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	2136279841 − 1 [3]	12 October 2024	41,024,320
2	282589933 − 1 [4]	7 December 2018	24,862,048
3	277232917 − 1 [5]	26 December 2017	23,249,425
4	274207281 − 1 [6]	7 January 2016	22,338,618
5	257885161 − 1 [7]	25 January 2013	17,425,170
6	25241902097152 + 1 [8]	12 October 2025	13,426,224
7	243112609 − 1 [9]	23 August 2008	12,978,189
8	242643801 − 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	237156667 − 1 [9]	6 September 2008	11,185,272
12	232582657 − 1 [13]	4 September 2006	9,808,358
13	10223×231172165 + 1 [14]	31 October 2016	9,383,761
14	230402457 − 1 [15]	15 December 2005	9,152,052
15	4×511786358 + 1	1 October 2024	8,238,312
16	225964951 − 1 [16]	18 February 2005	7,816,230
17	4052186×694052186 + 1 [17]	16 April 2025	7,451,366
18	69×224612729 − 1	13 August 2024	7,409,172
19	224036583 − 1 [18]	15 May 2004	7,235,733
20	53362841048576 + 1 [19]	31 October 2025	7,054,022
21	107347×223427517 − 1	4 August 2024	7,052,391
22	3×223157875 − 1 [20]	25 June 2025	6,971,216
23	38432361048576 + 1 [21]	17 December 2024	6,904,556
24	3×222103376 − 1 [22]	30 September 2024	6,653,780
25	19637361048576 + 1 [23]	24 September 2022	6,598,776
26	19517341048576 + 1 [24]	9 August 2022	6,595,985
27	202705×221320516 + 1 [25]	25 November 2021	6,418,121
28	220996011 − 1 [26]	17 November 2003	6,320,430
29	10590941048576 + 1 [27]	31 October 2018	6,317,602
30	3×220928756 − 1 [28]	5 July 2023	6,300,184
31	9194441048576 + 1 [29]	29 August 2017	6,253,210
32	81×220498148 + 1	13 June 2023	6,170,560
33	7×220267500 + 1	21 July 2022	6,101,127
34	4×58431178 + 1	2 January 2024	5,893,142
35	168451×219375200 + 1 [30]	17 September 2017	5,832,522
36	69×219374980 − 1	3 July 2022	5,832,452
37	3×218924888 − 1 [31]	24 March 2022	5,696,990
38	69×218831865 − 1	16 December 2021	5,668,959
39	2×311879700 + 1	22 June 2024	5,668,058
40	97139×218397548 − 1	23 April 2023	5,538,219
41	7×218233956 + 1	1 October 2020	5,488,969
42	3×218196595 − 1 [32]	8 January 2022	5,477,722
43	4×311279466 + 1	10 September 2024	5,381,674
44	3×217748034 − 1 [33]	6 September 2021	5,342,692
45	${\displaystyle \Phi _{3}(-123447^{524288})}$	23 February 2017	5,338,805
46	3622×57558139 − 1	18 February 2022	5,282,917
47	7×66772401 + 1	9 September 2019	5,269,954
48	2×310852677 + 1	8 January 2023	5,178,044
49	8508301×217016603 − 1 [34]	21 March 2018	5,122,515
50	8×105112848 − 1	30 January 2024	5,112,848
51	13×216828072 + 1	11 October 2023	5,065,756
52	3×216819291 − 1 [35]	20 January 2021	5,063,112
53	5287180×310574360 − 1	3 November 2024	5,045,259
54	3×216408818 + 1 [36]	25 October 2020	4,939,547
55	2329989×216309923 − 1	13 February 2024	4,909,783
56	69×215866556 + 1	20 August 2021	4,776,312
57	2036×310009192 + 1	15 February 2024	4,775,602
58	2525332×732525332 + 1 [37]	28 August 2021	4,705,888
59	1419499×215614489 + 1	9 February 2024	4,700,436
60	11×215502315 + 1	8 January 2023	4,666,663
61	(102332974 + 1)2 − 2	20 February 2024	4,665,949
62	37×215474010 + 1	8 November 2022	4,658,143
63	93839×215337656 − 1	28 November 2022	4,617,100
64	215317227+27658614 + 1	31 July 2020	4,610,945
65	13×215294536 + 1	30 September 2023	4,604,116
66	6×56546983 + 1	13 June 2020	4,576,146
67	4788920×39577840 − 1	14 February 2024	4,569,798
68	31×215145093 − 1	9 February 2025	4,559,129
69	69×214977631 − 1	3 December 2021	4,508,719
70	192971×214773498 − 1	7 March 2021	4,447,272
71	4×39214845 + 1	10 September 2024	4,396,600
72	9145334×39145334 + 1	25 December 2023	4,363,441
73	4×56181673 − 1	15 July 2022	4,320,805
74	396101×214259638 − 1	3 February 2024	4,292,585
75	6962×312863120 − 1	29 February 2020	4,269,952
76	37×214166940 + 1	24 June 2022	4,264,676
77	99739×214019102 + 1 [38]	24 December 2019	4,220,176
78	69×213832885 − 1	17 January 2022	4,164,116
79	9562633# + 1	25 June 2025	4,151,498
80	404849×213764867 + 1	10 March 2021	4,143,644
81	25×213719266 + 1	20 September 2022	4,129,912
82	81×213708272 + 1	11 October 2022	4,126,603
83	2740879×213704395 − 1	26 October 2019	4,125,441
