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	4052186×69^4052186 + 1 ^[16]	16 April 2025	7,451,366
17	69×2^24612729 − 1	13 August 2024	7,409,172
18	2^24036583 − 1 ^[17]	15 May 2004	7,235,733
19	107347×2^23427517 − 1	4 August 2024	7,052,391
20	3843236^1048576 + 1 ^[18]	17 December 2024	6,904,556
21	3×2^22103376 − 1 ^[19]	30 September 2024	6,653,780
22	1963736^1048576 + 1 ^[20]	24 September 2022	6,598,776
23	1951734^1048576 + 1 ^[21]	9 August 2022	6,595,985
24	202705×2^21320516 + 1 ^[22]	25 November 2021	6,418,121
25	2^20996011 − 1 ^[23]	17 November 2003	6,320,430
26	1059094^1048576 + 1 ^[24]	31 October 2018	6,317,602
27	3×2^20928756 − 1 ^[25]	5 July 2023	6,300,184
28	919444^1048576 + 1 ^[26]	29 August 2017	6,253,210
29	81×2^20498148 + 1	13 June 2023	6,170,560
30	7×2^20267500 + 1	21 July 2022	6,101,127
31	4×5^8431178 + 1	2 January 2024	5,893,142
32	168451×2^19375200 + 1 ^[27]	17 September 2017	5,832,522
33	69×2^19374980 − 1	3 July 2022	5,832,452
34	3×2^18924888 − 1 ^[28]	24 March 2022	5,696,990
35	69×2^18831865 − 1	16 December 2021	5,668,959
36	2×3^11879700 + 1	22 June 2024	5,668,058
37	97139×2^18397548 − 1	23 April 2023	5,538,219
38	7×2^18233956 + 1	1 October 2020	5,488,969
39	3×2^18196595 − 1 ^[29]	8 January 2022	5,477,722
40	4×3^11279466 + 1	10 September 2024	5,381,674
41	3×2^17748034 − 1 ^[30]	6 September 2021	5,342,692
42	$\Phi _{3}(-123447^{524288})$	23 February 2017	5,338,805
43	3622×5^7558139 − 1	18 February 2022	5,282,917
44	7×6^6772401 + 1	9 September 2019	5,269,954
45	2×3^10852677 + 1	8 January 2023	5,178,044
46	8508301×2^17016603 − 1 ^[31]	21 March 2018	5,122,515
47	8×10^5112848 − 1	30 January 2024	5,112,848
48	13×2^16828072 + 1	11 October 2023	5,065,756
49	3×2^16819291 − 1 ^[32]	20 January 2021	5,063,112
50	5287180×3^10574360 − 1	3 November 2024	5,045,259
51	3×2^16408818 + 1 ^[33]	25 October 2020	4,939,547
52	2329989×2^16309923 − 1	13 February 2024	4,909,783
53	69×2^15866556 + 1	20 August 2021	4,776,312
54	2036×3^10009192 + 1	15 February 2024	4,775,602
55	2525332×73^2525332 + 1 ^[34]	28 August 2021	4,705,888
56	1419499×2^15614489 + 1	9 February 2024	4,700,436
57	11×2^15502315 + 1	8 January 2023	4,666,663
58	(10^2332974 + 1)² − 2	20 February 2024	4,665,949
59	37×2^15474010 + 1	8 November 2022	4,658,143
60	93839×2^15337656 − 1	28 November 2022	4,617,100
61	2^15317227+2^7658614 + 1	31 July 2020	4,610,945
62	13×2^15294536 + 1	30 September 2023	4,604,116
63	6×5^6546983 + 1	13 June 2020	4,576,146
64	4788920×3^9577840 − 1	14 February 2024	4,569,798
65	31×2^15145093 − 1	9 February 2025	4,559,129
66	69×2^14977631 − 1	3 December 2021	4,508,719
67	192971×2^14773498 − 1	7 March 2021	4,447,272
68	4×3^9214845 + 1	10 September 2024	4,396,600
69	9145334×3^9145334 + 1	25 December 2023	4,363,441
