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
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| Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
| 4001 | 2^543989+2793047 | 163758 | Enzo Doria | 02/2016 |
| 4002 | (28*10^163709+113)/3 | 163710 | Robert Price | 03/2020 |
| 4003 | (2^543398)/(543398^2) | 163568 | Henri Lifchitz | 05/2025 |
| 4004 | (2013^49729-1)/(2013^223-1) | 163561 | Ryan Propper | 11/2023 |
| 4005 | L(2*543272)%(2^543272) | 163541 | Henri Lifchitz | 07/2025 |
| 4006 | (23*10^163523+301)/9 | 163524 | Robert Price | 06/2021 |
| 4007 | (68*10^163521-329)/9 | 163522 | Robert Price | 03/2021 |
| 4008 | 35820^35899+35899^35820 | 163489 | Norbert Schneider | 11/2021 |
| 4009 | 2^542870-69551 | 163421 | Enzo Doria | 12/2015 |
| 4010 | 2^542502+24799 | 163310 | Enzo Doria | 10/2023 |
| 4011 | 2^542395+72533 | 163278 | Enzo Doria | 04/2016 |
| 4012 | 2^542258+216949 | 163236 | Enzo Doria | 12/2023 |
| 4013 | 2^542072-3683 | 163180 | Yves Minet | 03/2017 |
| 4014 | fibonacci(780566)-4 | 163129 | Jon Grantham | 08/2023 |
| 4015 | (682*10^163106-7)/9 | 163108 | Robert Price | 08/2021 |
| 4016 | 2^541779-1867357 | 163092 | Enzo Doria | 04/2016 |
| 4017 | (29*10^163056+313)/9 | 163057 | Robert Price | 04/2021 |
| 4018 | 2^541476+214743 | 163001 | Enzo Doria | 11/2023 |
| 4019 | 13^142159+14^142159-2 | 162933 | Harsh Aggarwal | 05/2024 |
| 4020 | 8*10^162924+9 | 162925 | Robert Price | 12/2015 |
| 4021 | 2^540905+81557 | 162829 | Enzo Doria | 08/2016 |
| 4022 | 2^540628-2939 | 162746 | Yves Minet | 09/2014 |
| 4023 | 919^54919-918^54919 | 162743 | Jean-Louis Charton | 01/2013 |
| 4024 | (203*10^162689+1)/3 | 162691 | Robert Price | 03/2020 |
| 4025 | 3*10^162620-59 | 162621 | Robert Price | 09/2018 |
| 4026 | 2^540180+26791 | 162611 | Enzo Doria | 12/2023 |
| 4027 | 3^340694-112960 | 162553 | Enzo Doria | 07/2014 |
| 4028 | 2^539925+81 | 162534 | Henri Lifchitz | 11/2024 |
| 4029 | 2^539807-114081 | 162499 | Enzo Doria | 12/2014 |
| 4030 | 414^62093+62093^414 | 162498 | Norbert Schneider | 03/2022 |
| 4031 | 2^539654-114893 | 162453 | Enzo Doria | 05/2015 |
| 4032 | 9*10^162449-71 | 162450 | Robert Price | 11/2020 |
| 4033 | 2^539617-1851583 | 162441 | Enzo Doria | 08/2015 |
| 4034 | (509*10^162422+31)/9 | 162424 | Robert Price | 08/2022 |
| 4035 | (91*10^162410+11)/3 | 162412 | Robert Price | 02/2020 |
| 4036 | 2^539346+81049 | 162360 | Enzo Doria | 07/2016 |
| 4037 | 2^539220-115499 | 162322 | Enzo Doria | 07/2015 |
| 4038 | 2^539217-113713 | 162321 | Enzo Doria | 09/2014 |
| 4039 | 9^170099-8^170099 | 162316 | Jean-Louis Charton | 05/2005 |
| 4040 | 4*10^162263-39 | 162264 | Robert Price | 09/2020 |
