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

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	$\Phi _{3}(-516693^{1048576})$	2 October 2023	11,981,518
8	$\Phi _{3}(-465859^{1048576})$	31 May 2023	11,887,192
9	2^37156667 – 1 ^[6]	6 September 2008	11,185,272
10	2^32582657 – 1 ^[8]	4 September 2006	9,808,358
11	10223×2^31172165 + 1 ^[9]	31 October 2016	9,383,761
12	2^30402457 – 1 ^[10]	15 December 2005	9,152,052
13	2^25964951 – 1 ^[11]	18 February 2005	7,816,230
14	2^24036583 – 1 ^[12]	15 May 2004	7,235,733
15	1963736^1048576 + 1 ^[13]	24 September 2022	6,598,776
16	1951734^1048576 + 1 ^[14]	9 August 2022	6,595,985
17	202705×2^21320516 + 1 ^[15]	25 November 2021	6,418,121
18	2^20996011 – 1 ^[16]	17 November 2003	6,320,430
19	1059094^1048576 + 1 ^[17]	31 October 2018	6,317,602
20	3×2^20928756 - 1 ^[18]	5 July 2023	6,300,184
21	919444^1048576 + 1 ^[19]	29 August 2017	6,253,210
22	81×2^20498148 + 1	13 June 2023	6,170,560
23	7×2^20267500 + 1	21 July 2022	6,101,127
24	4×5^8431178 + 1	2 January 2024	5,893,142
25	168451×2^19375200 + 1 ^[20]	17 September 2017	5,832,522
26	69×2^19374980 - 1	3 July 2022	5,832,452
27	3×2^18924888 - 1 ^[21]	24 March 2022	5,696,990
28	69×2^18831865 - 1	16 December 2021	5,668,959
29	97139×2^18397548 - 1	23 April 2023	5,538,219
30	7×2^18233956 + 1	1 October 2020	5,488,969
31	3×2^18196595 - 1 ^[22]	8 January 2022	5,477,722
32	3×2^17748034 - 1 ^[23]	6 September 2021	5,342,692
33	$\Phi _{3}(-123447^{524288})$	23 February 2017	5,338,805
34	3622×5^7558139 - 1	18 February 2022	5,282,917
35	7×6^6772401 + 1	9 September 2019	5,269,954
36	2×3^10852677 + 1	8 January 2023	5,178,044
37	8508301×2^17016603-1 ^[24]	21 March 2018	5,122,515
38	13×2^16828072 + 1	11 October 2023	5,065,756
39	3×2^16819291-1 ^[25]	20 January 2021	5,063,112
40	3×2^16408818+1 ^[26]	25 October 2020	4,939,547
41	69×2^15866556+1	20 August 2021	4,776,312
42	2525332×73^2525332+1 ^[27]	28 August 2021	4,705,888
43	11×2^15502315+1	8 January 2023	4,666,663
44	37×2^15474010+1	8 November 2022	4,658,143
45	93839×2^15337656-1	28 November 2022	4,617,100
46	2^15317227+2^7658614+1	31 July 2020	4,610,945
47	13×2^15294536+1	30 September 2023	4,604,116
48	6×5^6546983+1	13 June 2020	4,576,146
49	69×2^14977631-1	3 December 2021	4,508,719
50	192971×2^14773498-1	7 March 2021	4,447,272
51	9145334×3^9145334+1	25 December 2023	4,363,441
52	4×5^6181673-1	15 July 2022	4,320,805
53	6962×31^2863120-1	29 February 2020	4,269,952
54	37×2^14166940+1	24 June 2022	4,264,676
55	99739×2^14019102-1 ^[28]	24 December 2019	4,220,176
56	69×2^13832885-1	17 January 2022	4,164,116
57	404849×2^13764867+1	10 March 2021	4,143,644
58	25×2^13719266+1	20 September 2022	4,129,912
59	81×2^13708272 + 1	11 October 2022	4,126,603
60	2740879×2^13704395-1	26 October 2019	4,125,441
61	479216×3^8625889-1	16 November 2019	4,115,601
62	$\Phi _{3}(-143332^{393216})$	30 January 2017	4,055,114
63	81×2^13470584 + 1	9 October 2022	4,055,052
64	2^13466917 – 1 ^[29]	14 November 2001	4,053,946
65	9×2^13334487 + 1	31 March 2020	4,014,082
66	206039×2^13104952 - 1	26 April 2021	3,944,989
67	2805222×5^5610444 + 1 ^[30]	2 September 2019	3,921,539
