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
Search by form
| Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
| 4001 | 2^490550+1179439 | 147671 | Enzo Doria | 06/2016 |
| 4002 | 27249^33292-33292^27249 | 147662 | Frank Doornink | 06/2024 |
| 4003 | (23*10^147649-59)/9 | 147650 | Robert Price | 05/2018 |
| 4004 | 2^490303+2793653 | 147596 | Enzo Doria | 03/2016 |
| 4005 | 2^490266+255255 | 147585 | Paul Bourdelais | 10/2021 |
| 4006 | 199^64181-2 | 147543 | Lelio R Paula | 11/2017 |
| 4007 | 32849^30958+30958^32849 | 147518 | Hans Havermann | 11/2020 |
| 4008 | 2^489871-286987 | 147466 | Enzo Doria | 07/2015 |
| 4009 | 2^489864-351899 | 147464 | Enzo Doria | 07/2015 |
| 4010 | 175^65724-2 | 147422 | Lelio R Paula | 11/2017 |
| 4011 | 2^489712+1874851 | 147419 | Enzo Doria | 06/2016 |
| 4012 | 34473^18830+18830^34473 | 147367 | Hans Havermann | 11/2020 |
| 4013 | 63^81896-2 | 147359 | Lelio R Paula | 10/2017 |
| 4014 | 34580^18237+18237^34580 | 147344 | Hans Havermann | 11/2020 |
| 4015 | (11*10^147313-107)/3 | 147314 | Robert Price | 09/2018 |
| 4016 | (397*10^147310+17)/9 | 147312 | Robert Price | 03/2022 |
| 4017 | 2^489305-59815 | 147296 | Enzo Doria | 10/2015 |
| 4018 | (2^489280-7)/6381 | 147285 | Lelio R Paula | 09/2015 |
| 4019 | 2*10^147264-61 | 147265 | Robert Price | 10/2021 |
| 4020 | 2*10^147260+29 | 147261 | Robert Price | 02/2021 |
| 4021 | 33556^24457+24457^33556 | 147258 | Hans Havermann | 11/2020 |
| 4022 | 12^136450-11 | 147255 | Riley Fisher | 12/2024 |
| 4023 | 2^489125+80357 | 147242 | Enzo Doria | 06/2016 |
| 4024 | 10^147240-40000001 | 147240 | Robert Price | 07/2022 |
| 4025 | 10^147240-371331 | 147240 | Alfred Reich | 09/2024 |
| 4026 | 10^147240-464727 | 147240 | Alfred Reich | 09/2024 |
| 4027 | 32835^30452+30452^32835 | 147220 | Hans Havermann | 12/2020 |
| 4028 | (19*10^147213-97)/3 | 147214 | Robert Price | 10/2021 |
| 4029 | 27123^33190-33190^27123 | 147143 | Frank Doornink | 01/2024 |
| 4030 | (148*10^147139-1)/3 | 147141 | Robert Price | 03/2020 |
| 4031 | 34338^19255+19255^34338 | 147123 | Hans Havermann | 11/2020 |
| 4032 | 2^488648-112799 | 147098 | Enzo Doria | 07/2014 |
| 4033 | 2^488627-350317 | 147092 | Enzo Doria | 06/2015 |
| 4034 | 33432^25075+25075^33432 | 147076 | Hans Havermann | 12/2020 |
| 4035 | (2^488441-1)/(61543567*30051203516986199) | 147012 | Dario Alpern | 12/2014 |
| 4036 | 2^488280-2165 | 146987 | Yves Minet | 07/2014 |
| 4037 | 2^488278+45 | 146987 | Lelio R Paula | 12/2017 |
| 4038 | 32568^32568+32561^32561 | 146973 | Henri Lifchitz | 08/2024 |
| 4039 | 2^487927-39 | 146881 | Lelio R Paula | 12/2017 |
| 4040 | (7*10^146860-13)/3 | 146861 | Robert Price | 07/2018 |
| 4041 | (26*10^146856-77)/3 | 146857 | Robert Price | 11/2019 |
| 4042 | 32948^28611+28611^32948 | 146834 | Hans Havermann | 11/2020 |
| 4043 | 42596^2799+2799^42596 | 146829 | Hans Havermann | 12/2020 |
| 4044 | 2^487726-1863341 | 146821 | Enzo Doria | 12/2015 |
| 4045 | 43838^2229+2229^43838 | 146775 | Hans Havermann | 11/2020 |
| 4046 | 35005^15594+15594^35005 | 146775 | Hans Havermann | 11/2020 |
| 4047 | (167*10^146764+7)/3 | 146766 | Robert Price | 04/2021 |
| 4048 | 53^85114+85114 | 146761 | Kellen Shenton | 05/2022 |
| 4049 | (59*10^146738+157)/9 | 146739 | Robert Price | 12/2021 |