| 4041 | 31243^36098-36098^31243 | 162252 | Frank Doornink | 01/2024 |
| 4042 | 31987^36000-36000^31987 | 162180 | Frank Doornink | 01/2024 |
| 4043 | (115*10^162153-1)/3 | 162155 | Serge Batalov | 12/2014 |
| 4044 | (10^162138+11)/3 | 162138 | Serge Batalov | 07/2015 |
| 4045 | (61*10^162100-403)/9 | 162101 | Robert Price | 10/2021 |
| 4046 | 2^538473-112723 | 162097 | Enzo Doria | 06/2014 |
| 4047 | 2^538157+79337 | 162002 | Enzo Doria | 06/2016 |
| 4048 | 2^538136-114749 | 161996 | Enzo Doria | 05/2015 |
| 4049 | 2^538104+1531 | 161986 | Lelio R Paula | 01/2013 |
| 4050 | (9*29^110727-1199)/14 | 161927 | Curtis Bright | 05/2015 |
| 4051 | ((2^179294-1)^3+2)/11 | 161918 | Serge Batalov | 03/2023 |
| 4052 | 31198^36027-36027^31198 | 161910 | Frank Doornink | 01/2024 |
| 4053 | 2^537815-22737 | 161899 | Enzo Doria | 07/2013 |
| 4054 | 2^537804-39839 | 161896 | Enzo Doria | 09/2015 |
| 4055 | (754*10^161816-7)/9 | 161818 | Robert Price | 05/2020 |
| 4056 | 2^537461+29867 | 161792 | Enzo Doria | 03/2024 |
| 4057 | 2^537458-59201 | 161791 | Enzo Doria | 10/2015 |
| 4058 | 2*10^161766+51 | 161767 | Robert Price | 05/2018 |
| 4059 | (7*10^161760+131)/3 | 161761 | Robert Price | 06/2020 |
| 4060 | 2^537209-49849 | 161717 | Enzo Doria | 10/2015 |
| 4061 | (58*10^161691+329)/9 | 161692 | Robert Price | 05/2019 |
| 4062 | 23*10^161668-3 | 161670 | Robert Price | 10/2021 |
| 4063 | 2^536937+1879397 | 161635 | Enzo Doria | 09/2016 |
| 4064 | 3*2^536868-5 | 161614 | Jon Grantham | 07/2023 |
| 4065 | 34*10^161593-9 | 161595 | Robert Price | 06/2020 |
| 4066 | (31*10^161582-1)/3 | 161584 | Robert Price | 02/2020 |
| 4067 | 24494^36813+36813^24494 | 161575 | Norbert Schneider | 11/2023 |
| 4068 | 2^536569-22881 | 161524 | Enzo Doria | 07/2013 |
| 4069 | (46*10^161505+593)/9 | 161506 | Robert Price | 04/2022 |
| 4070 | 10^161253+573493 | 161254 | Patrick De Geest | 07/2018 |
| 4071 | 10^161253-8001 | 161253 | Robert Price | 03/2018 |
| 4072 | 97*10^161247-3 | 161249 | Robert Price | 05/2020 |
| 4073 | 7*10^161192-9 | 161193 | Robert Price | 10/2015 |
| 4074 | 2^535415-19 | 161176 | Stefano Morozzi | 07/2022 |
| 4075 | 2^535269-113803 | 161133 | Enzo Doria | 09/2014 |
| 4076 | 2^535205-23295 | 161113 | Enzo Doria | 08/2013 |
| 4077 | (49*10^161105+437)/9 | 161106 | Robert Price | 09/2021 |
| 4078 | 2^534961+6561 | 161040 | Henri Lifchitz | 11/2024 |
| 4079 | (89^82609+1)/90 | 161036 | Paul Bourdelais | 10/2017 |
| 4080 | 35385^35385-17692^17692 | 160960 | Henri Lifchitz | 10/2024 |
| 4081 | 2^534429-19 | 160880 | Stefano Morozzi | 07/2022 |
| 4082 | 2^534359-23229 | 160859 | Enzo Doria | 08/2013 |
| 4083 | 10^160836-1001 | 160836 | Robert Price | 10/2022 |
