Proven GIGANTIC primes ( via CM )
Total: 681
Rank Expression Digits When Who Comment Certificate
1 R(109297)   109297 May 2025 Andreas Enge; Paul Underwood Repunit
2 R(86453)   86453 May 2023 Andreas Enge Repunit
3 5104824 + 1048245   73269 Feb 2023 Greg Childers Leyland plus form
4 M(221509) / 292391881   66673 Oct 2023 Andreas Enge; Paul Underwood Mersenne cofactor
5 M(216317) / 4036536904985126774592622545676909961173365710122848260271644315502006857   65046 Oct 2026 Oliver Kruse Mersenne cofactor
    new  
6 p(3000484833)   61012 Sep 2026 Greg Childers Partitions
    new  
7 3125330 + 1253303   59798 Dec 2022 Greg Childers Leyland plus form
8 Lucas(277273) / 11090921   57940 May 2026 Greg Childers Lucas cofactor
9 Τ(1994518)   57125 Sep 2022 Andreas Enge Ramanujan tau function
10 2176177 + 60947   53035 Oct 2025 Maia Karpovich Dual Sierpinski Problem
11 M(175631) / 30644889864000236404469033475809   52839 Oct 2026 Oliver Kruse Mersenne cofactor
    new  
12 M(174533) / 17794804010102394541862377900092223173807310609   52494 Nov 2022 Paul Underwood Mersenne cofactor
13 M(173867) / 52536637502689   52326 Oct 2026 Oliver Kruse; Paul Underwood Mersenne cofactor
    new  
14 (94017581 − 1) / 939   52268 Jan 2025 Ryan S. Propper Generalized repunit
15 p(2100982676)   51053 Aug 2026 Greg Childers Partitions
    new  
16 p(2100412931)   51046 Jul 2026 Greg Childers Partitions
17 1050000 + 65859   50001 May 2022 Andreas Enge Smallest 50001-digit prime
18 M(157457) / 1651348995090599153173927   47376 Jan 2026 Oliver Kruse Mersenne cofactor
19 M(151013) / 61157791169561859593299975690769   45428 Sep 2025 Paul Underwood Mersenne cofactor
20 2148227 + 60443   44621 Dec 2024 Maia Karpovich Dual Sierpinski Problem
21 Fib(208519) / 140875424305897   43564 Jul 2026 Greg Childers Fibonacci cofactor
22 (2141079 + 1) / 3   42469 Oct 2025 Paul Underwood Wagstaff
23 Lucas(202667)   42355 Nov 2023 Greg Childers Lucas
24 See PrimePages for more informations   42229 Oct 2025 Serge Batalov; Ryan Propper Part of BLS-proof of
  Lehmer number
25 2139964 + 35461   42134 Oct 2024 Maia Karpovich Dual Sierpinski Problem
26 Fib(201107)   42029 Sep 2023 Maia Karpovich Fibonacci number
27 − E(12146) / 1226039954339   41943 Aug 2025 Serge Batalov Euler irregular
28 (2138937 + 1) / 3   41824 Oct 2023 Andreas Enge; Paul Underwood Wagstaff
29 M(136883) / 536581361   41198 Aug 2025 Paul Underwood Mersenne cofactor
30 E(11848) / 7910215   40792 Aug 2022 David Broadhurst; Paul Underwood Euler irregular
31 Lucas(193201)   40377 Dec 2023 Greg Childers Lucas
32 1040000 + 14253   40001 Jun 2022 Andreas Enge Smallest 40001-digit prime
33 M(132929) / 2054179601105776846215055956722560390485432904126229271473   39959 Jan 2026 Oliver Kruse Mersenne cofactor
34 M(130439) / 260879   39261 Feb 2023 Alan Mock Mersenne cofactor
35 Τ(474176)   38404 Jun 2022 Andreas Enge Ramanujan tau function
36 Lucas(183089)   38264 Dec 2023 Greg Childers Lucas
37 (2127031 + 1) / 3   38240 Jan 2023 Paul Underwood Wagstaff
38 (34 • 1037957 − 61) / 9   37958 Dec 2025 Jason Parker-Burlingham Quasi-repdigit
39 Fib(179689) / 359377   37547 May 2026 Greg Childers Fibonacci cofactor
40 378296 + 782963   37357 Jul 2022 Greg Childers Leyland plus form
41 Φ(13875,124750) / 14963669110546259757220673451001   36661 Sep 2024 Tom Wu Part of BLS primality Proof of
  (12475027751 − 1) / 124749
42 6320018 + 2001863   36020 Jan 2023 Greg Childers Leyland plus form
43 2119087 − 1190872   35849 Mar 2024 Tengfei Wang Leyland minus form
44 (2117239 + 1) / 3   35292 Jul 2022 Ryan S. Propper Wagstaff
45 p(1000007396)   35219 Aug 2022 Greg Childers Partitions
46 1864754598 • Bern(12306) / 7988337402668760859   35160 Jul 2025 Serge Batalov Irregular
47 See complete expression   35085 Nov 2025 Maia Karpovich 3rd prime p , where tan(p) > p
48 239487993 − 239477993   35003 May 2026 Anonymous Generalized Mersenne
49 9 • 1034838 + 7   34839 Aug 2023 Markus Tervooren
50 E(10168) / 1097239206089665   34323 Oct 2023 Frank Doornink Euler irregular
51 Φ(717, − 1072)   34273 Aug 2025 Serge Batalov Unique
52 Lucas(159521)   33338 Nov 2023 Greg Childers Lucas
53 Φ(12345,92365) / 382141463174433542855941   32630 Jun 2024 Tom Wu Part of BLS primality Proof of
  (9236524691 − 1) / 92364
54 (1825667 − 1) / 17   32218 Jun 2022 Paul Underwood Generalized repunit
55 Φ(34051, − 10)   32033 Aug 2025 Serge Batalov Unique
56 2105789 + 48527   31846 Oct 2023 Maia Karpovich Dual Sierpinski Problem
57 Φ(23023, − 100)   31681 Aug 2025 Serge Batalov Unique
58 M(105269) /  
151888973648615898448098254186003467843831193426357780775029327271885867309638591059561  		 31603 Sep 2024 Serge Batalov Mersenne cofactor
59 Φ(4613, − 108)   31585 Aug 2025 Serge Batalov Unique
60 Φ(10295, − 104)   31360 Aug 2025 Serge Batalov Unique
61 2104095 + 7013   31336 Oct 2023 Maia Karpovich Dual Sierpinski Problem
62 2103766 + 17659   31237 Apr 2023 Maia Karpovich Dual Sierpinski Problem
63 − E(9266) / 2129452307358569777   30900 May 2023 Frank Doornink Euler irregular
64 Φ(11589, − 104)   30897 Oct 2022 Serge Batalov Unique
65 6402
∑ (n-th prime)n 
n=1  		 30763 Jan 2026 Oliver Kruse Sum (n-th prime)n
66 Lucas(145703) / 179214691   30442 Nov 2023 Greg Childers Lucas cofactor
67 Lucas(145193) / 38621339   30336 Nov 2023 Greg Childers Lucas cofactor
68 (7116384 + 1) / 2   30331 Apr 2023 Alan Mock Generalized half-Fermat
69 17013451 − 13451170   30002 Mar 2024 Tengfei Wang Leyland minus form
70 Φ(36547, − 10)   29832 Jun 2022 Serge Batalov Unique
71 299069 + 990692   29823 Jun 2022 Greg Childers Leyland plus form
72 Φ(18756,58425)   29744 Sep 2025 Tom Wu Part of BLS primality Proof of
  (5842518757 − 1) / 58424
73 See PrimePages for more informations   29210 Oct 2025 Serge Batalov; Ryan S. Propper Lehmer primitive part prime
74 1029028 − 2 • 108312 − 1   29028 Jul 2025 Tengfei Wang Near repdigit
75 Fib(138449) / 722703781   28925 Mar 2026 Greg Childers Fibonacci cofactor
76 Φ(21960,102936) / 5017642938047862206894175676419044635657201   28830 Jul 2024 Tom Wu Part of BLS primality Proof of
  (10293621961 − 1) / 102935
77 Lucas(137483) / 297756567358709   28718 May 2026 Serge Batalov Lucas cofactor
78 E(8668) / 5813137335705569364147662902195143235   28636 Oct 2026 Frank Doornink Euler irregular
    new  
79 1922182 − 2218219   28366 May 2025 Tengfei Wang Leyland minus form
80 (1111111102 • 1028243 − 1) / 9   28252 Apr 2024 Tengfei Wang
81 Fib(135221) / 240836845308529927941202189034491397   28224 Mar 2026 Greg Childers Fibonacci cofactor
82 Φ(8553,74968) / 12199774257779118942571063   27762 Sep 2025 Tom Wu Part of BLS primality Proof of
