What is a PRP ?
A PRP is a probable prime number, a number that nobody knows how to prove
or disprove its primality.
Here are some criterions that can be used to recognize these numbers
:
- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N
should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3.
N should pass the strong test in base b.
- or more (if someone has got an idea) !!!
Submit your PRPs
See the Top discoverers
See the Latest PRPs
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| Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
| 4001 | 89*10^159258-9 | 159260 | Robert Price | 05/2020 |
| 4002 | 2^528944-461315 | 159229 | Enzo Doria | 07/2015 |
| 4003 | (13*10^159147+161)/3 | 159148 | Robert Price | 11/2018 |
| 4004 | 2^528620-113879 | 159131 | Enzo Doria | 10/2014 |
| 4005 | 32125^35306-35306^32125 | 159119 | Frank Doornink | 02/2024 |
| 4006 | (47*10^159083+259)/9 | 159084 | Robert Price | 03/2022 |
| 4007 | (861^54181-1)/860 | 159019 | Jinyuan Wang | 11/2023 |
| 4008 | 2^528000-23307 | 158944 | Enzo Doria | 08/2013 |
| 4009 | (29*10^158909+61)/9 | 158910 | Robert Price | 08/2018 |
| 4010 | 2^527817+1876817 | 158889 | Enzo Doria | 07/2016 |
| 4011 | 2^527774-49451 | 158876 | Enzo Doria | 10/2015 |
| 4012 | 2^527745-291553 | 158868 | Enzo Doria | 07/2015 |
| 4013 | (91*10^158862+11)/3 | 158864 | Robert Price | 02/2020 |
| 4014 | 2^527644-1856999 | 158837 | Enzo Doria | 10/2015 |
| 4015 | (37200^37199-37198^37199)/(2^37199) | 158822 | Henri Lifchitz | 06/2013 |
| 4016 | (17*10^158819+7)/3 | 158820 | Robert Price | 06/2023 |
| 4017 | 2^527573-1863253 | 158816 | Enzo Doria | 12/2015 |
| 4018 | 2^527553-23401 | 158810 | Enzo Doria | 08/2013 |
| 4019 | (49*10^158783+437)/9 | 158784 | Robert Price | 09/2021 |
| 4020 | 10^158755+310207 | 158756 | Patrick De Geest | 08/2021 |
| 4021 | 10^158755-50001 | 158755 | Robert Price | 08/2020 |
| 4022 | (61*10^158748-619)/9 | 158749 | Robert Price | 03/2022 |
| 4023 | 11^152420-210 | 158730 | Enzo Doria | 09/2012 |
| 4024 | (13*10^158694+401)/9 | 158695 | Robert Price | 01/2018 |
| 4025 | 2^527052-69059 | 158659 | Enzo Doria | 11/2015 |
| 4026 | 2^526849-113233 | 158598 | Enzo Doria | 07/2014 |
| 4027 | 24286^36161+36161^24286 | 158579 | Norbert Schneider | 08/2023 |
| 4028 | (2^526763-lucasV(1,2,526763)+1)/2 | 158572 | Mike Oakes | 11/2016 |
| 4029 | (299*10^158544-17)/3 | 158546 | Robert Price | 04/2020 |
| 4030 | 2^526658-3551 | 158540 | Yves Minet | 03/2017 |
| 4031 | 7*10^158465-11 | 158466 | Robert Price | 06/2019 |
| 4032 | (7^187507-3^187507)/4 | 158462 | Jon Grantham | 08/2023 |
| 4033 | 2^526375-23115 | 158455 | Enzo Doria | 08/2013 |
| 4034 | (77*10^158407-293)/9 | 158408 | Robert Price | 09/2019 |
