Megaprime

A megaprime is a prime number with at least one million decimal digits.^[1]

A titanic prime, a term coined by Samuel Yates in the 1980s, is a prime number with at least 1,000 digits; and a gigantic prime has at least 10,000 digits.

The number of megaprimes found by year.

As of December 2018, 449 (probable) megaprimes are known, including 421 definite primes^[2] and 28 probable primes.^[3] The first to be found was the Mersenne prime 2^6972593−1 with 2,098,960 digits, discovered in 1999 by Nayan Hajratwala, a participant in the distributed computing project GIMPS,^[4]^[5] and was subject to a cooperative computing award.

The term bevaprime has been proposed as a term for a prime with at least 1,000,000,000 digits.^[6]

In fact, almost all primes are megaprimes, as the number of primes with less than a million digits is finite. However, the vast majority of known primes are not megaprimes.

Known megaprimes and mega PRPs[]

Entries labelled "Prime" have been proved prime; those labelled "PRP" have not. See the article Probable prime.

Rank (only for proven primes)^[7]	Number	Discovery date	Decimal digits	Prime / PRP
1	2^82589933 – 1 ^[8]	2018-12-07	24,862,048	Prime
2	2^77232917 – 1 ^[9]	2017-12-26	23,249,425	Prime
3	2^74207281 – 1	2016-01-07	22,338,618	Prime
4	2^57885161 – 1	2013-01-25	17,425,170	Prime
5	2^43112609 – 1	2008-08-23	12,978,189	Prime
6	2^42643801 – 1	2009-06-04	12,837,064	Prime
7	2^37156667 – 1	2008-09-06	11,185,272	Prime
8	2^32582657 – 1	2006-09-04	9,808,358	Prime
9	10223×2^31172165 + 1	2016-11	9,383,761	Prime
10	2^30402457 – 1	2005-12-15	9,152,052	Prime
11	2^25964951 – 1	2005-02-18	7,816,230	Prime
12	2^24036583 – 1	2004-05-15	7,235,733	Prime
13	2^20996011 – 1	2003-11-17	6,320,430	Prime
14	1059094^1048576 + 1	2018	6,317,602	Prime
15	919444^1048576 + 1 ^[10]	2017-09-02	6,253,210	Prime
16	168451×2^19375200 + 1	2017	5,832,522	Prime
17	$\Phi _{3}(-123447^{524288})$	2017	5,338,805	Prime
18	8508301*2^17016603-1	2018	5,122,515	Prime
19	$\Phi _{3}(-143332^{393216})$	2017	4,055,114	Prime
20	2^13466917 – 1	2001-11-14	4,053,946	Prime
-	${\tfrac {2^{13372531}+1}{3}}$ ^[3]	2013-09	4,025,533	PRP
-	${\tfrac {2^{13347311}+1}{3}}$ ^[3]	2013-09	4,017,941	PRP
21	19249×2^13018586 + 1 ^[2]	2007-03-26	3,918,990	Prime
22	3×2^11895718 − 1 ^[2]	2015-06	3,580,969	Prime
23	3×2^11731850 − 1 ^[11]	2015-03-13	3,531,640	Prime
24	3×2^11484018 − 1 ^[12]	2014-11-22	3,457,035	Prime