  (7496817107 − 1) / 74967
83 Lucas(132647) / 13578619295354715892634059   27697 May 2026 Serge Batalov Lucas cofactor
84 Fib(132409) / 2882138154561602271737   27651 Aug 2024 Serge Batalov Fibonacci cofactor
85 30111061 + 300   27416 Feb 2026 Alfred Reich Dual Williams
86 70877087 + 1616   27289 Jun 2025 Tengfei Wang Lifchitz plus form
87 9 • 1026725 + 7   26726 Aug 2023 Markus Tervooren
88 See PrimePages for more informations   26668 Sep 2025 Serge Batalov; Ryan Propper Part of CHG-proof of
  Lehmer number
89 Τ(1572206)   26643 Jul 2022 Greg Childers Ramanujan tau function
90 288071 + 88071   26513 Jun 2025 Tengfei Wang Dual Cullen prime
91 M(87691) / 806957040167570408395443233   26371 Nov 2022 Serge Batalov Mersenne cofactor
92 1026045 − 3   26045 Jan 2024 U.N.Owen Near repdigit
93 (11 • 1026000 − 17) / 3   26001 Aug 2022 Florian Piesker
94 M(86371) / 41681512921035887   25984 Jun 2022 Ryan S. Propper Mersenne cofactor
95 − E(7894) / 19   25790 May 2023 Frank Doornink Euler irregular
96 Lucas(122869) / 50429766416459430193411   25656 Apr 2024 Serge Batalov Lucas cofactor
97 primU(183537)   25571 Oct 2024 Serge Batalov Fibonacci primitive part
98 2119304 − 1930421   25525 Feb 2024 Tengfei Wang Leyland minus form
99 7391
( ∑ n! ) / 99  
n=1  		 25385 Jan 2026 Oliver Kruse Sum factorial cofactor
100 Fib(120937) / 3311205867595743073258613   25250 Apr 2024 Serge Batalov Fibonacci cofactor
101 Fib(120847) / 801583206855072663577903717598265772863698229236258027166465876287487690977   25181 May 2026 Serge Batalov Fibonacci cofactor
102 20927579 + 75792092   25167 Oct 2023 Anonymous Leyland plus form
103 51226753 + 67535122   25050 May 2022 Greg Childers Leyland plus form
104 primV(194181)   24908 Oct 2024 Serge Batalov Lucas primitive part
105 Lucas(119162) / 3   24903 Oct 2024 Serge Batalov Lucas cofactor
106 − E(7634) / 1559   24828 May 2023 Frank Doornink Euler irregular
107 primU(118319)   24553 Oct 2024 Serge Batalov Fibonacci primitive part
108 Fib(117167) / 17658707237   24476 Apr 2024 Serge Batalov Fibonacci cofactor
109 Lucas(116593) / 120790349    24359 Nov 2023 Greg Childers Lucas cofactor
110 (1520593 + 1) / 1317968   24214 Jul 2026 Michael Porter Generalized Wagstaff cofactor
111 280307 − 803072   24175 Jan 2024 Tengfei Wang Leyland minus form
112 primV(214470)   23895 Oct 2024 Serge Batalov Lucas primitive part
113 primU(115373)   23875 Oct 2024 Serge Batalov Fibonacci primitive part
114 primU(135421)   23725 Oct 2024 Serge Batalov Fibonacci primitive part
115 primV(143234)   23654 Oct 2024 Serge Batalov Lucas primitive part
116 M(78737) / 1590296767505866614563328548192658003295567890593   23654 May 2022 Ryan S. Propper Mersenne cofactor
117 primU(164185)   23524 Oct 2024 Serge Batalov Fibonacci primitive part
118 20097104 − 71042009   23465 Jun 2025 Tengfei Wang Leyland minus form
119 See complete expression   23429 Jun 2022 Andreas Enge
120 20127043 − 70432012   23268 May 2025 Tengfei Wang Leyland minus form
121 primU(166737)   23231 Oct 2024 Serge Batalov Fibonacci primitive part
122 See PrimePages for more informations   23130 Sep 2025 Serge Batalov; Ryan Propper Part of BLS-proof of
  Lehmer number
123 primA(275285)   23012 Mar 2024 Serge Batalov Lucas Aurifeuillian primitive part
124 primV(110723)   22997 Oct 2024 Serge Batalov Lucas primitive part
125 (1022973 + 53) / 9   22973 Mar 2024 U.N.Owen Near repunit
126 (34 • 1022925 − 61) / 9   22926 Jul 2025 Jason Parker-Burlingham
127 primV(180906)   22905 Sep 2024 Serge Batalov Lucas primitive part
128 1022822 − 1063 − 1   22822 Mar 2026 Serge Batalov Near Repdigit; Prime / Emirp
129 923840 − 238409   22750 Jan 2024 Tengfei Wang Leyland minus form
130 (32569 • 2615921 + 21) / 5   22532 Mar 2023 Florian Piesker
131 Fib(106663) / 35892566541651557   22275 Apr 2024 Serge Batalov Fibonacci cofactor
132 348054 • Bern(8286) / 1570865077944473903275073668721   22234 Dec 2022 Serge Batalov Irregular
133 p(398256632)   22223 Apr 2022 Serge Batalov Partitions
134 Fib(105509) / 144118801533126010445795676378394340544227572822879081   21997 Jul 2022 Serge Batalov Fibonacci cofactor
135 9911006 + 1100699   21964 Sep 2024 Oliver Kruse Leyland plus form
136 1021873 − 3   21873 Aug 2022 Markus Tervooren Near repdigit
137 3314398 − 1439833   21864 May 2025 Tengfei Wang Leyland minus form
138 primB(282035)   21758 Oct 2023 Serge Batalov Lucas Aurifeuillian primitive part
139 primA(276335)   21736 Mar 2024 Serge Batalov Lucas Aurifeuillian primitive part
140 1021717 + 7   21718 Apr 2024 U.N.Owen
141 primV(154281)   21495 Nov 2023 Greg Childers Lucas primitive part
142 (3131 • 271216 − 11) / 15   21441 Jul 2022 Florian Piesker
143 primA(296695)   21137 Oct 2023 Serge Batalov Lucas Aurifeuillian primitive part
144 primA(413205)   21127 Sep 2023 Serge Batalov Lucas Aurifeuillian primitive part
145 269999 + 35583   21072 Aug 2023 Frank Doornink Smallest 70000-bit prime
146 Φ(60266 , 5)   21062 Oct 2026 Michael Porter Cyclotomic polynomial
    new  
147 57612705200181 • 269801 + 5   21026 Jan 2026 Serge Batalov Part of a prime triplet
148 p(355646102)   21000 Jul 2022 Serge Batalov Partitions
149 (1120161 − 1) / 10   20995 Jun 2022 Florian Piesker Generalized repunit
150 14 • 1916415 + 381   20992 Jun 2022 Florian Piesker
151 (730985 + 1) / (76197 + 1) / 107869208339862414181   20929 Oct 2026 Michael Porter Generalized Wagstaff cofactor
    new  
152 Lucas(100417) /  
7130429037791016075118087990532064354948544338847967474370719436805470448849  		 20911 Apr 2024 Serge Batalov Lucas cofactor
153 p(350199893)   20838 Jul 2022 Charles H (Chuck) Lasher;
  David Broadhurst; Paul Underwood		 Partitions
154 1299820 + 9820129   20726 Sep 2024 Oliver Kruse Leyland plus form
155 primU(102689)   20715 Sep 2024 Serge Batalov Fibonacci primitive part
156 primU(105821)   20598 Sep 2022 Serge Batalov Fibonacci primitive part
157 ((((((25210088873 + 80)3 + 12)3 + 450)3 + 894)3 + 3636)3 + 70756)3 + 97220   20562 Jun 2022 Greg Childers Mills' prime
  re-certified via CM
158 (343063 − 1) / 2   20546 Nov 2023 Anonymous Generalized repunit
159 primU(172179)   20540 Sep 2022 Serge Batalov Fibonacci primitive part
160 Lucas(98081) / 84490439013599359615894385176643888515853963025217237339   20442 Apr 2024 Serge Batalov Lucas cofactor
161 See PrimePages for more informations   20401 Oct 2025 Serge Batalov; Ryan Propper Part of CHG-proof of
  Lehmer number
162 Τ(412296)   20367 Jun 2022 Greg Childers Ramanujan tau function
163 19986137 − 61371998   20256 Feb 2024 Tengfei Wang Leyland minus form
164 (3567937 + 1) / 357   20249 Jul 2022 Florian Piesker Generalized Wagstaff
