Proven GIGANTIC primes ( via Primo )
Total: 371
Rank Expression Digits When Who Comment Certificate
1 R(49081)   49081 Mar 2022 Paul Underwood Repunit
2 p(1289844341)   40000 Dec 2020 Paul Underwood Partitions
3 2116224 - 15905   34987 May 2019 Peter Kaiser
4 (14665 • 1034110 − 56641) / 9999   34111 Dec 2020 David Broadhurst; Paul Underwood Palindrome
5 Picture(57885161)   34093 Dec 2020 Paul Underwood show picture
6 M(106391) / 286105171290931103   32010 May 2025 Robert Gelhar Mersenne cofactor
7 Lucas(148091)   30950 Sep 2015 Paul Underwood Lucas
8 −Τ(331,2129)   29492 Dec 2020 Philippe Alsina; Pierre Gazzano;
  Nik Lygeros; Olivier Rozier; André Solaris		 Lehmer-Ramanujan
9 Lucas(140057)   29271 Dec 2014 Peter Kaiser; Paul Underwood Lucas
10 − 30 • Bern(10264) / 262578313564364605963   28506 May 2021 Robert Gelhar Irregular
11 (1027669 + 7) / 8313493832818655929448065598763458531111   27630 Jan 2021 Alfred Reich
12 546351925018076058 • Bern(9702) / 129255048976106804786904258880518941   26709 Jan 2021 Serge Batalov Irregular
13 M(86137) / 20021531730209833250959969231661791   25896 May 2022 Paul Underwood Mersenne cofactor
14 1025333 − 2 • 105182 − 3   25333 Aug 2020 Robert Gelhar
15 Φ(12345,7176) / 31531760245313526865033921   25331 Jun 2017 Tom Wu Part of BLS primality proof of
  (717624691 − 1) / 7175
16 M(84211) / 140050626828838622759681349695502902354485703679858928071137   25291 Dec 2020 Robert Gelhar Mersenne cofactor
17 (283339 + 1) / 3   25088 Sep 2014 Tom Wu Wagstaff
18 M(82939) / 883323903012540278033571819073   24938 Feb 2021 Paul Underwood Mersenne cofactor
19 −Τ(6911522)   23770 Mar 2014 Nik Lygeros; Olivier Rozier
20 1023769 + 23769   23770 Jan 2024 Tengfei Wang Dual Cullen prime
21 798 • Bern(8766) / 14670751334144820770719   23743 Jan 2021 Robert Gelhar Irregular
22 (10011867 + 1) / 101   23732 Dec 2021 Ray Chandler Generalized Wagstaff
23 826205 + 262058   23666 Sep 2023 Tengfei Wang Leyland plus form
24 Φ(35421,− 10)   23613 Jun 2021 Serge Batalov Unique
25 primV(67, − 1, 13081) / 65419672274940815357   23451 Oct 2019 Paul Underwood Helper to LucasU(67, − 1, 26161)
26 Τ(2571698)   22506 Apr 2014 Patrice Deloche; Nik Lygeros;
  Olivier Rozier
27 1022250 + 57913   22251 Jun 2014 Pierre Cami
28 273845 + 14717   22230 Dec 2013 Peter Kaiser Dual Sierpinski Problem
29 273360 + 10711   22084 Sep 2014 Peter Kaiser Dual Sierpinski Problem
30 Fib(104911)   21925 Oct 2015 Mathew Steine; Bouk de Water Fibonacci number
31 Φ(15072, 24741) / 30662286083704489057   21913 Jun 2024 Tom Wu Part of BLS primality proof of
  (2474115073 − 1) / 24740
32 345535 + 2   21726 Jun 2020 Robert Gelhar Dual Williams prime
33 20170108 • 1021700 + 39   21708 Nov 2016 Peter Kaiser
34 Φ(1203,1027)   21600 Nov 2021 Ray Chandler Unique
35 Φ(15438, 23340) / 15439   21487 Jul 2020 Tom Wu Part of BLS primality proof of
  (2334015439 − 1) / 23339
36 − E(6658) / 85079   21257 Dec 2020 Serge Batalov Euler irregular
37 Φ(39855, − 10)   21248 Nov 2020 Robert Gelhar Unique
38 Φ(15372, 64758) / 1244123140789621   20770 Jan 2018 Tom Wu Part of BLS primality proof of
  (6475815373 − 1) / 64757
39 Φ(23749, −10)   20160 Apr 2014 Ray Chandler Unique
40 4111286921397 • 266420 + 5   20008 Apr 2019 Peter Kaiser Part of a prime triplet
41 Lucas(94823)   19817 May 2014 Paul Underwood Lucas
42 Φ(8055,40734) / 96202794155883391141266863081244220084299983546056404017486521   19632 Mar 2015 Tom Wu Part of BLS primality proof of
  (4073416111 − 1) / 40733
43 M(63703) / 42808417   19169 Jan 2014 David Metcalfe Mersenne cofactor
44 Φ(7545,58729) / 2732693371   19143 Jun 2024 Tom Wu Part of BLS primality proof of
  (5872915091 − 1) / 58728
45 Lucas(89849)   18778 Sep 2014 Paul Underwood; Harvey Dubner Lucas
46 primV(145353)   18689 Dec 2013 Dana Jacobsen Lucas primitive part
47 Φ(14943, − 100)   18688 Mar 2014 Ray Chandler Unique
48 Φ(12040,43326) / 22911344130361   18683 Nov 2017 Tom Wu Part of BLS primality proof of
  (4332612041 − 1) / 43325
49 Φ(13338,63847) / 44250132909040111   18666 May 2013 Tom Wu Part of BLS primality proof of