68	19249×2^13018586 + 1 ^[31]	26 March 2007	3,918,990
69	2293×2^12918431 - 1	13 February 2021	3,888,839
70	81×2^12804541 + 1	19 September 2022	3,854,553
71	4×5^5380542 + 1	22 February 2023	3,760,839
72	9×2^12406887 + 1	29 March 2020	3,734,847
73	7×2^12286041 - 1	10 June 2023	3,698,468
74	69×2^12231580 - 1	27 July 2021	3,682,075
75	27×2^12184319 + 1	6 February 2021	3,667,847
76	3761×2^11978874 − 1	6 July 2022	3,606,004
77	3×2^11895718 − 1 ^[32]	23 June 2015	3,580,969
78	37×2^11855148 + 1	30 May 2022	3,568,757
79	6339004⁵²⁴²⁸⁸ + 1 ^[33]	8 June 2023	3,566,218
80	763795×6^4582771 + 1	11 December 2023	3,566,095
81	5897794⁵²⁴²⁸⁸ + 1 ^[31]	18 December 2022	3,549,792
82	3×2^11731850 − 1 ^[34]	13 March 2015	3,531,640
83	69×2^11718455 − 1 ^[31]	4 December 2020	3,527,609
84	41×2^11676439 + 1 ^[31]	20 June 2022	3,514,960
85	4896418⁵²⁴²⁸⁸ + 1 ^[35]	15 May 2022	3,507,424
86	81×2^11616017 + 1 ^[31]	30 August 2022	3,496,772
87	69×2^11604348 − 1 ^[31]	4 December 2020	3,493,259
88	4450871×6^4450871 + 1 ^[31]	17 September 2023	3,463,458
89	9×2^11500843 + 1 ^[31]	13 March 2020	3,462,100
90	3×2^11484018 − 1 ^[36]	22 November 2014	3,457,035
91	193997×2^11452891 +1 ^[37]	3 April 2018	3,447,670
92	3638450⁵²⁴²⁸⁸ +1 ^[38]	29 May 2020	3,439,810
93	9221×2^11392194 -1 ^[39]	7 February 2021	3,429,397
94	9×2^11366286 +1	26 March 2020	3,421,594
95	5×2^11355764 -1	2 October 2021	3,418,427
96	732050×6^4392301 +1	9 September 2023	3,417,881
97	3214654⁵²⁴²⁸⁸ +1 ^[40]	24 December 2019	3,411,613
98	146561×2^11280802 -1 ^[41]	16 November 2020	3,395,865
99	2985036⁵²⁴²⁸⁸ +1 ^[42]	18 September 2019	3,394,739
100	6929×2^11255424 -1	7 July 2022	3,388,225
101	2877652⁵²⁴²⁸⁸ +1 ^[43]	29 June 2019	3,386,397
102	2788032⁵²⁴²⁸⁸ +1 ^[44]	17 April 2019	3,379,193
103	2733014⁵²⁴²⁸⁸ +1 ^[45]	18 March 2019	3,374,655
104	9×2^11158963 +1	13 March 2020	3,359,184
105	9271×2^11134335 -1	17 January 2021	3,351,773
106	2312092⁵²⁴²⁸⁸+1 ^[46]	4 August 2018	3,336,572
107	2061748⁵²⁴²⁸⁸+1 ^[47]	20 March 2018	3,310,478
108	1880370⁵²⁴²⁸⁸ + 1 ^[48]	15 January 2018	3,289,511
109	27×2^10902757 - 1	7 March 2022	3,282,059
110	3×2^10829346 + 1 ^[49]	14 January 2014	3,259,959
111	11×2^10803449 + 1	29 May 2022	3,252,164
112	11×2^10797109 + 1	29 May 2022	3,250,255
113	7×2^10612737 - 1	19 May 2022	3,194,154
114	37×2^10599476 + 1	17 June 2022	3,190,762
115	5×2^10495620 - 1	26 September 2021	3,159,498
116	${\tfrac {\Phi _{3}(-3^{3304302}+1)}{3}}$	30 June 2023	3,153,105
117	5×2^10349000 - 1	26 September 2021	3,115,361
118	$\Phi _{3}(-844833^{262144})$	17 January 2017	3,107,335
119	52922×5^4399812-1	3 August 2023	3,075,342
120	$\Phi _{3}(-712012^{262144})$	14 January 2017	3,068,389
121	177742×5^4386703-1	24 July 2023	3,066,180
122	874208×54^1748416-1	26 September 2019	3,028,951
123	475856⁵²⁴²⁸⁸ + 1 ^[50]	8 August 2012	2,976,633
124	2×3^6236772+1	20 December 2022	2,975,697
125	15×3^9830108+1	19 August 2023	2,959,159
126	9×2^9778263+1	5 August 2020	2,943,552
127	1806676×41^1806676+1	11 March 2018	2,913,785
128	356926⁵²⁴²⁸⁸ + 1 ^[51]	20 June 2012	2,911,151
129	341112⁵²⁴²⁸⁸ + 1 ^[52]	15 June 2012	2,900,832