165 4404139952163 • 267002 − 5   20183 Jul 2024 Serge Batalov Part of a prime triplet
166 primV(112028)   20063 May 2022 Serge Batalov Lucas primitive part
167 53705370 + 44114411   20030 May 2024 Oliver Kruse Lifchitz plus form
168 26685841 + 58412668   20013 Dec 2022 Greg Childers Leyland plus form
169 (1020004 − 1) / 9 − 10228   20004 May 2025 Tengfei Wang Near repunit
170 1020000 + 56149   20001 Nov 2024 U.N.Owen Smallest 20001-digit prime
171 p(322610098)   20000 Jun 2022 Serge Batalov Partitions
172 266436 + 18181   20000 Jul 2022 Florian Piesker
173 1019999 + 1514722611   20000 Jun 2022 Paul Underwood Part of the smallest
  20000-digit twin prime
174 1019999 + 1514722609   20000 Jun 2022 Paul Underwood Part of the smallest
  20000-digit twin prime
175 1019999 + 110949   20000 Jun 2022 Paul Underwood Smallest 20000-digit prime
176 primV(151521)   19863 Jun 2022 Serge Batalov Lucas primitive part
177 See complete expression   19849 Sep 2026 Anonymous Mersenne cofactor
    new  
178 (9006659 + 1) / 901   19670 Aug 2026 Michael Porter Generalized Wagstaff
    new  
179 (224664493 + 1) / 22467   19548 Jun 2026 Michael Porter Generalized Wagstaff
180 264773 − 647732   19499 Jan 2024 Tengfei Wang Leyland minus form
181 39585411 + 54113958   19466 May 2022 Greg Childers Leyland plus form
182 (5824! − 1) / 1078163   19396 Apr 2026 Anonymous Factorial minus cofactor
183 M(66497) / M (2293) / 7140061530624311   19312 Sep 2025 Alex Kruppa Mersenne cofactor
184 M(64381) / 18252318785612645711774019109285438988204922542528174996118699181907547497   19308 Apr 2024 Serge Batalov Mersenne cofactor
185 Lucas(91943) / 12774901180031755171852992299   19187 Jul 2022 Serge Batalov Lucas cofactor
186 (V(428,1,8019) − 1) / (V(428,1,729) − 1)   19184 Jun 2022 Serge Batalov Lehmer primitive part
187 Lucas(91873) / 119273493071598409455551351   19175 Jul 2022 Serge Batalov Lucas cofactor
188 (2 • 1019153 + 691) / 9   19153 Jun 2022 Greg Childers
189 primU(137439)   19148 Jun 2022 Serge Batalov Fibonacci primitive part
190 ⌊(π • 1019176)⌋ % (1019128)   19128 Feb 2023 Oliver Kruse String in Pi
191 primU(107779)   18980 May 2022 Serge Batalov Fibonacci primitive part
192 ( U(162,1,8581) + U(162,1,8580) ) / ( U(162,1,66) + U(162,1,65) )   18814 Jun 2022 Serge Batalov Lehmer primitive part
193 See complete expression   18718 Jun 2022 Andreas Enge
194 (82 • 1018592 − 1) / 9   18593 Aug 2023 Markus Tervooren Near repunit
195 ( U(859,1,6385) − U(859,1,6384) ) / ( U(859,1,57) − U(859,1,56) )   18567 Jun 2022 Serge Batalov Lehmer primitive part
196 (505 • 1018470 − 1) / 9   18472 Jun 2022 Florian Piesker
197 primB(220895)   18465 Jun 2022 Serge Batalov Lucas Aurifeuillian primitive part
198 1748192 + 1218192   18355 Jan 2023 Youcef Lemsafer
199 primV(153279)   18283 May 2022 Serge Batalov Lucas primitive part
200 See complete expression   18192 Aug 2025 Alex Kruppa Mersenne cofactor of M(123435)
201 See complete expression   18190 Jul 2025 Alex Kruppa Cyclotomic polynomial cofactor
  of M(242730)
202 (721520 + 41) / 6   18186 Dec 2022 Florian Piesker Near repdigit in base 7
203 (10504 • 1018178 − 1) / 9   18182 Apr 2023 Florian Piesker
204 (34 • 1018155 − 7) / 9   18156 Jan 2026 Anonymous
205 259999 + 26453   18062 Oct 2023 Frank Doornink Smallest 60000-bit prime
206 259395 − 593952   17880 May 2025 Tengfei Wang Leyland minus form
207 primB(235015)   17856 May 2022 Serge Batalov Lucas Aurifeuillian primitive part
208 (1737 • 525415 − 1) / 4   17767 Oct 2022 Anonymous
209 1017753 + 3   17754 Mar 2024 U.N.Owen
210 (3407001 + 1) / 341   17721 Jul 2022 Florian Piesker Generalized Wagstaff
211 primV(148197)   17696 May 2022 Serge Batalov Lucas primitive part
212 ((236656 + 1)2 + 3) / ((27332 + 1)2 + 3) / 151   17653 Mar 2025 Alex Kruppa
213 918494 − 184949   17648 Jan 2024 Tengfei Wang Leyland minus form
214 (336913 − 1) / 2   17612 Dec 2022 Florian Piesker Generalized repunit
215 ( V(447,1,6723) + 1 ) / ( V(447,1,81) + 1 )   17604 Jun 2022 Serge Batalov Lehmer primitive part
216 (79 • 739339 − 1) / 6   17403 Jul 2022 Florian Piesker
217 1017343 + 777   17344 Dec 2023 U.N.Owen
218 primV(169830)   17335 May 2022 Serge Batalov Lucas primitive part
219 257285 + 572852   17245 Jun 2022 Greg Childers Leyland plus form
220 720366 − 203667   17212 Jan 2024 Tengfei Wang Leyland minus form
221 (257146 + 228573 + 1) / 1057378152607   17191 Oct 2024 Alex Kruppa Cyclotomic polynomial cofactor
  of M(171438)
222 (3816659 + 1) / 382   17184 Jul 2022 Florian Piesker Generalized Wagstaff
223 ( V(1578,1,5589) + 1 ) / ( V(1578,1,243) + 1 )   17098 Jun 2022 Serge Batalov Lehmer primitive part
224 M(19) • M(60287) / M(3173) / M(361)   17091 Sep 2024 Alex Kruppa Mersenne cofactor of M(60287)
225 (176874003 − 1) / 17686   17000 Mar 2024 Edwin Hall Generalized repunit
226 primV(101510)   16970 May 2022 Serge Batalov Lucas primitive part
227 (1016922 − 91) / 9   16922 May 2025 Tengfei Wang Near repunit
228 (17 • 1016918 + 7) / 3   16919 Aug 2023 Markus Tervooren
229 (3186733 + 1) / 319   16847 Jul 2022 Florian Piesker Generalized Wagstaff
230 See complete expression   16734 Jun 2022 Andreas Enge
231 See complete expression   16716 Sep 2024 Alex Kruppa Mersenne cofactor of M(69625)
232 (17 • 1016628 + 7) / 3   16629 Aug 2023 Markus Tervooren
233 (V(1240,1,5589) − 1) / (V(1240,1,243) − 1)   16538 Jun 2022 Serge Batalov Lehmer primitive part
234 primA(201485)   16535 May 2022 Serge Batalov Lucas Aurifeuillian primitive part
235 ( U(800,1,5725) − U(800,1,5724) ) / ( U(800,1,54) − U(800,1,53) )   16464 Jun 2022 Serge Batalov Lehmer primitive part
236 708853 − 885370   16335 Jun 2025 Tengfei Wang Leyland minus form
237 17484430616589 • 254201 + 5   16330 Jun 2024 Serge Batalov Part of a CPAP-3; d = 6
238 17484430616589 • 254201 − 7   16330 Jun 2024 Serge Batalov Part of a CPAP-3; d = 6
239 (4984! + 1) / 12823   16263 Mar 2026 Anonymous Factorial plus cofactor
240 (1427537 + 1) / 143   16220 Jul 2022 Florian Piesker Generalized Wagstaff
241 primB(225785)   16176 May 2022 Serge Batalov Lucas Aurifeuillian primitive part
242 (1214951 − 1) / 11   16134 Aug 2022 Florian Piesker Generalized repunit
243 (11023 • 1016097 − 1) / 3   16101 May 2023 Florian Piesker
244 1016076 + 67   16077 Nov 2023 U.N.Owen
245 (25453 • 1015998 − 1) / 9   16002 Apr 2023 Florian Piesker
246 (4695987 − 1) / 468   15990 Jul 2022 Florian Piesker Generalized repunit
247 (85 • 252665 − 1) / 578045658449   15844 Jun 2026 Michael Porter
248 19194818 − 48181919   15818 May 2025 Tengfei Wang Leyland minus form
