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 | (22*10^155543+47)/3 | 155544 | Robert Price | 06/2021 |
| 4002 | (19*10^155504+131)/3 | 155505 | Robert Price | 06/2020 |
| 4003 | 7*10^155496+61 | 155497 | Robert Price | 08/2019 |
| 4004 | 2^516440+1878421 | 155464 | Enzo Doria | 08/2016 |
| 4005 | 26012^35173-35173^26012 | 155295 | Frank Doornink | 03/2024 |
| 4006 | 2^515863-1867237 | 155291 | Enzo Doria | 03/2016 |
| 4007 | 2^515786-461861 | 155268 | Enzo Doria | 07/2015 |
| 4008 | 2^515644-113247 | 155225 | Enzo Doria | 07/2014 |
| 4009 | (7*10^155203+107)/3 | 155204 | Robert Price | 02/2018 |
| 4010 | 10^155163+206871 | 155164 | Patrick De Geest | 05/2021 |
| 4011 | 10^155163-40001 | 155163 | Robert Price | 01/2021 |
| 4012 | (17*10^155133-89)/9 | 155134 | Robert Price | 07/2018 |
| 4013 | 26024^35131-35131^26024 | 155117 | Frank Doornink | 03/2024 |
| 4014 | 2^515249+214457 | 155106 | Enzo Doria | 10/2023 |
| 4015 | 2^515227-114997 | 155099 | Enzo Doria | 06/2015 |
| 4016 | 26510^35061-35061^26510 | 155090 | Frank Doornink | 03/2024 |
| 4018 | EPrime(155025) | 155025 | Eric W. Weisstein | 10/2010 |
| 4017 | (14*10^155024-221)/9 | 155025 | Robert Price | 04/2018 |
| 4019 | (4*10^155022+173)/3 | 155023 | Robert Price | 02/2018 |
| 4020 | 2^514652+6561 | 154926 | Henri Lifchitz | 11/2024 |
| 4021 | (266*10^154897+1)/3 | 154899 | Robert Price | 04/2020 |
| 4022 | (115*10^154869-1)/3 | 154871 | Serge Batalov | 12/2014 |
| 4023 | (86*10^154853-221)/9 | 154854 | Robert Price | 09/2019 |
| 4024 | 2^514361+78167 | 154839 | Enzo Doria | 05/2016 |
| 4025 | 2^514281-115033 | 154815 | Enzo Doria | 06/2015 |
| 4026 | 25701^35104-35104^25701 | 154807 | Frank Doornink | 02/2024 |
| 4027 | 2^514194-3311 | 154788 | Yves Minet | 12/2014 |
| 4028 | 25930^35067-35067^25930 | 154779 | Frank Doornink | 03/2024 |
| 4029 | (14*10^154773+37)/3 | 154774 | Robert Price | 12/2018 |
| 4030 | (16*10^154748+131)/3 | 154749 | Robert Price | 03/2022 |
| 4031 | 6*10^154742-31 | 154743 | Robert Price | 07/2020 |
| 4032 | (14*10^154645+139)/9 | 154646 | Robert Price | 11/2021 |
| 4033 | 2^513690+216949 | 154637 | Enzo Doria | 12/2023 |
| 4034 | 5*10^154618-79 | 154619 | Robert Price | 03/2021 |
| 4035 | (167*10^154595+1)/3 | 154597 | Robert Price | 04/2021 |
| 4036 | 2^513437+1879337 | 154560 | Enzo Doria | 09/2016 |
| 4037 | 2^513306-113201 | 154521 | Enzo Doria | 07/2014 |
| 4038 | 26415^34942-34942^26415 | 154509 | Frank Doornink | 03/2024 |
| 4039 | (5^739314)%L(739314) | 154508 | Henri Lifchitz | 07/2025 |
| 4040 | 18^120818+19^120818-2 | 154497 | Harsh Aggarwal | 05/2024 |
| 4041 | (10^154494-13)/3 | 154494 | Robert Price | 12/2017 |