  (6384713339− 1) / 63846
50 587 • 43103# / 11# + 657402   18662 Oct 2013 Pierre Cami Part of a proven prime mega-gap
51 587 • 43103# / 11# − 455704   18662 Oct 2013 Pierre Cami Part of a proven prime mega-gap
52 261792 + 21661   18602 Dec 2012 Peter Kaiser Dual Sierpinski Problem
53 Φ(18827,10)   18480 May 2014 Ray Chandler Unique
54 R(21469) / R(3067) / 3945067990295736019201267346350493   18369 Jan 2018 Ray Chandler Repunit cofactor
55 Φ(106820 [C-D] ,10) / ​1037738269424921   18129 Aug 2017 Ray Chandler Cyclotomic polynomial cofactor
  of R(106820)
56 Lucas(86477) / 1042112515940998434071039   18049 Sep 2020 Serge Batalov Lucas cofactor
57 Φ(47560,10) / ​45260833352611441   17904 Jun 2017 Ray Chandler Cyclotomic polynomial cofactor
  of R(47560)
58 Φ(26601,10) / ​304368643   17724 Apr 2017 Ray Chandler Cyclotomic polynomial cofactor
  of R(26601)
59 M(58199) / 237604901713907577052391   17497 Jan 2015 David Metcalfe Mersenne cofactor
60 R(21865) / R(4373) / 2116024961761   17480 Jun 2017 Ray Chandler Repunit cofactor
61 Φ(52062,10)   17353 Apr 2014 Ray Chandler Cyclotomic polynomial cofactor
  of R(52062)
62 1199
86160983933969883031666688 • ∑ ( 248⋅n ) + 138585004357  
n=0  		 17351 May 2020 Robert Gelhar
63 108677 • Sm(2445) + Smr(2446)   17350 Jan 2022 Oliver Kruse Sm - Smarandache function
  Smr - reversed Sm
64 M(57131) / 61481396117165983261035042726614288722959856631   17152 Jan 2016 David Metcalfe Mersenne cofactor
65 1017135 − 5 • 101884 − 1   17135 Mar 2022 Ray Chandler Near repdigit; Part of a twin prime
66 1017135 − 5 • 101884 − 3   17135 Mar 2022 Ray Chandler Part of a twin prime
67 Lucas(81671)   17069 Sep 2013 Mathew Steine Lucas
68 256366 + 39079   16968 Oct 2012 Peter Kaiser Dual Sierpinski Problem
69 primV(86756)   16920 Jan 2015 Charles H (Chuck) Lasher;
  Harvey Dubner		 Lucas primitive part
70 39161# / 11# − 510478   16901 Apr 2013 Pierre Cami Part of an incomplete
  proven prime gap; d = 984108
71 primU(5617,−1,4769) / 38153   16869 Jul 2019 Serge Batalov
72 Lucas(80761) / 570100885555095451   16861 Aug 2020 Serge Batalov Lucas cofactor
73 6521953289619 • 255555 − 5   16737 Apr 2013 Peter Kaiser Part of a prime triplet
74 (45774577 + 45764576) / 5007522261204368020293    16733 Jan 2018 Richard Dickerson Lifchitz plus cofactor
75 255525 − 555252   16715 Dec 2023 Tengfei Wang Leyland minus form
76 6 • (Lucas(81836) − 1) / (Lucas(1996) − 1) / (Lucas(164) − 1)   16653 Jan 2021 Serge Batalov Lucas primitive part
77 p(221444161)   16569 APr 2017 Serge Batalov Partitions
78 Fib(78919) / 15574900936381642440917   16471 Sep 2020 Serge Batalov Fibonacci cofactor
79 −Τ(791570)   16386 Feb 2014 Nik Lygeros; Olivier Rozier
80 See complete expression   16312 Aug 2020 Ryan Propper Cyclotomic polynomial cofactor of
  (2850713830 − 1) / 28506
81 ⌊(π • 1016207)⌋   16208 Jun 2026 Robert Baillie String in Pi
82 primV(123573)   16198 May 2019 Serge Batalov Lucas primitive part
83 Φ(10356,50091) / 10304269521936621850713514888196023221889   16165 Nov 2016 Tom Wu Part of BLS primality proof of
  (5009110357 − 1) / 50090
84 Lucas(77417) / 313991497376559420151   16159 Aug 2020 Serge Batalov Lucas cofactor
85 Φ(64410,10) / 89083940360761   16115 Nov 2016 Ray Chandler Cyclotomic polynomial cofactor
  of R(64410)
86 M(53381) / 94649555180092174344611143949332081125424867221122582640412951   16008 Mar 2017 Paul Underwood Mersenne cofactor
87 − E(5186) / 295970922359784619239409649676896529941379763   15954 Mar 2018 Thomas Ritschel Euler irregular
88 primV(121227)   15890 May 2019 Serge Batalov Lucas primitive part
89 Φ(7545,9082) / 268247497918471   15882 Oct 2014 Tom Wu Part of BLS primality proof of
  (908215091 − 1) / 9081
90 See complete expression   15721 Apr 2014 Anonymous
91 718582 − 185827   15704 Dec 2023 Tengfei Wang Leyland minus form
92 primU(131481)   15695 Mar 2019 Serge Batalov Fibonacci primitive part
93 Φ(34474,10) / ​404621339   15652 Oct 2016 Ray Chandler Cyclotomic polynomial cofactor
