The table below lists the largest currently known prime numbers and probable primes (PRPs) as tracked by the University of Tennessee's PrimePages and Henri & Renaud Lifchitz' 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.

This is a dynamic list and may never be able to satisfy particular standards for completeness. You can help by adding missing items with reliable sources.

Rank^[1]	Number	Discovery date	Decimal digits
1	2^82589933 – 1 ^[2]	7 December 2018	24,862,048
2	2^77232917 – 1 ^[3]	26 December 2017	23,249,425
3	2^74207281 – 1 ^[4]	7 January 2016	22,338,618
4	2^57885161 – 1 ^[5]	25 January 2013	17,425,170
5	2^43112609 – 1 ^[6]	23 August 2008	12,978,189
6	2^42643801 – 1 ^[7]	4 June 2009	12,837,064
7	2^37156667 – 1 ^[6]	6 September 2008	11,185,272
8	2^32582657 – 1 ^[8]	4 September 2006	9,808,358
9	10223×2^31172165 + 1 ^[9]	31 October 2016	9,383,761
10	2^30402457 – 1 ^[10]	15 December 2005	9,152,052
11	2^25964951 – 1 ^[11]	18 February 2005	7,816,230
12	2^24036583 – 1 ^[12]	15 May 2004	7,235,733
13	1963736^1048576 + 1 ^[13]	24 September 2022	6,598,776
14	1951734^1048576 + 1 ^[14]	9 August 2022	6,595,985
15	202705×2^21320516 + 1 ^[15]	25 November 2021	6,418,121
16	2^20996011 – 1 ^[16]	17 November 2003	6,320,430
17	1059094^1048576 + 1 ^[17]	31 October 2018	6,317,602
18	919444^1048576 + 1 ^[18]	29 August 2017	6,253,210
19	7×2^20267500 + 1	21 July 2022	6,101,127
20	168451×2^19375200 + 1 ^[19]	17 September 2017	5,832,522
21	69×2^19374980 - 1	3 July 2022	5,832,452
22	3×2^18924888 - 1 ^[20]	24 March 2022	5,696,990
23	69×2^18831865 - 1	16 December 2021	5,668,959
24	7×2^18233956 + 1	1 October 2020	5,488,969
25	3×2^18196595 - 1 ^[21]	8 January 2022	5,477,722
26	3×2^17748034 - 1 ^[22]	6 September 2021	5,342,692
27	$\Phi _{3}(-123447^{524288})$	23 February 2017	5,338,805
28	3622×5^7558139 - 1	18 February 2022	5,282,917
29	7×6^6772401 + 1	9 September 2019	5,269,954
30	2×3^10852677 + 1	9 January 2023	5,178,044
31	8508301×2^17016603-1 ^[23]	21 March 2018	5,122,515
32	3×2^16819291-1 ^[24]	20 January 2021	5,063,112
33	3×2^16408818+1 ^[25]	25 October 2020	4,939,547
34	69×2^15866556+1	20 August 2021	4,776,312
35	2525332×73^2525332+1	28 August 2021	4,705,888
36	11×2^15502315+1	8 January 2023	4,666,663
37	37×2^15474010+1	8 November 2022	4,658,143
38	93839×2^15337656-1	28 November 2022	4,617,100
39	2^15317227+2^7658614+1	31 July 2020	4,610,945
40	6×5^6546983+1	13 June 2020	4,576,146
41	69×2^14977631-1	3 December 2021	4,508,719
42	192971×2^14773498-1	7 March 2021	4,447,272
43	4×5^6181673-1	15 July 2022	4,320,805
44	6962×31^2863120-1	29 February 2020	4,269,952
45	37×2^14166940+1	24 June 2022	4,264,676
46	99739×2^14019102-1 ^[26]	24 December 2019	4,220,176