130	213988×5^4138363-1	29 November 2022	2,892,597
131	43×2^9596983-1	28 February 2022	2,888,982
132	121×2^9584444+1 ^[53]	18 November 2020	2,885,208
133	11×2^9381365+1	7 March 2020	2,824,074
134	15×2^9312889+1	7 August 2023	2,803,461
135	49×2^9187790+1	11 September 2022	2,765,803
136	27653×2^9167433 + 1 ^[31]	8 June 2005	2,759,677
137	90527×2^9162167 + 1	30 June 2010	2,758,093
138	6795×2^9144320 - 1	31 March 2021	2,752,719
139	1323365×116^1323365+1 ^[54]	18 January 2018	2,732,038
140	75×2^9079482+1	25 July 2023	2,733,199
141	57×2^9075622-1	7 August 2022	2,732,037
142	63838×5^3887851-1 ^[55]	19 June 2022	2,717,497
143	13×2^8989858 + 1	10 March 2020	2,706,219
144	4159×2^8938471 - 1	19 April 2022	2,690,752
145	273809×2^8932416 − 1 ^[56]	13 December 2017	2,688,931
146	2×3^5570081 + 1	14 February 2020	2,657,605
147	25×2^8788628 + 1 ^[57]	1 March 2021	2,645,643
148	2038×366^1028507 − 1 ^[58]	4 April 2016	2,636,562
149	64598×5^3769854 - 1	14 June 2022	2,635,020
150	8×785⁹⁰⁰³²⁵ + 1	4 June 2022	2,606,325
151	17×2^8636199 + 1 ^[59]	17 February 2021	2,599,757
152	75898⁵²⁴²⁸⁸ + 1 ^[60]	19 November 2011	2,558,647
153	25×2^8456828 + 1 ^[61]	27 January 2021	2,545,761
154	39×2^8413422 + 1 ^[62]	23 January 2021	2,532,694
155	31×2^8348000 + 1 ^[63]	19 January 2021	2,513,000
156	27×2^8342438 - 1 ^[64]	1 February 2021	2,511,326
157	3867×2^8261084 - 1	14 April 2021	2,486,838
158	101×2^8152967 + 1	2 December 2023	2,454,290
159	273662×5^3493296 - 1 ^[65]	7 December 2021	2,441,715
160	81×2^8109236 + 1	9 September 2022	2,441,126
161	11×2^8103463 + 1	6 March 2020	2,439,387
162	102818×5^3440382 - 1 ^[66]	8 October 2021	2,404,729
163	11×2^7971110 - 1	25 November 2019	2,399,545
164	27×2^7963247 + 1 ^[67]	14 January 2021	2,397,178
165	3177×2^7954621 - 1	13 June 2021	2,394,584
166	39×2^7946769 + 1 ^[68]	14 January 2021	2,392,218
167	7×6^3072198 + 1	4 August 2019	2,390,636
168	3765×2^7904593 - 1	10 January 2021	2,379,524
169	29×2^7899985 + 1 ^[69]	14 January 2021	2,378,134
170	5113×2^7895471 - 1	27 November 2022	2,376,778
171	861×2^7895451 - 1	21 February 2021	2,376,771
172	75×2^7886683 + 1	4 September 2023	2,374,131
173	28433×2^7830457 + 1 ^[31]	31 December 2004	2,357,207
174	2589×2^7803339 - 1	21 August 2022	2,349,043
175	8401×2^7767655 - 1	24 April 2023	2,338,302
176	9693×2^7767343 - 1	17 November 2023	2,338,208
177	5×2^7755002 - 1	23 September 2021	2,334,489
178	2945×2^7753232 - 1	27 November 2022	2,333,959
179	2545×2^7732265 - 1	13 January 2021	2,327,648
180	5539×2^7730709 - 1	15 January 2021	2,327,180
181	4817×2^7719584 - 1	13 June 2021	2,323,831
182	1341174×53^1341174 + 1 ^[70]	21 August 2017	2,312,561
183	9467×2^7680034 - 1	20 February 2022	2,311,925
184	45×2^7661004 + 1 ^[71]	13 December 2020	2,306,194
185	15×2^7619838 + 1 ^[72]	6 December 2020	2,293,801
186	3597×2^7580693 - 1	10 January 2021	2,282,020
187	3129×2^2271443 - 1	14 March 2023	2,271,443
188	7401×2^7523295 - 1	21 February 2021	2,264,742
189	45×2^7513661 + 1 ^[73]	12 November 2020	2,261,839
190	$\Phi _{3}(-558640^{196608})$	11 January 2017	2,259,865
191	9×2^7479919 - 1	3 June 2023	2,251,681