70	4×5^6181673 − 1	15 July 2022	4,320,805
71	396101×2^14259638 − 1	3 February 2024	4,292,585
72	6962×31^2863120 − 1	29 February 2020	4,269,952
73	37×2^14166940 + 1	24 June 2022	4,264,676
74	99739×2^14019102 + 1 ^[35]	24 December 2019	4,220,176
75	69×2^13832885 − 1	17 January 2022	4,164,116
76	404849×2^13764867 + 1	10 March 2021	4,143,644
77	25×2^13719266 + 1	20 September 2022	4,129,912
78	81×2^13708272 + 1	11 October 2022	4,126,603
79	2740879×2^13704395 − 1	26 October 2019	4,125,441
80	479216×3^8625889 − 1	16 November 2019	4,115,601
81	13×2^13584543 − 1	30 May 2025	4,089,357
82	31×2^13514933 − 1	9 February 2025	4,068,402
83	$\Phi _{3}(-143332^{393216})$	30 January 2017	4,055,114
84	81×2^13470584 + 1	9 October 2022	4,055,052
85	2^13466917 − 1 ^[36]	14 November 2001	4,053,946
86	5778486×5^5778486 + 1	15 August 2024	4,038,996
87	9×2^13334487 + 1	31 March 2020	4,014,082
88	206039×2^13104952 − 1	26 April 2021	3,944,989
89	2805222×5^5610444 + 1 ^[37]	2 September 2019	3,921,539
90	5128×22^2919993 + 1	5 December 2024	3,919,869
91	19249×2^13018586 + 1 ^[38]	26 March 2007	3,918,990
92	2293×2^12918431 − 1	13 February 2021	3,888,839
93	81×2^12804541 + 1	19 September 2022	3,854,553
94	67612×5^5501582 + 1 ^[39]	8 April 2025	3,845,446
95	4×5^5380542 + 1	22 February 2023	3,760,839
96	13520762⁵²⁴²⁸⁸ + 1 ^[40]	25 February 2025	3,738,699
97	13427472⁵²⁴²⁸⁸ + 1 ^[41]	3 March 2025	3,737,122
98	9×2^12406887 + 1	29 March 2020	3,734,847
99	12900356⁵²⁴²⁸⁸ + 1 ^[42]	22 January 2025	3,728,004
100	12693488⁵²⁴²⁸⁸ + 1 ^[43]	6 January 2025	3,724,323
101	11937916⁵²⁴²⁸⁸ + 1 ^[44]	5 October 2024	3,710,349
102	7×2^12286041 − 1	10 June 2023	3,698,468
103	10913140⁵²⁴²⁸⁸ + 1 ^[45]	19 June 2024	3,689,913
104	69×2^12231580 − 1	27 July 2021	3,682,075
105	27×2^12184319 + 1	6 February 2021	3,667,847
106	9332124⁵²⁴²⁸⁸ + 1 ^[46]	22 June 2024	3,654,278
107	8630170⁵²⁴²⁸⁸ + 1 ^[47]	13 April 2024	3,636,472
108	863282×5^5179692 − 1	17 October 2024	3,620,456
109	670490×12^3352450 − 1	17 October 2024	3,617,907
110	4×3^7578378 + 1	9 September 2024	3,615,806
111	11×2^11993994 − 1	15 August 2024	3,610,554
112	3761×2^11978874 − 1	6 July 2022	3,606,004
113	95×2^11954552 − 1	28 May 2024	3,598,681
114	259072×5^5136295 − 1	28 October 2024	3,590,122
115	3×2^11895718 − 1 ^[48]	23 June 2015	3,580,969
116	37×2^11855148 + 1	30 May 2022	3,568,757
117	6339004⁵²⁴²⁸⁸ + 1 ^[49]	8 June 2023	3,566,218
118	763795×6^4582771 + 1	11 December 2023	3,566,095
119	5897794⁵²⁴²⁸⁸ + 1 ^[38]	18 December 2022	3,549,792
120	3×2^11731850 − 1 ^[50]	13 March 2015	3,531,640
121	69×2^11718455 − 1 ^[38]	4 December 2020	3,527,609
122	8629×2^11708579 − 1	19 September 2024	3,524,638
123	41×2^11676439 + 1 ^[38]	20 June 2022	3,514,960
124	4896418⁵²⁴²⁸⁸ + 1 ^[51]	15 May 2022	3,507,424
125	81×2^11616017 + 1 ^[38]	30 August 2022	3,496,772