47	69×2^13832885-1	17 January 2022	4,164,116
48	404849×2^13764867+1	10 March 2021	4,143,644
49	25×2^13719266+1	20 September 2022	4,129,912
50	81×2^13708272 + 1	11 October 2022	4,126,603
51	2740879×2^13704395-1	26 October 2019	4,125,441
52	479216×3^8625889-1	16 November 2019	4,115,601
53	$\Phi _{3}(-143332^{393216})$	30 January 2017	4,055,114
54	81×2^13470584 + 1	9 October 2022	4,055,052
55	2^13466917 – 1 ^[27]	14 November 2001	4,053,946
56	9×2^13334487 + 1	31 March 2020	4,014,082
57	206039×2^13104952 - 1	26 April 2021	3,944,989
58	2805222×5^5610444 + 1 ^[28]	2 September 2019	3,921,539
59	19249×2^13018586 + 1 ^[29]	26 March 2007	3,918,990
60	2293×2^12918431 - 1	13 February 2021	3,888,839
61	81×2^12804541 + 1	19 September 2022	3,854,553
62	9×2^12406887 + 1	29 March 2020	3,734,847
63	69×2^12231580 - 1	27 July 2021	3,682,075
64	27×2^12184319 + 1	6 February 2021	3,667,847
65	3761×2^11978874 − 1	6 July 2022	3,606,004
66	3×2^11895718 − 1 ^[29]	23 June 2015	3,580,969
67	37×2^11855148 + 1	30 May 2022	3,568,757
68	5897794⁵²⁴²⁸⁸ + 1 ^[29]	18 December 2022	3,549,792
69	3×2^11731850 − 1 ^[30]	13 March 2015	3,531,640
70	69×2^11718455 − 1 ^[29]	4 December 2020	3,527,609
71	41×2^11676439 + 1 ^[29]	20 June 2022	3,514,960
72	4896418⁵²⁴²⁸⁸ + 1 ^[29]	15 May 2022	3,507,424
73	81×2^11616017 + 1 ^[29]	30 August 2022	3,496,772
74	69×2^11604348 − 1 ^[29]	4 December 2020	3,493,259
75	9×2^11500843 + 1 ^[29]	13 March 2020	3,462,100
76	3×2^11484018 − 1 ^[31]	22 November 2014	3,457,035
77	193997×2^11452891 +1	3 April 2018	3,447,670
78	3638450⁵²⁴²⁸⁸ +1	29 May 2020	3,439,810
79	9221×2^11392194 -1	7 February 2021	3,429,397
80	9×2^11366286 +1	26 March 2020	3,421,594
81	5×2^11355764 -1	2 October 2021	3,418,427
82	3214654⁵²⁴²⁸⁸ +1	24 December 2019	3,411,613
83	146561×2^11280802 -1	16 November 2020	3,395,865
84	2985036⁵²⁴²⁸⁸ +1	18 September 2019	3,394,739
85	6929×2^11255424 -1	7 July 2022	3,388,225
86	2877652⁵²⁴²⁸⁸ +1	29 June 2019	3,386,397
87	2788032⁵²⁴²⁸⁸ +1	17 April 2019	3,379,193
88	2733014⁵²⁴²⁸⁸ +1	18 March 2019	3,374,655
89	9×2^11158963 +1	13 March 2020	3,359,184
90	9271×2^11134335 -1	17 January 2021	3,351,773
91	2312092⁵²⁴²⁸⁸+1	4 August 2018	3,336,572
92	2061748⁵²⁴²⁸⁸+1	20 March 2018	3,310,478
93	1880370⁵²⁴²⁸⁸ + 1	15 January 2018	3,289,511
94	27×2^10902757 - 1	7 March 2022	3,282,059
95	3×2^10829346 + 1 ^[32]	14 January 2014	3,259,959
96	11×2^10803449 + 1	29 May 2022	3,252,164
97	11×2^10797109 + 1	29 May 2022	3,250,255
98	7×2^10612737 - 1	19 May 2022	3,194,154
99	37×2^10599476 + 1	17 June 2022	3,190,762
100	5×2^10495620 - 1	26 September 2021	3,159,498
101	5×2^10349000 - 1	26 September 2021	3,115,361
102	$\Phi _{3}(-844833^{262144})$	17 January 2017	3,107,335
103	$\Phi _{3}(-712012^{262144})$	14 January 2017	3,068,389
