\tfrac {6^{3360347}-1}{5}}}$ [118]	October 2023	2,614,858
19	F(11964299) [118]	28 June 2025	2,500,391
20	${\displaystyle {\tfrac {2^{8247949}-1}{45487316822291087700751210632267642069671672071}}}$ [118]	3 June 2024	2,482,834
21	${\displaystyle {\tfrac {17^{1990523}-1}{16}}}$ [118]	August 2020	2,449,236
22	${\displaystyle {\tfrac {35963^{524288}+1}{2}}}$ [118]	August 2022	2,388,581
23	500186^54465 + 54465^500186 [118]	August 2024	2,368,940
24	${\displaystyle {\tfrac {11^{2264611}+1}{12}}}$ [118]	July 2021	2,358,349
25	${\displaystyle {\tfrac {5^{3300593}-1}{4}}}$ [118]	February 2022	2,307,015
26	${\displaystyle {\tfrac {3^{4694803}+2^{4694803}}{5}}}$ [118]	December 2023	2,239,990
27	${\displaystyle {\tfrac {2^{7313983}-1}{305492080276193}}}$ [118]	1 March 2018	2,201,714
28	${\displaystyle {\tfrac {3^{4571447}+2^{4571447}}{5}}}$ [118]	December 2023	2,181,134
29	${\displaystyle {\tfrac {15^{1848811}+1}{16}}}$ [118]	July 2024	2,174,370
30	F(10367321) [118]	10 August 2024	2,166,642
31	${\displaystyle {\tfrac {15^{1841911}+1}{16}}}$ [118]	July 2024	2,166,255
32	3^4532794 + 4532794^3 [118]	October 2023	2,162,693
33	F(10317107) [118]	27 July 2024	2,156,148
34	${\displaystyle {\tfrac {2^{7080247}-1}{17045259548603283727480473638587228614426296913631}}}$ [118]	27 October 2017	2,131,318
35	360834^356345 + 356345^360834 [118]	February 2024	2,003,304
36	360339^356572 + 356572^360339 [118]	May 2024	2,000,656

See also

• Largest known prime number

References

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.
8. Official announcement of discovery of 2524190^2097152 + 1, PrimeGrid
9. "Official press release of 45th and 46th Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 10 September 2008.
10. "Official press release of 47th Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 25 January 2013.
11. "PrimePage Primes: Phi(3, - 516693^1048576)". t5k.org. Retrieved 18 October 2024.
12. "PrimePage Primes: Phi(3, - 465859^1048576)". t5k.org. Retrieved 18 October 2024.
13. "Official press release of 44th Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 25 January 2013.
14. Official announcement of discovery of 10223×2^31172165 + 1, PrimeGrid
15. "Official press release of 43rd Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 25 January 2013.
16. "Official press release of 42nd Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 25 January 2013.
17. Official announcement of discovery of 4052186×69^4052186 + 1, PrimeGrid
18. "Official press release of 41st Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 25 January 2013.
19. Official announcement of discovery of 5336284^1048576 + 1, PrimeGrid
20. Official announcement of discovery of 3×2^23157875 − 1, PrimeGrid
21. Official announcement of discovery of 3843236^1048576 + 1, PrimeGrid
22. Official announcement of discovery of 3×2^22103376 − 1, PrimeGrid
23. Official announcement of discovery of 1963736^1048576 + 1, PrimeGrid
24. Official announcement of discovery of 1951734^1048576 + 1, PrimeGrid
25. Official announcement of discovery of 202705×2^21320516 + 1, PrimeGrid
26. "Official press release of 40th Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 25 January 2013.