249 (19 • 620238 + 2501) / 35   15748 Apr 2023 Florian Piesker
250 36574400 + 44003657   15678 Oct 2023 Anonymous Leyland plus form
251 See complete expression   15587 Aug 2025 Alex Kruppa
252 See complete expression   15587 Aug 2024 Alex Kruppa Mersenne cofactor of M(64165)
253 (619889 − 1) / 5   15476 Aug 2022 Florian Piesker Generalized repunit
254 See complete expression   15450 Apr 2023 Youcef Lemsafer Generalized repunit cofactor
255 (17 • 1015448 + 7) / 3   15449 Aug 2023 Markus Tervooren
256 (718251 + 1) / 8   15423 Aug 2022 Anonymous Generalized Wagstaff
257 22484537 + 45372248   15208 Aug 2022 Greg Childers Leyland plus form
258 1015103 − 63987   15103 Nov 2023 U.N.Owen
259 16094710 − 47101609   15103 Oct 2026 Oliver Kruse Leyland minus form
    new  
260 608491 − 849160   15099 Oct 2026 Oliver Kruse Leyland minus form
    new  
261 26384405 + 44052638   15071 May 2022 Greg Childers Leyland plus form
262 249999 + 24783   15052 Jul 2023 Maia Karpovich Smallest 50000-bit prime
263 14534752 − 47521453   15028 Feb 2024 Florian Piesker Leyland minus form
264 39114180 + 41803911   15016 Dec 2022 Greg Childers Leyland plus form
265 (31794291 − 42913179) / 8886701589272771624   15010 Apr 2024 Markus Tervooren Leyland minus form cofactor
266 (3010159 + 1) / 31   15005 May 2026 Michael Porter Generalized Wagstaff
267 (14774734 + 47341477) / 53   15003 Apr 2023 Youcef Lemsafer Leyland plus form cofactor
268 (210983952048 + 1) / 2   15000 Mar 2024 Edwin Hall Generalized half-Fermat
269 (41474147 + 2022) / 5435   15000 Mar 2024 Edwin Hall
270 ( V(1212,1,4887) + 1) / ( V(1212,1,27) + 1 )   14986 Jun 2022 Serge Batalov Lehmer primitive part
271 (1506883 + 1) / 151   14976 Jun 2022 Florian Piesker Generalized Wagstaff
272 1077372 + 7372107   14961 Oct 2023 Ryan S. Propper Leyland plus form
273 17164613 + 46131716   14921 Nov 2023 Ryan S. Propper Leyland plus form
274 3455876 + 5876345   14913 Nov 2023 Ryan S. Propper Leyland plus form
275 11594866 + 48661159   14910 Nov 2023 Anonymous Leyland plus form
276 (4616! + 1) / 3774283   14906 Mar 2026 Anonymous Factorial plus cofactor
277 5128801 + 8015128   14890 Oct 2025 Ryan S. Propper Leyland plus form
278 ((231 − 1)1597 − 1) / (231 − 2) / 634021777   14885 Jun 2022 Greg Childers
279 3765755 + 5755376   14821 Nov 2023 Anonymous Leyland plus form
280 17154558 + 45581715   14742 Nov 2023 Anonymous Leyland plus form
281 ( V(696,1,5211) + 1 ) / ( V(696,1,27) + 1 )   14737 Jun 2022 Serge Batalov Lehmer primitive part
282 19454476 + 44761945   14722 Nov 2023 Anonymous Leyland plus form
283 3815698 + 5698381   14707 Nov 2023 Anonymous Leyland plus form
284 See complete expression   14703 Jun 2022 Greg Childers
285 10874840 + 48401087   14696 Nov 2023 Anonymous Leyland plus form
286 33484163 + 41633348   14674 Jan 2024 Ryan S. Propper Leyland plus form
287 16374554 + 45541637   14637 Jan 2024 Ryan S. Propper Leyland plus form
288 φ(17003,10) / 215414318848365482017888228389199   14500 Sep 2024 Alfred Reich Cyclotomic polynomial cofactor
  of R(17003)
289 27724211 + 42112772   14498 Jan 2024 Ryan S. Propper Leyland plus form
290 40224022 + 20252025   14498 Jun 2025 Tengfei Wang Lifchitz plus form
291 (117514072048 + 1) / 2   14480 Nov 2024 Alfred Reich Generalized half-Fermat
292 25804241 + 42412580   14469 Jan 2024 Ryan S. Propper Leyland plus form
293 424019 − 324019   14461 Oct 2025 Ryan S. Propper Generalized Mersenne
294 8164949 + 4949816   14410 Jan 2024 Ryan S. Propper Leyland plus form
295 p(158221457)   14404 Jul 2022 Serge Batalov Partitions
296 19914342 + 43421991   14325 Oct 2023 Ryan S. Propper Leyland plus form
297 19164359 + 43591916   14308 Oct 2023 Ryan S. Propper Leyland plus form
298 917300 + 730091   14302 Oct 2023 Anonymous Leyland plus form
299 See complete expression   14297 Aug 2024 Alex Kruppa Mersenne cofactor of M(52193)
300 1113674 − 1367411   14241 Jan 2024 Tengfei Wang Leyland plus form
301 p(158931035)   14036 May 2026 Serge Batalov Partitions
302 p(158917403)   14035 May 2026 Serge Batalov Partitions
303 See complete expression   14035 Aug 2024 Alex Kruppa Mersenne cofactor of M(93195)
304 p(158898550)   14034 May 2026 Serge Batalov Partitions
305 p(158788742)   14029 May 2026 Serge Batalov Partitions
306 p(158635927)   14022 May 2026 Serge Batalov Partitions
307 p(158569348)   14020 May 2026 Serge Batalov Partitions
308 38 • (1014032 + 61) / 210606316076673   14020 Apr 2023 Youcef Lemsafer
309 p(158507386)   14017 May 2026 Serge Batalov Partitions
310 p(158447043)   14014 May 2026 Serge Batalov Partitions
311 p(158430002)   14013 May 2026 Serge Batalov Partitions
312 p(158381443)   14011 May 2026 Serge Batalov Partitions
313 p(158375386)   14011 Jul 2022 Serge Batalov Partitions
314 p(158295265)   14007 Jul 2022 Serge Batalov Partitions
315 21544153 + 41532154   13843 May 2022 Paul Leyland Leyland plus form
316 686303773648831000 + 68630377364882   13837 Apr 2026 Alfred Reich Dual Williams
317 1013808 + 32791   13809 Aug 2024 Alfred Reich
318 See complete expression   13786 Aug 2024 Alex Kruppa Mersenne cofactor of M(58315)
319 11 • (245616 + 1) / 3   13733 Jun 2022 Florian Piesker
320 (5045059 + 1) / 505   13669 Jun 2022 Florian Piesker Generalized Wagstaff
321 13354364 + 43641335   13640 Jan 2023 Greg Childers Leyland plus form
322 26073976 + 39762607   13583 Jan 2023 Greg Childers Leyland plus form
323 4995026 + 5026499   13561 Jan 2023 Greg Childers Leyland plus form
324 916918 + 691891   13553 Jan 2023 Greg Childers Leyland plus form
325 (4233! + 1) / 326022408531457943   13498 Mar 2026 Anonymous Factorial plus cofactor
326 17274162 + 41621727   13474 Jan 2023 Greg Childers Leyland plus form
327 23613992 + 39922361   13466 Jan 2023 Greg Childers Leyland plus form
328 29853874 + 38742985   13462 Jan 2023 Greg Childers Leyland plus form
329 1036682 + 6682103   13450 Jan 2023 Greg Childers Leyland plus form
330 10934414 + 44141093   13413 Jan 2023 Greg Childers Leyland plus form
331 (4215101 + 1) / 422   13384 Jun 2022 Florian Piesker Generalized Wagstaff
332 2295670 + 5670229   13381 Jan 2023 Greg Childers Leyland plus form
333 2245685 + 5685224   13362 Jan 2023 Greg Childers Leyland plus form
334 Lucas(64063) / 464426465381142115542697818362662865912299   13347 Aug 2024 Serge Batalov Lucas cofactor
335 See complete expression   13343 Aug 2024 Alex Kruppa Cyclotomic polynomial cofactor
  of M(180090)
336 p(141528106)   13244 Jul 2022 Charles H (Chuck) Lasher;
  David Broadhurst; Paul Underwood		 Partitions
337 p(141513546)   13244 Jul 2022 Charles H (Chuck) Lasher;
  David Broadhurst; Paul Underwood		 Partitions