84	479216×38625889 − 1	16 November 2019	4,115,601
85	13×213584543 − 1	30 May 2025	4,089,357
86	31×213514933 − 1	9 February 2025	4,068,402
87	${\displaystyle \Phi _{3}(-143332^{393216})}$	30 January 2017	4,055,114
88	81×213470584 + 1	9 October 2022	4,055,052
89	213466917 − 1 [39]	14 November 2001	4,053,946
90	5778486×55778486 + 1	15 August 2024	4,038,996
91	9×213334487 + 1	31 March 2020	4,014,082
92	206039×213104952 − 1	26 April 2021	3,944,989
93	2805222×55610444 + 1 [40]	2 September 2019	3,921,539
94	5128×222919993 + 1	5 December 2024	3,919,869
95	19249×213018586 + 1 [41]	26 March 2007	3,918,990
96	2293×212918431 − 1	13 February 2021	3,888,839
97	81×212804541 + 1	19 September 2022	3,854,553
98	67612×55501582 + 1 [42]	8 April 2025	3,845,446
99	18703062524288 + 1 [43]	9 December 2025	3,812,577
100	18529322524288 + 1 [44]	30 November 2025	3,810,452
101	18099898524288 + 1	1 September 2025	3,805,113
102	17997078524288 + 1 [45]	20 November 2025	3,803,816
103	17544674524288 + 1 [46]	25 October 2025	3,798,019
104	17502532524288 + 1 [47]	23 October 2025	3,797,471
105	17445908524288 + 1 [48]	19 October 2025	3,796,734
106	17177670524288 + 1 [49]	5 October 2025	3,793,205
107	16211276524288 + 1 [50]	9 August 2025	3,780,021
108	15958750524288 + 1 [51]	15 July 2025	3,776,446
109	15852200524288 + 1 [52]	8 July 2025	3,774,921
110	751882!/751879# + 1	7 December 2025	3,765,621
111	4×55380542 + 1	22 February 2023	3,760,839
112	13520762524288 + 1 [53]	25 February 2025	3,738,699
113	13427472524288 + 1 [54]	3 March 2025	3,737,122
114	9×212406887 + 1	29 March 2020	3,734,847
115	12900356524288 + 1 [55]	22 January 2025	3,728,004
116	12693488524288 + 1 [56]	6 January 2025	3,724,323
117	11937916524288 + 1 [57]	5 October 2024	3,710,349
118	7×212286041 − 1	10 June 2023	3,698,468
119	10913140524288 + 1 [58]	19 June 2024	3,689,913
120	69×212231580 − 1	27 July 2021	3,682,075
121	27×212184319 + 1	6 February 2021	3,667,847
122	9332124524288 + 1 [59]	22 June 2024	3,654,278
123	8630170524288 + 1 [60]	13 April 2024	3,636,472
124	863282×55179692 − 1	17 October 2024	3,620,456
125	670490×123352450 − 1	17 October 2024	3,617,907
126	4×37578378 + 1	9 September 2024	3,615,806
127	11×211993994 − 1	15 August 2024	3,610,554
128	3761×211978874 − 1	6 July 2022	3,606,004
129	95×211954552 − 1	28 May 2024	3,598,681
130	259072×55136295 − 1	28 October 2024	3,590,122
131	3×211895718 − 1 [61]	23 June 2015	3,580,969
132	37×211855148 + 1	30 May 2022	3,568,757
133	6339004524288 + 1 [62]	8 June 2023	3,566,218
134	763795×64582771 + 1	11 December 2023	3,566,095
135	5897794524288 + 1 [41]	18 December 2022	3,549,792
136	3×211731850 − 1 [63]	13 March 2015	3,531,640
137	69×211718455 − 1 [41]	4 December 2020	3,527,609
138	8629×211708579 − 1	19 September 2024	3,524,638
139	41×211676439 + 1 [41]	20 June 2022	3,514,960
140	4896418524288 + 1 [64]	15 May 2022	3,507,424
141	81×211616017 + 1 [41]	30 August 2022	3,496,772
142	69×211604348 − 1 [41]	4 December 2020	3,493,259
143	4450871×64450871 + 1 [41]	17 September 2023	3,463,458
144	9×211500843 + 1 [41]	13 March 2020	3,462,100
145	3×211484018 − 1 [65]	22 November 2014	3,457,035
146	193997×211452891 + 1 [66]	3 April 2018	3,447,670
147	29914×54930904 + 1	27 September 2024	3,446,559
148	3638450524288 + 1 [67]	29 May 2020	3,439,810
149	9221×211392194 − 1 [68]	7 February 2021	3,429,397
150	9×211366286 + 1	26 March 2020	3,421,594
151	${\displaystyle \Phi _{3}(-3328218^{262144})}$	29 December 2025	3,419,518
152	5×211355764 − 1	2 October 2021	3,418,427
153	732050×64392301 + 1	9 September 2023	3,417,881
154	${\displaystyle \Phi _{3}(-3268739^{262144})}$	10 November 2025	3,415,412
155	3214654524288 + 1 [69]	24 December 2019	3,411,613
156	632760! − 1	20 October 2024	3,395,992
157	146561×211280802 − 1 [70]	16 November 2020	3,395,865
158	51208×54857576 + 1	6 June 2024	3,395,305
159	2985036524288 + 1 [71]	18 September 2019	3,394,739
160	4591×211270837 − 1	2 January 2025	3,392,864
161	6929×211255424 − 1	7 July 2022	3,388,225