25	193997*2^11452891 +1	2018	3,447,670	Prime
26	2312092⁵²⁴²⁸⁸+1	2018	3,336,572	Prime
27	2061748⁵²⁴²⁸⁸+1	2018	3,310,478	Prime
28	1880370⁵²⁴²⁸⁸ + 1	2018	3,289,511	Prime
29	3×2^10829346 + 1 ^[13]	2014-01-14	3,259,959	Prime
30	$\Phi _{3}(-844833^{262144})$	2017	3,107,335	Prime
31	$\Phi _{3}(-712012^{262144})$	2017	3,068,389	Prime
32	475856⁵²⁴²⁸⁸ + 1 ^[14]	2012-08-08	2,976,633	Prime
33	1806676*41^1806676+1	2018	2,913,785	Prime
34	356926⁵²⁴²⁸⁸ + 1 ^[15]	2012-06-20	2,911,151	Prime
35	341112⁵²⁴²⁸⁸ + 1 ^[16]	2012-06-15	2,900,832	Prime
36	27653×2^9167433 + 1 ^[2]	2005	2,759,677	Prime
37	90527×2^9162167 + 1	2010	2,758,093	Prime
-	2^9092392 + 40291 ^[3]	2011-02	2,737,083	PRP
38	1323365*116^1323365+1	2018	2,732,038	Prime
39	273809×2^8932416 − 1 ^[17]	2017	2,688,931	Prime
40	2038×366^1028507 − 1 ^[17]	2016	2,636,562	Prime
41	75898⁵²⁴²⁸⁸ + 1 ^[18]	2011-11-19	2,558,647	Prime
42	28433×2^7830457 + 1 ^[2]	2004	2,357,207	Prime
43	1341174×53^1341174 + 1	2017	2,312,561	Prime
44	$\Phi _{3}(-558640^{196608})$	2017	2,259,865	Prime
-	${\tfrac {2^{7313983}-1}{305492080276193}}$ ^[3]	2018	2,201,714	PRP
45	737×2^7269322 − 1	2017	2,188,287	Prime
46	502573×2^7181987 − 1 ^[19]	2014-10-04	2,162,000	Prime
47	402539×2^7173024 − 1 ^[20]	2014-10-02	2,159,301	Prime
48	3343×2^7166019 - 1	2016	2,157,191	Prime
49	161041×2^7107964 + 1	2015-01	2,139,716	Prime
-	${\tfrac {2^{7080247}-1}{17045259548603283727480473638587228614426296913631}}$	2017-10	2,131,318	PRP
50	27*2^7046834+1	2018	2,121,310	Prime
51	3×2^7033641 + 1 ^[21]	2011-02-21	2,117,338	Prime
52	33661×2^7031232 + 1 ^[2]	2007	2,116,617	Prime
53	$\Phi _{3}(-237804^{196608})$	2017	2,114,016	Prime
54	2^6972593 – 1	1999-06-01	2,098,960	Prime
55	4×72^1119849 − 1 ^[17]	2016	2,079,933	Prime
56	127*2^6836153-1	2018	2,057,890	Prime
57	40597×2^6808509 – 1 ^[22]	2013-12-25	2,049,571	Prime
58	6679881×2^6679881 + 1 ^[23]	2009-07-25	2,010,852	Prime
59	37×2^6660841 − 1 ^[17]	2014	2,005,115	Prime
60	304207×2^6643565 – 1 ^[24]	2013-10-10	1,999,918	Prime
61	398023×2^6418059 – 1 ^[25]	2013-10-05	1,932,034	Prime
62	1582137x2^6328550 + 1 ^[26]	2009-04-20	1,905,090	Prime
63	194368*5^2638045-1	2018	1,843,920	Prime
64	66916*5^2628609-1	2018	1,837,324	Prime
65	3×2^6090515 – 1 ^[27]	2010-04-24	1,833,429	Prime
66	1583×2^5989282 − 1	2015	1,802,957	Prime
67	327926*5^2542838-1	2018	1,777,374	Prime
68	81556*5^2539960+1	2018	1,775,361	Prime
69	5828034²⁶²¹⁴⁴+1	2018	1,773,542	Prime
70	5205422²⁶²¹⁴⁴+1	2018	1,760,679	Prime