| 4042 | 23462^35343+35343^23462 | 154462 | Norbert Schneider | 04/2023 |
| 4043 | 2^513042-113787 | 154442 | Enzo Doria | 09/2014 |
| 4044 | (151*10^154434-7)/9 | 154436 | Robert Price | 01/2020 |
| 4045 | (118*10^154428+11)/3 | 154430 | Robert Price | 03/2022 |
| 4046 | 2^512987+29153 | 154425 | Enzo Doria | 02/2024 |
| 4047 | (14*10^154413+139)/9 | 154414 | Robert Price | 11/2021 |
| 4048 | (77*10^154389-149)/9 | 154390 | Robert Price | 03/2022 |
| 4049 | 32184^34247-34247^32184 | 154374 | Frank Doornink | 02/2024 |
| 4050 | (27393*35^99972-499)/34 | 154367 | Eric Chen | 05/2025 |
| 4051 | 10^154359+49 | 154360 | Robert Price | 02/2023 |
| 4052 | 2^512628-114053 | 154317 | Enzo Doria | 11/2014 |
| 4053 | 2^512529-49783 | 154287 | Enzo Doria | 10/2015 |
| 4054 | (355573#+6991)/(6991*2031599) | 154285 | Makoto Morimoto | 06/2019 |
| 4055 | 2^512315-115297 | 154223 | Enzo Doria | 06/2015 |
| 4056 | (47*10^154221+241)/9 | 154222 | Robert Price | 06/2022 |
| 4057 | (7*10^154211+173)/9 | 154211 | Robert Price | 01/2022 |
| 4058 | 2^512243+22703 | 154201 | Enzo Doria | 09/2023 |
| 4059 | 2^512168+79561 | 154178 | Enzo Doria | 06/2016 |
| 4060 | (77*10^154175+67)/9 | 154176 | Robert Price | 12/2021 |
| 4061 | (59*19^120562-5)/18 | 154170 | Anonymous | 12/2023 |
| 4062 | (5*10^154158-311)/9 | 154158 | Robert Price | 12/2021 |
| 4063 | 27169^34758-34758^27169 | 154120 | Frank Doornink | 01/2024 |
| 4064 | (89*10^154103-737)/9 | 154104 | Robert Price | 01/2022 |
| 4065 | 2^511857+23327 | 154085 | Enzo Doria | 10/2023 |
| 4066 | 4*10^154078-57 | 154079 | Robert Price | 10/2018 |
| 4067 | 26242^34863-34863^26242 | 154060 | Frank Doornink | 03/2024 |
| 4068 | (355049#+1859)/(11*13*10148891*62587751) | 154051 | Makoto Morimoto | 06/2019 |
| 4069 | 7*10^154038-57 | 154039 | Robert Price | 06/2020 |
| 4070 | 2^511658-114371 | 154025 | Enzo Doria | 02/2015 |
| 4071 | (57^87719+1)/58 | 154022 | Paul Bourdelais | 11/2017 |
| 4072 | 2^511580-1846679 | 154001 | Enzo Doria | 07/2015 |
| 4073 | (259*10^153998-1)/3 | 154000 | Robert Price | 12/2020 |
| 4074 | 2^511541-113713 | 153990 | Enzo Doria | 09/2014 |
| 4075 | 49958^32768+49957^32768 | 153965 | Kellen Shenton | 11/2020 |
| 4076 | 10^153935+970801 | 153936 | Patrick De Geest | 05/2021 |
| 4077 | 10^153935-1000001 | 153935 | Robert Price | 08/2020 |
| 4078 | (16*10^153868-73)/3 | 153869 | Robert Price | 07/2020 |
| 4079 | 9*10^153851-67 | 153852 | Robert Price | 11/2020 |
| 4080 | 2^511077-112723 | 153850 | Enzo Doria | 06/2014 |
| 4081 | 69^83653-68^83653 | 153826 | Robert Price | 12/2013 |
| 4082 | 2^510963-113707 | 153816 | Enzo Doria | 09/2014 |
| 4083 | (154*10^153810-1)/9 | 153812 | Serge Batalov | 12/2014 |