162	2877652524288 + 1 [72]	29 June 2019	3,386,397
163	2788032524288 + 1 [73]	17 April 2019	3,379,193
164	2733014524288 + 1 [74]	18 March 2019	3,374,655
165	${\displaystyle \Phi _{3}(-2637072^{262144})}$	4 December 2025	3,366,518
166	9×211158963 + 1	13 March 2020	3,359,184
167	9271×211134335 − 1	17 January 2021	3,351,773
168	136804×54777253 − 1	1 March 2024	3,339,162
169	2312092524288 + 1 [75]	4 August 2018	3,336,572
170	987324×481974648 − 1	12 October 2024	3,319,866
171	2061748524288 + 1 [76]	20 March 2018	3,310,478
172	1880370524288 + 1 [77]	15 January 2018	3,289,511
173	27×210902757 − 1	7 March 2022	3,282,059
174	3×210829346 + 1 [78]	14 January 2014	3,259,959
175	11×210803449 + 1	29 May 2022	3,252,164
176	11×210797109 + 1	29 May 2022	3,250,255
177	7×210612737 − 1	19 May 2022	3,194,154
178	7351117# + 1	14 September 2024	3,191,401
179	37×210599476 + 1	17 June 2022	3,190,762
180	5×210495620 − 1	26 September 2021	3,159,498
181	${\displaystyle {\tfrac {\Phi _{3}(-3^{3304302}+1)}{3}}}$	30 June 2023	3,153,105
182	5×210349000 − 1	26 September 2021	3,115,361
183	${\displaystyle \Phi _{3}(-844833^{262144})}$	17 January 2017	3,107,335
184	17×210248660 − 1	8 August 2025	3,085,156
185	52922×54399812 − 1	3 August 2023	3,075,342
186	${\displaystyle \Phi _{3}(-712012^{262144})}$	14 January 2017	3,068,389
187	177742×54386703 − 1	24 July 2023	3,066,180
188	4×36402015 + 1	9 September 2024	3,054,539
189	874208×541748416 − 1	26 September 2019	3,028,951
190	475856524288 + 1 [79]	8 August 2012	2,976,633
191	2×36236772 + 1	20 December 2022	2,975,697
192	15×39830108 + 1	19 August 2023	2,959,159
193	9×29778263 + 1	5 August 2020	2,943,552
194	198×5581061348 + 1	30 August 2024	2,915,138
195	1806676×411806676 + 1	11 March 2018	2,913,785
196	356926524288 + 1 [80]	20 June 2012	2,911,151
197	341112524288 + 1 [81]	15 June 2012	2,900,832
198	213988×54138363 − 1	29 November 2022	2,892,597
199	43×29596983 − 1	28 February 2022	2,888,982
200	121×29584444 + 1 [82]	18 November 2020	2,885,208
201	15×29482269 − 1	14 August 2024	2,854,449
202	6533299# − 1	18 August 2024	2,835,864
203	11×29381365 + 1	7 March 2020	2,824,074
204	15×29312889 + 1	7 August 2023	2,803,461
205	97×29305542 + 1	10 May 2025	2,801,250
206	93×29235048 + 1	7 May 2025	2,780,029
207	49×29187790 + 1	11 September 2022	2,765,803
208	6369619# + 1	12 August 2024	2,765,105
209	27653×29167433 + 1 [41]	8 June 2005	2,759,677
210	6354977# − 1	12 August 2024	2,758,832
211	90527×29162167 + 1	30 June 2010	2,758,093
212	6795×29144320 − 1	31 March 2021	2,752,719
213	31×29088085 − 1	27 August 2024	2,735,788
214	75×29079482 + 1	25 July 2023	2,733,199
215	1323365×1161323365 + 1 [83]	18 January 2018	2,732,038
216	57×29075622 − 1	7 August 2022	2,732,037
217	102718281 − 5×101631138 − 5×101087142 − 1	6 August 2024	2,718,281
218	63838×53887851 − 1 [84]	19 June 2022	2,717,497
219	13×28989858 + 1	10 March 2020	2,706,219
220	271357×28943013 − 1	13 October 2025	2,692,121
221	4159×28938471 − 1	19 April 2022	2,690,752
222	273809×28932416 − 1 [85]	13 December 2017	2,688,931
223	93×28898285 + 1	4 March 2024	2,678,653
224	2×35570081 + 1	14 February 2020	2,657,605
225	25×28788628 + 1 [86]	1 March 2021	2,645,643
226	2038×3661028507 − 1 [87]	4 April 2016	2,636,562
227	64598×53769854 − 1	14 June 2022	2,635,020
228	63×28741225 + 1	6 May 2024	2,631,373
229	8×785900325 + 1	4 June 2022	2,606,325
230	17×28636199 + 1 [88]	17 February 2021	2,599,757
231	75898524288 + 1 [89]	19 November 2011	2,558,647
232	25×28456828 + 1 [90]	27 January 2021	2,545,761
233	39×28413422 + 1 [91]	23 January 2021	2,532,694
234	31×28348000 + 1 [92]	19 January 2021	2,513,000
235	27×28342438 − 1 [93]	1 February 2021	2,511,326
236	17×28330892 − 1	16 July 2025	2,507,850
237	3867×28261084 − 1	14 April 2021	2,486,838
238	101×28152967 + 1	2 December 2023	2,454,290
239	9×28128075 − 1	8 July 2025	2,446,796
240	273662×53493296 − 1 [94]	7 December 2021	2,441,715
241	81×28109236 + 1	9 September 2022	2,441,126
242	11×28103463 + 1	6 March 2020	2,439,387