71	5152128²⁶²¹⁴⁴+1	2018	1,759,508	Prime
72	4489246²⁶²¹⁴⁴+1	2018	1,743,828	Prime
73	7×2^5775996 + 1 ^[28]	2012-11-02	1,738,749	Prime
74	4246258²⁶²¹⁴⁴+1	2018	1,737,493	Prime
75	3933508²⁶²¹⁴⁴+1	2018	1,728,783	Prime
76	3853792²⁶²¹⁴⁴+1	2018	1,726,452	Prime
77	3673932²⁶²¹⁴⁴ + 1	2017	1,721,010	Prime
78	3596074²⁶²¹⁴⁴ + 1	2017	1,718,572	Prime
79	3547726²⁶²¹⁴⁴ + 1	2017	1,717,031	Prime
80	1243×2^5686715 - 1	2016	1,711,875	Prime
81	3060772²⁶²¹⁴⁴ + 1	2017	1,700,222	Prime
82	9×2^5642513 + 1	2013	1,698,567	Prime
83	2622×11^1621920 – 1 ^[17]	2015	1,689,060	Prime
84	2676404²⁶²¹⁴⁴ + 1	2017	1,684,945	Prime
86	301562×5^2408646 - 1	2017	1,683,577	Prime
86	2611294²⁶²¹⁴⁴ + 1	2017	1,682,141	Prime
87	171362×5^2400996 − 1	2017	1,678,230	Prime
88	2514168²⁶²¹⁴⁴ + 1	2017	1,677,825	Prime
89	252191×2^5497878 – 1 ^[29]	2012-06-23	1,655,032	Prime
90	2042774²⁶²¹⁴⁴ + 1	2016	1,654,187	Prime
91	1828858²⁶²¹⁴⁴+1	2016	1,641,593	Prime
92	258317 × 2^5450519+1	2008	1,640,776	Prime
93	5*2^5429494-1	2017	1,634,442	Prime
94	43*2^5408183-1	2018	1,628,027	Prime
94	1615588²⁶²¹⁴⁴ + 1	2016	1,627,477	Prime
95	1349×2^5385004 − 1	2017	1,621,051	Prime
96	1488256²⁶²¹⁴⁴ + 1	2016	1,618,131	Prime
97	1415198²⁶²¹⁴⁴ + 1	2016	1,612,400	Prime
98	$\Phi _{3}(-1082083^{131072})$	2017	1,581,846	Prime
-	${\tfrac {2^{5240707}-1}{75392810903}}$ ^[3]	2016-07	1,577,600	PRP
99	180062×5^2249192 − 1	2016	1,572,123	Prime
100	27×2^5213635 + 1	2015	1,569,462	Prime
101	$\Phi _{3}(-843575^{131072})$	2017	1,553,498	Prime
102	53546×5^2216664-1	2016	1,549,387	Prime
-	2^5146295 + 41693 ^[3]	2009-11	1,549,190	PRP
103	773620²⁶²¹⁴⁴ + 1 ^[30]	2012-04-19	1,543,643	Prime
104	51×2^5085142 - 1	2014	1,530,782	Prime
105	3×2^5082306 + 1 ^[31]	2009-04-03	1,529,928	Prime
106	676754²⁶²¹⁴⁴+1	2012	1,528,413	Prime
107	296024 × 5^2185270 − 1	2016	1,527,444	Prime
108	5359 × 2^5054502+1	2003	1,521,561	Prime
109	13×2^4998362 + 1	2014	1,504,659	Prime
110	525094²⁶²¹⁴⁴+1	2012	1,499,526	Prime
111	92158×5^2145024 + 1	2016	1,499,313	Prime
112	77072×5^2139921 + 1	2016	1,495,746	Prime
113	306398 × 5^2112410 − 1	2016	1,476,517	Prime
114	265711 × 2^4858008+1	2008	1,462,412	Prime
115	154222 × 5^2091432 + 1	2015	1,461,854	Prime
116	1271 × 2^4850526-1	2012	1,460,157	Prime
117	$\Phi _{3}(-362978^{131072})$	2015	1,457,490	Prime
118	361658²⁶²¹⁴⁴+1	2011	1,457,075	Prime
-	${\tfrac {2^{4834891}-1}{120254426180274428677241}}$ ^[3]	2017-01	1,455,425	PRP
119	100186 × 5^2079747 − 1	2015	1,453,686	Prime
120	$\Phi _{19168228L}(2)$ ^[*]	2014	1,442,553	Prime