| 4035 | 31209^35242-35242^31209 | 158388 | Frank Doornink | 01/2024 |
| 4036 | 32071^35144-35144^32071 | 158363 | Frank Doornink | 01/2024 |
| 4037 | 2^526028-112793 | 158351 | Enzo Doria | 07/2014 |
| 4038 | (229*10^158339-1)/3 | 158341 | Robert Price | 07/2020 |
| 4039 | 32042^35123-35123^32042 | 158255 | Frank Doornink | 01/2024 |
| 4040 | 2^525690-9221 | 158249 | Lelio R Paula | 01/2013 |
| 4041 | 2*10^158242-7 | 158243 | Robert Price | 10/2015 |
| 4042 | 2^525667-525667^2 | 158242 | Henri Lifchitz | 12/2017 |
| 4043 | (56*10^158230+187)/9 | 158231 | Robert Price | 10/2021 |
| 4044 | 10^158209-7000000001 | 158209 | Robert Price | 12/2021 |
| 4045 | 31050^35207-35207^31050 | 158153 | Frank Doornink | 01/2024 |
| 4046 | 2^525186-1857431 | 158097 | Enzo Doria | 10/2015 |
| 4047 | 31527^35108-35108^31527 | 157940 | Frank Doornink | 01/2024 |
| 4048 | 2^524515-23245 | 157895 | Enzo Doria | 08/2013 |
| 4049 | 2^524499-109087 | 157890 | Enzo Doria | 04/2014 |
| 4050 | 2^524384-219533 | 157856 | Enzo Doria | 03/2024 |
| 4052 | 2^18067*(2^506221+1)-1 | 157827 | Makoto Morimoto | 05/2014 |
| 4053 | 2^524288+189093 | 157827 | Makoto Morimoto | 01/2016 |
| 4051 | 2^524288-164073 | 157827 | Matthias Baur | 03/2020 |
| 4054 | (2^(2^19)-9333)/(19*23*463*1213*31973) | 157814 | Makoto Morimoto | 09/2017 |
| 4055 | (10^157792+359)/9 | 157792 | Serge Batalov | 12/2014 |
| 4056 | 2^524154+25 | 157787 | Stefano Morozzi | 04/2021 |
| 4057 | 2^523924+1876591 | 157717 | Enzo Doria | 07/2016 |
| 4058 | (17*10^157705+67)/3 | 157706 | Robert Price | 01/2019 |
| 4059 | (46^94841+1)/47 | 157696 | Robert Price | 01/2014 |
| 4060 | 2^523774+77839 | 157672 | Enzo Doria | 05/2016 |
| 4061 | 2^523587+2799143 | 157616 | Enzo Doria | 04/2016 |
| 4062 | 2^523496+220141 | 157588 | Enzo Doria | 03/2024 |
| 4063 | 2^523371+1872113 | 157551 | Enzo Doria | 05/2016 |
| 4064 | 8*10^157477+27 | 157478 | Robert Price | 09/2021 |
| 4065 | p(30987)#-p(30987+1) | 157417 | Henri Lifchitz | 11/2024 |
| 4066 | 32268^34909-34909^32268 | 157397 | Frank Doornink | 02/2024 |
| 4067 | (8*10^157368+49)/3 | 157369 | Robert Price | 05/2020 |
| 4068 | (82*10^157319+449)/9 | 157320 | Robert Price | 11/2019 |
| 4069 | 2^522535-351457 | 157299 | Enzo Doria | 07/2015 |
| 4070 | 25401^35704-35704^25401 | 157271 | Frank Doornink | 01/2024 |
| 4071 | 2^522226+2799079 | 157206 | Enzo Doria | 04/2016 |
| 4072 | (134*10^157191-11)/3 | 157193 | Robert Price | 01/2022 |
| 4073 | 2^522134-1849451 | 157178 | Enzo Doria | 08/2015 |
| 4074 | 9*10^157152+71 | 157153 | Robert Price | 08/2020 |
| 4075 | 4*10^157150+93 | 157151 | Robert Price | 08/2018 |
| 4076 | 31227^34952-34952^31227 | 157093 | Frank Doornink | 01/2024 |
| 4077 | (32^104347+5^104347)/37 | 157057 | Anonymous | 12/2023 |