243	102818×53440382 − 1 [95]	8 October 2021	2,404,729
244	9×27979119 − 1	8 July 2025	2,401,956
245	11×27971110 − 1	25 November 2019	2,399,545
246	27×27963247 + 1 [96]	14 January 2021	2,397,178
247	3177×27954621 − 1	13 June 2021	2,394,584
248	39×27946769 + 1 [97]	14 January 2021	2,392,218
249	7×63072198 + 1	4 August 2019	2,390,636
250	3765×27904593 − 1	10 January 2021	2,379,524
251	29×27899985 + 1 [98]	14 January 2021	2,378,134
252	5113×27895471 − 1	27 November 2022	2,376,778
253	861×27895451 − 1	21 February 2021	2,376,771
254	75×27886683 + 1	4 September 2023	2,374,131
255	3243959×27862047 + 1	3 December 2025	2,366,719
256	2661×27861390 − 1	28 December 2024	2,366,518
257	21×27838882 − 1	15 August 2025	2,359,740
258	30397×27838120 + 1	17 August 2025	2,359,514
259	99×27830910 + 1	24 April 2024	2,357,341
260	28433×27830457 + 1 [41]	31 December 2004	2,357,207
261	2589×27803339 − 1	21 August 2022	2,349,043
262	59×27792307 + 1	24 April 2024	2,345,720
263	101×27784453 + 1	24 April 2024	2,343,356
264	95×27778585 + 1	24 April 2024	2,341,590
265	8401×27767655 − 1	24 April 2023	2,338,302
266	9693×27767343 − 1	17 November 2023	2,338,208
267	5×27755002 − 1	23 September 2021	2,334,489
268	2945×27753232 − 1	27 November 2022	2,333,959
269	2×836798431 + 1	10 September 2024	2,333,181
270	63×27743186 + 1	24 April 2024	2,330,934
271	2545×27732265 − 1	13 January 2021	2,327,648
272	5539×27730709 − 1	15 January 2021	2,327,180
273	4817×27719584 − 1	13 June 2021	2,323,831
274	183×558842752 + 1	23 August 2024	2,314,734
275	1341174×531341174 + 1 [99]	21 August 2017	2,312,561
276	9467×27680034 − 1	20 February 2022	2,311,925
277	45×27661004 + 1 [100]	13 December 2020	2,306,194
278	15×27619838 + 1 [101]	6 December 2020	2,293,801
279	3645×27610003 − 1	28 August 2025	2,290,843
280	3597×27580693 − 1	10 January 2021	2,282,020
281	5256037# + 1	6 August 2024	2,281,955
282	38118498221×27552807 + 1	7 October 2025	2,273,633
283	3129×27545557 − 1	14 March 2023	2,271,443
284	7401×27523295 − 1	21 February 2021	2,264,742
285	45×27513661 + 1 [102]	12 November 2020	2,261,839
286	${\displaystyle \Phi _{3}(-558640^{196608})}$	11 January 2017	2,259,865
287	2739×27483537 − 1	1 May 2025	2,252,773
288	9×27479919 − 1	3 June 2023	2,251,681
289	1875×27474308 − 1	21 August 2022	2,249,995
290	69×27452023 + 1	23 March 2023	2,243,285
291	1281879×27447178 + 1	27 December 2023	2,241,831
292	9107×27417464 − 1	3 May 2025	2,232,884
293	4×53189669 − 1	12 July 2022	2,229,484
294	19×27383785 − 1	11 July 2025	2,222,743
295	29×27374577 + 1 [103]	27 October 2020	2,219,971
296	2653×27368343 − 1	18 September 2024	2,218,096
297	21555×27364128 − 1	4 September 2024	2,216,828
298	3197×27359542 − 1	27 November 2022	2,215,447
299	109838×53168862 − 1 [104]	13 August 2020	2,214,945
300	95×27354869 + 1	25 September 2023	2,214,039
301	101×27345194 − 1	5 October 2019	2,211,126
302	85×27333444 + 1	25 September 2023	2,207,589
303	15×27300254 + 1 [105]	25 October 2020	2,197,597
304	6733×27285527 − 1	26 October 2025	2,193,166
305	422429! + 1	21 February 2022	2,193,027
306	1759×27284439 − 1	28 August 2021	2,192,838
307	1909683×141909683 + 1	27 May 2023	2,188,748
308	737×27269322 − 1	10 August 2017	2,188,287
309	6909×27258896 − 1	18 September 2024	2,185,150
310	93×27241494 + 1	25 September 2023	2,179,909
311	118568×53112069 + 1 [106]	1 May 2020	2,175,248
312	4215×27221386 − 1	27 December 2024	2,173,858
313	40×257901632 + 1	11 September 2024	2,172,875
314	1685×27213108 − 1	13 April 2025	2,171,366
315	580633×27208783 − 1	15 February 2024	2,170,066
316	6039×27207973 − 1	24 March 2021	2,169,820
317	1871×27207954 − 1	26 September 2025	2,169,814
318	502573×27181987 − 1 [107]	4 October 2014	2,162,000
319	402539×27173024 − 1 [108]	2 October 2014	2,159,301
320	3343×27166019 − 1	29 September 2016	2,157,191
321	4137×27132569 − 1	11 April 2025	2,147,121
322	161041×27107964 + 1 [109]	6 January 2015	2,139,716
323	294×213918952 − 1	19 September 2023	2,139,672
324	17×27101254 − 1	11 July 2025	2,137,692
325	27×27046834 + 1 [110]	11 October 2018	2,121,310