126	69×2^11604348 − 1 ^[38]	4 December 2020	3,493,259
127	4450871×6^4450871 + 1 ^[38]	17 September 2023	3,463,458
128	9×2^11500843 + 1 ^[38]	13 March 2020	3,462,100
129	3×2^11484018 − 1 ^[52]	22 November 2014	3,457,035
130	193997×2^11452891 + 1 ^[53]	3 April 2018	3,447,670
131	29914×5^4930904 + 1	27 September 2024	3,446,559
132	3638450⁵²⁴²⁸⁸ + 1 ^[54]	29 May 2020	3,439,810
133	9221×2^11392194 − 1 ^[55]	7 February 2021	3,429,397
134	9×2^11366286 + 1	26 March 2020	3,421,594
135	5×2^11355764 − 1	2 October 2021	3,418,427
136	732050×6^4392301 + 1	9 September 2023	3,417,881
137	3214654⁵²⁴²⁸⁸ + 1 ^[56]	24 December 2019	3,411,613
138	632760! − 1	20 October 2024	3,395,992
139	146561×2^11280802 − 1 ^[57]	16 November 2020	3,395,865
140	51208×5^4857576 + 1	6 June 2024	3,395,305
141	2985036⁵²⁴²⁸⁸ + 1 ^[58]	18 September 2019	3,394,739
142	4591×2^11270837 − 1	2 January 2025	3,392,864
143	6929×2^11255424 − 1	7 July 2022	3,388,225
144	2877652⁵²⁴²⁸⁸ + 1 ^[59]	29 June 2019	3,386,397
145	2788032⁵²⁴²⁸⁸ + 1 ^[60]	17 April 2019	3,379,193
146	2733014⁵²⁴²⁸⁸ + 1 ^[61]	18 March 2019	3,374,655
147	9×2^11158963 + 1	13 March 2020	3,359,184
148	9271×2^11134335 − 1	17 January 2021	3,351,773
149	136804×5^4777253 − 1	1 March 2024	3,339,162
150	2312092⁵²⁴²⁸⁸ + 1 ^[62]	4 August 2018	3,336,572
151	987324×48^1974648 − 1	12 October 2024	3,319,866
152	2061748⁵²⁴²⁸⁸ + 1 ^[63]	20 March 2018	3,310,478
153	1880370⁵²⁴²⁸⁸ + 1 ^[64]	15 January 2018	3,289,511
154	27×2^10902757 − 1	7 March 2022	3,282,059
155	3×2^10829346 + 1 ^[65]	14 January 2014	3,259,959
156	11×2^10803449 + 1	29 May 2022	3,252,164
157	11×2^10797109 + 1	29 May 2022	3,250,255
158	7×2^10612737 − 1	19 May 2022	3,194,154
159	7351117# + 1	14 September 2024	3,191,401
160	37×2^10599476 + 1	17 June 2022	3,190,762
161	5×2^10495620 − 1	26 September 2021	3,159,498
162	${\tfrac {\Phi _{3}(-3^{3304302}+1)}{3}}$	30 June 2023	3,153,105
163	5×2^10349000 − 1	26 September 2021	3,115,361
164	$\Phi _{3}(-844833^{262144})$	17 January 2017	3,107,335
165	52922×5^4399812 − 1	3 August 2023	3,075,342
166	$\Phi _{3}(-712012^{262144})$	14 January 2017	3,068,389
167	177742×5^4386703 − 1	24 July 2023	3,066,180
168	4×3^6402015 + 1	9 September 2024	3,054,539
169	874208×54^1748416 − 1	26 September 2019	3,028,951
170	475856⁵²⁴²⁸⁸ + 1 ^[66]	8 August 2012	2,976,633
171	2×3^6236772 + 1	20 December 2022	2,975,697
172	15×3^9830108 + 1	19 August 2023	2,959,159
173	9×2^9778263 + 1	5 August 2020	2,943,552
174	198×558^1061348 + 1	30 August 2024	2,915,138
175	1806676×41^1806676 + 1	11 March 2018	2,913,785
176	356926⁵²⁴²⁸⁸ + 1 ^[67]	20 June 2012	2,911,151
177	341112⁵²⁴²⁸⁸ + 1 ^[68]	15 June 2012	2,900,832
178	213988×5^4138363 − 1	29 November 2022	2,892,597
179	43×2^9596983 − 1	28 February 2022	2,888,982