| 4078 | fibonacci(751442)-2 | 157042 | Jon Grantham | 08/2023 |
| 4079 | 2^521401-29593 | 156958 | Enzo Doria | 08/2015 |
| 4080 | 7*10^156956+87 | 156957 | Robert Price | 07/2019 |
| 4081 | 2^521348-23397 | 156942 | Enzo Doria | 08/2013 |
| 4082 | Phi(572849,2) | 156922 | Henri Lifchitz | 02/2026 |
| 4083 | 10^156902+34509 | 156903 | Patrick De Geest | 08/2021 |
| 4085 | 10^156902-80000001 | 156902 | Robert Price | 04/2021 |
| 4084 | 10^156902-69789 | 156902 | Patrick De Geest | 08/2021 |
| 4086 | (98^78797+1)/99 | 156901 | Paul Bourdelais | 12/2017 |
| 4087 | 65^86522+64 | 156857 | Lelio R Paula | 04/2016 |
| 4088 | 8^173687-7^173687 | 156855 | Jean-Louis Charton | 09/2004 |
| 4089 | 2^520977-1858183 | 156830 | Enzo Doria | 10/2015 |
| 4090 | (8*10^156718-101)/3 | 156719 | Robert Price | 08/2018 |
| 4091 | (10^156640+7)/53 | 156639 | Alfred Reich | 07/2021 |
| 4092 | 2^520314-1849481 | 156631 | Enzo Doria | 08/2015 |
| 4093 | Phi(51227,11#) | 156610 | Henri Lifchitz | 12/2025 |
| 4094 | (16*10^156563-637)/9 | 156564 | Robert Price | 09/2022 |
| 4095 | (13*10^156522+89)/3 | 156523 | Robert Price | 09/2018 |
| 4096 | (2^(6*86654+1)-5)/3 | 156513 | Kevin Acres | 12/2013 |
| 4097 | (2^519925-5)/3 | 156513 | Stefano Morozzi | 08/2022 |
| 4098 | (4*10^156501+119)/3 | 156502 | Robert Price | 12/2021 |
| 4099 | (83*10^156476-101)/9 | 156477 | Robert Price | 08/2021 |
| 4100 | 3*10^156435-97 | 156436 | Robert Price | 07/2018 |
| 4101 | 10^156428+111 | 156429 | Boyan Hu | 10/2024 |
| 4102 | (8*10^156371-77)/3 | 156372 | Robert Price | 07/2018 |
| 4103 | 53^90679-52^90679 | 156356 | Robert Price | 01/2013 |
| 4104 | 31267^34782-34782^31267 | 156349 | Frank Doornink | 01/2024 |
| 4105 | (418*10^156309-31)/9 | 156311 | Robert Price | 05/2022 |
| 4106 | 2^519106-59141 | 156267 | Enzo Doria | 10/2015 |
| 4107 | 25929^35404-35404^25929 | 156266 | Frank Doornink | 03/2024 |
| 4108 | 2^519053+6077 | 156251 | Enzo Doria | 02/2016 |
| 4109 | 31199^34764-34764^31199 | 156235 | Frank Doornink | 01/2024 |
| 4110 | 2^518968-1860989 | 156225 | Enzo Doria | 11/2015 |
| 4111 | (25*10^156221-7)/9 | 156222 | Robert Price | 05/2018 |
| 4112 | 2^518931-2782297 | 156214 | Enzo Doria | 09/2015 |
| 4113 | 2^518608-2939 | 156117 | Yves Minet | 09/2014 |
| 4114 | 10*27^109005+697 | 156027 | Curtis Bright | 05/2015 |
| 4115 | (49*10^155933-319)/9 | 155934 | Robert Price | 10/2021 |
| 4116 | 2^517967-113485 | 155924 | Enzo Doria | 08/2014 |
| 4117 | (103*10^155904+17)/3 | 155906 | Robert Price | 08/2020 |
| 4118 | (8*10^155887-719)/9 | 155887 | Robert Price | 03/2021 |
| 4119 | 2^517789+29231 | 155871 | Enzo Doria | 02/2024 |
| 4120 | 4*10^155853-39 | 155854 | Robert Price | 09/2020 |
| 4121 | 2^517698+4429 | 155843 | Lelio R Paula | 01/2013 |