192	1875×2^7474308 - 1	21 August 2022	2,249,995
193	69×2^7452023 + 1	23 March 2023	2,243,285
194	1281879×2^7447178 + 1	27 December 2023	2,241,831
195	4×5^3189669 - 1	12 July 2022	2,229,484
196	29×2^7374577 + 1 ^[74]	27 October 2020	2,219,971
197	3197×2^7359542 - 1	27 November 2022	2,215,447
198	109838×5^3168862 - 1 ^[75]	13 August 2020	2,214,945
199	95×2^7354869 + 1	25 September 2023	2,214,039
200	101×2^7345194 - 1	5 October 2019	2,211,126
201	85×2^7333444 + 1	25 September 2023	2,207,589
202	15×2^7300254 + 1 ^[76]	25 October 2020	2,197,597
203	422429! + 1	21 February 2022	2,193,027
204	1759×2^7284439 - 1	28 August 2021	2,192,838
205	1909683×14^1909683 + 1	27 May 2023	2,188,748
206	737×2^7269322 − 1	10 August 2017	2,188,287
207	95×2^7241494 + 1	25 September 2023	2,179,909
208	118568×5^3112069 + 1 ^[77]	1 May 2020	2,175,248
209	6039×2^7207973 − 1	24 March 2021	2,169,820
210	502573×2^7181987 − 1 ^[78]	4 October 2014	2,162,000
211	402539×2^7173024 − 1 ^[79]	2 October 2014	2,159,301
212	3343×2^7166019 - 1	29 September 2016	2,157,191
213	161041×2^7107964 + 1 ^[80]	6 January 2015	2,139,716
214	294×213⁹¹⁸⁹⁵²-1	19 September 2023	2,139,672
215	27×2^7046834+1 ^[81]	11 October 2018	2,121,310
216	1759×2^7046791 - 1	28 August 2021	2,121,299
217	327×2^7044001 - 1	13 January 2021	2,120,459
218	5×2^7037188 - 1	22 September 2021	2,118,406
219	3×2^7033641 + 1 ^[82]	21 February 2011	2,117,338
220	33661×2^7031232 + 1 ^[31]	30 October 2007	2,116,617
221	$\Phi _{3}(-237804^{196608})$	6 January 2017	2,114,016
222	207494×5^3017502-1	16 March 2020	2,109,149
223	15×2^6993631-1	25 August 2021	2,105,294
224	8943501×2^6972593-1	8 January 2022	2,098,967
225	6020095×2^6972593-1	4 September 2022	2,098,967
226	2^6972593 – 1 ^[83]	1 June 1999	2,098,960
227	273×2^6963847-1	16 November 2022	2,096,330
228	6219×2^6958945-1	7 January 2021	2,094,855
229	51×2^6945567+1	26 May 2020	2,090,826
230	238694×5^2979422-1 ^[84]	12 March 2020	2,082,532
231	4×72^1119849 − 1 ^[58]	7 September 2016	2,079,933
232	33×2^6894190-1	27 July 2021	2,075,360
233	2345×2^6882320-1	13 April 2022	2,071,789
234	57×2^6857990+1	17 August 2023	2,064,463
235	146264×5^2953282-1 ^[85]	9 March 2020	2,064,261
236	69×2^6838971-1	1 March 2020	2,058,738
237	35816×5^2945294-1 ^[86]	5 March 2020	2,058,677
238	127×2^6836153-1	25 June 2018	2,057,890
239	19×2^6833086+1 ^[87]	24 October 2020	2,056,966
240	65×2^6810465 + 1	22 September 2023	2,050,157
241	40597×2^6808509 – 1 ^[88]	25 December 2013	2,049,571
242	283×2^6804701-1	19 January 2020	2,048,431
243	1861209×2^6789999+1	2 December 2020	2,044,000
244	5817×2^6789459-1	9 January 2021	2,043,835
245	8435×2^6786180-1	7 January 2021	2,042,848
246	51×2^6753404+1	26 May 2020	2,032,979
247	93×2^6750726+1	18 September 2023	2,032,173
248	69×2^6745775+1	21 March 2023	2,030,683
249	9995×2^6711008-1	31 December 2020	2,020,219
250	39×2^6684941+1 ^[89]	20 October 2020	2,012,370
251	6679881×2^6679881 + 1 ^[90]	25 July 2009	2,010,852
252	37×2^6660841 − 1 ^[58]	30 July 2014	2,005,115
253	39×2^6648997+1 ^[91]	20 October 2020	2,001,550
254	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.