| 4084 | 457^60454+60454^457 | 160803 | Norbert Schneider | 07/2021 |
| 4085 | 8*10^160782+53 | 160783 | Robert Price | 08/2020 |
| 4086 | 67^88037-66^88037 | 160763 | Robert Price | 10/2013 |
| 4087 | (88*10^160761-637)/9 | 160762 | Robert Price | 11/2020 |
| 4088 | 2^533981+81 | 160745 | Henri Lifchitz | 11/2024 |
| 4089 | 2^533948-1852559 | 160735 | Enzo Doria | 08/2015 |
| 4090 | (2^769082)%F(769082) | 160728 | Henri Lifchitz | 05/2025 |
| 4091 | 2^533665-23335 | 160650 | Enzo Doria | 08/2013 |
| 4092 | 2^533600+217981 | 160630 | Enzo Doria | 01/2024 |
| 4093 | (19*10^160619+77)/3 | 160620 | Robert Price | 05/2019 |
| 4094 | 2^533350-5 | 160555 | Stefano Morozzi | 07/2022 |
| 4095 | (38*10^160508+151)/9 | 160509 | Robert Price | 03/2022 |
| 4096 | 3^336353-2^336353 | 160482 | Mike Oakes | 10/2007 |
| 4097 | 26134^36315-36315^26134 | 160411 | Frank Doornink | 03/2024 |
| 4098 | 25821^36358-36358^25821 | 160411 | Frank Doornink | 03/2024 |
| 4099 | 2*10^160339-63 | 160340 | Robert Price | 01/2022 |
| 4100 | 24419^36532+36532^24419 | 160293 | Norbert Schneider | 10/2023 |
| 4101 | (91*10^160249+11)/3 | 160251 | Robert Price | 02/2020 |
| 4102 | (772*10^160239-7)/9 | 160241 | Robert Price | 06/2022 |
| 4103 | (2*10^160226+187)/9 | 160226 | Robert Price | 06/2022 |
| 4104 | 2^532253+1868417 | 160225 | Enzo Doria | 04/2016 |
| 4105 | 2^532108-291989 | 160181 | Enzo Doria | 07/2015 |
| 4106 | (28*10^160171-79)/3 | 160172 | Robert Price | 02/2021 |
| 4107 | (26*10^160166-131)/3 | 160167 | Robert Price | 10/2019 |
| 4108 | 55*10^160145+9 | 160147 | Robert Price | 03/2022 |
| 4109 | (17*10^160143+67)/3 | 160144 | Robert Price | 01/2019 |
| 4110 | (394^61637-1)/393 | 159977 | Jinyuan Wang | 04/2023 |
| 4111 | (3^765357)%F(765357) | 159950 | Henri Lifchitz | 07/2025 |
| 4112 | (19*10^159921-49)/3 | 159922 | Robert Price | 05/2019 |
| 4113 | (47^95621-5^95621)/42 | 159887 | Robert Price | 05/2026 |
| 4114 | 2^531110-1853771 | 159881 | Enzo Doria | 09/2015 |
| 4115 | 2^531088+48451 | 159874 | Enzo Doria | 07/2025 |
| 4116 | (275^65536+53^65536)/2 | 159864 | Kellen Shenton | 11/2020 |
| 4117 | 2^530992-1845299 | 159845 | Enzo Doria | 07/2015 |
| 4118 | 2^530810+25 | 159790 | Stefano Morozzi | 04/2021 |
| 4119 | 25590^36241-36241^25590 | 159753 | Frank Doornink | 02/2024 |
| 4120 | (136*10^159736-1)/9 | 159738 | Serge Batalov | 12/2014 |
| 4121 | 2^530417-113833 | 159672 | Enzo Doria | 09/2014 |
| 4122 | 2^530406-69701 | 159669 | Enzo Doria | 02/2016 |
| 4123 | 5*10^159656+41 | 159657 | Robert Price | 03/2019 |
| 4124 | 8*10^159614+29 | 159615 | Robert Price | 11/2021 |