326	1759×27046791 − 1	28 August 2021	2,121,299
327	327×27044001 − 1	13 January 2021	2,120,459
328	5×27037188 − 1	22 September 2021	2,118,406
329	3×27033641 + 1 [111]	21 February 2011	2,117,338
330	625783×27031319 − 1	10 February 2024	2,116,644
331	33661×27031232 + 1 [41]	30 October 2007	2,116,617
332	${\displaystyle \Phi _{3}(-237804^{196608})}$	6 January 2017	2,114,016
333	207494×53017502 − 1	16 March 2020	2,109,149
334	15×26993631 − 1	25 August 2021	2,105,294
335	8943501×26972593 − 1	8 January 2022	2,098,967
336	6020095×26972593 − 1	4 September 2022	2,098,967
337	26972593 − 1 [112]	1 June 1999	2,098,960
338	273×26963847 − 1	16 November 2022	2,096,330
339	6219×26958945 − 1	7 January 2021	2,094,855
340	51×26945567 + 1	26 May 2020	2,090,826
341	8×102084563 − 1	1 June 2025	2,084,564
342	3323×26921196 − 1	18 September 2024	2,083,492
343	238694×52979422 − 1 [113]	12 March 2020	2,082,532
344	4×721119849 − 1 [87]	7 September 2016	2,079,933
345	129×26900230 + 1	5 June 2025	2,077,179
346	33×26894190 − 1	27 July 2021	2,075,360
347	4778027# − 1	31 July 2024	2,073,926
348	105×26884697 + 1	2 June 2025	2,072,503
349	2345×26882320 − 1	13 April 2022	2,071,789
350	76013952262144 + 1	25 December 2025	2,065,929
351	75810636262144 + 1	20 December 2025	2,065,624
352	75753274262144 + 1	20 December 2025	2,065,538
353	57×26857990 + 1	17 August 2023	2,064,463
354	146264×52953282 − 1 [114]	9 March 2020	2,064,261
355	74732694262144 + 1	10 December 2025	2,063,994
356	74716572262144 + 1	10 December 2025	2,063,970
357	74399970262144 + 1	5 December 2025	2,063,486
358	74336726262144 + 1	4 December 2025	2,063,389
359	73597220262144 + 1	25 November 2025	2,062,251
360	73589294262144 + 1	24 November 2025	2,062,239
361	73465436262144 + 1	21 November 2025	2,062,047
362	73116844262144 + 1	13 November 2025	2,061,505
363	72862906262144 + 1	9 November 2025	2,061,109
364	72752758262144 + 1	4 November 2025	2,060,937
365	72718062262144 + 1	4 November 2025	2,060,883
366	72071732262144 + 1	22 October 2025	2,059,866
367	71737620262144 + 1	18 October 2025	2,059,337
368	71380700262144 + 1	13 October 2025	2,058,770
369	69×26838971 − 1	1 March 2020	2,058,738
370	35816×52945294 − 1 [115]	5 March 2020	2,058,677
371	71107798262144 + 1	11 October 2025	2,058,333
372	127×26836153 − 1	25 June 2018	2,057,890
373	105×26835099 + 1	26 May 2025	2,057,572
374	70520422262144 + 1	29 September 2025	2,057,389
375	70349734262144 + 1	27 September 2025	2,057,113
376	19×26833086 + 1 [116]	24 October 2020	2,056,966
377	69844790262144 + 1	22 September 2025	2,056,293
378	69810332262144 + 1	22 September 2025	2,056,237
379	69290228262144 + 1	20 September 2025	2,055,386
380	69170386262144 + 1	13 September 2025	2,055,189
381	68717884262144 + 1	30 August 2025	2,054,441
382	68000464262144 + 1	10 August 2025	2,053,246
383	67886950262144 + 1	9 August 2025	2,053,056
384	67673558262144 + 1	5 August 2025	2,052,698
385	67535128262144 + 1	2 August 2025	2,052,465
386	67433562262144 + 1	2 August 2025	2,052,293
387	67167678262144 + 1	24 July 2025	2,051,844
388	67141518262144 + 1	24 July 2025	2,051,799
389	67062340262144 + 1	22 July 2025	2,051,665
390	66498472262144 + 1	8 July 2025	2,050,704
391	66342922262144 + 1	4 July 2025	2,050,437
392	66266188262144 + 1	3 July 2025	2,050,305
393	65×26810465 + 1	22 September 2023	2,050,157
394	40597×26808509 − 1 [117]	25 December 2013	2,049,571
395	283×26804701 − 1	19 January 2020	2,048,431
396	65136498262144 + 1	20 June 2025	2,048,348
397	64989720262144 + 1	18 June 2025	2,048,091
398	64074894262144 + 1	30 May 2025	2,046,447
399	64010198262144 + 1	30 May 2025	2,046,362
400	63833640262144 + 1	27 May 2025	2,046,047
401	8×102045966 − 1	31 May 2025	2,045,967
402	63784742262144 + 1	26 May 2025	2,045,960
403	63558122262144 + 1	27 May 2025	2,045,555
404	63448958262144 + 1	22 May 2025	2,045,359
405	63286690262144 + 1	19 May 2025	2,045,068
406	62767176262144 + 1	9 May 2025	2,044,129
407	62747994262144 + 1	9 May 2025	2,044,095
408	1861209×26789999 + 1	2 December 2020	2,044,000