338 p(141512238)   13244 Jul 2022 Charles H (Chuck) Lasher;
  David Broadhurst; Paul Underwood		 Partitions
339 1935792 − 5792193   13238 Feb 2023 Youcef Lemsafer Leyland minus form
340 p(141255053)   13232 Jul 2022 Charles H (Chuck) Lasher;
  David Broadhurst; Paul Underwood		 Partitions
341 M(44431) / M(283) / M(157) / 430619564833   13231 Aug 2024 Alex Kruppa Mersenne cofactor
342 6694682 + 4682669   13229 Jan 2023 Greg Childers Leyland plus form
343 p(141150528)   13227 Jul 2022 Charles H (Chuck) Lasher;
  David Broadhurst; Paul Underwood		 Partitions
344 p(141112026)   13225 Jul 2022 Charles H (Chuck) Lasher;
  David Broadhurst; Paul Underwood		 Partitions
345 p(141111278)   13225 Jul 2022 Charles H (Chuck) Lasher;
  David Broadhurst; Paul Underwood		 Partitions
346 See complete expression   13217 Aug 2024 Alex Kruppa Cyclotomic polynomial cofactor
  of M(133962)
347 p(140859260)   13213 Jul 2022 Charles H (Chuck) Lasher;
  David Broadhurst; Paul Underwood		 Partitions
348 p(140807155)   13211 Jul 2022 Charles H (Chuck) Lasher;
  David Broadhurst; Paul Underwood		 Partitions
349 p(140791396)   13210 Jul 2022 Charles H (Chuck) Lasher;
  David Broadhurst; Paul Underwood		 Partitions
350 p(140760498)   13208 Jun 2022 Charles H (Chuck) Lasher;
  David Broadhurst; Paul Underwood		 Partitions
351 p(140710320)   13206 Jun 2022 Charles H (Chuck) Lasher;
  David Broadhurst; Paul Underwood		 Partitions
352 See complete expression   13202 Sep 2024 Alex Kruppa Cyclotomic polynomial cofactor
  of M(134034)
353 p(140593907)   13201 Jun 2022 Charles H (Chuck) Lasher;
  David Broadhurst; Paul Underwood		 Partitions
354 p(140560280)   13199 Jun 2022 Charles H (Chuck) Lasher;
  David Broadhurst; Paul Underwood		 Partitions
355 p(140552343)   13199 Jun 2022 Charles H (Chuck) Lasher;
  David Broadhurst; Paul Underwood		 Partitions
356 p(140535370)   13198 Jun 2022 Charles H (Chuck) Lasher;
  David Broadhurst; Paul Underwood		 Partitions
357 p(140533925)   13198 Jun 2022 Charles H (Chuck) Lasher;
  David Broadhurst; Paul Underwood		 Partitions
358 p(140519816)   13197 Jun 2022 Charles H (Chuck) Lasher;
  David Broadhurst; Paul Underwood		 Partitions
359 25723867 + 38672572   13188 Jan 2023 Greg Childers Leyland plus form
360 19244015 + 40151924   13187 Jan 2023 Greg Childers Leyland plus form
361 See complete expression   13186 Nov 2024 Alfred Reich
362 1013172 + 22947   13173 Aug 2024 Alfred Reich
363 1013170 + 2697   13171 Aug 2024 Alfred Reich
364 1013162 + 87729   13163 Aug 2024 Alfred Reich
365 1013161 + 51729   13162 Aug 2024 Alfred Reich
366 1013160 + 11161   13161 Aug 2024 Alfred Reich
367 1013159 + 1807   13160 Aug 2024 Alfred Reich
368 29323789 + 37892932   13138 Jan 2023 Greg Childers Leyland plus form
369 34293712 + 37123429   13123 Dec 2022 Anonymous Leyland plus form
370 4614926 + 4926461   13122 Dec 2022 Anonymous Leyland plus form
371 25803841 + 38412580   13105 Dec 2022 Florian Piesker Leyland plus form
372 (243502 + 221751 + 1) / 71426334276062353   13079 Aug 2024 Alex Kruppa Cyclotomic polynomial cofactor
  of M(130506)
373 See complete expression   13007 Oct 2024 Alfred Reich Leyland minus form cofactor
374 1013002 − 8 • 108 − 1   13002 Dec 2023 U.N.Owen Near repdigit
375 24453836 + 38362445   12998 Dec 2022 Greg Childers Leyland plus form
376 21093908 + 39082109   12991 Dec 2022 Greg Childers Leyland plus form
377 17783993 + 39931778   12977 Aug 2022 Greg Childers Leyland plus form
378 See complete expression   12947 Aug 2024 Alex Kruppa Mersenne cofactor of M(67235)
379 21073894 + 38942107   12943 Aug 2022 Greg Childers Leyland plus form
380 (50233491 − 1) / 35068626   12913 Mar 2023 Youcef Lemsafer Generalized repunit cofactor
381 14674076 + 40761467   12907 Jul 2022 Greg Childers Leyland plus form
382 Sm10(3506) / 7937021247923634 ; See complete expression   12901 Jan 2023 Youcef Lemsafer Smarandache base 10 cofactor
383 10274278 + 42781027   12884 Jul 2022 Greg Childers Leyland plus form
384 1595852 + 5852159   12883 Jul 2022 Greg Childers Leyland plus form
385 (242737 + 1) / 3   12865 May 2022 Greg Childers Wagstaff
386 primV(97240) / 2054798130239231521   12822 Feb 2026 Paul Underwood Lucas primitive part
387 See complete expression   12814 Aug 2024 Alex Kruppa Mersenne cofactor of M(48127)
388 20953858 + 38582095   12814 Jul 2022 Greg Childers Leyland plus form
389 (367 • 715118 − 1) / 6   12778 Jun 2022 Florian Piesker Near redigit in base 7
390 (326633 + 1) / 4   12707 Aug 2022 Florian Piesker Generalized Wagstaff
391 242210 + 91549   12707 Mar 2023 Anonymous
392 (77 • 1012720 − 41) / 80794157024576083501251   12699 Mar 2023 Youcef Lemsafer
393 (3499 • 1012689 − 1) / 3   12693 Apr 2023 Florian Piesker
394 16893926 + 39261689   12672 Jul 2022 Greg Childers Leyland plus form
395 24823729 + 37292482   12660 Jul 2022 Greg Childers Leyland plus form
396 (4994691 − 1) / 498   12655 Jun 2022 Florian Piesker Generalized repunit
397 2575248 + 5248257   12648 Jul 2022 Greg Childers Leyland plus form
398 M(53977) / M(701) / M(7711) / M(4907) / M(77) • 259969    12644 Jul 2024 Alex Kruppa Mersenne cofactor of M(53977)
399 13784023 + 40231378   12630 Jul 2022 Greg Childers Leyland plus form
400 (26383687 + 36872638) / 530650435937411   12600 Mar 2023 Youcef Lemsafer Leyland plus form cofactor
401 (2055449 + 1) / 206   12595 Jun 2022 Florian Piesker Generalized Wagstaff
402 (2305333 − 1) / 229   12593 Jun 2022 Florian Piesker Generalized repunit
403 R(12611) / 151596145122775505868566782271   12581 Sep 2024 Alfred Reich Repunit cofactor
404 Sm10(3418) / 10541062 ; See complete expression   12558 Jan 2023 Youcef Lemsafer Smarandache base 10 cofactor
405 (239509 − 1) / (23257 − 1) / 11002902177363902238826201639790642566112031151441   12550 Mar 2023 Youcef Lemsafer Generalized repunit cofactor
406 (241614 + 220807 + 1) / 231896371365555042937   12507 Jul 2024 Alex Kruppa
407 (8 • 1012527 − 11) / 66426466217992706366987547351   12500 Feb 2023 Youcef Lemsafer
408 26133650 + 36502613   12473 Jul 2022 Greg Childers Leyland plus form
409 35123512 + 33   12452 May 2025 Tengfei Wang Lifchitz plus form
410 10504096 + 10134096   12375 Jan 2023 Youcef Lemsafer
411 30523543 + 35433052   12346 May 2022 Greg Childers Leyland plus form
412 23893646 + 36462389   12317 May 2022 Greg Childers Leyland plus form
413 25773602 + 36022577   12287 May 2022 Greg Childers Leyland plus form
414 31723507 + 35073172   12280 May 2022 Greg Childers Leyland plus form
415 13253924 + 39241325   12252 May 2022 Greg Childers Leyland plus form
416 (1211353 +1) / 13   12251 Aug 2022 Florian Piesker Generalized Wagstaff