| 4125 | 7^188858-188858^7 | 159604 | Norbert Schneider | 05/2018 |
| 4126 | 28^110278+27 | 159590 | Alfred Reich | 02/2024 |
| 4127 | (45^96517-2^96517)/43 | 159562 | Robert Price | 11/2024 |
| 4128 | 7*10^159553-27 | 159554 | Robert Price | 11/2022 |
| 4129 | 3^334409-5*2^334409 | 159554 | Jon Grantham | 08/2023 |
| 4130 | (24^115597-1)/23 | 159547 | Paul Bourdelais | 09/2017 |
| 4131 | 25472^36209-36209^25472 | 159540 | Frank Doornink | 01/2024 |
| 4132 | (17*10^159438-377)/9 | 159439 | Robert Price | 03/2018 |
| 4133 | (49^94321+2^94321)/51 | 159420 | Robert Price | 06/2025 |
| 4134 | (203*10^159381+1)/3 | 159383 | Robert Price | 03/2020 |
| 4135 | 32282^35343-35343^32282 | 159361 | Frank Doornink | 02/2024 |
| 4136 | 2^529215+219383 | 159310 | Enzo Doria | 02/2024 |
| 4137 | 89*10^159258-9 | 159260 | Robert Price | 05/2020 |
| 4138 | 2^528944-461315 | 159229 | Enzo Doria | 07/2015 |
| 4139 | (13*10^159147+161)/3 | 159148 | Robert Price | 11/2018 |
| 4140 | 2^528620-113879 | 159131 | Enzo Doria | 10/2014 |
| 4141 | 32125^35306-35306^32125 | 159119 | Frank Doornink | 02/2024 |
| 4142 | (47*10^159083+259)/9 | 159084 | Robert Price | 03/2022 |
| 4143 | (861^54181-1)/860 | 159019 | Jinyuan Wang | 11/2023 |
| 4144 | 2^528000-23307 | 158944 | Enzo Doria | 08/2013 |
| 4145 | (29*10^158909+61)/9 | 158910 | Robert Price | 08/2018 |
| 4146 | 2^527817+1876817 | 158889 | Enzo Doria | 07/2016 |
| 4147 | 399^61084+398 | 158878 | Alfred Reich | 03/2026 |
| 4148 | 2^527774-49451 | 158876 | Enzo Doria | 10/2015 |
| 4149 | 2^527745-291553 | 158868 | Enzo Doria | 07/2015 |
| 4150 | (91*10^158862+11)/3 | 158864 | Robert Price | 02/2020 |
| 4151 | 2^527644-1856999 | 158837 | Enzo Doria | 10/2015 |
| 4152 | (37200^37199-37198^37199)/(2^37199) | 158822 | Henri Lifchitz | 06/2013 |
| 4153 | (17*10^158819+7)/3 | 158820 | Robert Price | 06/2023 |
| 4154 | 2^527573-1863253 | 158816 | Enzo Doria | 12/2015 |
| 4155 | 2^527553-23401 | 158810 | Enzo Doria | 08/2013 |
| 4156 | (49*10^158783+437)/9 | 158784 | Robert Price | 09/2021 |
| 4157 | 10^158755+310207 | 158756 | Patrick De Geest | 08/2021 |
| 4158 | 10^158755-50001 | 158755 | Robert Price | 08/2020 |
| 4159 | (61*10^158748-619)/9 | 158749 | Robert Price | 03/2022 |
| 4160 | 11^152420-210 | 158730 | Enzo Doria | 09/2012 |
| 4161 | (13*10^158694+401)/9 | 158695 | Robert Price | 01/2018 |
| 4162 | 2^527052-69059 | 158659 | Enzo Doria | 11/2015 |
| 4163 | 2^526849-113233 | 158598 | Enzo Doria | 07/2014 |
| 4164 | 24286^36161+36161^24286 | 158579 | Norbert Schneider | 08/2023 |
| 4165 | (2^526763-lucasV(1,2,526763)+1)/2 | 158572 | Mike Oakes | 11/2016 |
| 4166 | (299*10^158544-17)/3 | 158546 | Robert Price | 04/2020 |