180	121×2^9584444 + 1 ^[69]	18 November 2020	2,885,208
181	15×2^9482269 − 1	14 August 2024	2,854,449
182	6533299# − 1	18 August 2024	2,835,864
183	11×2^9381365 + 1	7 March 2020	2,824,074
184	15×2^9312889 + 1	7 August 2023	2,803,461
185	97×2^9305542 + 1	10 May 2025	2,801,250
186	93×2^9235048 + 1	7 May 2025	2,780,029
187	49×2^9187790 + 1	11 September 2022	2,765,803
188	6369619# + 1	12 August 2024	2,765,105
189	27653×2^9167433 + 1 ^[38]	8 June 2005	2,759,677
190	6354977# − 1	12 August 2024	2,758,832
191	90527×2^9162167 + 1	30 June 2010	2,758,093
192	6795×2^9144320 − 1	31 March 2021	2,752,719
193	31×2^9088085 − 1	27 August 2024	2,735,788
194	75×2^9079482 + 1	25 July 2023	2,733,199
195	1323365×116^1323365 + 1 ^[70]	18 January 2018	2,732,038
196	57×2^9075622 − 1	7 August 2022	2,732,037
197	10^2718281 − 5×10^1631138 − 5×10^1087142 − 1	6 August 2024	2,718,281
198	63838×5^3887851 − 1 ^[71]	19 June 2022	2,717,497
199	13×2^8989858 + 1	10 March 2020	2,706,219
200	4159×2^8938471 − 1	19 April 2022	2,690,752
201	273809×2^8932416 − 1 ^[72]	13 December 2017	2,688,931
202	93×2^8898285 + 1	4 March 2024	2,678,653
203	2×3^5570081 + 1	14 February 2020	2,657,605
204	25×2^8788628 + 1 ^[73]	1 March 2021	2,645,643
205	2038×366^1028507 − 1 ^[74]	4 April 2016	2,636,562
206	64598×5^3769854 − 1	14 June 2022	2,635,020
207	63×2^8741225 + 1	6 May 2024	2,631,373
208	8×785⁹⁰⁰³²⁵ + 1	4 June 2022	2,606,325
209	17×2^8636199 + 1 ^[75]	17 February 2021	2,599,757
210	75898⁵²⁴²⁸⁸ + 1 ^[76]	19 November 2011	2,558,647
211	25×2^8456828 + 1 ^[77]	27 January 2021	2,545,761
212	39×2^8413422 + 1 ^[78]	23 January 2021	2,532,694
213	31×2^8348000 + 1 ^[79]	19 January 2021	2,513,000
214	27×2^8342438 − 1 ^[80]	1 February 2021	2,511,326
215	3867×2^8261084 − 1	14 April 2021	2,486,838
216	101×2^8152967 + 1	2 December 2023	2,454,290
217	273662×5^3493296 − 1 ^[81]	7 December 2021	2,441,715
218	81×2^8109236 + 1	9 September 2022	2,441,126
219	11×2^8103463 + 1	6 March 2020	2,439,387
220	102818×5^3440382 − 1 ^[82]	8 October 2021	2,404,729
221	11×2^7971110 − 1	25 November 2019	2,399,545
222	27×2^7963247 + 1 ^[83]	14 January 2021	2,397,178
223	3177×2^7954621 − 1	13 June 2021	2,394,584
224	39×2^7946769 + 1 ^[84]	14 January 2021	2,392,218
225	7×6^3072198 + 1	4 August 2019	2,390,636
226	3765×2^7904593 − 1	10 January 2021	2,379,524
227	29×2^7899985 + 1 ^[85]	14 January 2021	2,378,134
228	5113×2^7895471 − 1	27 November 2022	2,376,778
229	861×2^7895451 − 1	21 February 2021	2,376,771
230	75×2^7886683 + 1	4 September 2023	2,374,131
231	2661×2^7861390 − 1	28 December 2024	2,366,518
232	99×2^7830910 + 1	24 April 2024	2,357,341
233	28433×2^7830457 + 1 ^[38]	31 December 2004	2,357,207
234	2589×2^7803339 − 1	21 August 2022	2,349,043
235	59×2^7792307 + 1	24 April 2024	2,345,720
236	101×2^7784453 + 1	24 April 2024	2,343,356