Rank^[92]	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	${\tfrac {2^{15135397}+1}{3}}$ ^[92]	June 2021	4,556,209
4	${\tfrac {3^{8530117}-1}{2}}$ ^[92]	November 2023	4,069,900
5	2^13380298 – 27	March 2021	4,027,872
6	${\tfrac {2^{13372531}+1}{3}}$ ^[92]	September 2013	4,025,533
7	${\tfrac {2^{13347311}+1}{3}}$ ^[92]	September 2013	4,017,941
8	${\tfrac {2^{12720787}-1}{1666870069020922905132673131516413926009285199}}$ ^[92]	3 July 2022	3,829,294
9	${\tfrac {3^{7973131}-1}{2}}$ ^[92]	November 2023	3,804,150
10	${\tfrac {2^{12588091}-1}{32075464348897282169539424801}}$ ^[92]	10 April 2023	3,789,365
11	${\tfrac {2^{12503723}-2^{6251862}+1}{5}}$ ^[92]	July 2020	3,763,995
12	${\tfrac {2^{10443557}-1}{37289325994807}}$ ^[92]	9 July 2020	3,143,811
13	2^9092392 + 40291 ^[92]	February 2011	2,737,083
14	${\tfrac {6^{3360347}-1}{5}}$ ^[92]	October 2023	2,614,858
15	${\tfrac {17^{1990523}-1}{16}}$ ^[92]	August 2020	2,449,236
16	${\tfrac {35963^{524288}+1}{2}}$ ^[92]	August 2022	2,388,581
17	${\tfrac {11^{2264611}+1}{12}}$ ^[92]	July 2021	2,358,349
18	${\tfrac {5^{3300593}-1}{4}}$ ^[92]	February 2022	2,307,015
19	${\tfrac {3^{4694803}+2^{4694803}}{5}}$ ^[92]	December 2023	2,239,990
20	${\tfrac {2^{7313983}-1}{305492080276193}}$ ^[92]	1 March 2018	2,201,714
21	${\tfrac {3^{4571447}+2^{4571447}}{5}}$ ^[92]	December 2023	2,181,134
22	3^4532794 + 4532794³	October 2023	2,162,693
23	${\tfrac {2^{7080247}-1}{17045259548603283727480473638587228614426296913631}}$	27 October 2017	2,131,318