121	653 × 10^1435026 − 1 ^[17]	2014	1,435,029	Prime
122	1229 x 2^4703492-1	2018	1,415,896
123	144052× 5^2018290 + 1	2015	1,410,730	Prime
124	9 × 2^4683555 − 1	2012	1,409,892	Prime
125	34x993⁴⁶⁹²⁴⁵+1	2018	1,406,305	Prime
126	79x2^4658115-1	2018	1,402,235	Prime
127	11 × 2^4643238 − 1	2014	1,397,755	Prime
128	68×995⁴⁶⁵⁹⁰⁸ − 1 ^[17]	2017	1,396,712	Prime
129	$\Phi _{3}(-192098^{131072})$	2015	1,385,044	Prime
130	27 × 2^4583717 − 1	2014	1,379,838	Prime
-	2^4583176 + 2131 ^[3]	2009-09	1,379,674	PRP
131	121×2^4553899 – 1 ^[32]	2012-02-25	1,370,863	Prime
132	27× 2^4542344 − 1	2014	1,367,384	Prime
-	$\Phi _{18132292M}(2)$ ^[*] ^[3]	2014-03	1,364,591	PRP
133	4×797⁴⁶⁸⁷⁰² + 1 ^[17]	2017	1,359,920	Prime
134	145310²⁶²¹⁴⁴+1	2011	1,353,265	Prime
135	36772 × 6^1723287 − 1	2014	1,340,983	Prime
-	${\tfrac {13^{1199467}+1}{14}}$ ^[3]	2015-12	1,336,138	PRP
136	151×2^4424321 − 1	2016	1,331,856	Prime
-	${\tfrac {5^{1888279}-1}{4}}$ ^[3]	2018	1,319,850	PRP
137	49x2^4365175-1	2017	1,314,051	Prime
138	49x2^4360869-1	2017	1,312,755	Prime
139	13x2^4333087-1	2018	1,304,391	Prime
140	353159×2^4331116 – 1 ^[33]	2011-05-31	1,303,802	Prime
141	682156×79⁶⁸²¹⁵⁶ + 1	2016	1,294,484	Prime
142	141941×2^4299438 – 1 ^[34]	2011-05-26	1,294,265	Prime
143	15 × 2^4246384+1	2013	1,278,291	Prime
144	3×2^4235414 – 1 ^[35]	2008-03-23	1,274,988	Prime
145	109208 × 5^1816285 + 1	2014	1,269,534	Prime
146	1091x2^4215518-1	2018	1,269,001
147	191 × 2^4203426-1	2012	1,265,360	Prime
148	1259 × 2^4196028-1	2016	1,263,134	Prime
-	${\tfrac {2^{4194304}+1026473}{3}}$ ^[3]	2017-07	1,262,611	PRP
149	325918x5^1803339-1	2014	1,260,486	Prime
-	${\tfrac {2^{4187251}-1}{72234342371519}}$ ^[3]	2016-05	1,260,475	PRP
-	${\tfrac {14^{1091401}+1}{15}}$ ^[3]	2014-03	1,250,885	PRP
150	133778x5^1785689+1	2014	1,248,149	Prime
151	17x2^4107544-1	2015	1,236,496	Prime
152	24032x5^1768249+1	2014	1,235,958	Prime
153	172×159⁵⁶¹³¹⁹ − 1 ^[17]	2017	1,235,689	Prime
-	${\tfrac {16^{1025393}+1}{17}}$ ^[3]	2014-08	1,234,695	PRP
154	1031×2^4054974−1	2017	1,220,672	Prime
-	${\tfrac {2^{4031399}+1}{3}}$ ^[3]	2010-02	1,213,572	PRP
155	39653×430⁴⁶⁰³⁹⁷-1 ^[17]	2016	1,212,446	Prime
156	40734²⁶²¹⁴⁴+1	2011	1,208,473	Prime
157	9 × 2^4005979 - 1	2012	1,205,921	Prime
158	12 × 68⁶⁵⁶⁹²¹ + 1 ^[17]	2016	1,203,815	Prime
159	67×688⁴²³⁸⁹³ + 1 ^[17]	2017	1,202,836	Prime
160	1993191 × 4^1993191 − 1	2015	1,200,027	Prime
161	138172x5^1714207-1	2014	1,198,185	Prime