237	95×2^7778585 + 1	24 April 2024	2,341,590
238	8401×2^7767655 − 1	24 April 2023	2,338,302
239	9693×2^7767343 − 1	17 November 2023	2,338,208
240	5×2^7755002 − 1	23 September 2021	2,334,489
241	2945×2^7753232 − 1	27 November 2022	2,333,959
242	2×836⁷⁹⁸⁴³¹ + 1	10 September 2024	2,333,181
243	63×2^7743186 + 1	24 April 2024	2,330,934
244	2545×2^7732265 − 1	13 January 2021	2,327,648
245	5539×2^7730709 − 1	15 January 2021	2,327,180
246	4817×2^7719584 − 1	13 June 2021	2,323,831
247	183×558⁸⁴²⁷⁵² + 1	23 August 2024	2,314,734
248	1341174×53^1341174 + 1 ^[86]	21 August 2017	2,312,561
249	9467×2^7680034 − 1	20 February 2022	2,311,925
250	45×2^7661004 + 1 ^[87]	13 December 2020	2,306,194
251	15×2^7619838 + 1 ^[88]	6 December 2020	2,293,801
252	3597×2^7580693 − 1	10 January 2021	2,282,020
253	5256037# + 1	6 August 2024	2,281,955
254	3129×2^7545557 − 1	14 March 2023	2,271,443
255	7401×2^7523295 − 1	21 February 2021	2,264,742
256	45×2^7513661 + 1 ^[89]	12 November 2020	2,261,839
257	$\Phi _{3}(-558640^{196608})$	11 January 2017	2,259,865
258	2739×2^7483537 − 1	1 May 2025	2,252,773
259	9×2^7479919 − 1	3 June 2023	2,251,681
260	1875×2^7474308 − 1	21 August 2022	2,249,995
261	69×2^7452023 + 1	23 March 2023	2,243,285
262	1281879×2^7447178 + 1	27 December 2023	2,241,831
263	9107×2^7417464 − 1	3 May 2025	2,232,884
264	4×5^3189669 − 1	12 July 2022	2,229,484
265	29×2^7374577 + 1 ^[90]	27 October 2020	2,219,971
266	2653×2^7368343 − 1	18 September 2024	2,218,096
267	21555×2^7364128 − 1	4 September 2024	2,216,828
268	3197×2^7359542 − 1	27 November 2022	2,215,447
269	109838×5^3168862 − 1 ^[91]	13 August 2020	2,214,945
270	95×2^7354869 + 1	25 September 2023	2,214,039
271	101×2^7345194 − 1	5 October 2019	2,211,126
272	85×2^7333444 + 1	25 September 2023	2,207,589
273	15×2^7300254 + 1 ^[92]	25 October 2020	2,197,597
274	422429! + 1	21 February 2022	2,193,027
275	1759×2^7284439 − 1	28 August 2021	2,192,838
276	1909683×14^1909683 + 1	27 May 2023	2,188,748
277	737×2^7269322 − 1	10 August 2017	2,188,287
278	6909×2^7258896 − 1	18 September 2024	2,185,150
279	93×2^7241494 + 1	25 September 2023	2,179,909
280	118568×5^3112069 + 1 ^[93]	1 May 2020	2,175,248
281	4215×2^7221386 − 1	27 December 2024	2,173,858
282	40×257⁹⁰¹⁶³² + 1	11 September 2024	2,172,875
283	1685×2^7213108 − 1	13 April 2025	2,171,366
284	580633×2^7208783 − 1	15 February 2024	2,170,066
285	6039×2^7207973 − 1	24 March 2021	2,169,820
286	502573×2^7181987 − 1 ^[94]	4 October 2014	2,162,000
287	402539×2^7173024 − 1 ^[95]	2 October 2014	2,159,301
288	3343×2^7166019 − 1	29 September 2016	2,157,191
289	4137×2^7132569 − 1	11 April 2025	2,147,121
290	161041×2^7107964 + 1 ^[96]	6 January 2015	2,139,716
291	294×213⁹¹⁸⁹⁵² − 1	19 September 2023	2,139,672
292	27×2^7046834 + 1 ^[97]	11 October 2018	2,121,310