References

↑ Caldwell, Chris K. "THE LARGEST KNOWN PRIMES (The 5,000 largest known primes)". Retrieved 23 November 2018.
↑ "Official press release of 51st Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 7 December 2018.
↑ "Official press release of 50th Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 26 December 2017.
↑ "Official press release of 49th Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 7 January 2016.
↑ "Official press release of 48th Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 25 January 2013.
1 2 "Official press release of 45th and 46th Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 10 September 2008.
↑ "Official press release of 47th Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 25 January 2013.
↑ "Official press release of 44th Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 25 January 2013.
↑ Official announcement of discovery of 10223×2^31172165 + 1, PrimeGrid
↑ "Official press release of 43rd Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 25 January 2013.
↑ "Official press release of 42nd Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 25 January 2013.
↑ "Official press release of 41st Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 25 January 2013.
↑ Official announcement of discovery of 1963736^1048576 + 1, PrimeGrid
↑ Official announcement of discovery of 1951734^1048576 + 1, PrimeGrid
↑ Official announcement of discovery of 202705×2^21320516 + 1, PrimeGrid
↑ "Official press release of 40th Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 25 January 2013.
↑ Official announcement of discovery of 1059094^1048576 + 1, PrimeGrid
↑ Official announcement of discovery of 3×2^20928756 - 1, PrimeGrid
↑ Official announcement of discovery of 919444^1048576 + 1, PrimeGrid
↑ Official announcement of discovery of 168451×2^19375200 + 1, PrimeGrid
↑ Official announcement of discovery of 3×2^18924888 - 1, PrimeGrid
↑ Official announcement of discovery of 3×2^18196595 - 1, PrimeGrid
↑ Official announcement of discovery of 3×2^17748034 - 1, PrimeGrid
↑ Official announcement of discovery of 8508301×2^17016603-1, PrimeGrid
↑ Official announcement of discovery of 3×2^16819291-1, PrimeGrid
↑ Official announcement of discovery of 3×2^16408818+1, PrimeGrid
↑ Official announcement of discovery of 2525332×73^2525332+1, PrimeGrid
↑ Official announcement of discovery of 99739×2^14019102-1, PrimeGrid
↑ "Official press release of 39th Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 25 January 2013.
↑ Official announcement of discovery of 2805222×5^5610444 + 1, PrimeGrid
1 2 3 4 5 6 7 8 9 10 11 Chris Caldwell, The Largest Known Primes at The PrimePages.
↑ Official announcement of discovery of 3×2^11895718−1, PrimeGrid
↑ Official announcement of discovery of 6339004⁵²⁴²⁸⁸ + 1, PrimeGrid
↑ Official announcement of discovery of 3×2^11731850 − 1, PrimeGrid
↑ Official announcement of discovery of 4896418⁵²⁴²⁸⁸ + 1, PrimeGrid
↑ Official announcement of discovery of 3×2^11484018 − 1, PrimeGrid
↑ Official announcement of discovery of 193997×2^11452891 + 1, PrimeGrid
↑ Official announcement of discovery of 3638450⁵²⁴²⁸⁸ + 1, PrimeGrid
↑ Official announcement of discovery of 9221×2^11392194 -1, PrimeGrid
↑ Official announcement of discovery of 3214654⁵²⁴²⁸⁸ + 1, PrimeGrid
↑ Official announcement of discovery of 146561×2^11280802 -1, PrimeGrid