| 4167 | 2^526658-3551 | 158540 | Yves Minet | 03/2017 |
| 4168 | 7*10^158465-11 | 158466 | Robert Price | 06/2019 |
| 4169 | (7^187507-3^187507)/4 | 158462 | Jon Grantham | 08/2023 |
| 4170 | 2^526375-23115 | 158455 | Enzo Doria | 08/2013 |
| 4171 | (77*10^158407-293)/9 | 158408 | Robert Price | 09/2019 |
| 4172 | 31209^35242-35242^31209 | 158388 | Frank Doornink | 01/2024 |
| 4173 | 32071^35144-35144^32071 | 158363 | Frank Doornink | 01/2024 |
| 4174 | 2^526028-112793 | 158351 | Enzo Doria | 07/2014 |
| 4175 | (229*10^158339-1)/3 | 158341 | Robert Price | 07/2020 |
| 4176 | 32042^35123-35123^32042 | 158255 | Frank Doornink | 01/2024 |
| 4177 | 2^525690-9221 | 158249 | Lelio R Paula | 01/2013 |
| 4178 | 2*10^158242-7 | 158243 | Robert Price | 10/2015 |
| 4179 | 2^525667-525667^2 | 158242 | Henri Lifchitz | 12/2017 |
| 4180 | (56*10^158230+187)/9 | 158231 | Robert Price | 10/2021 |
| 4181 | 10^158209-7000000001 | 158209 | Robert Price | 12/2021 |
| 4182 | 31050^35207-35207^31050 | 158153 | Frank Doornink | 01/2024 |
| 4183 | 2^525186-1857431 | 158097 | Enzo Doria | 10/2015 |
| 4184 | 31527^35108-35108^31527 | 157940 | Frank Doornink | 01/2024 |
| 4185 | 2^524515-23245 | 157895 | Enzo Doria | 08/2013 |
| 4186 | 2^524499-109087 | 157890 | Enzo Doria | 04/2014 |
| 4187 | 2^524384-219533 | 157856 | Enzo Doria | 03/2024 |
| 4189 | 2^18067*(2^506221+1)-1 | 157827 | Makoto Morimoto | 05/2014 |
| 4190 | 2^524288+189093 | 157827 | Makoto Morimoto | 01/2016 |
| 4188 | 2^524288-164073 | 157827 | Matthias Baur | 03/2020 |
| 4191 | (2^(2^19)-9333)/(19*23*463*1213*31973) | 157814 | Makoto Morimoto | 09/2017 |
| 4192 | (10^157792+359)/9 | 157792 | Serge Batalov | 12/2014 |
| 4193 | 2^524154+25 | 157787 | Stefano Morozzi | 04/2021 |
| 4194 | 2^523924+1876591 | 157717 | Enzo Doria | 07/2016 |
| 4195 | (17*10^157705+67)/3 | 157706 | Robert Price | 01/2019 |
| 4196 | (46^94841+1)/47 | 157696 | Robert Price | 01/2014 |
| 4197 | 2^523774+77839 | 157672 | Enzo Doria | 05/2016 |
| 4198 | 2^523587+2799143 | 157616 | Enzo Doria | 04/2016 |
| 4199 | 2^523496+220141 | 157588 | Enzo Doria | 03/2024 |
| 4200 | 2^523371+1872113 | 157551 | Enzo Doria | 05/2016 |
| 4201 | 8*10^157477+27 | 157478 | Robert Price | 09/2021 |
| 4202 | p(30987)#-p(30987+1) | 157417 | Henri Lifchitz | 11/2024 |
| 4203 | 32268^34909-34909^32268 | 157397 | Frank Doornink | 02/2024 |
| 4204 | (8*10^157368+49)/3 | 157369 | Robert Price | 05/2020 |
| 4205 | (82*10^157319+449)/9 | 157320 | Robert Price | 11/2019 |
| 4206 | 2^522535-351457 | 157299 | Enzo Doria | 07/2015 |
| 4207 | 25401^35704-35704^25401 | 157271 | Frank Doornink | 01/2024 |
| 4208 | 2^522226+2799079 | 157206 | Enzo Doria | 04/2016 |