293	1759×2^7046791 − 1	28 August 2021	2,121,299
294	327×2^7044001 − 1	13 January 2021	2,120,459
295	5×2^7037188 − 1	22 September 2021	2,118,406
296	3×2^7033641 + 1 ^[98]	21 February 2011	2,117,338
297	625783×2^7031319 − 1	10 February 2024	2,116,644
298	33661×2^7031232 + 1 ^[38]	30 October 2007	2,116,617
299	$\Phi _{3}(-237804^{196608})$	6 January 2017	2,114,016
300	207494×5^3017502 − 1	16 March 2020	2,109,149
301	15×2^6993631 − 1	25 August 2021	2,105,294
302	8943501×2^6972593 − 1	8 January 2022	2,098,967
303	6020095×2^6972593 − 1	4 September 2022	2,098,967
304	2^6972593 − 1 ^[99]	1 June 1999	2,098,960
305	273×2^6963847 − 1	16 November 2022	2,096,330
306	6219×2^6958945 − 1	7 January 2021	2,094,855
307	51×2^6945567 + 1	26 May 2020	2,090,826
308	8×10^2084563 − 1	1 June 2025	2,084,564
309	3323×2^6921196 − 1	18 September 2024	2,083,492
310	238694×5^2979422 − 1 ^[100]	12 March 2020	2,082,532
311	4×72^1119849 − 1 ^[74]	7 September 2016	2,079,933
312	129×2^6900230 + 1	5 June 2025	2,077,179
313	33×2^6894190 − 1	27 July 2021	2,075,360
314	4778027# − 1	31 July 2024	2,073,926
315	105×2^6884697 + 1	2 June 2025	2,072,503
316	2345×2^6882320 − 1	13 April 2022	2,071,789
317	57×2^6857990 + 1	17 August 2023	2,064,463
318	146264×5^2953282 − 1 ^[101]	9 March 2020	2,064,261
319	69×2^6838971 − 1	1 March 2020	2,058,738
320	35816×5^2945294 − 1 ^[102]	5 March 2020	2,058,677
321	127×2^6836153 − 1	25 June 2018	2,057,890
322	105×2^6835099 + 1	26 May 2025	2,057,572
323	19×2^6833086 + 1 ^[103]	24 October 2020	2,056,966
324	65×2^6810465 + 1	22 September 2023	2,050,157
325	40597×2^6808509 − 1 ^[104]	25 December 2013	2,049,571
326	283×2^6804701 − 1	19 January 2020	2,048,431
327	65136498²⁶²¹⁴⁴ + 1	20 June 2025	2,048,348
328	64989720²⁶²¹⁴⁴ + 1	18 June 2025	2,048,091
329	64074894²⁶²¹⁴⁴ + 1	30 May 2025	2,046,447
330	64010198²⁶²¹⁴⁴ + 1	30 May 2025	2,046,362
331	63833640²⁶²¹⁴⁴ + 1	27 May 2025	2,046,047
332	8×10^2045966 − 1	31 May 2025	2,045,967
333	63784742²⁶²¹⁴⁴ + 1	26 May 2025	2,045,960
334	63558122²⁶²¹⁴⁴ + 1	27 May 2025	2,045,555
335	63448958²⁶²¹⁴⁴ + 1	22 May 2025	2,045,359
336	63286690²⁶²¹⁴⁴ + 1	19 May 2025	2,045,068
337	62767176²⁶²¹⁴⁴ + 1	9 May 2025	2,044,129
338	62747994²⁶²¹⁴⁴ + 1	9 May 2025	2,044,095
339	1861209×2^6789999 + 1	2 December 2020	2,044,000
340	5817×2^6789459 − 1	9 January 2021	2,043,835
341	62311952²⁶²¹⁴⁴ + 1	3 May 2025	2,043,301
342	62199610²⁶²¹⁴⁴ + 1	5 May 2025	2,043,095
343	62152830²⁶²¹⁴⁴ + 1	1 May 2025	2,043,010
344	62136706²⁶²¹⁴⁴ + 1	2 May 2025	2,042,980
345	8435×2^6786180 − 1	7 January 2021	2,042,848
346	61238184²⁶²¹⁴⁴ + 1	21 April 2025	2,041,322
347	119×2^6777781 + 1	18 May 2025	2,040,318
348	59145944²⁶²¹⁴⁴ + 1	29 March 2025	2,037,364
349	58936230²⁶²¹⁴⁴ + 1	28 March 2025	2,036,960
350	58870004²⁶²¹⁴⁴ + 1	28 March 2025	2,036,832