27. Official announcement of discovery of 1059094^1048576 + 1, PrimeGrid
28. Official announcement of discovery of 3×2^20928756 − 1, PrimeGrid
29. Official announcement of discovery of 919444^1048576 + 1, PrimeGrid
30. Official announcement of discovery of 168451×2^19375200 + 1, PrimeGrid
31. Official announcement of discovery of 3×2^18924888 − 1, PrimeGrid
32. Official announcement of discovery of 3×2^18196595 − 1, PrimeGrid
33. Official announcement of discovery of 3×2^17748034 − 1, PrimeGrid
34. Official announcement of discovery of 8508301×2^17016603 − 1, PrimeGrid
35. Official announcement of discovery of 3×2^16819291 − 1, PrimeGrid
36. Official announcement of discovery of 3×2^16408818 + 1, PrimeGrid
37. Official announcement of discovery of 2525332×73^2525332 + 1, PrimeGrid
38. Official announcement of discovery of 99739×2^14019102 + 1, PrimeGrid
39. "Official press release of 39th Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 25 January 2013.
40. Official announcement of discovery of 2805222×5^5610444 + 1, PrimeGrid
41. Chris Caldwell, The Largest Known Primes at The PrimePages.
42. Official announcement of discovery of 67612×5^5501582 + 1, PrimeGrid
43. Official announcement of discovery of 17544674⁵²⁴²⁸⁸ + 1, PrimeGrid
44. Official announcement of discovery of 17502532⁵²⁴²⁸⁸ + 1, PrimeGrid
45. Official announcement of discovery of 17177670⁵²⁴²⁸⁸ + 1, PrimeGrid
46. Official announcement of discovery of 17177670⁵²⁴²⁸⁸ + 1, PrimeGrid
47. Official announcement of discovery of 16211276⁵²⁴²⁸⁸ + 1, PrimeGrid
48. Official announcement of discovery of 15958750⁵²⁴²⁸⁸ + 1, PrimeGrid
49. Official announcement of discovery of 15852200⁵²⁴²⁸⁸ + 1, PrimeGrid
50. Official announcement of discovery of 13520762⁵²⁴²⁸⁸ + 1, PrimeGrid
51. Official announcement of discovery of 13427472⁵²⁴²⁸⁸ + 1, PrimeGrid
52. Official announcement of discovery of 12900356⁵²⁴²⁸⁸ + 1, PrimeGrid
53. Official announcement of discovery of 12693488⁵²⁴²⁸⁸ + 1, PrimeGrid
54. Official announcement of discovery of 11937916⁵²⁴²⁸⁸ + 1, PrimeGrid
55. Official announcement of discovery of 10913140⁵²⁴²⁸⁸ + 1, PrimeGrid
56. Official announcement of discovery of 9332124⁵²⁴²⁸⁸ + 1, PrimeGrid
57. Official announcement of discovery of 8630170⁵²⁴²⁸⁸ + 1, PrimeGrid
58. Official announcement of discovery of 3×2^11895718−1, PrimeGrid
59. Official announcement of discovery of 6339004⁵²⁴²⁸⁸ + 1, PrimeGrid
60. Official announcement of discovery of 3×2^11731850 − 1, PrimeGrid
61. Official announcement of discovery of 4896418⁵²⁴²⁸⁸ + 1, PrimeGrid
62. Official announcement of discovery of 3×2^11484018 − 1, PrimeGrid
63. Official announcement of discovery of 193997×2^11452891 + 1, PrimeGrid
64. Official announcement of discovery of 3638450⁵²⁴²⁸⁸ + 1, PrimeGrid
65. Official announcement of discovery of 9221×2^11392194 − 1, PrimeGrid
66. Official announcement of discovery of 3214654⁵²⁴²⁸⁸ + 1, PrimeGrid
67. Official announcement of discovery of 146561×2^11280802 − 1, PrimeGrid
68. Official announcement of discovery of 2985036⁵²⁴²⁸⁸ + 1, PrimeGrid
69. Official announcement of discovery of 2877652⁵²⁴²⁸⁸ + 1, PrimeGrid
70. Official announcement of discovery of 2788032⁵²⁴²⁸⁸ + 1, PrimeGrid