| 4209 | (134*10^157191-11)/3 | 157193 | Robert Price | 01/2022 |
| 4210 | 2^522134-1849451 | 157178 | Enzo Doria | 08/2015 |
| 4211 | 9*10^157152+71 | 157153 | Robert Price | 08/2020 |
| 4212 | 4*10^157150+93 | 157151 | Robert Price | 08/2018 |
| 4213 | 31227^34952-34952^31227 | 157093 | Frank Doornink | 01/2024 |
| 4214 | (32^104347+5^104347)/37 | 157057 | Anonymous | 12/2023 |
| 4215 | fibonacci(751442)-2 | 157042 | Jon Grantham | 08/2023 |
| 4216 | 2^521401-29593 | 156958 | Enzo Doria | 08/2015 |
| 4217 | 7*10^156956+87 | 156957 | Robert Price | 07/2019 |
| 4218 | 2^521348-23397 | 156942 | Enzo Doria | 08/2013 |
| 4219 | Phi(572849,2) | 156922 | Henri Lifchitz | 02/2026 |
| 4220 | 10^156902+34509 | 156903 | Patrick De Geest | 08/2021 |
| 4222 | 10^156902-80000001 | 156902 | Robert Price | 04/2021 |
| 4221 | 10^156902-69789 | 156902 | Patrick De Geest | 08/2021 |
| 4223 | (98^78797+1)/99 | 156901 | Paul Bourdelais | 12/2017 |
| 4224 | 65^86522+64 | 156857 | Lelio R Paula | 04/2016 |
| 4225 | 8^173687-7^173687 | 156855 | Jean-Louis Charton | 09/2004 |
| 4226 | 2^520977-1858183 | 156830 | Enzo Doria | 10/2015 |
| 4227 | (8*10^156718-101)/3 | 156719 | Robert Price | 08/2018 |
| 4228 | (10^156640+7)/53 | 156639 | Alfred Reich | 07/2021 |
| 4229 | 2^520314-1849481 | 156631 | Enzo Doria | 08/2015 |
| 4230 | Phi(51227,11#) | 156610 | Henri Lifchitz | 12/2025 |
| 4231 | (16*10^156563-637)/9 | 156564 | Robert Price | 09/2022 |
| 4232 | (13*10^156522+89)/3 | 156523 | Robert Price | 09/2018 |
| 4233 | (2^(6*86654+1)-5)/3 | 156513 | Kevin Acres | 12/2013 |
| 4234 | (2^519925-5)/3 | 156513 | Stefano Morozzi | 08/2022 |
| 4235 | (4*10^156501+119)/3 | 156502 | Robert Price | 12/2021 |
| 4236 | (83*10^156476-101)/9 | 156477 | Robert Price | 08/2021 |
| 4237 | 3*10^156435-97 | 156436 | Robert Price | 07/2018 |
| 4238 | 10^156428+111 | 156429 | Boyan Hu | 10/2024 |
| 4239 | (8*10^156371-77)/3 | 156372 | Robert Price | 07/2018 |
| 4240 | 53^90679-52^90679 | 156356 | Robert Price | 01/2013 |
| 4241 | 31267^34782-34782^31267 | 156349 | Frank Doornink | 01/2024 |
| 4242 | (418*10^156309-31)/9 | 156311 | Robert Price | 05/2022 |
| 4243 | 2^519106-59141 | 156267 | Enzo Doria | 10/2015 |
| 4244 | 25929^35404-35404^25929 | 156266 | Frank Doornink | 03/2024 |
| 4245 | 2^519053+6077 | 156251 | Enzo Doria | 02/2016 |
| 4246 | 31199^34764-34764^31199 | 156235 | Frank Doornink | 01/2024 |
| 4247 | 2^518968-1860989 | 156225 | Enzo Doria | 11/2015 |
| 4248 | (25*10^156221-7)/9 | 156222 | Robert Price | 05/2018 |
| 4249 | 2^518931-2782297 | 156214 | Enzo Doria | 09/2015 |
| 4250 | 2^518608-2939 | 156117 | Yves Minet | 09/2014 |