| 4084 | (181*25^109991-75077)/8 | 153763 | Curtis Bright | 05/2015 |
| 4085 | 2*10^153746-3 | 153747 | Robert Price | 07/2015 |
| 4086 | 2^510626+1179379 | 153714 | Enzo Doria | 05/2016 |
| 4087 | (7*10^153664+113)/3 | 153665 | Robert Price | 02/2018 |
| 4088 | 2^510448+24991 | 153661 | Enzo Doria | 11/2023 |
| 4089 | 2^510420+81121 | 153652 | Enzo Doria | 07/2016 |
| 4090 | (197*7^181761-1)/2 | 153608 | Karsten Bonath | 05/2017 |
| 4091 | 2^509894-459161 | 153494 | Enzo Doria | 05/2015 |
| 4092 | (74*10^153489+673)/9 | 153490 | Robert Price | 02/2022 |
| 4093 | (49*10^153484-211)/9 | 153485 | Robert Price | 06/2022 |
| 4094 | 2^509841+71657 | 153478 | Enzo Doria | 04/2016 |
| 4095 | 9*10^153446+41 | 153447 | Robert Price | 08/2020 |
| 4096 | 2^509533-1846723 | 153385 | Enzo Doria | 07/2015 |
| 4097 | 2^509468-39989 | 153366 | Enzo Doria | 09/2015 |
| 4098 | 70^83117-69^83117 | 153360 | Robert Price | 01/2014 |
| 4099 | (209246*34^99997-81)/11 | 153148 | Eric Chen | 08/2023 |
| 4100 | (7*10^153116-1)/3 | 153117 | Robert Price | 08/2022 |
| 4101 | (112*10^153025-1)/3 | 153027 | Serge Batalov | 12/2014 |
| 4102 | 31912^33975-33975^31912 | 153022 | Frank Doornink | 01/2024 |
| 4103 | (19*10^153010+131)/3 | 153011 | Robert Price | 06/2020 |
| 4104 | 2^508174-1855151 | 152976 | Enzo Doria | 09/2015 |
| 4105 | 181^67757-2 | 152974 | Lelio R Paula | 12/2017 |
| 4106 | 2^508160-1864829 | 152972 | Enzo Doria | 01/2016 |
| 4107 | 10^152960+412563 | 152961 | Patrick De Geest | 05/2021 |
| 4108 | 10^152960-50000000001 | 152960 | Robert Price | 12/2020 |
| 4109 | 10^152960-423749 | 152960 | Patrick De Geest | 05/2021 |
| 4110 | (71*10^152933-143)/9 | 152934 | Robert Price | 10/2021 |
| 4111 | 32109^33932-33932^32109 | 152919 | Frank Doornink | 02/2024 |
| 4112 | 2^507857-1848199 | 152881 | Enzo Doria | 07/2015 |
| 4113 | 2^507638-115361 | 152815 | Enzo Doria | 07/2015 |
| 4114 | 2^507551-114025 | 152789 | Enzo Doria | 11/2014 |
| 4115 | (6^196337+1)/7 | 152780 | Paul Bourdelais | 02/2010 |
| 4116 | (22*10^152670-13)/9 | 152671 | Robert Price | 06/2018 |
| 4117 | 2^507085+28517 | 152648 | Enzo Doria | 01/2024 |
| 4118 | 2^506917+28847 | 152598 | Enzo Doria | 02/2024 |
| 4119 | 2^506451-22339 | 152457 | Enzo Doria | 07/2013 |
| 4120 | 26463^34460-34460^26463 | 152405 | Frank Doornink | 03/2024 |
| 4121 | 31898^33837-33837^31898 | 152394 | Frank Doornink | 01/2024 |
| 4122 | 2^505995-113185 | 152320 | Enzo Doria | 07/2014 |
| 4123 | (8*10^152260-17)/9 | 152260 | Serge Batalov | 11/2022 |
| 4124 | (4*10^152253+149)/9 | 152253 | Robert Price | 04/2018 |
| 4125 | 33530^33643-33643^33530 | 152250 | Norbert Schneider | 04/2024 |
| 4126 | 578^55117-577^55117 | 152230 | Jean-Louis Charton | 08/2012 |