162	$\Phi _{3}(-1202113^{98304})$	2016	1,195,366	Prime
163	$\Phi _{3}(-1110815^{98304})$	2016	1,188,622	Prime
164	22478x5^1675150-1	2014	1,170,884	Prime
165	1199x2^3889576-1	2018	1,170,883	Prime
166	298989x2^3886857+1	2014	1,170,067	Prime
167	27×2^3855094 – 1 ^[36]	2012-02-28	1,160,501	Prime
168	164x978³⁸⁷⁹²⁰-1	2018	1,160,015	Prime
169	30x514⁴²⁴⁶⁵²-1	2017	1,151,218	Prime
170	24518²⁶²¹⁴⁴+1	2008	1,150,678	Prime
171	$\Phi _{3}(-700219^{98304})$	2016	1,149,220	Prime
172	109x980³⁸³⁶⁶⁹-1	2018	1,147,643	Prime
173	123547×2^3804809 – 1 ^[37]	2011-05-08	1,145,367	Prime
174	2564x75⁶¹⁰⁷⁵³+1	2014	1,145,203	Prime
175	$\Phi _{3}(-660955^{98304})$	2016	1,144,293	Prime
176	326834x5^1634978-1	2014	1,142,807	Prime
177	415267×2^3771929 – 1 ^[38]	2011-05-08	1,135,470	Prime
178	11 × 2^3771821+1	2013	1,135,433	Prime
179	938237 × 2^3752950-1	2007	1,129,757	Prime
180	207394x5^1612573-1	2014	1,127,146	Prime
181	684×10^1127118 + 1 ^[17]	2017	1,127,121	Prime
182	$\Phi _{3}(-535386^{98304})$	2016	1,126,302	Prime
183	104944x5^1610735-1	2014	1,125,861	Prime
184	23451 × 2^3739388 + 1 ^[17]	2015	1,125,673	Prime
185	2^3704053 + 2^1852027 + 1	2014	1,115,032	Prime
186	330286×5^1584399 – 1 ^[39]	2014-03-21	1,107,453	Prime
187	13x2^3675223-1	2016	1,106,354	Prime
188	15×2^3668194 – 1	2013	1,104,238	Prime
189	13*2^3664703-1	2016	1,103,187	Prime
190	$\Phi _{3}(-406515^{98304})$	2016	1,102,790	Prime
191	33300×430⁴¹⁷⁸⁴⁹-1 ^[17]	2016	1,100,397	Prime
192	65531 × 2^3629342-1	2011	1,092,546	Prime
193	113x2^3628034-1	2014	1,092,150	Prime
-	${\tfrac {106\cdot 23^{800873}-7}{11}}$ ^[3]	2015-05	1,090,573	PRP
194	29x920³⁶⁷⁸¹⁰-1	2015	1,090,113	Prime
195	14641x2^3618876+1	2018	1,089,395	Prime
196	485767 × 2^3609357-1	2008	1,086,531	Prime
197	189x2^3596375+1	2016	1,082,620	Prime
198	35x2^3587843+1	2014	1,080,050	Prime
199	275x2^3585539+1	2016	1,079,358	Prime
200	2x59⁶⁰⁸⁶⁸⁵+1	2014	1,077,892	Prime
201	309x2^3577339+1	2016	1,076,889	Prime
202	251x2^3574535+1	2016	1,076,045	Prime
203	35x2^3570777+1	2014	1,074,913	Prime
204	33x2^3570132+1	2014	1,074,719	Prime
205	5 × 2^3569154-1	2009	1,074,424	Prime
206	81 × 492³⁹⁹⁰⁹⁵ − 1 ^[17]	2015	1,074,352	Prime
207	22934×5^1536762 – 1 ^[40]	2014-02-06	1,074,155	Prime
208	771x2^3564109+1	2018	1,072,907	Prime
209	381x2^3563676+1	2016	1,072,776	Prime
210	555x2^3563328+1	2018	1,072,672	Prime
211	1183x2^3560584+1	2018	1,071,846	Prime
212	415x2^3559614+1	2016	1,071,554	Prime
213	1103x2^3558176-1	2018	1,071,121	Prime
214	1379x2^3557072-1	2018	1,070,789	Prime