  of R(34474)
94 primV(120258)   15649 May 2019 Serge Batalov Lucas primitive part
95 Φ(32302,10) / 1451105224587147287   15582 Oct 2016 Ray Chandler Cyclotomic polynomial cofactor
  of R(32302)
96 M(51487) / 992759464401015098867323676444574243990277591   15455 Nov 2018 Serge Batalov Mersenne cofactor
97 primB(183835)   15368 Mar 2019 Serge Batalov Lucas Aurifeuillian primitive part
98 Φ(71400,10) / ​176358001   15352 Dec 2016 Ray Chandler Cyclotomic polynomial cofactor
  of R(71400)
99 primU(77387)   15319 Mar 2019 Serge Batalov Fibonacci primitive part
100 (42244224 + 42234223) / 43228896852681817   15299 Mar 2016 Richard Dickerson Lifchitz plus cofactor
101 Φ(285,− 2637124) / 13082397832081   15267 Feb 2012 Tom Wu Part of BLS primality proof of
  (2637113681 − 1) / 26370
102 728192 + 438192   15216 Oct 2012 Youcef Lemsafer
103 primB(181705)   15189 Feb 2012 Serge Batalov Lucas Aurifeuillian primitive part
104 4183192700 + 418318   15179 Dec 2023 Alfred Reich
105 Φ(10092,44497)   15098 Jun 2016 Tom Wu Part of BLS primality proof of
  (4449710093 − 1) / 44496
106 1015093 + 7   15094 Apr 2021 Alfred Reich
107 249989 − 499892   15049 Oct 2023 Tengfei Wang Leyland minus form
108 Fib(71983) / 2043438054776977   15028 Dec 2018 Serge Batalov Fibonacci cofactor
109 2494779036241 • 249800 + 13   15004 Apr 2022 Serge Batalov Part of a CPAP-3
110 2494779036241 • 249800 + 7   15004 Apr 2022 Serge Batalov Part of a CPAP-3
111 1015000 − 8621   15000 Jan 2025 U.N.Owen
112 primB(268665)   14972 Apr 2019 Serge Batalov Lucas Aurifeuillian primitive part
113 primV(75316)   14897 Dec 2015 Charles H (Chuck) Lasher;
  Harvey Dubner		 Lucas primitive part
114 Φ(5015, − 10000)   14848 Apr 2013 Ray Chandler Unique
115 primV(91322)   14847 Feb 2016 Charles H (Chuck) Lasher;
  Harvey Dubner		 Lucas primitive part
116 Φ(13476,1852) / 38475181770440710933448053   14640 Aug 2015 Tom Wu Part of BLS primality proof of
  (185213477 − 1) / 1851
117 primA(284895)   14626 Apr 2019 Serge Batalov Lucas Aurifeuillian primitive part
118 1014600 + 7   14601 Jul 2020 Alfred Reich
119 Φ(30452,10) / 9702901620338905487971475229839576180195475686611321   14469 Jul 2016 Ray Chandler Cyclotomic polynomial cofactor
  of R(30452)
120 Fib(69239) / 1384781   14464 Sep 2018 Serge Batalov Fibonacci cofactor
121 M(48617) / M(797) / M(61)   14377 May 2019 Anonymous Mersenne cofactor
122 1014357 − 2 • 1013570 − 3   14357 Mar 2022 Ray Chandler
123 Φ(9336,42417) / 46299256179289281554796097   14339 Jun 2024 Tom Wu Part of BLS primality proof of
  (424179337 − 1) / 42416
124 primA(170575)   14258 Jan 2019 Serge Batalov Lucas Aurifeuillian primitive part
125 Lucas(68213) / 7290202116115634431   14237 Aug 2018 Serge Batalov Lucas cofactor
126 R(16597) / R(2371) / 29505775938311   14213 Jun 2016 Ray Chandler Repunit cofactor
127 Φ(43566,10) / ​130699   14139 Aug 2016 Ray Chandler Cyclotomic polynomial cofactor
  of R(43566)
128 Φ(9318,36210) / 4494536789839233596781125043007   14130 Jun 2024 Tom Wu Part of BLS primality proof of
  (362109319 − 1) / 36209
129 See complete expression   14078 Aug 2019 Serge Batalov
130 R(14011) / 3122892204966673507876545735955200724341171845519631387   13957 Jun 2016 Ray Chandler Repunit cofactor
131 Φ(11490,38284) / 266998459447149619398404835337978513293521552530531   13956 Mar 2013 Tom Wu Part of BLS primality proof of
  (3828411491 − 1) / 38283
132 Fib(67703) / Fib(857) / 14472334024676221   13954 Jul 2018 Serge Batalov Fibonacci cofactor
133 Fib(66947) / 12485272838388758877279873712131648167413   13951 Apr 2017 Serge Batalov Fibonacci cofactor
134 Lucas(66533) / 2128184670585621839884209100279   13875 Dec 2018 Serge Batalov Lucas cofactor
135 6 • Bern(5534) / 226840561549600012633271691723599339   13862 Feb 2014 David Metcalfe; Thomas Ritschel;
  Jens Kruse Andersen		 Irregular
136 B(66242)   13847 Apr 2018 Jared M. Polzer Brady number
137 4410546 • Bern(5526) / 9712202742835546740714595866405369616019   13840 Apr 2018 Thomas Ritschel Irregular
138 1013820 − 3   13820 Jun 2022 Markus Tervooren Near repdigit