417 (23671 • 1012192 − 1) / 9   12196 Apr 2022 Florian Piesker
418 M(55495) / M(11099) / M(5045) • M(1009) / 567767102431   12138 Jul 2024 Alex Kruppa Mersenne cofactor of M(55495)
419 5354444 + 4444535   12125 May 2022 Greg Childers Leyland plus form
420 239999 + 18065   12041 Jul 2023 Oliver Kruse Smallest 40000-bit prime
421 239999 + 1411862541   12041 Oct 2023 Frank Doornink Part of smallest 40000-bit prime twin
422 239999 + 1411862543   12041 Oct 2023 Frank Doornink Part of smallest 40000-bit prime twin
423 (714221 − 1) / 6   12018 Aug 2022 Florian Piesker Generalized repunit
424 1012000 − 11319   12000 Dec 2023 U.N.Owen Largest 12000 digit prime
425 397542 − 98   12000 Mar 2024 Edwin Hall
426 (2235110 − 405) / 4   12000 Mar 2024 Edwin Hall
427 417440 + 952   12000 Mar 2024 Edwin Hall
428 1011999 + 76621   12000 Oct 2023 U.N.Owen
429 1011999 + 72577   12000 Jan 2023 Frank Doornink
430 1011999 + 12757   12000 Jan 2024 U.N.Owen Smallest 12000 digit prime
431 M(42991) / M(3307) / M(13)   11943 Jul 2024 Alex Kruppa Mersenne cofactor of M(42991)
432 30703423 + 34233070   11937 May 2022 Greg Childers Leyland plus form
433 976006 − 600697   11933 Apr 2025 Tengfei Wang Leyland minus form
434 (886 • 199291 − 1) / 3   11884 Jun 2022 Florian Piesker
435 1310633 − 50   11845 Jun 2022 Florian Piesker
436 298096 + 10   11840 Jul 2022 Florian Piesker
437 (313 • 324761 − 1) / 2   11817 Jul 2022 Florian Piesker
438 (4589 • 516892 − 1) / 4   11811 Dec 2022 Anonymous
439 3 • 1011799 − 37   11800 Mar 2023 Youcef Lemsafer
440 (22683515 + 35152268) / 787343    11790 Feb 2023 Youcef Lemsafer Leyland plus form cofactor
441 (3752! + 1) / 104478008869009   11770 Mar 2026 Anonymous Factorial plus cofactor
442 (3732! + 1) / 5504713034011   11700 Feb 2026 Anonymous Factorial plus cofactor
443 M(58389) / M(19463) / 501545671318332018168553   11695 Jul 2024 Alex Kruppa Mersenne cofactor of M(58389)
444 14073712 + 37121407   11687 May 2022 Greg Childers Leyland plus form
445 25603423 + 34232560   11667 Jun 2022 Greg Childers Leyland plus form
446 22483469 + 34692248   11628 Jun 2022 Greg Childers Leyland plus form
447 (29153354 + 33542915) / 16793707319901665479   11602 Apr 2023 Youcef Lemsafer Leyland plus form cofactor
448 26693378 + 33782669   11575 Jun 2022 Greg Childers Leyland plus form
449 (516519 − 1) / 4   11546 Aug 2022 Florian Piesker Generalized repunit
450 Φ(45067 , 2) / 10140976011912241   11544 Oct 2026 Jiahao He Cyclotomic polynomial cofactor
    new  
451 See complete expression   11522 Jul 2024 Alex Kruppa Mersenne cofactor of M(62439)
452 21973442 + 34422197   11503 Jun 2022 Greg Childers Leyland plus form
453 1975000 − 5000197   11473 Sep 2024 Oliver Kruse Leyland minus form
454 (22213422 − 34222221) / 11   11451 Dec 2023 U.N.Owen Leyland minus form cofactor
455 See complete expression   11377 Sep 2025 Serge Batalov
456 (201 • 1415279 − 1) / 20   11347 Jun 2022 Florian Piesker
457 (4327 • 1011330 − 7) / 9   11333 Jun 2022 Florian Piesker
458 (1110867 − 1) / 10   11316 Aug 2022 Florian Piesker Generalized repunit
459 15163557 + 35571516   11314 Jun 2022 Greg Childers Leyland plus form
460 1137 • 367259 + 19   11301 Apr 2023 Florian Piesker
461 4964189 + 4189496   11292 Jun 2022 Greg Childers Leyland plus form
462 9223805 + 3805922   11281 Jun 2022 Greg Childers Leyland plus form
463 4724217 + 4217472   11277 Jun 2022 Greg Childers Leyland plus form
464 13249 • 248131 − 49   11227 Jun 2022 Florian Piesker
465 7653892 + 3892765   11224 Jun 2022 Paul Leyland Leyland plus form
466 19663395 + 33951966   11182 Jun 2022 Greg Childers Leyland plus form
467 See complete expression   11155 Jul 2024 Alex Kruppa
468 (19 • 1011149 + 611) / 9   11150 Jul 2024 Alfred Reich
469 M(47435) • M(179) • M(53) • M(5) / M(9487) / M895) / M(265)   11146 Jul 2024 Alex Kruppa Mersenne cofactor of M(47435)
470 31823182 + 33   11146 May 2025 Tengfei Wang Lifchitz plus form
471 29423213 + 32132942   11145 Jun 2022 Greg Childers Leyland plus form
472 (3570! + 1) / 1653141738351157   11120 Feb 2026 Anonymous Factorial plus cofactor
473 (3134451 + 1) / 314   11106 Jun 2022 Florian Piesker Generalized Wagstaff
474 179021 + 25   11100 Jun 2022 Florian Piesker
475 See complete expression   11064 Aug 2025 Serge Batalov
476 (5034093 − 1) / 502   11055 May 2023 Tom Wu Generalized repunit
477 (17 • 1011046 + 7) / 3   11047 Aug 2023 Markus Tervooren
478 24823243 + 32432482   11010 May 2022 Greg Childers Leyland plus form
479 1011000 + 11973   11001 Jul 2024 Alfred Reich
480 (293869752365940771791281143446653 • 1010968 − 1) / 3   11000 Jun 2026 Anonymous Prime / Emirp
481 (1011000 + 46652354920208825626736445697937) / 3   11000 Jun 2026 Anonymous Prime / Emirp
482 1010999 + 24439   11000 Nov 2023 U.N.Owen
483 (133 • 1005496 − 1) / 33   10993 Jun 2022 Florian Piesker
484 12623543 + 35431262   10988 May 2022 Oliver Kruse Leyland plus form
485 27813188 + 31882781   10981 May 2022 Oliver Kruse Leyland plus form
486 30893142 + 31423089   10966 May 2022 Oliver Kruse Leyland plus form
487 13303509 + 35091330   10962 May 2022 Oliver Kruse Leyland plus form
488 995488 + 548899   10953 May 2022 Oliver Kruse Leyland plus form
489 17663369 + 33691766   10940 May 2022 Oliver Kruse Leyland plus form
490 (4794079 + 1) / 480   10931 Jun 2022 Florian Piesker Generalized Wagstaff
491 5393996 + 3996539   10916 May 2022 Oliver Kruse Leyland plus form
492 (64 • 1010906 + 53) / 9   10907 May 2022 Greg Childers Palindrome
493 M(36433) / 22829723232843819182760759315930113665799992643755857550482474537913   10901 Dec 2025 Oliver Kruse Mersenne cofactor
494 30703121 + 31213070   10884 May 2022 Oliver Kruse Leyland plus form
495 12713502 + 35021271   10871 May 2022 Oliver Kruse Leyland plus form
496 (237651 + 1) / (21637 + 1) / 2796203   10835 Jul 2024 Alex Kruppa Wagstaff cofactor
497 347035 + 703534   10774 May 2022 Greg Childers Leyland plus form
498 5793896 + 3896579   10764 May 2022 Oliver Kruse Leyland plus form
499 Sm3(3228) / 6690369309511780988346 ; See complete expression   10738 May 2026 Youcef Lemsafer Smarandache base 3 cofactor
500 286 • 414 + 286 − 1   10718 May 2026 Alfred Reich Dual Williams
501 21183217 + 32172118   10700 May 2022 Oliver Kruse Leyland plus form
502 Lucas(51169)   10694 Jan 2026 Anonymous Lucas; recertified
503 2984309 + 4309298   10662 May 2022 Oliver Kruse Leyland plus form
504 11733470 + 34701173   10651 May 2022 Oliver Kruse Leyland plus form
505 292 • 384 + 292 − 1   10635 May 2026 Alfred Reich Dual Williams
506 17553268 + 32681755   10603 May 2022 Oliver Kruse Leyland plus form
507 (19 • 1010613 − 73) / 20376889065137331   10598 Jul 2024 Alfred Reich