215	681x2^3553141+1	2018	1,069,605	Prime
216	599x2^3551793+1	2018	1,069,200	Prime
217	621x2^3551472+1	2018	1,069,103	Prime
-	${\tfrac {7^{1264699}-1}{6}}$ ^[3]	2014-01	1,068,794	PRP
218	773x2^3550373+1	2018	1,068,772	Prime
219	1199x2^3548380-1	2018	1,068,172	Prime
220	191x2^3548117+1	2015	1,068,092	Prime
221	867x2^3547711+1	2018	1,067,971	Prime
222	$\Phi _{3}(3^{1118781}+1)/3$	2014	1,067,588	Prime
223	351x2^3545752+1	2016	1,067,381	Prime
224	93x2^3544744+1	2014	1,067,077	Prime
225	1159x2^3543702+1	2018	1,066,764	Prime
226	178658x5^1525224 – 1 ^[41]	2014-01-31	1,066,092	Prime
227	1085x2^3539671+1	2018	1,065,551	Prime
228	465×2^3536871 – 1 ^[42]	2016-09-30	1,064,707	Prime
229	1019 × 2^3536312-1	2012	1,064,539	Prime
230	1179x2^3534450+1	2018	1,063,979	Prime
231	447x2^3533656+1	2016	1,063,740	Prime
232	1059x2^3533550+1	2016	1,063,529	Prime
234	553x2^3532758+1	2018	1,063,469	Prime
235	141x2^3529287+1	2015	1,062,424	Prime
236	13x2^3527315-1	2016	1,061,829	Prime
237	1393x2^3525571-1	2017	1,061,306	Prime
238	1071x2^3523944+1	2018	1,060,816	Prime
239	329x2^3518451+1	2016	1,059,162	Prime
240	135x2^3518338+1	2015	1,059,128	Prime
241	2×10^1059002 – 1	2013	1,059,003	Prime
242	64x10^1058794+1	2017	1,058,796	Prime
243	599x2^3515959+1	2018	1,058,412	Prime
244	7 × 2^3511774+1	2008	1,057,151	Prime
245	1135x2^3510890+1	2018	1,056,887	Prime
246	428639 × 2^3506452-1	2011	1,055,553	Prime
247	555x2^3502765+1	2018	1,054,441	Prime
248	643x2^3501974+1	2018	1,054,203	Prime
249	2x23⁷⁷⁴¹⁰⁹+1	2014	1,054,127	Prime
250	1159x2^3501490+1	2018	1,054,057	Prime
253	9×2^3497442 + 1 ^[43]	2012-10-23	1,052,836	Prime
256	51×2^3490971 + 1	2014	1,050,889	Prime
261	59912×5^1500861 + 1 ^[44]	2014-01-17	1,049,062	Prime
-	${\tfrac {2^{3464473}-1}{604874508299177}}$ ^[3]	2014-10	1,042,896	PRP
274	37292×5^1487989 + 1 ^[45]	2013-12-29	1,040,065	Prime
275	1273 × 2^3448551-1	2012	1,038,121	Prime
293	191249 × 2^3417696-1	2010	1,028,835	Prime
298	59 × 2^3408416-1	2010	1,026,038	Prime
302	24 × 414³⁹¹¹⁷⁹ + 1 ^[17]	2016	1,023,717	Prime
307	342924651×2^3394939 – 1	2017	1,021,988	Prime
312	67×2^3391385 – 1	2014	1,020,911	Prime
315	173198×5^1457792 – 1 ^[46]	2013-12-04	1,018,959	Prime
356	81×2^3352924 + 1 ^[47]	2012-01-17	1,009,333	Prime
384	1087 × 2^3336385-1	2012	1,004,355	Prime
410	464253×2^3321908 – 1	2013	1,000,000	Prime
412	191273×2^3321908 – 1 ^[2]	2013	1,000,000	Prime
-	10⁹⁹⁹⁹⁹⁹ + 593499 ^[3] ^[48]	2012-12-24	1,000,000	PRP