409	5817×26789459 − 1	9 January 2021	2,043,835
410	62311952262144 + 1	3 May 2025	2,043,301
411	62199610262144 + 1	5 May 2025	2,043,095
412	62152830262144 + 1	1 May 2025	2,043,010
413	62136706262144 + 1	2 May 2025	2,042,980
414	8435×26786180 − 1	7 January 2021	2,042,848
415	61238184262144 + 1	21 April 2025	2,041,322
416	119×26777781 + 1	18 May 2025	2,040,318
417	59145944262144 + 1	29 March 2025	2,037,364
418	58936230262144 + 1	28 March 2025	2,036,960
419	58870004262144 + 1	28 March 2025	2,036,832
420	58846688262144 + 1	28 March 2025	2,036,787
421	58333324262144 + 1	28 March 2025	2,035,789
422	58288282262144 + 1	28 March 2025	2,035,701
423	57643582262144 + 1	28 March 2025	2,034,435
424	57594478262144 + 1	28 March 2025	2,034,338
425	57478518262144 + 1	28 March 2025	2,034,108
426	57429230262144 + 1	27 March 2025	2,034,111
427	51×26753404 + 1	26 May 2020	2,032,979
428	93×26750726 + 1	18 September 2023	2,032,173
429	56303352262144 + 1	27 March 2025	2,031,757
430	56295176262144 + 1	26 March 2025	2,031,740
431	55952434262144 + 1	26 March 2025	2,031,045
432	55892864262144 + 1	27 March 2025	2,030,920
433	69×26745775 + 1	21 March 2023	2,030,683
434	55702322262144 + 1	27 March 2025	2,030,535
435	55695224262144 + 1	25 March 2025	2,030,520
436	55169618262144 + 1	25 March 2025	2,029,441
437	55007338262144 + 1	25 March 2025	2,029,105
438	54852328262144 + 1	25 March 2025	2,028,784
439	54528918262144 + 1	26 March 2025	2,028,111
440	54044092262144 + 1	24 March 2025	2,027,094
441	53903472262144 + 1	24 March 2025	2,026,797
442	53750036262144 + 1	24 March 2025	2,026,473
443	53616962262144 + 1	28 March 2025	2,026,191
444	53311612262144 + 1	24 March 2025	2,025,540
445	4681×26728157 − 1	25 August 2025	2,025,381
446	53008094262144 + 1	23 March 2025	2,024,890
447	52648144262144 + 1	21 March 2025	2,024,115
448	52599274262144 + 1	20 March 2025	2,024,009
449	52592976262144 + 1	21 March 2025	2,023,995
450	117×26719464 + 1	10 May 2025	2,022,763
451	51992174262144 + 1	16 March 2025	2,022,687
452	51852794262144 + 1	14 March 2025	2,022,382
453	51714136262144 + 1	13 March 2025	2,022,077
454	51283286262144 + 1	9 March 2025	2,021,124
455	51125138262144 + 1	7 March 2025	2,020,773
456	9995×26711008 − 1	31 December 2020	2,020,219
457	50454356262144 + 1	1 March 2025	2,019,269
458	50449664262144 + 1	28 February 2025	2,019,259
459	50366208262144 + 1	28 February 2025	2,019,070
460	50121532262144 + 1	27 February 2025	2,018,516
461	49536902262144 + 1	25 February 2025	2,017,180
462	49235348262144 + 1	23 February 2025	2,016,485
463	49209090262144 + 1	23 February 2025	2,016,424
464	48055302262144 + 1	18 February 2025	2,013,723
465	47707672262144 + 1	16 February 2025	2,012,896
466	39×26684941 + 1 [118]	20 October 2020	2,012,370
467	47351862262144 + 1	15 February 2025	2,012,044
468	47281922262144 + 1	13 February 2025	2,011,876
469	47255958262144 + 1	13 February 2025	2,011,813
470	6679881×26679881 + 1 [119]	25 July 2009	2,010,852
471	46831458262144 + 1	11 February 2025	2,010,786
472	46378776262144 + 1	8 February 2025	2,009,680
473	45073202262144 + 1	21 January 2025	2,006,469
474	45007104262144 + 1	19 January 2025	2,006,202
475	44819108262144 + 1	14 January 2025	2,005,786
476	44666524262144 + 1	12 January 2025	2,005,397
477	37×26660841 − 1 [87]	30 July 2014	2,005,115
478	44144624262144 + 1	29 December 2024	2,004,059
479	44030166262144 + 1	30 December 2024	2,003,764
480	43330794262144 + 1	3 December 2024	2,001,941
481	39×26648997 + 1 [120]	20 October 2020	2,001,550
482	42781592262144 + 1	18 November 2024	2,000,489
483	102000007 − 101127194 − 10872812 − 1	12 January 2024	2,000,007
484	102000005 − 101051046 − 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 [121]	Number	Discovery date	Decimal digits
1	${\displaystyle {\tfrac {10^{8177207}-1}{9}}}$ [121]	8 May 2021	8,177,207
2	${\displaystyle {\tfrac {10^{5794777}-1}{9}}}$ [121]	19 April 2021	5,794,777
3	${\displaystyle {\tfrac {2^{15135397}+1}{3}}}$ [121]	June 2021	4,556,209