139 1013807 + 13807    13808 Nov 2023 Anonymous Dual Cullen prime
140 (1013784 + 7) / 27771161176334419   13768 Mar 2021 Alfred Reich
141 4715140 + 5140471    13740 Mar 2023 Tengfei Wang Leyland plus form
142 1013726 − 5 • 1013419 − 3   13726 Mar 2022 Ray Chandler
143 1013681 − 5 • 102824 − 1   13681 Mar 2022 Ray Chandler Part of a twin prime
144 1013681 − 5 • 102824 − 3   13681 Feb 2022 Ray Chandler Part of a twin prime
145 primB(163595)   13675 Jul 2018 Serge Batalov Lucas Aurifeuillian primitive part
146 4250! + 850! + 1   13578 Feb 2020 Peter Košinár
147 (418388 + 40) / 6353091241359073016116549653451   13498 May 2024 Alfred Reich Dual Williams cofactor
148 Φ(41470,10) / ​1658801   13434 Apr 2016 Ray Chandler Cyclotomic polynomial cofactor
  of R(41470)
149 (37593759 + 37583758) / 8408153197032643414637   13417 Apr 2015 Richard Dickerson Lifchitz plus cofactor
150 56667641271 • 244441 + 5   13389 Apr 2022 Oliver Kruse; Stephan Schöler Part of a prime triplet
151 p(140380916)   13191 May 2022 Chuck Lasher Partitions
152 p(140303751)   13187 May 2022 Chuck Lasher Partitions
153 primU(94551)   13174 Apr 2018 Serge Batalov Fibonacci primitive part
154 1013069 − 5 • 1012385 − 3   13069 Feb 2022 Ray Chandler
155 (1013023 + 7) / 6453389   13017 Mar 2021 Alfred Reich
156 primB(242295)   13014 Jun 2018 Serge Batalov Lucas Aurifeuillian primitive part
157 See complete expression   12998 Dec 2018 Serge Baralov
158 Φ(26008,10) / 4216522190067097972291840975367635579445657   12958 Apr 2016 Ray Chandler Cyclotomic polynomial cofactor
  of R(26008)
159 Φ(75740 [C+D] ,10) / ​204043561   12953 Apr 2016 Ray Chandler Cyclotomic polynomial cofactor
  of R(75740)
160 Φ(28455,10) / 5258291515652656797947926184778372614764081094641   12912 Mar 2016 Ray Chandler Cyclotomic polynomial cofactor
  of R(28455)
161 Φ(12972,1549) / 33320592661   12903 Sep 2011 Tom Wu Part of BLS primality proof of
  (154912973 − 1) / 1548
162 Fib(61813) / 2236143226659081266701   12897 Dec 2018 Serge Batalov Fibonacci cofactor
163 Φ(64060 [C-D] ,10)   12809 Mar 2016 Ray Chandler Cyclotomic polynomial cofactor
  of R(64060)
164 (1012817 + 7) / 3030281866046117   12802 Feb 2021 Alfred Reich
165 primU(62771)   12791 Apr 2018 Serge Batalov Fibonacci primitive part
166 (1012809 + 7) / 34790386359869004143   12790 Oct 2020 Alfred Reich
167 Φ(27472,10) / 4532606311701334388113   12779 Mar 2016 Ray Chandler Cyclotomic polynomial cofactor
  of R(27472)
168 p(131328565)   12758 Mar 2017 Serge Batalov Partitions
169 primA(154415)   12728 Jun 2018 Serge Batalov Lucas Aurifeuillian primitive part
170 (1012602 − 1) / 9 − 106301   12602 Mar 2023 Tengfei Wang Near repunit
171 primA(263865)   12570 Jun 2018 Serge Batalov Lucas Aurifeuillian primitive part
172 6 • Bern(5078) / 643283455240626084534218914061   12533 May 2013 Thomas Ritschel Irregular
173 M(41681) / 50021504124824209998331027904313150125767065389449583   12495 Apr 2015 Serge Batalov Mersenne cofactor
174 M(41521) / 41602235382028197528613357724450752065089   12459 Aug 2012 Tom Wu Mersenne cofactor
175 (1012454 + 7) / 465514545959   12443 Aug 2020 Alfred Reich
176 (22 • 268773+ 53) / 25   12414 Feb 2015 Anonymous
177 M(41263) / 1379707143199991617049286121   12395 Oct 2012 David Metcalfe Mersenne cofactor
178 R(12413) / 71981093659479847827654672018603   12382 Feb 2016 Ray Chandler Repunit cofactor
179 Φ(93420 [C-D] ,10) / 5026930200001   12372 Feb 2016 Ray Chandler Cyclotomic polynomial cofactor
  of R(93420)
180 Fib(59369) / 24424236691484660394583037561699885688092693836440759407570209763004757   12337 Apr 2015 Serge Batalov Fibonacci cofactor
181 p(122110618)   12302 Apr 2015 Serge Batalov Partitions
182 Φ(24832,10) / 216817628929793   12274 Jan 2016 Ray Chandler Cyclotomic polynomial cofactor
  of R(24832)
183 See complete expression   12266 Jan 2021 Paul S. Vanderveen
184 Φ(30650,10) / 55082730049767601   12224 Jan 2016 Ray Chandler Cyclotomic polynomial cofactor
  of R(30650)