All numbers from 10⁹⁹⁹⁹⁹⁹ through 10⁹⁹⁹⁹⁹⁹ + 593498 are known to be composite, and there is a very high probability 10⁹⁹⁹⁹⁹⁹ + 593499, a strong PRP, is actually the smallest megaprime.^[48]

The last prime that is not a megaprime is almost certainly 10⁹⁹⁹⁹⁹⁹ - 172473.^[3]

Notes[]

^{^ *} $\Phi _{nL}(b)$ = gcd( $\Phi _{n}(b)$ , the aurifeuillean L part of $b^{n}-1$ ), $\Phi _{nM}(b)$ = gcd( $\Phi _{n}(b)$ ,the aurifeuillean M part of $b^{n}-1$ ).

References[]

^ Chris Caldwell, The Prime Glossary: megaprime at The Prime Pages. Retrieved on 2008-01-04.
^ Jump up to: ^a ^b ^c ^d ^e ^f ^g Chris Caldwell, The Largest Known Primes at The Prime Pages.
^ Jump up to: ^a ^b ^c ^d ^e ^f ^g ^h ⁱ ^j ^k ^l ^m ⁿ ^o ^p ^q ^r ^s ^t ^u ^v Henri Lifchitz & Renaud Lifchitz, Probable Primes Top 10000, primenumbers.net
^ GIMPS press release, GIMPS Finds First Million-Digit Prime. Retrieved on 2008-01-04.
^ Chris Caldwell, The Largest Known Prime by Year: A Brief History at The Prime Pages. Retrieved on 2008-09-28.
^ "Chris Caldwell, The Largest Known Prime by Year: A Brief History". Archived from the original on 2016-01-01. Retrieved 2008-01-04.CS1 maint: bot: original URL status unknown (link)
^ Caldwell, Chris K. "THE LARGEST KNOWN PRIMES (The 5,000 largest known primes)". Retrieved 23 November 2018.
^ Entry for the number
^ Entry for the number
^ Entry for the number, http://primes.utm.edu
^ Official announcement of discovery of 3×2^11731850 − 1, PrimeGrid
^ Official announcement of discovery of 3×2^11484018 − 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
^ Jump up to: ^a ^b ^c ^d ^e ^f ^g ^h ⁱ ^j ^k ^l ^m ⁿ ^o ^p ^q Generalized Sierpinski/Riesel primes
^ Official announcement of discovery of 75898⁵²⁴²⁸⁸ + 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 3×2^7033641 + 1, PrimeGrid
^ Official announcement of discovery of 40597×2^6808509 – 1, PrimeGrid
^ Official announcement of discovery of 6679881×2^6679881 + 1, PrimeGrid
^ Official announcement of discovery of 304207×2^6643565 – 1, PrimeGrid
^ Official announcement of discovery of 398023×2^6418059 – 1, PrimeGrid
^ Official announcement of discovery of 6328548×2^6328548 + 1, PrimeGrid
^ Official announcement of discovery of 3×2^6090515 – 1, PrimeGrid
^ Official announcement of discovery of 7×2^5775996 + 1, PrimeGrid
^ Official announcement of discovery of 252191×2^5497878 – 1, PrimeGrid
^ Official announcement of discovery of 773620²⁶²¹⁴⁴ + 1, PrimeGrid
^ Official announcement of discovery of 3×2^5082306 + 1, PrimeGrid
^ Official announcement of discovery of 121×2^4553899 – 1, PrimeGrid
^ Official announcement of discovery of 353159×2^4331116 – 1, PrimeGrid
^ Official announcement of discovery of 141941×2^4299438 – 1, PrimeGrid
^ Official announcement of discovery of 3×2^4235414 – 1, PrimeGrid
^ Official announcement of discovery of 27×2^3855094 – 1, PrimeGrid
^ Official announcement of discovery of 123547×2^3804809 – 1, PrimeGrid
^ Official announcement of discovery of 415267×2^3771929 – 1, PrimeGrid
^ Official announcement of discovery of 330286×5^1584399 – 1, PrimeGrid
^ Official announcement of discovery of 22934×5^1536762 – 1, PrimeGrid
^ Official announcement of discovery of 178658×5^1525224 – 1, PrimeGrid
^ Official announcement of discovery of 465×2^3536871 – 1, PrimeGrid
^ Official announcement of discovery of 9×2^3497442 + 1, PrimeGrid
^ Official announcement of discovery of 59912×5^1500861 + 1, PrimeGrid
^ Official announcement of discovery of 37292×5^1487989 + 1, PrimeGrid
^ Official announcement of discovery of 173198×5^1457792 – 1, PrimeGrid
^ Official announcement of discovery of 81×2^3352924 + 1, PrimeGrid
^ Jump up to: ^a ^b Patrick De Geest, 10^999999 + y, World!Of Numbers

External links[]

Chris Caldwell, The Largest Known Primes Database at The Prime Pages
Top PRPs
A text file for the top primes
PrimeGrid’s 321 Prime Search, about the discovery of 3×2^6090515−1

[1] Chris Caldwell, The Prime Glossary: megaprime at The Prime Pages. Retrieved on 2008-01-04.