| 4122 | 32015^34584-34584^32015 | 155814 | Frank Doornink | 01/2024 |
| 4123 | 2^517543-113257 | 155796 | Enzo Doria | 07/2014 |
| 4124 | (14*10^155740-143)/3 | 155741 | Robert Price | 11/2018 |
| 4125 | 31959^34564-34564^31959 | 155697 | Frank Doornink | 01/2024 |
| 4126 | 31^104309-30^104309 | 155563 | Henri Lifchitz | 08/2013 |
| 4127 | 2^516742-39851 | 155555 | Enzo Doria | 09/2015 |
| 4128 | (22*10^155543+47)/3 | 155544 | Robert Price | 06/2021 |
| 4129 | (19*10^155504+131)/3 | 155505 | Robert Price | 06/2020 |
| 4130 | 7*10^155496+61 | 155497 | Robert Price | 08/2019 |
| 4131 | 2^516440+1878421 | 155464 | Enzo Doria | 08/2016 |
| 4132 | 26012^35173-35173^26012 | 155295 | Frank Doornink | 03/2024 |
| 4133 | 2^515863-1867237 | 155291 | Enzo Doria | 03/2016 |
| 4134 | 2^515786-461861 | 155268 | Enzo Doria | 07/2015 |
| 4135 | 2^515644-113247 | 155225 | Enzo Doria | 07/2014 |
| 4136 | (7*10^155203+107)/3 | 155204 | Robert Price | 02/2018 |
| 4137 | 10^155163+206871 | 155164 | Patrick De Geest | 05/2021 |
| 4138 | 10^155163-40001 | 155163 | Robert Price | 01/2021 |
| 4139 | (17*10^155133-89)/9 | 155134 | Robert Price | 07/2018 |
| 4140 | 26024^35131-35131^26024 | 155117 | Frank Doornink | 03/2024 |
| 4141 | 2^515249+214457 | 155106 | Enzo Doria | 10/2023 |
| 4142 | 2^515227-114997 | 155099 | Enzo Doria | 06/2015 |
| 4143 | 26510^35061-35061^26510 | 155090 | Frank Doornink | 03/2024 |
| 4145 | EPrime(155025) | 155025 | Eric W. Weisstein | 10/2010 |
| 4144 | (14*10^155024-221)/9 | 155025 | Robert Price | 04/2018 |
| 4146 | (4*10^155022+173)/3 | 155023 | Robert Price | 02/2018 |
| 4147 | 2^514652+6561 | 154926 | Henri Lifchitz | 11/2024 |
| 4148 | (266*10^154897+1)/3 | 154899 | Robert Price | 04/2020 |
| 4149 | (115*10^154869-1)/3 | 154871 | Serge Batalov | 12/2014 |
| 4150 | (86*10^154853-221)/9 | 154854 | Robert Price | 09/2019 |
| 4151 | 2^514361+78167 | 154839 | Enzo Doria | 05/2016 |
| 4152 | 2^514281-115033 | 154815 | Enzo Doria | 06/2015 |
| 4153 | 25701^35104-35104^25701 | 154807 | Frank Doornink | 02/2024 |
| 4154 | 2^514194-3311 | 154788 | Yves Minet | 12/2014 |
| 4155 | 25930^35067-35067^25930 | 154779 | Frank Doornink | 03/2024 |
| 4156 | (14*10^154773+37)/3 | 154774 | Robert Price | 12/2018 |
| 4157 | (16*10^154748+131)/3 | 154749 | Robert Price | 03/2022 |
| 4158 | 6*10^154742-31 | 154743 | Robert Price | 07/2020 |
| 4159 | (14*10^154645+139)/9 | 154646 | Robert Price | 11/2021 |
| 4160 | 2^513690+216949 | 154637 | Enzo Doria | 12/2023 |
| 4161 | 5*10^154618-79 | 154619 | Robert Price | 03/2021 |
| 4162 | (167*10^154595+1)/3 | 154597 | Robert Price | 04/2021 |
| 4163 | 2^513437+1879337 | 154560 | Enzo Doria | 09/2016 |
| 4164 | 2^513306-113201 | 154521 | Enzo Doria | 07/2014 |