185 primU(809,1,8662)   12214 Jul 2019 Serge Batalov Fibonacci primitive part
186 p(120052058)   12198 Dec 2012 David Metcalfe Partitions
187 (8008450840 • 240501 + 1) / 14886194409995637157139753229   12174 May 2017 Anonymous Proth cofactor
188 Φ(5655,34120) / 2271359859904984234411620898291   12155 Mar 2012 Tom Wu Part of BLS primality proof of
  (3412011311− 1) / 34119
189 (1012143 + 7) / 42686281893173706680658963579615275995302772319   12097 Sep 2020 Alfred Reich
190 (1012092 + 7) / 17674680705494895280031   12070 Sep 2020 Alfred Reich
191 (1012036 + 7) / 34769374508226918531515812507   12008 Mar 2024 Alfred Reich
192 664342014133 • 239840 − 29   12005 Mar 2020 Serge Batalov Part of a CPAP-3
193 664342014133 • 239840 − 59   12005 Apr 2020 Serge Batalov Part of a CPAP-3
194 1011999 + 63699   12000 Mar 2026 Tjark Koopmann
195 (25153532 + 35322515) / 58788056567   12000 Oct 2018 Edwin Hall Leyland plus form cofactor
196 (200602792 − 200601396 + 1) / 6978841365608175696640474868614878036235777   11970 May 2015 Serge Batalov Cyclotomic polynomial cofactor
197 (33773377 + 33763376) / 10748454158666113155842929899   11888 Aug 2013 Richard Dickerson Lifchitz plus cofactor
198 R(14825) / R(2965) / 2385593169023127848787616597709045781314051389601   11812 Jan 2016 Ray Chandler Repunit cofactor
199 Sm10(3231) / 453699 ;See complete expression   11811 Dec 2021 Youcef Lemsafer Smarandache base 10 cofactor
200 Φ(27496,10) / 168030249266363848764289   11737 Jan 2016 Ray Chandler Cyclotomic polynomial cofactor
  of R(27496)
201 primA(143705)   11703 Apr 2017 Serge Batalov Lucas Aurifeuillian primitive part
202 1011659 − 5 • 101092 − 1   11659 Feb 2022 Ray Chandler Part of a prime twin; near repdigit
203 1011659 − 5 • 101092 − 3   11659 Feb 2022 Ray Chandler Part of a prime twin
204 4207993863 • 238624 + 5   11637 Jun 2021 Frank Doornink Part of a prime triplet
205 primV(83481)   11631 May 2015 Chuck Lasher Lucas primitive part
206 primU(73025)   11587 Apr 2015 Serge Batalov Fibonacci primitive part
207 primU(67781)   11587 Apr 2015 Serge Batalov Fibonacci primitive part
208 (32953295 + 32943294) / 12740953   11585 Jun 2013 Richard Dickerson Lifchitz plus cofactor
209 R(14485) / R(2897) / 51188280415874381036921   11566 Dec 2015 Ray Chandler Repunit cofactor
210 primB(219165)   11557 May 2015 Serge Batalov Lucas Aurifeuillian primitive part
211 primV(56356)   11557 Jun 2015 Chuck Lasher Lucas primitive part
212 primV(131040)   11557 Mar 2015 Chuck Lasher Lucas primitive part
213 primV(58672)   11557 Feb 2015 Chuck Lasher Lucas primitive part
214 Φ(57740 [C+D] ,10)   11545 Dec 2015 Ray Chandler Cyclotomic polynomial cofactor
  of R(57740)
215 ⌊(√2 • 1011539)⌋   11540 Jun 2026 Robert Baillie String in √2
216 1011504 − 5 • 1010085 − 3   11504 Feb 2022 Ray Chandler
217 Φ(47520,10) / ​11493924613839361   11504 Dec 2015 Ray Chandler Cyclotomic polynomial cofactor
  of R(47520)
218 Φ(35712,10) / ​5391064400230083022849   11499 Dec 2015 Ray Chandler Cyclotomic polynomial cofactor
  of R(35712)
219 Φ(86340 [C+D] ,10) / 32427678822181   11491 Dec 2015 Ray Chandler Cyclotomic polynomial cofactor
  of R(86340)
220 238090 + 47269   11467 Feb 2012 Norman Luhn Dual Sierpinski Problem
221 Φ(23572,10) / ​243203586324449   11466 Nov 2015 Ray Chandler Repunit cofactor of R(23572)
222 Fib(54799) / 4661437953906084533621577211561   11422 Jan 2015 David Broadhurst; Bouk de Water Fibonacci cofactor
223 (26 • 1011373 minus; 449) / 9   11374 Jan 2021 Thomas Ritschel
224 Fib(54521) / 6403194135342743624071073   11370 Jan 2015 David Broadhurst; Bouk de Water Fibonacci cofactor
225 327511 − 751132   11306 Nov 2023 Tengfei Wang Leyland minus form
226 (19 • 1011286 − 91) / 32297260888735659   11271 Nov 2023 Alfred Reich
227 Φ(24466,10) / ​1312096417987559179   11262 Nov 2015 Ray Chandler Cyclotomic polynomial cofactor
  of R(24466)
228 ⌊(√2 • 1011259)⌋   11260 Jun 2026 Robert Baillie String in √2
229 1011225 − 8 • 109840 − 3   11225 Feb 2022 Ray Chandler
230 p(100077222)   11136 Nov 2012 David Metcalfe Partitions