| 4127 | 2^505431-505431 | 152150 | Henri Lifchitz | 04/2005 |
| 4128 | (203*10^152143+1)/3 | 152145 | Robert Price | 03/2020 |
| 4129 | 31730^33787-33787^31730 | 152092 | Frank Doornink | 01/2024 |
| 4130 | 2^505089+217787 | 152047 | Enzo Doria | 01/2024 |
| 4131 | 33565^33594-33594^33565 | 152043 | Norbert Schneider | 04/2024 |
| 4132 | 2^505053+73097 | 152037 | Enzo Doria | 04/2016 |
| 4133 | 22*10^151998+3 | 152000 | Robert Price | 01/2020 |
| 4134 | (238*10^151979-1)/3 | 151981 | Robert Price | 04/2020 |
| 4135 | (2^504793-7)/46765 | 151954 | Lelio R Paula | 12/2017 |
| 4136 | 3^318465+4 | 151947 | Aurel Gibier | 09/2024 |
| 4137 | 350377#+797581 | 151937 | Nicolas PALAU | 08/2017 |
| 4138 | (79*10^151906-529)/9 | 151907 | Robert Price | 01/2022 |
| 4139 | 2^504618-343991 | 151906 | Enzo Doria | 07/2015 |
| 4140 | 2^504259+211193 | 151798 | Enzo Doria | 08/2023 |
| 4141 | 2^504212-461939 | 151783 | Enzo Doria | 07/2015 |
| 4142 | 7*10^151772-41 | 151773 | Robert Price | 08/2021 |
| 4143 | 2^504054-2231 | 151736 | Yves Minet | 10/2011 |
| 4144 | 25237^34458-34458^25237 | 151686 | Frank Doornink | 11/2023 |
| 4145 | (28*10^151682+191)/3 | 151683 | Robert Price | 02/2020 |
| 4146 | 2^503817+23961 | 151665 | Enzo Doria | 10/2023 |
| 4147 | 2^503475-933075 | 151562 | Paul Bourdelais | 06/2021 |
| 4148 | 2^503371+26289 | 151530 | Enzo Doria | 12/2023 |
| 4149 | 2^503361-39883 | 151527 | Enzo Doria | 09/2015 |
| 4150 | 2^503225+382667 | 151486 | Enzo Doria | 10/2016 |
| 4151 | (206*10^151483-11)/3 | 151485 | Robert Price | 02/2022 |
| 4152 | (844*10^151396-7)/9 | 151398 | Robert Price | 05/2021 |
| 4153 | (26*10^151391-503)/9 | 151392 | Robert Price | 07/2018 |
| 4154 | 2^502769+1877567 | 151349 | Enzo Doria | 08/2016 |
| 4155 | 2^502576-4019 | 151291 | Yves Minet | 10/2011 |
| 4156 | 5*10^151257+41 | 151258 | Robert Price | 03/2019 |
| 4157 | 2^502290-2792501 | 151205 | Enzo Doria | 02/2016 |
| 4158 | 2^502181+1868417 | 151172 | Enzo Doria | 04/2016 |
| 4159 | 2^502055+22583 | 151134 | Enzo Doria | 09/2023 |
| 4160 | (3*23^110967+41)/22 | 151106 | Anonymous | 12/2023 |
| 4161 | 6*10^151063-77 | 151064 | Robert Price | 09/2021 |
| 4162 | 2^501781-1850503 | 151052 | Enzo Doria | 08/2015 |
| 4163 | (2^82589933-1)%(10^151020) | 151020 | Anonymous | 05/2025 |
| 4164 | (5*10^151007+37)/3 | 151008 | Robert Price | 03/2018 |
| 4165 | 3^316494+5*2^316494 | 151007 | Jon Grantham | 08/2023 |
| 4166 | 2^501627-991 | 151005 | Yves Minet | 02/2014 |
| 4167 | 2^501577-115333 | 150990 | Enzo Doria | 07/2015 |
| 4168 | 25239^34298-34298^25239 | 150983 | Frank Doornink | 12/2023 |
| 4169 | (19*10^150977-7)/3 | 150978 | Robert Price | 12/2023 |