| 4050 | ((10^73362-1)*10000/9+6701)*10^73362+(10^73362-1)/9 | 146728 | Hans Havermann | 09/2019 |
| 4051 | 32963^28234+28234^32963 | 146711 | Hans Havermann | 12/2020 |
| 4052 | (22*10^146661-19)/3 | 146662 | Robert Price | 04/2019 |
| 4053 | 33958^20825+20825^33958 | 146651 | Hans Havermann | 12/2020 |
| 4054 | 26289^33178-33178^26289 | 146640 | Frank Doornink | 03/2024 |
| 4055 | 2^487121-39523 | 146639 | Enzo Doria | 09/2015 |
| 4056 | 61063^252+252^61063 | 146637 | Hans Havermann | 12/2020 |
| 4057 | (7*2^486967+1)/39 | 146591 | Lelio R Paula | 09/2015 |
| 4058 | 34099^19900+19900^34099 | 146587 | Hans Havermann | 11/2020 |
| 4059 | 2^486893-79 | 146570 | Yves Minet | 09/2017 |
| 4060 | 36818^9567+9567^36818 | 146565 | Hans Havermann | 12/2020 |
| 4061 | 2^486840+1879141 | 146554 | Enzo Doria | 08/2016 |
| 4062 | 2^486774-87 | 146534 | Lelio R Paula | 12/2017 |
| 4063 | 38655^6176+6176^38655 | 146530 | Hans Havermann | 11/2020 |
| 4064 | 8*10^146522-81 | 146523 | Robert Price | 02/2021 |
| 4065 | 32820^29059+29059^32820 | 146485 | Hans Havermann | 12/2020 |
| 4066 | 37261^8530+8530^37261 | 146472 | Hans Havermann | 12/2020 |
| 4067 | 66953^154+154^66953 | 146462 | Hans Havermann | 12/2020 |
| 4068 | 96^73877-95^73877 | 146445 | Robert Price | 10/2015 |
| 4069 | 8*10^146421+81 | 146422 | Robert Price | 08/2019 |
| 4070 | 33153^26090+26090^33153 | 146420 | Hans Havermann | 11/2020 |
| 4071 | 2^486275+23961 | 146384 | Enzo Doria | 10/2023 |
| 4072 | (52^85259+1)/53 | 146304 | Paul Bourdelais | 09/2017 |
| 4073 | 179^64935+2 | 146290 | Lelio R Paula | 10/2017 |
| 4074 | 32595^30758+30758^32595 | 146285 | Hans Havermann | 11/2020 |
| 4075 | 34972^15157+15157^34972 | 146205 | Hans Havermann | 12/2020 |
| 4076 | (16*10^146200+131)/3 | 146201 | Robert Price | 03/2022 |
| 4077 | (19*10^146181-49)/3 | 146182 | Robert Price | 05/2019 |
| 4078 | 2^485531-114621 | 146160 | Enzo Doria | 05/2015 |
| 4079 | 2^485473-933075 | 146142 | Paul Bourdelais | 06/2021 |
| 4080 | (2^485461-9)/4249 | 146135 | Lelio R Paula | 09/2015 |
| 4081 | (22*10^146130-193)/9 | 146131 | Robert Price | 07/2022 |
| 4082 | 2^485389+81887 | 146117 | Enzo Doria | 08/2016 |
| 4083 | 32554^30773+30773^32554 | 146108 | Hans Havermann | 11/2020 |
| 4084 | 28075^32844-32844^28075 | 146101 | Frank Doornink | 06/2024 |
| 4085 | (10^146063+71)/9 | 146063 | Serge Batalov | 07/2015 |
| 4086 | 2*10^146051-63 | 146052 | Robert Price | 01/2022 |
| 4087 | (2^485119+7)/2745 | 146032 | Lelio R Paula | 09/2015 |
| 4088 | (22*10^146029+257)/9 | 146030 | Robert Price | 06/2018 |
| 4089 | 7*10^145982-53 | 145983 | Robert Price | 06/2020 |
| 4090 | 2^484743+1872923 | 145923 | Enzo Doria | 05/2016 |
| 4091 | 33140^25287+25287^33140 | 145913 | Hans Havermann | 01/2021 |
| 4092 | 37875^7112+7112^37875 | 145895 | Hans Havermann | 01/2021 |
| 4093 | 30542^32529-32529^30542 | 145890 | Frank Doornink | 06/2024 |
| 4094 | 32862^27473+27473^32862 | 145872 | Hans Havermann | 01/2021 |
| 4095 | V(1046652)/2093303 | 145817 | Serge Batalov | 07/2024 |
| 4096 | 32836^27587+27587^32836 | 145815 | Hans Havermann | 01/2021 |
| 4097 | 2^484341+1879157 | 145802 | Enzo Doria | 08/2016 |
| 4098 | 2*10^145784-91 | 145785 | Robert Price | 04/2020 |
| 4099 | 2^484271-51 | 145781 | Lelio R Paula | 11/2017 |
| 4100 | (188*10^145750-11)/3 | 145752 | Robert Price | 02/2022 |