71. Official announcement of discovery of 2733014⁵²⁴²⁸⁸ + 1, PrimeGrid
72. Official announcement of discovery of 2312092⁵²⁴²⁸⁸ + 1, PrimeGrid
73. Official announcement of discovery of 2061748⁵²⁴²⁸⁸ + 1, PrimeGrid
74. Official announcement of discovery of 1880370⁵²⁴²⁸⁸ + 1, PrimeGrid
75. Official announcement of discovery of 3×2^10829346 + 1, PrimeGrid
76. Official announcement of discovery of 475856⁵²⁴²⁸⁸ + 1, PrimeGrid
77. Official announcement of discovery of 356926⁵²⁴²⁸⁸ + 1, PrimeGrid
78. Official announcement of discovery of 341112⁵²⁴²⁸⁸ + 1, PrimeGrid
79. Official announcement of discovery of 121×2^9584444 + 1, PrimeGrid
80. Official announcement of discovery of 1323365×116^1323365 + 1, PrimeGrid
81. Official announcement of discovery of 63838×5^3887851 − 1, PrimeGrid
82. Official announcement of discovery of 273809×2^8932416 − 1, PrimeGrid
83. Official announcement of discovery of 25×2^8788628 + 1, PrimeGrid
84. "CRUS - Proven Conjectures". www.noprimeleftbehind.net.
85. Official announcement of discovery of 17×2^8636199 + 1, PrimeGrid
86. Official announcement of discovery of 75898⁵²⁴²⁸⁸ + 1, PrimeGrid
87. Official announcement of discovery of 25×2^8456828 + 1, PrimeGrid
88. Official announcement of discovery of 39×2^8413822 + 1, PrimeGrid
89. Official announcement of discovery of 31×2^8348000 + 1, PrimeGrid
90. Official announcement of discovery of 27×2^8342438 − 1, PrimeGrid
91. Official announcement of discovery of 273662×5^3493296 + 1, PrimeGrid
92. 102818×5^3440382 − 1, PrimeGrid
93. Official announcement of discovery of 27×2^7963247 + 1, PrimeGrid
94. Official announcement of discovery of 39×2^7946769 + 1, PrimeGrid
95. Official announcement of discovery of 29×2^7899985 + 1, PrimeGrid
96. Official announcement of discovery of 1341174×53^1341174 + 1, PrimeGrid
97. Official announcement of discovery of 45×2^7661004 + 1, PrimeGrid
98. Official announcement of discovery of 15×2^7619838 + 1, PrimeGrid
99. Official announcement of discovery of 45×2^7513661 + 1, PrimeGrid
100. Official announcement of discovery of 29×2^7374577 + 1, PrimeGrid
101. 109838×5^3168862 − 1, PrimeGrid
102. Official announcement of discovery of 29×2^7300254 + 1, PrimeGrid
103. 118568×5^3112069 + 1, PrimeGrid
104. Official announcement of discovery of 502573×2^7181987 − 1, PrimeGrid
105. Official announcement of discovery of 402539×2^7173024 − 1, PrimeGrid
106. Official announcement of discovery of 161041×2^7107964 + 1, PrimeGrid
107. Official announcement of discovery of 27×2^7046834 + 1, PrimeGrid
108. Official announcement of discovery of 3×2^7033641 + 1, PrimeGrid
109. GIMPS press release, GIMPS Finds First Million-Digit Prime. Retrieved on 2008-01-04.
110. 238694×5^2979422 − 1, PrimeGrid
111. 146264×5^2953282 − 1, PrimeGrid
112. 35816×5^2945294 − 1, PrimeGrid
113. Official announcement of discovery of 19×2^6833086 + 1, PrimeGrid
114. Official announcement of discovery of 40597×2^6808509 − 1, PrimeGrid
115. Official announcement of discovery of 39×2^6684941 + 1, PrimeGrid
116. Official announcement of discovery of 6679881×2^6679881 + 1, PrimeGrid
117. Official announcement of discovery of 39×2^6648997 + 1, PrimeGrid
118. 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