351	58846688²⁶²¹⁴⁴ + 1	28 March 2025	2,036,787
352	58333324²⁶²¹⁴⁴ + 1	28 March 2025	2,035,789
353	58288282²⁶²¹⁴⁴ + 1	28 March 2025	2,035,701
354	57643582²⁶²¹⁴⁴ + 1	28 March 2025	2,034,435
355	57594478²⁶²¹⁴⁴ + 1	28 March 2025	2,034,338
356	57478518²⁶²¹⁴⁴ + 1	28 March 2025	2,034,108
357	57429230²⁶²¹⁴⁴ + 1	27 March 2025	2,034,111
358	51×2^6753404 + 1	26 May 2020	2,032,979
359	93×2^6750726 + 1	18 September 2023	2,032,173
360	56303352²⁶²¹⁴⁴ + 1	27 March 2025	2,031,757
361	56295176²⁶²¹⁴⁴ + 1	26 March 2025	2,031,740
362	55952434²⁶²¹⁴⁴ + 1	26 March 2025	2,031,045
363	55892864²⁶²¹⁴⁴ + 1	27 March 2025	2,030,920
364	69×2^6745775 + 1	21 March 2023	2,030,683
365	55702322²⁶²¹⁴⁴ + 1	27 March 2025	2,030,535
366	55695224²⁶²¹⁴⁴ + 1	25 March 2025	2,030,520
367	55169618²⁶²¹⁴⁴ + 1	25 March 2025	2,029,441
368	55007338²⁶²¹⁴⁴ + 1	25 March 2025	2,029,105
369	54852328²⁶²¹⁴⁴ + 1	25 March 2025	2,028,784
370	54528918²⁶²¹⁴⁴ + 1	26 March 2025	2,028,111
371	54044092²⁶²¹⁴⁴ + 1	24 March 2025	2,027,094
372	53903472²⁶²¹⁴⁴ + 1	24 March 2025	2,026,797
373	53750036²⁶²¹⁴⁴ + 1	24 March 2025	2,026,473
374	53616962²⁶²¹⁴⁴ + 1	28 March 2025	2,026,191
375	53311612²⁶²¹⁴⁴ + 1	24 March 2025	2,025,540
376	53008094²⁶²¹⁴⁴ + 1	23 March 2025	2,024,890
377	52648144²⁶²¹⁴⁴ + 1	21 March 2025	2,024,115
378	52599274²⁶²¹⁴⁴ + 1	20 March 2025	2,024,009
379	52592976²⁶²¹⁴⁴ + 1	21 March 2025	2,023,995
380	117×2^6719464 + 1	10 May 2025	2,022,763
381	51992174²⁶²¹⁴⁴ + 1	16 March 2025	2,022,687
382	51852794²⁶²¹⁴⁴ + 1	14 March 2025	2,022,382
383	51714136²⁶²¹⁴⁴ + 1	13 March 2025	2,022,077
384	51283286²⁶²¹⁴⁴ + 1	9 March 2025	2,021,124
385	51125138²⁶²¹⁴⁴ + 1	7 March 2025	2,020,773
386	9995×2^6711008 − 1	31 December 2020	2,020,219
387	50454356²⁶²¹⁴⁴ + 1	1 March 2025	2,019,269
388	50449664²⁶²¹⁴⁴ + 1	28 February 2025	2,019,259
389	50366208²⁶²¹⁴⁴ + 1	28 February 2025	2,019,070
390	50121532²⁶²¹⁴⁴ + 1	27 February 2025	2,018,516
391	49536902²⁶²¹⁴⁴ + 1	25 February 2025	2,017,180
392	49235348²⁶²¹⁴⁴ + 1	23 February 2025	2,016,485
393	49209090²⁶²¹⁴⁴ + 1	23 February 2025	2,016,424
394	48055302²⁶²¹⁴⁴ + 1	18 February 2025	2,013,723
395	47707672²⁶²¹⁴⁴ + 1	16 February 2025	2,012,896
396	39×2^6684941 + 1 ^[105]	20 October 2020	2,012,370
397	47351862²⁶²¹⁴⁴ + 1	15 February 2025	2,012,044
398	47281922²⁶²¹⁴⁴ + 1	13 February 2025	2,011,876
399	47255958²⁶²¹⁴⁴ + 1	13 February 2025	2,011,813
400	6679881×2^6679881 + 1 ^[106]	25 July 2009	2,010,852
401	46831458²⁶²¹⁴⁴ + 1	11 February 2025	2,010,786
402	46378776²⁶²¹⁴⁴ + 1	8 February 2025	2,009,680
403	45073202²⁶²¹⁴⁴ + 1	21 January 2025	2,006,469
404	45007104²⁶²¹⁴⁴ + 1	19 January 2025	2,006,202
405	44819108²⁶²¹⁴⁴ + 1	14 January 2025	2,005,786
406	44666524²⁶²¹⁴⁴ + 1	12 January 2025	2,005,397
407	37×2^6660841 − 1 ^[74]	30 July 2014	2,005,115