231 Fib(53189) / 69431662887136064191105625570683133711989   11075 Dec 2014 David Broadhurst; Bouk de Water Fibonacci cofactor
232 primU(61733)   11058 Mar 2015 Serge Batalov Fibonacci primitive part
233 14059969053 • 236672 − 5   11050 Jun 2018 Serge Batalov Part of a prime triplet
234 Φ(41550,10) / ​2659201   11034 Nov 2015 Ray Chandler Repunit cofactor of R(41550)
235 Lucas(52859) / 1124137922466041911   11029 Oct 2014 David Broadhurst; Bouk de Water Lucas cofactor
236 1011021 + 3   11022 Oct 2023 Alfred Reich
237 (145 • 236579 + 1) / 80640950291793   11000 May 2021 Anonymous Proth cofactor
238 See complete expression   11000 May 2018 Edwin Hall
239 Φ(28952,10) / 6252357514486529280922692142551049114423577   10998 Nov 2015 Ray Chandler Cyclotomic polynomial cofactor
  of R(28952)
240 (11 • 1010981 + 3 • 1010965 + 2 • 109715 + 107314 + 102593 − 3 • 103218 − 51) / 9   10982 Oct 2025 Jason Yuen
241 (31413141 + 31403140) / 508719649   10976 May 2013 Richard Dickerson Lifchitz plus cofactor
242 Φ(34278,10) / 1678861663294594133263   10955 Oct 2015 Maksym Voznyy Cyclotomic polynomial cofactor
  of R(34278)
243 (1010903 + 7) / 70972859   10896 Aug 2020 Alfred Reich
244 5553964 − 3964555   10879 Dec 2023 Tengfei Wang Leyland minus form
245 Φ(23698,10) / ​11095752925475302853   10861 Aug 2016 Maksym Voznyy Cyclotomic polynomial cofactor
  of R(23698)
246 Lucas(52201) / 70585804042896975505694709575919458733851279868446609   10857 Mar 2015 David Broadhurst; Bouk de Water Lucas cofactor
247 Lucas(52009) / 39772636393178951550299332730909   10838 Mar 2015 David Broadhurst; Bouk de Water Lucas cofactor
248 19803281 − 32811980   10817 Dec 2023 Tengfei Wang Leyland minus form
249 Lucas(51941) / 2808052157610902114547210696868337380250300924116591143641642866931   10789 Jan 2015 David Broadhurst; Bouk de Water Lucas cofactor
250 3554226 − 4226355   10778 Dec 2023 Tengfei Wang Leyland minus form
251 1554914 − 4914155   10764 Dec 2023 Tengfei Wang Leyland minus form
252 417877 + 3   10764 Sep 2015 Frank Schickel Dual Williams prime
253 745755 − 575574   10758 Nov 2023 Tengfei Wang Leyland minus form
254 3428602715439 • 235678 + 13   10753 Apr 2020 Serge Batalov Part of a sexy prime triple
255 3428602715439 • 235678 + 7   10753 Apr 2020 Serge Batalov Part of a sexy prime triple
256 (235851 + 1) / 270128075618416280186665624066753024458414196059   10745 Aug 2019 Paul Underwood Wagstaff cofactor
257 811889 + 118898   10737 Feb 2012 Andrey V. Kulsha Leyland plus form
258 2394506 + 2384505   10718 Nov 2024 Jason Yuen
259 Lucas(51349) / 224417260052884218046541   10708 Sep 2014 David Broadhurst; Bouk de Water Lucas cofactor
260 (235677 + 1) / 15923710079918268519082938436557873216969746649   10694 Feb 2020 Anand S Nair Wagstaff cofactor
261 Φ(21368,10) / 27699508108389263492021113   10659 May 2013 Alfred Reich Cyclotomic polynomial cofactor
  of R(21368)
262 188489 − 848918   10657 Oct 2023 Tengfei Wang Leyland minus form
263 Fib(51031) / 95846689435051369   10648 Sep 2014 David Broadhurst; Bouk de Water Lucas cofactor
264 322316 + 2   10648 Oct 2015 Frank Schickel Dual Williams prime
265 Lucas(50989) / 69818796119453411   10640 Aug 2014 David Broadhurst; Bouk de Water Lucas cofactor
266 (245363571 • 235426 − 3) / 4840728260155155493606341384372091137139023   10630 Jun 2010 Tom Wu Part of sequence of four
  consecutively factored integers
267 (1010647 + 7) / 582839970850610767067   10627 Aug 2020 Alfred Reich
268 Φ(26570,10)   10625 Dec 2012 Ray Chandler Cyclotomic polynomial cofactor
  of R(26570)
269 φ(32184,10) / 149901609248398286998426345085780865697841494496161969   10603 Nov 2015 Ray Chandler Cyclotomic polynomial cofactor
  of R(32184)
270 2683143625525 • 235176 + 13   10602 Dec 2019 Gerd Lamprecht; Norman Luhn Part of a sexy prime triple
271 2683143625525 • 235176 + 7   10602 Dec 2019 Gerd Lamprecht; Norman Luhn Part of a sexy prime triple
272 5223899 − 3899522   10597 Jan 2024 Tengfei Wang Leyland minus form
273 p(90048122)   10563 Oct 2012 David Metcalfe Partitions