| 4165 | 26415^34942-34942^26415 | 154509 | Frank Doornink | 03/2024 |
| 4166 | (5^739314)%L(739314) | 154508 | Henri Lifchitz | 07/2025 |
| 4167 | 18^120818+19^120818-2 | 154497 | Harsh Aggarwal | 05/2024 |
| 4168 | (10^154494-13)/3 | 154494 | Robert Price | 12/2017 |
| 4169 | 23462^35343+35343^23462 | 154462 | Norbert Schneider | 04/2023 |
| 4170 | 2^513042-113787 | 154442 | Enzo Doria | 09/2014 |
| 4171 | (151*10^154434-7)/9 | 154436 | Robert Price | 01/2020 |
| 4172 | (118*10^154428+11)/3 | 154430 | Robert Price | 03/2022 |
| 4173 | 2^512987+29153 | 154425 | Enzo Doria | 02/2024 |
| 4174 | (14*10^154413+139)/9 | 154414 | Robert Price | 11/2021 |
| 4175 | (77*10^154389-149)/9 | 154390 | Robert Price | 03/2022 |
| 4176 | 32184^34247-34247^32184 | 154374 | Frank Doornink | 02/2024 |
| 4177 | (27393*35^99972-499)/34 | 154367 | Eric Chen | 05/2025 |
| 4178 | 10^154359+49 | 154360 | Robert Price | 02/2023 |
| 4179 | Phi(p(4426),-4426) | 154358 | Henri Lifchitz | 12/2025 |
| 4180 | 2^512628-114053 | 154317 | Enzo Doria | 11/2014 |
| 4181 | 2^512529-49783 | 154287 | Enzo Doria | 10/2015 |
| 4182 | (355573#+6991)/(6991*2031599) | 154285 | Makoto Morimoto | 06/2019 |
| 4183 | 2^512315-115297 | 154223 | Enzo Doria | 06/2015 |
| 4184 | (47*10^154221+241)/9 | 154222 | Robert Price | 06/2022 |
| 4185 | (7*10^154211+173)/9 | 154211 | Robert Price | 01/2022 |
| 4186 | 2^512243+22703 | 154201 | Enzo Doria | 09/2023 |
| 4187 | 2^512168+79561 | 154178 | Enzo Doria | 06/2016 |
| 4188 | (77*10^154175+67)/9 | 154176 | Robert Price | 12/2021 |
| 4189 | (59*19^120562-5)/18 | 154170 | Anonymous | 12/2023 |
| 4190 | (5*10^154158-311)/9 | 154158 | Robert Price | 12/2021 |
| 4191 | 27169^34758-34758^27169 | 154120 | Frank Doornink | 01/2024 |
| 4192 | (89*10^154103-737)/9 | 154104 | Robert Price | 01/2022 |
| 4193 | 2^511857+23327 | 154085 | Enzo Doria | 10/2023 |
| 4194 | 4*10^154078-57 | 154079 | Robert Price | 10/2018 |
| 4195 | 26242^34863-34863^26242 | 154060 | Frank Doornink | 03/2024 |
| 4196 | (355049#+1859)/(11*13*10148891*62587751) | 154051 | Makoto Morimoto | 06/2019 |
| 4197 | 7*10^154038-57 | 154039 | Robert Price | 06/2020 |
| 4198 | 2^511658-114371 | 154025 | Enzo Doria | 02/2015 |
| 4199 | (57^87719+1)/58 | 154022 | Paul Bourdelais | 11/2017 |
| 4200 | 2^511580-1846679 | 154001 | Enzo Doria | 07/2015 |
| 4201 | (259*10^153998-1)/3 | 154000 | Robert Price | 12/2020 |
| 4202 | 2^511541-113713 | 153990 | Enzo Doria | 09/2014 |
| 4203 | 49958^32768+49957^32768 | 153965 | Kellen Shenton | 11/2020 |
| 4204 | 10^153935+970801 | 153936 | Patrick De Geest | 05/2021 |
| 4205 | 10^153935-1000001 | 153935 | Robert Price | 08/2020 |
| 4206 | (16*10^153868-73)/3 | 153869 | Robert Price | 07/2020 |