408	44144624²⁶²¹⁴⁴ + 1	29 December 2024	2,004,059
409	44030166²⁶²¹⁴⁴ + 1	30 December 2024	2,003,764
410	43330794²⁶²¹⁴⁴ + 1	3 December 2024	2,001,941
411	39×2^6648997 + 1 ^[107]	20 October 2020	2,001,550
412	42781592²⁶²¹⁴⁴ + 1	18 November 2024	2,000,489
413	10^2000007 − 10^1127194 − 10⁸⁷²⁸¹² − 1	12 January 2024	2,000,007
414	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^[108]	Number	Discovery date	Decimal digits
1	${\tfrac {10^{8177207}-1}{9}}$ ^[108]	8 May 2021	8,177,207
2	${\tfrac {10^{5794777}-1}{9}}$ ^[108]	20 April 2021	5,794,777
3	${\tfrac {2^{15135397}+1}{3}}$ ^[108]	June 2021	4,556,209
4	${\tfrac {3^{8530117}-1}{2}}$ ^[108]	November 2023	4,069,900
5	2^13380298 − 27 ^[108]	March 2021	4,027,872
6	${\tfrac {2^{13372531}+1}{3}}$ ^[108]	September 2013	4,025,533
7	${\tfrac {2^{13347311}+1}{3}}$ ^[108]	September 2013	4,017,941
8	${\tfrac {2^{12720787}-1}{1666870069020922905132673131516413926009285199}}$ ^[108]	3 July 2022	3,829,294
9	${\tfrac {3^{7973131}-1}{2}}$ ^[108]	November 2023	3,804,150
10	${\tfrac {2^{12588091}-1}{32075464348897282169539424801}}$ ^[108]	10 April 2023	3,789,365
11	${\tfrac {2^{12503723}-2^{6251862}+1}{5}}$ ^[108]	July 2020	3,763,995
12	${\tfrac {5^{5154509}-1}{4}}$ ^[108]	February 2024	3,602,847
13	${\tfrac {5^{4939471}-1}{4}}$ ^[108]	January 2024	3,452,542
14	${\tfrac {3^{7034611}+1}{4}}$ ^[108]	December 2024	3,356,362
15	${\tfrac {2^{10443557}-1}{37289325994807}}$ ^[108]	9 July 2020	3,143,811
16	2^9092392 + 40291 ^[108]	February 2011	2,737,083
17	${\tfrac {14^{2307467}+1}{15}}$ ^[108]	June 2025	2,644,652
18	${\tfrac {6^{3360347}-1}{5}}$ ^[108]	October 2023	2,614,858
19	${\tfrac {2^{8247949}-1}{45487316822291087700751210632267642069671672071}}$ ^[108]	3 June 2024	2,482,834
20	${\tfrac {17^{1990523}-1}{16}}$ ^[108]	August 2020	2,449,236
21	${\tfrac {35963^{524288}+1}{2}}$ ^[108]	August 2022	2,388,581
22	500186⁵⁴⁴⁶⁵ + 54465⁵⁰⁰¹⁸⁶ ^[108]	August 2024	2,368,940
23	${\tfrac {11^{2264611}+1}{12}}$ ^[108]	July 2021	2,358,349
24	${\tfrac {5^{3300593}-1}{4}}$ ^[108]	February 2022	2,307,015
25	${\tfrac {3^{4694803}+2^{4694803}}{5}}$ ^[108]	December 2023	2,239,990
26	${\tfrac {2^{7313983}-1}{305492080276193}}$ ^[108]	1 March 2018	2,201,714
27	${\tfrac {3^{4571447}+2^{4571447}}{5}}$ ^[108]	December 2023	2,181,134
28	${\tfrac {15^{1848811}+1}{16}}$ ^[108]	July 2024	2,174,370
29	F(10367321) ^[108]	10 August 2024	2,166,642
30	${\tfrac {15^{1841911}+1}{16}}$ ^[108]	July 2024	2,166,255
31	3^4532794 + 4532794³ ^[108]	October 2023	2,162,693
32	F(10317107) ^[108]	27 July 2024	2,156,148
33	${\tfrac {2^{7080247}-1}{17045259548603283727480473638587228614426296913631}}$ ^[108]	27 October 2017	2,131,318
34	360834³⁵⁶³⁴⁵ + 356345³⁶⁰⁸³⁴ ^[108]	February 2024	2,003,304
35	360339³⁵⁶⁵⁷² + 356572³⁶⁰³³⁹ ^[108]	May 2024	2,000,656