↑ Official announcement of discovery of 2985036⁵²⁴²⁸⁸ + 1, PrimeGrid
↑ Official announcement of discovery of 2877652⁵²⁴²⁸⁸ + 1, PrimeGrid
↑ Official announcement of discovery of 2788032⁵²⁴²⁸⁸ + 1, PrimeGrid
↑ Official announcement of discovery of 2733014⁵²⁴²⁸⁸ + 1, PrimeGrid
↑ Official announcement of discovery of 2312092⁵²⁴²⁸⁸ + 1, PrimeGrid
↑ Official announcement of discovery of 2061748⁵²⁴²⁸⁸ + 1, PrimeGrid
↑ Official announcement of discovery of 1880370⁵²⁴²⁸⁸ + 1, PrimeGrid
↑ Official announcement of discovery of 3×2^10829346 + 1, PrimeGrid
↑ Official announcement of discovery of 475856⁵²⁴²⁸⁸ + 1, PrimeGrid
↑ Official announcement of discovery of 356926⁵²⁴²⁸⁸ + 1, PrimeGrid
↑ Official announcement of discovery of 341112⁵²⁴²⁸⁸ + 1, PrimeGrid
↑ Official announcement of discovery of 121×2^9584444+1, PrimeGrid
↑ Official announcement of discovery of 1323365×116^1323365 + 1, PrimeGrid
↑ Official announcement of discovery of 63838×5^3887851-1, PrimeGrid
↑ Official announcement of discovery of 273809×2^8932416 -1, PrimeGrid
↑ Official announcement of discovery of 25×2^8788628 + 1, PrimeGrid
1 2 3 "CRUS - Proven Conjectures". www.noprimeleftbehind.net.
↑ Official announcement of discovery of 17×2^8636199 + 1, PrimeGrid
↑ Official announcement of discovery of 75898⁵²⁴²⁸⁸ + 1, PrimeGrid
↑ Official announcement of discovery of 25×2^8456828 + 1, PrimeGrid
↑ Official announcement of discovery of 39×2^8413822 + 1, PrimeGrid
↑ Official announcement of discovery of 31×2^8348000 + 1, PrimeGrid
↑ Official announcement of discovery of 27×2^8342438 - 1, PrimeGrid
↑ Official announcement of discovery of 273662×5^3493296 + 1, PrimeGrid
↑ 102818×5^3440382-1, PrimeGrid
↑ Official announcement of discovery of 27×2^7963247 + 1, PrimeGrid
↑ Official announcement of discovery of 39×2^7946769 + 1, PrimeGrid
↑ Official announcement of discovery of 29×2^7899985 + 1, PrimeGrid
↑ Official announcement of discovery of 1341174×53^1341174 + 1, PrimeGrid
↑ Official announcement of discovery of 45×2^7661004 + 1, PrimeGrid
↑ Official announcement of discovery of 15×2^7619838 + 1, PrimeGrid
↑ Official announcement of discovery of 45×2^7513661 + 1, PrimeGrid
↑ Official announcement of discovery of 29×2^7374577 + 1, PrimeGrid
↑ 109838×5^3168862-1, PrimeGrid
↑ Official announcement of discovery of 29×2^7300254 + 1, PrimeGrid
↑ 118568×5^3112069+1, PrimeGrid
↑ Official announcement of discovery of 502573×2^7181987 − 1, PrimeGrid
↑ Official announcement of discovery of 402539×2^7173024 − 1, PrimeGrid
↑ Official announcement of discovery of 161041×2^7107964 + 1, PrimeGrid
↑ Official announcement of discovery of 27×2^7046834 + 1, PrimeGrid
↑ Official announcement of discovery of 3×2^7033641 + 1, PrimeGrid
↑ GIMPS press release, GIMPS Finds First Million-Digit Prime. Retrieved on 2008-01-04.
↑ 238694×5^2979422-1, PrimeGrid
↑ 146264×5^2953282-1, PrimeGrid
↑ 35816×5^2945294-1, PrimeGrid
↑ Official announcement of discovery of 19×2^6833086 + 1, PrimeGrid
↑ Official announcement of discovery of 40597×2^6808509 – 1, PrimeGrid
↑ Official announcement of discovery of 39×2^6684941 + 1, PrimeGrid
↑ Official announcement of discovery of 6679881×2^6679881 + 1, PrimeGrid
↑ Official announcement of discovery of 39×2^6648997 + 1, PrimeGrid
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 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