[The_largest_known_primes-2] Jump up to: ^a ^b ^c ^d ^e ^f ^g Chris Caldwell, The Largest Known Primes at The Prime Pages.

[PRPTop-3] Jump up to: ^a ^b ^c ^d ^e ^f ^g ^h ⁱ ^j ^k ^l ^m ⁿ ^o ^p ^q ^r ^s ^t ^u ^v Henri Lifchitz & Renaud Lifchitz, Probable Primes Top 10000, primenumbers.net

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

[largest-5] Chris Caldwell, The Largest Known Prime by Year: A Brief History at The Prime Pages. Retrieved on 2008-09-28.

[6] "Chris Caldwell, The Largest Known Prime by Year: A Brief History". Archived from the original on 2016-01-01. Retrieved 2008-01-04.CS1 maint: bot: original URL status unknown (link)

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

[8] Entry for the number

[9] Entry for the number

[10] Entry for the number, http://primes.utm.edu

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

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

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

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

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

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

[GSRP-17] Jump up to: ^a ^b ^c ^d ^e ^f ^g ^h ⁱ ^j ^k ^l ^m ⁿ ^o ^p ^q Generalized Sierpinski/Riesel primes

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

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

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

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

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

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

[24] Official announcement of discovery of 304207×2^6643565 – 1, PrimeGrid

[25] Official announcement of discovery of 398023×2^6418059 – 1, PrimeGrid

[26] Official announcement of discovery of 6328548×2^6328548 + 1, PrimeGrid

[27] Official announcement of discovery of 3×2^6090515 – 1, PrimeGrid

[28] Official announcement of discovery of 7×2^5775996 + 1, PrimeGrid

[29] Official announcement of discovery of 252191×2^5497878 – 1, PrimeGrid

[30] Official announcement of discovery of 773620²⁶²¹⁴⁴ + 1, PrimeGrid

[31] Official announcement of discovery of 3×2^5082306 + 1, PrimeGrid

[32] Official announcement of discovery of 121×2^4553899 – 1, PrimeGrid

[33] Official announcement of discovery of 353159×2^4331116 – 1, PrimeGrid

[34] Official announcement of discovery of 141941×2^4299438 – 1, PrimeGrid

[35] Official announcement of discovery of 3×2^4235414 – 1, PrimeGrid

[36] Official announcement of discovery of 27×2^3855094 – 1, PrimeGrid

[37] Official announcement of discovery of 123547×2^3804809 – 1, PrimeGrid

[38] Official announcement of discovery of 415267×2^3771929 – 1, PrimeGrid

[39] Official announcement of discovery of 330286×5^1584399 – 1, PrimeGrid

[40] Official announcement of discovery of 22934×5^1536762 – 1, PrimeGrid

[41] Official announcement of discovery of 178658×5^1525224 – 1, PrimeGrid

[42] Official announcement of discovery of 465×2^3536871 – 1, PrimeGrid

[43] Official announcement of discovery of 9×2^3497442 + 1, PrimeGrid

[44] Official announcement of discovery of 59912×5^1500861 + 1, PrimeGrid

[45] Official announcement of discovery of 37292×5^1487989 + 1, PrimeGrid

[46] Official announcement of discovery of 173198×5^1457792 – 1, PrimeGrid

[47] Official announcement of discovery of 81×2^3352924 + 1, PrimeGrid

[worldofnumbers-48] Jump up to: ^a ^b Patrick De Geest, 10^999999 + y, World!Of Numbers

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show v t 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
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 ( $n - 1, n + 1, 2 n - 1, 2 n + 1, \dots$ ) 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
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

Megaprime

Contents

Known megaprimes and mega PRPs[]

Notes[]

See also[]

References[]

External links[]