274 M(35339) / 49098843038498904028395440486235033667674267835480981233904512709297747031041   10562 Apr 2015 Serge Batalov Mersenne cofactor
275 1213266377 • 235000 + 4859   10546 Mar 2014 David Broadhurst Part of a CPAP-3; d = 2430
276 1213266377 • 235000 + 2429   10546 Mar 2014 David Broadhurst Part of a CPAP-3; d = 2430
277 1043085905 • 235000 + 18197   10546 Feb 2014 David Broadhurst Part of a CPAP-3; d = 18198
278 1043085905 • 235000 − 18199   10546 Feb 2014 David Broadhurst Part of a CPAP-3; d = 18198
279 109061779 • 235003 + 11855   10545 Feb 2014 David Broadhurst Part of a CPAP-3; d = 5928
280 109061779 • 235003 + 5927   10545 Feb 2014 David Broadhurst Part of a CPAP-3; d = 5928
281 350049825 • 235000 + 7703   10545 Feb 2014 David Broadhurst Part of a CPAP-3; d = 3852
282 350049825 • 235000 + 3851   10545 Feb 2014 David Broadhurst Part of a CPAP-3; d = 3852
283 146462479 • 235001 − 8767   10545 Dec 2013 David Broadhurst Part of a CPAP-3; d = 8766
284 (19 • 1010515 + 287) / 9   10516 Jul 2022 Alfred Reich
285 primU(55297)   10483 Sep 2014 David Broadhurst; Bouk de Water Fibonacci primitive part
286 1415^3324-3324^1415   10474 Oct 2026 Anonymous Leyland minus form
    new  
287 Φ(561,43669) / 361212114583   10472 Jun 2012 Andrew A. D. Steward
288 (234772 + 1) / 24665523763537   10455 Feb 2020 Anonymous
289 1215018 − 5018121   10452 Nov 2023 Tengfei Wang Leyland minus form
290 21213140 − 31402121   10446 Nov 2023 Tengfei Wang Leyland minus form
291 (19 • 1010435 + 521) / 9   10436 Jul 2024 Alfred Reich
292 234653 + 346532   10432 Sep 2010 Andrey V. Kulsha Leyland plus form
293 3221449497221499 • 234567 + 5   10422 Aug 2015 Peter Kaiser Part of a prime triplet
294 1288726869465789 • 234567 − 5   10421 Apr 2014 Peter Kaiser Part of a prime triplet
295 Φ(31254,10) / ​1531447   10410 Nov 2015 Ray Chandler Cyclotomic polynomial cofactor
  of R(31254)
296 Φ(10679,10) / 2801351900096504446401206289755362971854729   10398 Nov 2015 Ray Chandler Cyclotomic polynomial cofactor
  of R(10679)
297 (1010393 + 7) / 96851   10389 May 2021 Alfred Reich
298 8733530 − 3530873   10382 Dec 2023 Tengfei Wang Leyland minus form
299 Φ(4641,32556) / 21822667391000664007   10378 Jul 2012 Tom Wu Part of BLS primality proof of
  of (325569283 − 1) / 32555
300 See complete expression   10376 Nov 2018 Serge Batalov
301 417226 − 3   10372 Dec 2023 Matteo D'Aniello Dual Williams prime
302 Φ(34386,10) / 6573271911379053751098633975048464359927832533   10355 Oct 2023 Alfred Reich Cyclotomic polynomial cofactor
  of R(34386)
303 ( 19 • 1010338 + 719) / 9   10339 Jun 2024 Alfred Reich
304 See complete expression   10313 May 2025 Anonymous
305 Lucas(49391) / 298414424560419239   10305 Jun 2013 David Broadhurst; Bouk de Water Lucas cofactor
306 (19 • 1010296 − 1) / 9   10297 Feb 2012 Markus Tervooren
307 379 • 1010274 + 9   10277 Jan 2025 Jason Yuen
308 (234127 − 2) / 34127 + 1   10269 Mar 2025 Jason Yuen
309 26802987 + 29872680   10240 Oct 2017 Richard Dickerson Leyland plus form
310 27352974 + 29742735   10222 Sep 2017 Richard Dickerson Leyland plus form
311 ⌊(√42 • 1010212)⌋ % 1010212   10212 Jan 2016 Anonymous first 10212 digits of √42
312 613030 + 5   10140 Aug 2015 Frank Schickel Dual Williams prime
313 647935598824239 • 233619 + 5   10136 May 2019 Peter Kaiser Part of a prime triplet
314 209102639346537 • 233620 + 5   10135 May 2019 Peter Kaiser Part of a prime triplet
315 185353103135997 • 233620 + 5   10135 May 2019 Peter Kaiser Part of a prime triplet
316 162615027598677 • 233620 + 5   10135 May 2019 Peter Kaiser Part of a prime triplet
317 667674063382677 • 233608 + 7   10132 Feb 2019 Peter Kaiser Part of first known
  gigantic prime quadruplet
318 667674063382677 • 233608 + 5   10132 Feb 2019 Peter Kaiser Part of first known
  gigantic prime quadruplet
319 primV(77292)   10112 Jun 2014 Charles H (Chuck) Lasher; Harvey Dubner Lucas primitive part
320 p(82479677)   10109 Sep 2012 David Metcalfe Partitions
321 621988357825221 • 233505 + 5   10101 Sep 2018 Peter Kaiser Part of a prime triplet