| 4207 | 9*10^153851-67 | 153852 | Robert Price | 11/2020 |
| 4208 | 2^511077-112723 | 153850 | Enzo Doria | 06/2014 |
| 4209 | 69^83653-68^83653 | 153826 | Robert Price | 12/2013 |
| 4210 | 2^510963-113707 | 153816 | Enzo Doria | 09/2014 |
| 4211 | (154*10^153810-1)/9 | 153812 | Serge Batalov | 12/2014 |
| 4212 | (181*25^109991-75077)/8 | 153763 | Curtis Bright | 05/2015 |
| 4213 | 2*10^153746-3 | 153747 | Robert Price | 07/2015 |
| 4214 | 2^510626+1179379 | 153714 | Enzo Doria | 05/2016 |
| 4215 | (7*10^153664+113)/3 | 153665 | Robert Price | 02/2018 |
| 4216 | 2^510448+24991 | 153661 | Enzo Doria | 11/2023 |
| 4217 | 2^510420+81121 | 153652 | Enzo Doria | 07/2016 |
| 4218 | (197*7^181761-1)/2 | 153608 | Karsten Bonath | 05/2017 |
| 4219 | 2^509894-459161 | 153494 | Enzo Doria | 05/2015 |
| 4220 | (74*10^153489+673)/9 | 153490 | Robert Price | 02/2022 |
| 4221 | (49*10^153484-211)/9 | 153485 | Robert Price | 06/2022 |
| 4222 | 2^509841+71657 | 153478 | Enzo Doria | 04/2016 |
| 4223 | 9*10^153446+41 | 153447 | Robert Price | 08/2020 |
| 4224 | 2^509533-1846723 | 153385 | Enzo Doria | 07/2015 |
| 4225 | 2^509468-39989 | 153366 | Enzo Doria | 09/2015 |
| 4226 | 70^83117-69^83117 | 153360 | Robert Price | 01/2014 |
| 4227 | (209246*34^99997-81)/11 | 153148 | Eric Chen | 08/2023 |
| 4228 | (7*10^153116-1)/3 | 153117 | Robert Price | 08/2022 |
| 4229 | (112*10^153025-1)/3 | 153027 | Serge Batalov | 12/2014 |
| 4230 | 31912^33975-33975^31912 | 153022 | Frank Doornink | 01/2024 |
| 4231 | (19*10^153010+131)/3 | 153011 | Robert Price | 06/2020 |
| 4232 | 2^508174-1855151 | 152976 | Enzo Doria | 09/2015 |
| 4233 | 181^67757-2 | 152974 | Lelio R Paula | 12/2017 |
| 4234 | 2^508160-1864829 | 152972 | Enzo Doria | 01/2016 |
| 4235 | 10^152960+412563 | 152961 | Patrick De Geest | 05/2021 |
| 4236 | 10^152960-50000000001 | 152960 | Robert Price | 12/2020 |
| 4237 | 10^152960-423749 | 152960 | Patrick De Geest | 05/2021 |
| 4238 | (71*10^152933-143)/9 | 152934 | Robert Price | 10/2021 |
| 4239 | 32109^33932-33932^32109 | 152919 | Frank Doornink | 02/2024 |
| 4240 | 2^507857-1848199 | 152881 | Enzo Doria | 07/2015 |
| 4241 | 2^507638-115361 | 152815 | Enzo Doria | 07/2015 |
| 4242 | 2^507551-114025 | 152789 | Enzo Doria | 11/2014 |
| 4243 | (6^196337+1)/7 | 152780 | Paul Bourdelais | 02/2010 |
| 4244 | (22*10^152670-13)/9 | 152671 | Robert Price | 06/2018 |
| 4245 | 86*17^124075+13 | 152670 | Eric Chen | 01/2026 |
| 4246 | 2^507085+28517 | 152648 | Enzo Doria | 01/2024 |
| 4247 | 2^506917+28847 | 152598 | Enzo Doria | 02/2024 |
| 4248 | 2^506451-22339 | 152457 | Enzo Doria | 07/2013 |
| 4249 | 26463^34460-34460^26463 | 152405 | Frank Doornink | 03/2024 |
| 4250 | 31898^33837-33837^31898 | 152394 | Frank Doornink | 01/2024 |