104	874208×54^1748416-1	26 September 2019	3,028,951
105	475856⁵²⁴²⁸⁸ + 1 ^[33]	8 August 2012	2,976,633
106	2×3^6236772+1	20 December 2022	2,975,697
107	9×2^9778263+1	5 August 2020	2,943,552
108	1806676×41^1806676+1	11 March 2018	2,913,785
109	356926⁵²⁴²⁸⁸ + 1 ^[34]	20 June 2012	2,911,151
110	341112⁵²⁴²⁸⁸ + 1 ^[35]	15 June 2012	2,900,832
111	213988×5^4138363-1	29 November 2022	2,892,597
112	43×2^9596983-1	28 February 2022	2,888,982
113	121×2^9584444+1	18 November 2020	2,885,208
114	11×2^9381365+1	7 March 2020	2,824,074
115	49×2^9187790+1	11 September 2022	2,765,803
116	27653×2^9167433 + 1 ^[29]	8 June 2005	2,759,677
117	90527×2^9162167 + 1	30 June 2010	2,758,093
118	6795×2^9144320 - 1	31 March 2021	2,752,719
119	1323365×116^1323365+1	18 January 2018	2,732,038
120	57×2^9075622-1	7 August 2022	2,732,037
121	63838×5^3887851-1	19 June 2022	2,717,497
122	13×2^8989858 + 1	10 March 2020	2,706,219
123	4159×2^8938471 - 1	19 April 2022	2,690,752
124	273809×2^8932416 − 1 ^[36]	13 December 2017	2,688,931
125	2×3^5570081 + 1	14 February 2020	2,657,605
126	25×2^8788628 + 1	1 March 2021	2,645,643
127	2038×366^1028507 − 1 ^[36]	4 April 2016	2,636,562
128	64598×5^3769854 - 1	14 June 2022	2,635,020
129	8×785⁹⁰⁰³²⁵ + 1	4 June 2022	2,606,325
130	17×2^8636199 + 1	17 February 2021	2,599,757
131	75898⁵²⁴²⁸⁸ + 1 ^[37]	19 November 2011	2,558,647
132	25×2^8456828 + 1	27 January 2021	2,545,761
133	39×2^8413422 + 1	23 January 2021	2,532,694
134	31×2^8348000 + 1	19 January 2021	2,513,000
135	27×2^8342438 - 1	1 February 2021	2,511,326
136	3867×2^8261084 - 1	14 April 2021	2,486,838
137	273662×5^3493296 - 1 ^[38]	7 December 2021	2,441,715
138	81×2^8109236 + 1	9 September 2022	2,441,126
139	11×2^8103463 + 1	6 March 2020	2,439,387
140	102818×5^3440382 - 1 ^[39]	8 October 2021	2,404,729
141	11×2^7971110 - 1	25 November 2019	2,399,545
142	27×2^7963247 + 1	14 January 2021	2,397,178
143	3177×2^7954621 - 1	13 June 2021	2,394,584
144	39×2^7946769 + 1	14 January 2021	2,392,218
145	7×6^3072198 + 1	4 August 2019	2,390,636
146	3765×2^7904593 - 1	10 January 2021	2,379,524
147	29×2^7899985 + 1	14 January 2021	2,378,134
148	5113×2^7895471 - 1	27 November 2022	2,376,778
149	861×2^7895451 - 1	21 February 2021	2,376,771
150	28433×2^7830457 + 1 ^[29]	31 December 2004	2,357,207
151	2589×2^7803339 - 1	21 August 2022	2,349,043
152	5×2^7755002 - 1	23 September 2021	2,334,489
153	2945×2^7753232 - 1	27 November 2022	2,333,959
154	2545×2^7732265 - 1	13 January 2021	2,327,648
155	5539×2^7730709 - 1	15 January 2021	2,327,180
156	4817×2^7719584 - 1	13 June 2021	2,323,831
157	1341174×53^1341174 + 1	21 August 2017	2,312,561
158	9467×2^7680034 - 1	20 February 2022	2,311,925
159	45×2^7661004 + 1	13 December 2020	2,306,194