508 1010584 + 26191   10585 Aug 2024 Alfred Reich
509 (19 • 1010554 + 341) / 9   10555 Jul 2024 Alfred Reich
510 146462479 • 235001 + 8765   10545 Oct 2025 Paul Underwood Part of a CPAP-3; d = 8766
511 21193160 + 31602119   10511 May 2022 Oliver Kruse Leyland plus form
512 (129739 − 1) / 11   10510 Jul 2022 Florian Piesker Generalized repunit
513 24473100 + 31002447   10505 May 2022 Oliver Kruse Leyland plus form
514 (34 • 1010499 − 61) / 9   10500 Dec 2022 Jason Parker-Burlingham
515 1010470 + 3   10471 Aug 2022 Florian Piesker
516 12093392 + 33921209   10456 May 2022 Greg Childers Leyland plus form
517 26613052 − 30522661   10454 Jun 2025 Tengfei Wang Leyland minus form
518 29183013 − 30132918   10441 Jun 2025 Tengfei Wang Leyland minus form
519 16783225 + 32251678   10400 May 2022 Greg Childers Leyland plus form
520 17723201 + 32011772   10399 May 2022 Greg Childers Leyland plus form
521 (82 • 1010394 + 71) / 9   10395 Nov 2023 Richard G. Palindrome
522 19663155 + 31551966   10392 May 2022 Anonymous Leyland plus form
523 (2 • 1010391 + 61) / 9   10391 Jan 2023 Florian Baur Near repdigit
524 (419 • 712274 − 5) / 6   10375 Sep 2022 Florian Piesker
525 1010371 + 24679   10372 Aug 2024 Alfred Reich
526 1010370 + 7891   10371 Aug 2024 Alfred Reich
527 1010369 + 20863   10370 Aug 2024 Alfred Reich
528 27693008 − 30082769   10355 Jun 2025 Tengfei Wang Leyland minus form
529 17483193 − 31931748   10354 Feb 2024 Tengfei Wang Leyland minus form
530 See complete expression   10350 Jul 2024 Alex Kruppa Mersenne cofactor of M(47575)
531 24483053 − 30532448   10347 Jun 2025 Tengfei Wang Leyland minus form
532 6 • Bern(4306) / 2153   10342 Jun 2022 Greg Childers Irregular
533 29172982 − 29822917   10333 Jun 2025 Tengfei Wang Leyland minus form
534 8513522 + 3522851   10320 May 2022 Paul Leyland Leyland plus form
535 See complete expression   10317 Nov 2025 Anonymous Repunit cofactor of R(40404)
536 2124431 − 4431212   10308 Jun 2023 Florian Piesker Leyland minus form
537 See complete expression   10305 May 2024 Richard G.
538 See complete expression   10300 Sep 2024 Alex Kruppa Cyclotomic polynomial cofactor
  of M(119994)
539 19513128 − 31281951   10292 Jun 2023 Florian Piesker Leyland minus form
540 (4341 • 514720 − 1) / 4   10292 Oct 2022 Anonymous
541 (158741 − 1) / 14   10280 Jul 2022 Florian Piesker Generalized repunit
542 613206 + 217   10277 Feb 2024 Florian Piesker
543 59056921173 • 234030 + 7   10255 Jun 2022 Greg Childers Part of sexy prime pair
544 6973594 + 3594697   10219 May 2022 Greg Childers Leyland plus form
545 10613372 − 33721061   10203 Jun 2023 Florian Piesker Leyland minus form
546 (191 • 1055045 + 1) / 8   10199 Jun 2022 Florian Piesker
547 8123505 − 3505812   10198 Jun 2023 Florian Piesker Leyland minus form
548 See complete expression   10195 Jul 2024 Alex Kruppa Cyclotomic polynomial cofactor
  of M(103206)
549 22313042 + 30422231   10187 May 2022 Oliver Kruse Leyland plus form
550 24293000 − 30002429   10157 Jun 2023 Florian Piesker Leyland minus form
551 15433178 + 31781543   10133 May 2022 Paul Leyland Leyland plus form
552 M(42145) / M(8429) / 13604811874892518060205885792305751   10116 Jul 2024 Alex Kruppa Mersenne cofactor of M(42145)
553 11413308 − 33081141   10114 Jun 2023 Florian Piesker Leyland minus form
554 12343265 + 32651234   10094 Jun 2022 Greg Childers Leyland plus form
555 Φ(23912,10)   10081 Jun 2022 David Broadhurst Cyclotomic polynomial cofactor
  of R(23912)
556 (29092910 − 29102909) / 41   10078 Jan 2023 Youcef Lemsafer Leyland minus form cofactor
557 27392930 + 29302739   10073 Jun 2022 Greg Childers Leyland plus form
558 259692281 − 259682281   10069 Jun 2026 Ryan S. Propper Generalized Mersenne
559 29072907 + 18981898   10069 Dec 2025 Oliver Kruse Lifchitz plus form
560 See complete expression   10068 Jul 2024 Alex Kruppa Cyclotomic polynomial cofactor
  of M(117222)
561 7433506 + 742   10066 May 2026 Alfred Reich Dual Williams
562 2314253 − 2304253   10053 Jun 2026 Ryan S. Propper Generalized Mersenne
563 789102053 − 789092053   10053 Jun 2026 Ryan S. Propper Generalized Mersenne
564 8083456 + 807   10049 May 2026 Alfred Reich Dual Williams
565 2072644824759 • 233333 + 5   10047 Jun 2022 Greg Childers Part of first known gigantic prime
  triplet; re-certified via CM
566 3783896 + 377   10042 May 2026 Alfred Reich Dual Williams
567 6483571 + 3571648   10041 May 2022 Greg Childers Leyland plus form
568 6843538 + 683   10031 May 2026 Alfred Reich Dual Williams
569 769832053 − 769822053   10031 Jun 2026 Ryan S. Propper Generalized Mersenne
570 769472053 − 769462053   10030 Jun 2026 Ryan S. Propper Generalized Mersenne
571 19813042 − 30421981   10030 May 2023 Anonymous Leyland minus form
572 763942053 − 763932053   10024 Jun 2026 Ryan S. Propper Generalized Mersenne
573 (3262! + 1) / 3091890367590330237362029   10022 Feb 2026 Anonymous Factorial plus cofactor
574 915115 + 90   10021 May 2026 Alfred Reich Dual Williams
575 1010020 + 16657   10021 Aug 2024 Alfred Reich
576 See complete expression   10020 May 2026 Anonymous
577 See complete expression   10020 May 2026 Anonymous
578 1010020 − 237   10020 Aug 2024 Alfred Reich
579 28942894 + 20532053   10018 May 2024 Oliver Kruse Leyland plus form
580 8313430 + 830   10015 May 2026 Alfred Reich Dual Williams
581 (61 • 1010016 − 7) / 5193   10015 Jul 2026 Anonymous
582 See complete expression   10014 Jul 2024 Alex Kruppa Mersenne cofactor of M(42679)
583 (44 • 1010021 − 71) / 4788509679   10013 Jul 2026 Anonymous
584 244992281 − 244982281   10011 Jun 2026 Ryan S. Propper Generalized Mersenne
585 (69032609 − 1) / 3997631498   10007 May 2026 Michael Porter Generalized repunit cofactor
586 (1213911 − 1) / (124637 − 1) / 157   10007 May 2026 Michael Porter Generalized repunit cofactor
587 28912891 − 922922   10006 Oct 2026 Oliver Kruse Lifchitz minus form
    new  
588 (45 • 233283 − 1) / 2265199868100403   10006 May 2026 Michael Porter Riesel cofactor
589 (71 • 233238 − 1) / 109   10006 May 2026 Michael Porter Riesel cofactor
590 (1098 • 2394211 + 1) / 12688219834129   10006 May 2026 Michael Porter Generalized Proth cofactor
591 (186292347 + 1) / 80942219296714530   10006 May 2026 Michael Porter Generalized Wagstaff cofactor
592 (96132518 + 1) / 423844875449528964456890   10006 May 2026 Michael Porter
593 (185112351 − 1) / 4987222285699423705427686770   10006 May 2026 Michael Porter Generalized repunit cofactor
594 (138999 + 1) / 58926919603466247634   10005 May 2026 Michael Porter Generalized Wagstaff cofactor
595 (73142593 − 1) / 1752533160363107   10005 May 2026 Michael Porter Generalized repunit cofactor