4	${\displaystyle {\tfrac {3^{8530117}-1}{2}}}$ [121]	November 2023	4,069,900
5	213380298 − 27 [121]	March 2021	4,027,872
6	${\displaystyle {\tfrac {2^{13372531}+1}{3}}}$ [121]	September 2013	4,025,533
7	${\displaystyle {\tfrac {2^{13347311}+1}{3}}}$ [121]	September 2013	4,017,941
8	${\displaystyle {\tfrac {2^{12720787}-1}{1666870069020922905132673131516413926009285199}}}$ [121]	3 July 2022	3,829,294
9	${\displaystyle {\tfrac {3^{7973131}-1}{2}}}$ [121]	November 2023	3,804,150
10	${\displaystyle {\tfrac {2^{12588091}-1}{32075464348897282169539424801}}}$ [121]	10 April 2023	3,789,365
11	${\displaystyle {\tfrac {2^{12503723}-2^{6251862}+1}{5}}}$ [121]	July 2020	3,763,995
12	${\displaystyle {\tfrac {5^{5154509}-1}{4}}}$ [121]	February 2024	3,602,847
13	${\displaystyle {\tfrac {5^{4939471}-1}{4}}}$ [121]	January 2024	3,452,542
14	${\displaystyle {\tfrac {3^{7034611}+1}{4}}}$ [121]	December 2024	3,356,362
15	${\displaystyle {\tfrac {2^{10443557}-1}{37289325994807}}}$ [121]	9 July 2020	3,143,811
16	29092392 + 40291 [121]	February 2011	2,737,083
17	${\displaystyle {\tfrac {14^{2307467}+1}{15}}}$ [121]	June 2025	2,644,652
18	${\displaystyle {\tfrac {6^{3360347}-1}{5}}}$ [121]	October 2023	2,614,858
19	F(11964299) [121]	28 June 2025	2,500,391
20	${\displaystyle {\tfrac {2^{8247949}-1}{45487316822291087700751210632267642069671672071}}}$ [121]	3 June 2024	2,482,834
21	${\displaystyle {\tfrac {17^{1990523}-1}{16}}}$ [121]	August 2020	2,449,236
22	${\displaystyle {\tfrac {35963^{524288}+1}{2}}}$ [121]	August 2022	2,388,581
23	50018654465 + 54465500186 [121]	August 2024	2,368,940
24	${\displaystyle {\tfrac {11^{2264611}+1}{12}}}$ [121]	July 2021	2,358,349
25	${\displaystyle {\tfrac {5^{3300593}-1}{4}}}$ [121]	February 2022	2,307,015
26	${\displaystyle {\tfrac {3^{4694803}+2^{4694803}}{5}}}$ [121]	December 2023	2,239,990
27	${\displaystyle {\tfrac {2^{7313983}-1}{305492080276193}}}$ [121]	1 March 2018	2,201,714
28	${\displaystyle {\tfrac {3^{4571447}+2^{4571447}}{5}}}$ [121]	December 2023	2,181,134
29	${\displaystyle {\tfrac {15^{1848811}+1}{16}}}$ [121]	July 2024	2,174,370
30	F(10367321) [121]	10 August 2024	2,166,642
31	${\displaystyle {\tfrac {15^{1841911}+1}{16}}}$ [121]	July 2024	2,166,255
32	34532794 + 45327943 [121]	October 2023	2,162,693
33	F(10317107) [121]	27 July 2024	2,156,148
34	${\displaystyle {\tfrac {2^{7080247}-1}{17045259548603283727480473638587228614426296913631}}}$ [121]	27 October 2017	2,131,318
35	360834356345 + 356345360834 [121]	February 2024	2,003,304
36	360339356572 + 356572360339 [121]	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 18703062⁵²⁴²⁸⁸ + 1, PrimeGrid
44. Official announcement of discovery of 18529322⁵²⁴²⁸⁸ + 1, PrimeGrid
45. Official announcement of discovery of 17997078⁵²⁴²⁸⁸ + 1, PrimeGrid
46. Official announcement of discovery of 17544674⁵²⁴²⁸⁸ + 1, PrimeGrid
47. Official announcement of discovery of 17502532⁵²⁴²⁸⁸ + 1, PrimeGrid
48. Official announcement of discovery of 17177670⁵²⁴²⁸⁸ + 1, PrimeGrid
49. Official announcement of discovery of 17177670⁵²⁴²⁸⁸ + 1, PrimeGrid
50. Official announcement of discovery of 16211276⁵²⁴²⁸⁸ + 1, PrimeGrid
51. Official announcement of discovery of 15958750⁵²⁴²⁸⁸ + 1, PrimeGrid
52. Official announcement of discovery of 15852200⁵²⁴²⁸⁸ + 1, PrimeGrid
53. Official announcement of discovery of 13520762⁵²⁴²⁸⁸ + 1, PrimeGrid
54. Official announcement of discovery of 13427472⁵²⁴²⁸⁸ + 1, PrimeGrid
55. Official announcement of discovery of 12900356⁵²⁴²⁸⁸ + 1, PrimeGrid
56. Official announcement of discovery of 12693488⁵²⁴²⁸⁸ + 1, PrimeGrid
57. Official announcement of discovery of 11937916⁵²⁴²⁸⁸ + 1, PrimeGrid
58. Official announcement of discovery of 10913140⁵²⁴²⁸⁸ + 1, PrimeGrid
59. Official announcement of discovery of 9332124⁵²⁴²⁸⁸ + 1, PrimeGrid
60. Official announcement of discovery of 8630170⁵²⁴²⁸⁸ + 1, PrimeGrid
61. Official announcement of discovery of 3×2^11895718−1, PrimeGrid
62. Official announcement of discovery of 6339004⁵²⁴²⁸⁸ + 1, PrimeGrid