160	15×2^7619838 + 1	6 December 2020	2,293,801
161	3597×2^7580693 - 1	10 January 2021	2,282,020
162	7401×2^7523295 - 1	21 February 2021	2,264,742
163	45×2^7513661 + 1	12 November 2020	2,261,839
164	$\Phi _{3}(-558640^{196608})$	11 January 2017	2,259,865
165	1875×2^7474308 - 1	21 August 2022	2,249,995
166	4×5^3189669 - 1	12 July 2022	2,229,484
167	29×2^7374577 + 1	27 October 2020	2,219,971
168	3197×2^7359542 - 1	27 November 2022	2,215,447
169	109838×5^3168862 - 1	13 August 2020	2,214,945
170	101×2^7345194 - 1	5 October 2019	2,211,126
171	15×2^7300254 + 1	25 October 2020	2,197,597
172	422429! + 1	21 February 2022	2,193,027
173	1759×2^7284439 - 1	28 August 2021	2,192,838
174	737×2^7269322 − 1	10 August 2017	2,188,287
175	118568×5^3112069 + 1	1 May 2020	2,175,248
176	6039×2^7207973 − 1	24 March 2021	2,169,820
177	502573×2^7181987 − 1 ^[40]	4 October 2014	2,162,000
178	402539×2^7173024 − 1 ^[41]	2 October 2014	2,159,301
179	3343×2^7166019 - 1	29 September 2016	2,157,191
180	161041×2^7107964 + 1	6 January 2015	2,139,716
181	27×2^7046834+1	11 October 2018	2,121,310
182	1759×2^7046791 - 1	28 August 2021	2,121,299
183	327×2^7044001 - 1	13 January 2021	2,120,459
184	5×2^7037188 - 1	22 September 2021	2,118,406
185	3×2^7033641 + 1 ^[42]	21 February 2011	2,117,338
186	33661×2^7031232 + 1 ^[29]	30 October 2007	2,116,617
187	$\Phi _{3}(-237804^{196608})$	6 January 2017	2,114,016
188	207494×5^3017502-1	16 March 2020	2,109,149
189	15×2^6993631-1	25 August 2021	2,105,294
190	8943501×2^6972593-1	8 January 2022	2,098,967
191	6020095×2^6972593-1	4 September 2022	2,098,967
192	2^6972593 – 1 ^[43]	1 June 1999	2,098,960
193	273×2^6963847-1	16 November 2022	2,096,330
194	6219×2^6958945-1	7 January 2021	2,094,855
195	51×2^6945567+1	26 May 2020	2,090,826
196	238694×5^2979422-1	12 March 2020	2,082,532
197	4×72^1119849 − 1 ^[36]	7 September 2016	2,079,933
198	33×2^6894190-1	27 July 2021	2,075,360
199	2345×2^6882320-1	13 April 2022	2,071,789
200	146264×5^2953282-1	9 March 2020	2,064,261
201	69×2^6838971-1	1 March 2020	2,058,738
202	35816×5^2945294-1	5 March 2020	2,058,677
203	127×2^6836153-1	25 June 2018	2,057,890
204	19×2^6833086+1	24 October 2020	2,056,966
205	40597×2^6808509 – 1 ^[44]	25 December 2013	2,049,571
206	283×2^6804701-1	19 January 2020	2,048,431
207	1861209×2^6789999+1	2 December 2020	2,044,000
208	5817×2^6789459-1	9 January 2021	2,043,835
209	8435×2^6786180-1	7 January 2021	2,042,848
210	51×2^6753404+1	26 May 2020	2,032,979
211	9995×2^6711008-1	31 December 2020	2,020,219
212	39×2^6684941+1	20 October 2020	2,012,370
213	6679881×2^6679881 + 1 ^[45]	25 July 2009	2,010,852
214	37×2^6660841 − 1 ^[36]	30 July 2014	2,005,115
215	39×2^6648997+1	20 October 2020	2,001,550