322 489294113456196 • 233505 + 5   10101 Sep 2018 Peter Kaiser Part of a prime triplet
323 p(82352631)   10101 Sep 2012 Larry Soule Partitions
324 429915684905751 • 233505 + 5   10101 Sep 2018 Peter Kaiser Part of a prime triplet
325 79417260617886 • 233505 + 5   10100 Aug 2018 Peter Kaiser Part of a prime triplet
326 68048224519176 • 233505 + 5   10100 Aug 2018 Peter Kaiser Part of a prime triplet
327 56107655772636 • 233505 + 5   10100 Aug 2018 Peter Kaiser Part of a prime triplet
328 50917051471806 • 233505 + 5   10100 Jul 2018 Peter Kaiser Part of a prime triplet
329 90585694774959 • 233503 + 5   10100 Jul 2018 Peter Kaiser Part of a prime triplet
330 633669130955577 • 233500 + 5   10100 Jul 2018 Peter Kaiser Part of a prime triplet
331 596754028175112 • 233500 + 5   10100 Jul 2018 Peter Kaiser Part of a prime triplet
332 558173000087697 • 233500 + 5   10100 Jul 2018 Peter Kaiser Part of a prime triplet
333 551381480912562 • 233500 + 5   10100 Jul 2018 Peter Kaiser Part of a prime triplet
334 13994628271791 • 233505 + 5   10100 Jul 2018 Peter Kaiser Part of a prime triplet
335 442066703275842 • 233500 + 5   10100 Jul 2018 Peter Kaiser Part of a prime triplet
336 405970802435022 • 233500 + 5   10100 Jul 2018 Peter Kaiser Part of a prime triplet
337 356410982223402 • 233500 + 5   10100 Jul 2018 Peter Kaiser Part of a prime triplet
338 233548 + 4471   10099 Jul 2012 Norman Luhn Dual Sierpinski Problem
339 171013289842167 • 233500 + 5   10099 Jul 2018 Peter Kaiser Part of a prime triplet
340 145360980646197 • 233500 + 5   10099 Jul 2018 Peter Kaiser Part of a prime triplet
341 140892134560437 • 233500 + 5   10099 Jul 2018 Peter Kaiser Part of a prime triplet
342 28387857090561 • 233501 + 5   10099 Jul 2018 Peter Kaiser Part of a prime triplet
343 81505264551807 • 233444 + 5   10082 Jul 2012 Peter Kaiser Part of a prime triplet
344 296886 + 688629   10071 Jul 2021 Oliver Kruse Leyland plus form
345 See complete expression   10066 Feb 2013 Rocke Verser Cyclotomic polynomial cofactor
  of (569300 − 1) / 4
346 φ(22575,10) / 567394760213977999801   10060 Oct 2015 Maksym Voznyy Cyclotomic polynomial cofactor
  of R(22575)
347 1191713 • 233337 − 6269   10042 Nov 2013 Pierre Cami Part of a CPAP-3; d = 6270
348 1191713 • 233337 − 12539   10042 Nov 2013 Pierre Cami Part of a CPAP-3; d = 6270
349 5073712 + 3712507   10041 Aug 2019 Dylan Delgado Leyland plus form
350 18416522281203 • 233222 + 11   10015 Jan 2020 Peter Kaiser Part of a sexy prime triplet
351 18416522281203 • 233222 + 5   10015 Jan 2020 Peter Kaiser Part of a sexy prime triplet
352 (7 • 1010014 + 11) / 9 + 2 • 103046   10014 Jan 2015 Serge Batalov Part of a prime twin
353 (7 • 1010014 - 7) / 9 + 2 • 103046   10014 Jan 2015 Serge Batalov Part of a prime twin; near repdigit
354 1010010 + 1392367683   10011 Oct 2025 Stephan Schöler Reversible prime (emirp)
355 (86 • 1010003 + 13) / 9   10004 Apr 2026 Anonymous
356 (1010002 − 1) / 9 − 102872   10002 Feb 2023 Tengfei Wang Near repunit
357 See complete expression   10001 Sep 2012 Anonymous
358 956157 • 109994 + 711826   10000 Dec 2014 Anonymous
359 905832 • 109994 + 711826   10000 Mar 2018 Ben Chaffin
360 840879 • 109994 + 711826   10000 May 2023 Anonymous
361 233219 + 957645   10000 Mar 2026 Tjark Koopmann
362 See complete expression   10000 Jun 2018 Dennis Sydekum
363 1524583 − 1514583   10000 Sep 2012 Mike Oakes Generalized Mersenne
364 (7863457 + 3457786) / 14356930135   10000 May 2018 Edwin Hall Leyland plus form cofactor
365 Fib(47848)+87736   10000 Mar 2024 Anonymous
366 ((11476 • 1035 + 9731)256 + 1) / 2   10000 Jul 2020 Anonymous Generalized half-Fermat
367 109999 + 2 • 102000 + 1   10000 Jun 2026 Robert Baillie
368 109999 + 2421018649   10000 Jun 2021 Norman Luhn Part of smallest
  10000-digit prime twin
369 109999 + 2421018651   10000 Jun 2021 Norman Luhn Part of smallest
  10000-digit prime twin
370 109999 + 131673   10000 May 2024 Mohammad Raja
371 109999 + 33603   10000 Apr 2013 Alfred Reich Smallest giantic prime
  re-certified via Primo