63. Official announcement of discovery of 3×2^11731850 − 1, PrimeGrid
64. Official announcement of discovery of 4896418⁵²⁴²⁸⁸ + 1, PrimeGrid
65. Official announcement of discovery of 3×2^11484018 − 1, PrimeGrid
66. Official announcement of discovery of 193997×2^11452891 + 1, PrimeGrid
67. Official announcement of discovery of 3638450⁵²⁴²⁸⁸ + 1, PrimeGrid
68. Official announcement of discovery of 9221×2^11392194 − 1, PrimeGrid
69. Official announcement of discovery of 3214654⁵²⁴²⁸⁸ + 1, PrimeGrid
70. Official announcement of discovery of 146561×2^11280802 − 1, PrimeGrid
71. Official announcement of discovery of 2985036⁵²⁴²⁸⁸ + 1, PrimeGrid
72. Official announcement of discovery of 2877652⁵²⁴²⁸⁸ + 1, PrimeGrid
73. Official announcement of discovery of 2788032⁵²⁴²⁸⁸ + 1, PrimeGrid
74. Official announcement of discovery of 2733014⁵²⁴²⁸⁸ + 1, PrimeGrid
75. Official announcement of discovery of 2312092⁵²⁴²⁸⁸ + 1, PrimeGrid
76. Official announcement of discovery of 2061748⁵²⁴²⁸⁸ + 1, PrimeGrid
77. Official announcement of discovery of 1880370⁵²⁴²⁸⁸ + 1, PrimeGrid
78. Official announcement of discovery of 3×2^10829346 + 1, PrimeGrid
79. Official announcement of discovery of 475856⁵²⁴²⁸⁸ + 1, PrimeGrid
80. Official announcement of discovery of 356926⁵²⁴²⁸⁸ + 1, PrimeGrid
81. Official announcement of discovery of 341112⁵²⁴²⁸⁸ + 1, PrimeGrid
82. Official announcement of discovery of 121×2^9584444 + 1, PrimeGrid
83. Official announcement of discovery of 1323365×116^1323365 + 1, PrimeGrid
84. Official announcement of discovery of 63838×5^3887851 − 1, PrimeGrid
85. Official announcement of discovery of 273809×2^8932416 − 1, PrimeGrid
86. Official announcement of discovery of 25×2^8788628 + 1, PrimeGrid
87. "CRUS - Proven Conjectures". www.noprimeleftbehind.net.
88. Official announcement of discovery of 17×2^8636199 + 1, PrimeGrid
89. Official announcement of discovery of 75898⁵²⁴²⁸⁸ + 1, PrimeGrid
90. Official announcement of discovery of 25×2^8456828 + 1, PrimeGrid
91. Official announcement of discovery of 39×2^8413822 + 1, PrimeGrid
92. Official announcement of discovery of 31×2^8348000 + 1, PrimeGrid
93. Official announcement of discovery of 27×2^8342438 − 1, PrimeGrid
94. Official announcement of discovery of 273662×5^3493296 + 1, PrimeGrid
95. 102818×5^3440382 − 1, PrimeGrid
96. Official announcement of discovery of 27×2^7963247 + 1, PrimeGrid
97. Official announcement of discovery of 39×2^7946769 + 1, PrimeGrid
98. Official announcement of discovery of 29×2^7899985 + 1, PrimeGrid
99. Official announcement of discovery of 1341174×53^1341174 + 1, PrimeGrid
100. Official announcement of discovery of 45×2^7661004 + 1, PrimeGrid
101. Official announcement of discovery of 15×2^7619838 + 1, PrimeGrid
102. Official announcement of discovery of 45×2^7513661 + 1, PrimeGrid
103. Official announcement of discovery of 29×2^7374577 + 1, PrimeGrid
104. 109838×5^3168862 − 1, PrimeGrid
105. Official announcement of discovery of 29×2^7300254 + 1, PrimeGrid
106. 118568×5^3112069 + 1, PrimeGrid
107. Official announcement of discovery of 502573×2^7181987 − 1, PrimeGrid
108. Official announcement of discovery of 402539×2^7173024 − 1, PrimeGrid
109. Official announcement of discovery of 161041×2^7107964 + 1, PrimeGrid
110. Official announcement of discovery of 27×2^7046834 + 1, PrimeGrid
111. Official announcement of discovery of 3×2^7033641 + 1, PrimeGrid
112. GIMPS press release, GIMPS Finds First Million-Digit Prime. Retrieved on 2008-01-04.
113. 238694×5^2979422 − 1, PrimeGrid
114. 146264×5^2953282 − 1, PrimeGrid
115. 35816×5^2945294 − 1, PrimeGrid
116. Official announcement of discovery of 19×2^6833086 + 1, PrimeGrid
117. Official announcement of discovery of 40597×2^6808509 − 1, PrimeGrid
118. Official announcement of discovery of 39×2^6684941 + 1, PrimeGrid
119. Official announcement of discovery of 6679881×2^6679881 + 1, PrimeGrid
120. Official announcement of discovery of 39×2^6648997 + 1, PrimeGrid
121. 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