| 4170 | 8*10^150975+3 | 150976 | Robert Price | 08/2015 |
| 4171 | 2^501512-113669 | 150971 | Enzo Doria | 09/2014 |
| 4172 | 34180^26101+26101^34180 | 150962 | Norman Luhn | 04/2024 |
| 4173 | U(1083477)/2166953 | 150949 | Serge Batalov | 07/2024 |
| 4174 | (83*10^150908+493)/9 | 150909 | Robert Price | 12/2021 |
| 4175 | 36267^14482+14482^36267 | 150901 | Norman Luhn | 04/2024 |
| 4176 | 2*10^150818+83 | 150819 | Robert Price | 12/2021 |
| 4177 | 48753^1240+1240^48753 | 150814 | Norman Luhn | 04/2024 |
| 4178 | (12^139739+1)/13 | 150803 | Paul Bourdelais | 09/2011 |
| 4179 | (31^101111-1)/30 | 150792 | Alexander Zhirkov | 11/2010 |
| 4180 | 2^500899-500899 | 150786 | Henri Lifchitz | 04/2005 |
| 4181 | 2^500832+1876801 | 150766 | Enzo Doria | 07/2016 |
| 4182 | (23*10^150763-59)/9 | 150764 | Robert Price | 05/2018 |
| 4183 | 46002^1891+1891^46002 | 150735 | Norman Luhn | 04/2024 |
| 4184 | 32001^33458-33458^32001 | 150734 | Frank Doornink | 01/2024 |
| 4185 | 2^500699+1884953 | 150726 | Enzo Doria | 02/2017 |
| 4186 | (13*10^150675-37)/3 | 150676 | Robert Price | 01/2019 |
| 4187 | (2^500527+lucasV(1,2,500527)+1)/4 | 150674 | Mike Oakes | 11/2016 |
| 4188 | 35365^18204+18204^35365 | 150661 | Norman Luhn | 05/2024 |
| 4190 | 2^500337-71101 | 150617 | Enzo Doria | 04/2016 |
| 4189 | (74*10^150616+133)/9 | 150617 | Robert Price | 06/2019 |
| 4191 | (2*10^150612-17)/3 | 150612 | Serge Batalov | 11/2022 |
| 4192 | 4*10^150577+91 | 150578 | Robert Price | 08/2018 |
| 4193 | 5649^40132+40132^5649 | 150575 | Norbert Schneider | 04/2024 |
| 4194 | 2^500160+80071 | 150564 | Enzo Doria | 06/2016 |
| 4195 | (2^500120+5)/9 | 150551 | Lelio R Paula | 12/2017 |
| 4197 | (43*10^150515-421)/9 | 150516 | Robert Price | 01/2019 |
| 4196 | 4695^40994+40994^4695 | 150516 | Norbert Schneider | 11/2023 |
| 4198 | 2^499999+15981 | 150515 | Norman Luhn | 08/2023 |
| 4199 | (10^150551-1)/9/385207015049/57498437921/7808738631274081 | 150512 | Maksym Voznyy | 08/2014 |
| 4200 | (10^150551-1)/1556587827131683185788921941743157225041 | 150512 | Robert Price | 07/2016 |
| 4201 | 26614^34005-34005^26614 | 150476 | Frank Doornink | 03/2024 |
| 4202 | 2^499861-29503 | 150474 | Enzo Doria | 08/2015 |
| 4203 | 2^499653-113533 | 150411 | Enzo Doria | 08/2014 |
| 4204 | (14*10^150391-191)/3 | 150392 | Robert Price | 10/2020 |
| 4205 | 29033^33696+33696^29033 | 150382 | Norbert Schneider | 10/2023 |
| 4206 | 2^499534-221 | 150375 | Yves Minet | 06/2012 |
| 4207 | 30110^33567+33567^30110 | 150337 | Norbert Schneider | 10/2023 |
| 4208 | 26212^34023-34023^26212 | 150331 | Frank Doornink | 03/2024 |
| 4209 | (28*10^150294+41)/3 | 150295 | Robert Price | 07/2021 |
| 4210 | 2^499225+49727 | 150282 | Enzo Doria | 09/2016 |