Largest known probable primes (PRPs)

These are probable primes. Primality has not been proven because it is too hard for general numbers of this size but they are expected to be primes.

Rank^[46]	Number	Discovery date	Decimal digits
1	${\tfrac {10^{8177207}-1}{9))$	8 May 2021	8,177,207
2	${\tfrac {10^{5794777}-1}{9))$	20 April 2021	5,794,777
3	${\tfrac {2^{15135397}+1}{3))$ ^[46]	June 2021	4,556,209
4	2^13380298 – 27	March 2021	4,027,872
5	${\tfrac {2^{13372531}+1}{3))$ ^[46]	September 2013	4,025,533
6	${\tfrac {2^{13347311}+1}{3))$ ^[46]	September 2013	4,017,941
7	${\tfrac {2^{12720787}-1}{1666870069020922905132673131516413926009285199))$ ^[46]	October 2022	3,829,294
8	${\tfrac {2^{12503723}-2^{6251862}+1}{5))$ ^[46]	July 2020	3,763,995
9	${\tfrac {2^{10443557}-1}{37289325994807))$ ^[46]	9 July 2020	3,143,811
10	2^9092392 + 40291 ^[46]	February 2011	2,737,083
11	${\tfrac {17^{1990523}-1}{16))$ ^[46]	August 2020	2,449,236
12	${\tfrac {35963^{524288}+1}{2))$ ^[46]	August 2022	2,388,581
13	${\tfrac {11^{2264611}+1}{12))$ ^[46]	July 2021	2,358,349
14	${\tfrac {5^{3300593}-1}{4))$ ^[46]	February 2022	2,307,015
15	${\tfrac {2^{7313983}-1}{305492080276193))$ ^[46]	March 2018	2,201,714
16	${\tfrac {2^{7080247}-1}{17045259548603283727480473638587228614426296913631))$	October 2017	2,131,318

References

External links

Prime number classes

Prime number classes
By formula	Fermat ( $2 2 n + 1$ ) Mersenne ( $2 p - 1$ ) Double Mersenne ( $2 2 p -1 - 1$ ) Wagstaff $(2 p + 1)/3$ Proth ( $k \cdot2 n + 1$ ) Factorial ( $n! \pm 1$ ) Primorial ( $p n # \pm 1$ ) Euclid ( $p n # + 1$ ) Pythagorean ( $4 n + 1$ ) Pierpont ( $2 m \cdot3 n + 1$ ) Quartan ( $x 4 + y 4$ ) Solinas ( $2 m \pm 2 n \pm 1$ ) Cullen ( $n \cdot2 n + 1$ ) Woodall ( $n \cdot2 n - 1$ ) Cuban ( $x 3 - y 3)/(x - y$ ) Leyland ( $x y + y x$ ) Thabit ( $3\cdot2 n - 1$ ) Williams ( $(b -1)\cdot b n - 1$ ) Mills ( $⌊ A 3 n ⌋$ )
By integer sequence	Fibonacci Lucas Pell Newman–Shanks–Williams Perrin Partitions Bell Motzkin
By property	Wieferich (pair) Wall–Sun–Sun Wolstenholme Wilson Lucky Fortunate Ramanujan Pillai Regular Strong Stern Supersingular (elliptic curve) Supersingular (moonshine theory) Good Super Higgs Highly cototient Unique
Base-dependent	Palindromic Emirp Repunit $(10 n - 1)/9$ Permutable Circular Truncatable Minimal Delicate Primeval Full reptend Unique Happy Self Smarandache–Wellin Strobogrammatic Dihedral Tetradic
Patterns	Twin ( $p, p + 2$ ) Bi-twin chain ( $n \pm 1, 2 n \pm 1, 4 n \pm 1, \dots$ ) Triplet ( $p, p + 2 or p + 4, p + 6$ ) Quadruplet ( $p, p + 2, p + 6, p + 8$ ) k-tuple Cousin ( $p, p + 4$ ) Sexy ( $p, p + 6$ ) Chen Sophie Germain/Safe ( $p, 2 p + 1$ ) Cunningham ( $p, 2 p \pm 1, 4 p \pm 3, 8 p \pm 7, ...$ ) Arithmetic progression ( $p + a\cdotn, n = 0, 1, 2, 3, ...$ ) Balanced ( $consecutive p - n, p, p + n$ )
By size	Mega (1,000,000+ digits) Largest known list
Complex numbers	Eisenstein prime Gaussian prime
Composite numbers	Pseudoprime Catalan Elliptic Euler Euler–Jacobi Fermat Frobenius Lucas Somer–Lucas Strong Carmichael number Almost prime Semiprime Interprime Pernicious
Related topics	Probable prime Industrial-grade prime Illegal prime Formula for primes Prime gap
First 60 primes	2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281
List of prime numbers

Largest known primes

Largest known probable primes (PRPs)

See also

References

External links