596 (84692549 − 1) / 43178332   10005 May 2026 Michael Porter Generalized repunit cofactor
597 (135622426 + 1) / 877117813951457959945   10005 May 2026 Michael Porter
598 (1034 • 2394211 + 1) / 241143046561091   10005 May 2026 Michael Porter
599 (79 • 233263 − 1) / 115516295447   10004 May 2026 Michael Porter Riesel cofactor
600 (162222381 − 1) / 702336971660428797573   10004 Apr 2026 Michael Porter Generalized repunit cofactor
601 (111342473 − 1) / 11133   10004 May 2026 Michael Porter Generalized repunit
602 (74 • 1010017 − 1) / 7003079578422563   10004 May 2026 Michael Porter
603 (10491721663 + 1) / 1049173   10003 May 2026 Michael Porter Generalized Wagstaff cofactor
604 (39 • 233291 − 1) / 371972862859286220829   10003 Apr 2026 Michael Porter Riesel cofactor
605 (125232446 + 1) / 286050143722457924330   10003 Apr 2026 Michael Porter
606 (48782713 − 1) / 4877   10003 Apr 2026 Michael Porter Generalized repunit
607 (128902437 + 1) / 167222679108477   10003 May 2026 Michael Porter Generalized Wagstaff cofactor
608 746152053 − 746142053   10003 Jun 2026 Ryan S. Propper Generalized Mersenne
609 (127 • 233220 − 1) / 3   10002 Apr 2026 Michael Porter Riesel cofactor
610 (191 • 233262 − 1) / 26524711363663   10002 Apr 2026 Michael Porter Riesel cofactor
611 (55 • 233282 − 1) / 19295840380197014631   10002 Apr 2026 Michael Porter Riesel cofactor
612 (76542579 + 1) / 1730325449096005   10002 May 2026 Michael Porter Generalized Wagstaff cofactor
613 515857 − 505857   10002 Apr 2025 Anonymous Generalized Mersenne
614 (58262659 − 1) / 94295059225   10002 Apr 2026 Michael Porter Generalized repunit cofactor
615 (111592474 + 1) / 6161536516642   10002 Apr 2026 Michael Porter
616 1010001 + 28331593   10002 May 2024 Anonymous
617 (46062731 + 1) / 4607   10001 Apr 2026 Michael Porter Generalized Wagstaff
618 (33238 • 233239 + 1) / 4104169815   10001 Apr 2026 Michael Porter Near Cullen cofactor
619 (197852333 − 1) / 34638852192398078083384   10001 Apr 2026 Michael Porter
620 (52 • 1010000 + 11) / 9   10001 Mar 2023 Youcef Lemsafer
621 (133572428 + 1) / 31829931492483602   10001 Apr 2026 Michael Porter
622 (73 • 233241 + 1) / 61024593   10001 Apr 2026 Michael Porter Proth cofactor
623 (153122393 + 1) / 225232767773903   10001 Apr 2026 Michael Porter Generalized Wagstaff cofactor
624 (137782417 + 1) / 13779   10001 Apr 2026 Michael Porter Generalized Wagstaff
625 12843217 − 12833217   10001 Apr 2025 Anonymous Generalized Mersenne
626 1010000 + 1017363   10001 Aug 2024 Alfred Reich
627 1010000 + 165031   10001 Aug 2024 Alfred Reich
628 1010000 + 65277   10001 Oct 2023 U.N.Owen
629 1010000 + 28579   10001 Oct 2023 U.N.Owen
630 1010000 − 22403   10000 Aug 2024 Alfred Reich
631 1010000 − 47717   10000 Aug 2024 Alfred Reich
632 1010000 − 65403   10000 Jan 2026 Alfred Reich
633 1010000 − 322497   10000 Sep 2024 Alfred Reich
634 894297 • 109994 + 711826   10000 Aug 2024 Alfred Reich
635 233219 − 52545   10000 Jul 2024 Alfred Reich
636 (46572732 + 1) / 2516045064327004328914   10000 Apr 2026 Michael Porter
637 (82302558 + 1) / 6158727069636769   10000 Apr 2026 Anonymous
638 631101 • 109994 + 711826   10000 Aug 2024 Alfred Reich
639 Fib(47850) + 20841   10000 Dec 2023 Tengfei Wang
640 (237371 + 397) / 41745703454270394607773342228304835316   10000 Jul 2024 Alfred Reich
641 (237344 + 231) / 8   10000 Jul 2022 Florian Piesker
642 (114952467 − 1) / 536935319091017126   10000 Apr 2026 Anonymous Generalized repunit cofactor
643 299667 • 109994 + 711826   10000 Aug 2024 Alfred Reich
644 240708 • 109994 + 711826   10000 Aug 2024 Alfred Reich
645 233217 + 111   10000 May 2022 Anonymous
646 233217 − 721155   10000 Mar 2024 Edwin Hall
647 See complete expression   10000 Aug 2024 Alfred Reich
648 See complete expression   10000 Aug 2024 Alfred Reich Leyland plus form cofactor
649 Fib(47847) + 26679   10000 Jul 2024 Alfred Reich
650 (1010000 − 1) / 9 + 7 • 10885   10000 Aug 2024 Alfred Reich Near repunit
651 233216 + 281577   10000 Mar 2023 Youcef Lemsafer
652 ((11476 • 1035 + 4113)256 + 1) / 2   10000 Aug 2024 Alfred Reich Generalized half-Fermat
653 (33875430588693130699512 + 1) / 2   10000 Feb 2026 Anonymous Generalized half-Fermat
654 (33875430588693094381512 + 1) / 2   10000 Aug 2024 Alfred Reich Generalized half-Fermat
655 (33875430588693072115512 + 1) / 2   10000 Apr 2026 Anonymous Generalized half-Fermat
656 (33875430588693069661512 + 1) / 2   10000 Apr 2026 Anonymous Generalized half-Fermat
657 (33875430588693069511512 + 1) / 2   10000 Feb 2026 Anonymous Generalized half-Fermat
658 (33875430588693064859512 + 1) / 2   10000 Feb 2026 Anonymous Generalized half-Fermat
659 (33875430588693062819512 + 1) / 2   10000 Feb 2026 Anonymous Generalized half-Fermat
660 (33875430588693060889512 + 1) / 2   10000 Feb 2026 Anonymous Generalized half-Fermat
661 (33875430588693060787512 + 1) / 2   10000 Feb 2026 Anonymous Generalized half-Fermat
662 (33875430588693059443512 + 1) / 2   10000 Feb 2026 Anonymous Generalized half-Fermat
663 (33875430588693058083512 + 1) / 2   10000 Feb 2026 Anonymous Generalized half-Fermat
664 (33875430588693055871512 + 1) / 2   10000 Aug 2024 Alfred Reich Generalized half-Fermat
665 1309747264300589758110032419673347620959731068338635399869049806286716959555931128 + 2   10000 Aug 2024 Alfred Reich
666 10 • (104999 + 520488)2 + 7   10000 Aug 2024 Alfred Reich
667 10 • (104999 + 517910)2 + 7   10000 Aug 2024 Alfred Reich
668 10 • (104999 + 86414)2 + 7   10000 Aug 2024 Alfred Reich
669 109999 + 1527231836097   10000 Mar 2026 Anonymous
670 109999 + 21870245691511147257   10000 Jul 2024 Alfred Reich
671 109999 + 7066834558999   10000 Aug 2024 Alfred Reich
672 109999 + 274366375363   10000 Jun 2023 Oliver Kruse Part of the smallest gigantic triplet
  to pattern d = 0, 2, 6
673 109999 + 274366375359   10000 Jun 2023 Oliver Kruse Part of the smallest gigantic triplet
  to pattern d = 0, 2, 6
674 109999 + 274366375357   10000 Jun 2023 Oliver Kruse Part of the smallest gigantic triplet
  to pattern d = 0, 2, 6
675 109999 + 194011932123   10000 Jun 2023 Oliver Kruse Part of the smallest gigantic triplet
  to pattern d = 0, 4, 6
676 109999 + 194011932121   10000 Jun 2023 Oliver Kruse Part of the smallest gigantic triplet
  to pattern d = 0, 4, 6
677 109999 + 194011932117   10000 Jun 2023 Oliver Kruse Part of the smallest gigantic triplet
  to pattern d = 0, 4, 6
678 109999 + 11147257   10000 May 2022 Anonymous
679 109999 + 780199   10000 Jul 2024 Alfred Reich
680 109999 + 78571   10000 Nov 2024 Alfred Reich
681 109999 + 70999   10000 Oct 2023 U.N.Owen