This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.

[1] Caldwell, Chris K. "THE LARGEST KNOWN PRIMES (The 5,000 largest known primes)". Retrieved 23 November 2018.

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

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

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

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

[4546prime-6] 1 2 "Official press release of 45th and 46th Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 10 September 2008.

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

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

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

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

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

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

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

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

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

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

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

[18] Official announcement of discovery of 3×2^20928756 - 1, PrimeGrid

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

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

[21] Official announcement of discovery of 3×2^18924888 - 1, PrimeGrid

[22] Official announcement of discovery of 3×2^18196595 - 1, PrimeGrid

[23] Official announcement of discovery of 3×2^17748034 - 1, PrimeGrid

[24] Official announcement of discovery of 8508301×2^17016603-1, PrimeGrid

[25] Official announcement of discovery of 3×2^16819291-1, PrimeGrid

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

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

[28] Official announcement of discovery of 99739×2^14019102-1, PrimeGrid

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

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

[The_largest_known_primes-31] 1 2 3 4 5 6 7 8 9 10 11 Chris Caldwell, The Largest Known Primes at The PrimePages.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[55] Official announcement of discovery of 63838×5^3887851-1, PrimeGrid

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

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

[GSRP-58] 1 2 3 "CRUS - Proven Conjectures". www.noprimeleftbehind.net.

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

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

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

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

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

[64] Official announcement of discovery of 27×2^8342438 - 1, PrimeGrid

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

[66] 102818×5^3440382-1, PrimeGrid

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

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

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

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

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

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

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

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

[75] 109838×5^3168862-1, PrimeGrid

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

[77] 118568×5^3112069+1, PrimeGrid

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

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

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

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

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

[1stmegaprime-83] GIMPS press release, GIMPS Finds First Million-Digit Prime. Retrieved on 2008-01-04.

[84] 238694×5^2979422-1, PrimeGrid

[85] 146264×5^2953282-1, PrimeGrid

[86] 35816×5^2945294-1, PrimeGrid

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

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

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

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

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

[PRPTop-92] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Henri Lifchitz & Renaud Lifchitz, Probable Primes Top 10000, primenumbers.net

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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 Perrin Somer–Lucas Strong Carmichael number Almost prime Semiprime Sphenic number 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