| 4211 | (695*10^150274+7)/9 | 150276 | Robert Price | 12/2021 |
| 4212 | 2^499054-29261 | 150231 | Enzo Doria | 07/2015 |
| 4213 | 18580^35187+35187^18580 | 150215 | Norbert Schneider | 10/2023 |
| 4214 | (844*10^150196-7)/9 | 150198 | Robert Price | 05/2021 |
| 4215 | 2^498907-933075 | 150186 | Paul Bourdelais | 06/2021 |
| 4216 | (2^498898-7)/9 | 150183 | Lelio R Paula | 10/2015 |
| 4217 | 3*10^150182+17 | 150183 | Robert Price | 07/2018 |
| 4218 | 5*10^150175+63 | 150176 | Robert Price | 09/2020 |
| 4219 | 29273^33618-33618^29273 | 150154 | Frank Doornink | 06/2024 |
| 4220 | 32363^33292+33292^32363 | 150149 | Norbert Schneider | 07/2022 |
| 4221 | 32^99753-99753^32 | 150144 | Henri Lifchitz | 08/2024 |
| 4222 | (77*10^150128+67)/9 | 150129 | Robert Price | 12/2021 |
| 4223 | (7*10^(2*75062+1)-9*10^75062-7)/9 | 150125 | Robert Price | 12/2023 |
| 4224 | 2^498623+1866983 | 150101 | Enzo Doria | 03/2016 |
| 4225 | 33194^33194-213^213 | 150073 | Serge Batalov | 04/2024 |
| 4226 | 27868^33759-33759^27868 | 150063 | Frank Doornink | 06/2024 |
| 4227 | (25*10^150050-403)/9 | 150051 | Robert Price | 12/2020 |
| 4228 | numbpart(18140942830) | 150033 | Serge Batalov | 04/2017 |
| 4229 | 10^150029+4381 | 150030 | Patrick De Geest | 05/2016 |
| 4230 | 10^150029-41 | 150029 | Serge Batalov | 12/2014 |
| 4231 | 33185^33185+618^618 | 150028 | Serge Batalov | 04/2024 |
| 4232 | 9*34^97952+529 | 150013 | Eric Chen | 08/2023 |
| 4233 | 10^150000+1158603 | 150001 | Patrick De Geest | 09/2018 |
| 4234 | 10^150000-245703 | 150000 | Patrick De Geest | 09/2018 |
| 4235 | (38*10^149999+691)/9 | 150000 | Robert Price | 10/2018 |
| 4236 | 2043563126843649194^8192+2043563126843649185^8192 | 150000 | Youcef Lemsafer | 01/2023 |
| 4237 | (2043563126843649232^8192+2043563126843649201^8192)/147457 | 149994 | Youcef Lemsafer | 01/2023 |
| 4238 | 2^498238-53 | 149985 | Lelio R Paula | 12/2017 |
| 4239 | 45728^1905+1905^45728 | 149984 | Hans Havermann | 10/2020 |
| 4240 | (211^65024+1)/(211^512+1) | 149945 | Martin Hopf | 12/2023 |
| 4241 | 5*10^149907+23 | 149908 | Robert Price | 03/2019 |
| 4242 | 32^99585-829 | 149891 | Eric Chen | 11/2023 |
| 4243 | 39347^6442+6442^39347 | 149874 | Hans Havermann | 09/2020 |
| 4244 | 2^497850+81049 | 149868 | Enzo Doria | 07/2016 |
| 4245 | V(1075416) | 149830 | Serge Batalov | 07/2024 |
| 4246 | 37228^10575+10575^37228 | 149816 | Hans Havermann | 10/2020 |
| 4247 | (5*2^497673+1)/2743 | 149812 | Lelio R Paula | 10/2015 |
| 4248 | (5*2^497671+1)/373703 | 149810 | Lelio R Paula | 10/2015 |
| 4249 | (2*10^149803-143)/3 | 149803 | Robert Price | 03/2018 |
| 4250 | 33845^26604+26604^33845 | 149763 | Hans Havermann | 09/2020 |