| 4101 | 70^78989-69^78989 | 145743 | Robert Price | 01/2014 |
| 4102 | 51^85334+2 | 145714 | Robert Price | 07/2015 |
| 4103 | 10^2^72843+72843^2^10 | 145687 | Henri Lifchitz | 03/2025 |
| 4104 | 2^483886-1857101 | 145665 | Enzo Doria | 10/2015 |
| 4105 | 29312^32607-32607^29312 | 145657 | Frank Doornink | 06/2024 |
| 4106 | 33350^23307+23307^33350 | 145656 | Hans Havermann | 01/2021 |
| 4107 | (19*10^145585+131)/3 | 145586 | Robert Price | 06/2020 |
| 4108 | 31815^32332-32332^31815 | 145580 | Frank Doornink | 01/2024 |
| 4109 | 2^483563-1863457 | 145567 | Enzo Doria | 12/2015 |
| 4110 | 4*10^145563-69 | 145564 | Robert Price | 01/2022 |
| 4111 | 2^483516-1861409 | 145553 | Enzo Doria | 11/2015 |
| 4112 | 2^483384-115019 | 145514 | Enzo Doria | 06/2015 |
| 4113 | (259*10^145501-1)/3 | 145503 | Robert Price | 12/2020 |
| 4114 | (19*10^145499-61)/3 | 145500 | Robert Price | 05/2019 |
| 4115 | 2^483302-3221 | 145489 | Lelio R Paula | 12/2012 |
| 4116 | (23*10^145463+61)/3 | 145464 | Robert Price | 01/2022 |
| 4117 | 35523^12434+12434^35523 | 145453 | Hans Havermann | 01/2021 |
| 4118 | (29121^32761-1)/(29121^181-1) | 145444 | Ryan Propper | 11/2023 |
| 4119 | 2^483046+1874029 | 145412 | Enzo Doria | 06/2016 |
| 4120 | 2^482991-2789317 | 145395 | Enzo Doria | 12/2015 |
| 4121 | 2^482978-2789711 | 145391 | Enzo Doria | 12/2015 |
| 4122 | 2^482966-2789711 | 145388 | Enzo Doria | 12/2015 |
| 4123 | 2^482817-1858843 | 145343 | Enzo Doria | 10/2015 |
| 4124 | 2^482751-113635 | 145323 | Enzo Doria | 08/2014 |
| 4125 | 2^482705-459763 | 145309 | Enzo Doria | 05/2015 |
| 4126 | (4^241306+11)/3 | 145281 | Robert Price | 03/2017 |
| 4127 | (238*10^145276-1)/3 | 145278 | Robert Price | 04/2020 |
| 4128 | (19*2^482534+1)/7 | 145258 | Lelio R Paula | 09/2015 |
| 4129 | 53^84239-52^84239 | 145252 | Robert Price | 01/2013 |
| 4130 | U(1042497) | 145243 | Serge Batalov | 07/2024 |
| 4131 | 2^482386+212419 | 145213 | Enzo Doria | 08/2023 |
| 4132 | 47952^1067+1067^47952 | 145207 | Hans Havermann | 01/2021 |
| 4133 | (2^482333+5)/9287 | 145193 | Lelio R Paula | 09/2015 |
| 4134 | 2^482087+72623 | 145123 | Enzo Doria | 04/2016 |
| 4135 | 2^482016-286565 | 145102 | Enzo Doria | 07/2015 |
| 4136 | (19*10^145093+101)/3 | 145094 | Robert Price | 09/2019 |
| 4137 | 2^481956+121 | 145084 | Stefano Morozzi | 04/2021 |
| 4138 | 27535^32676-32676^27535 | 145078 | Frank Doornink | 06/2024 |
| 4139 | 2^481840+15 | 145049 | Robert Price | 09/2015 |
| 4140 | (23*10^145040+7)/3 | 145041 | Robert Price | 05/2023 |
| 4141 | 2^481801-481801 | 145037 | Henri Lifchitz | 03/2005 |
| 4142 | 2^481775+1869083 | 145029 | Enzo Doria | 05/2016 |
| 4143 | 29^99167+2 | 145022 | Ray Chandler | 08/2011 |
| 4144 | 2^481663+1875653 | 144996 | Enzo Doria | 07/2016 |
| 4145 | 8*10^144977+27 | 144978 | Robert Price | 09/2021 |
| 4146 | 29840^32393-32393^29840 | 144953 | Frank Doornink | 06/2024 |
| 4147 | 36486^9379+9379^36486 | 144929 | Hans Havermann | 12/2020 |
| 4148 | 31580^32209-32209^31580 | 144922 | Frank Doornink | 01/2024 |
| 4149 | 35111^13378+13378^35111 | 144882 | Hans Havermann | 01/2021 |
| 4150 | 2^481149-459073 | 144841 | Enzo Doria | 05/2015 |
| 4151 | 2^481113+181419 | 144830 | Boyan Hu | 04/2024 |
| 4152 | 34619^15246+15246^34619 | 144817 | Hans Havermann | 01/2021 |
| 4153 | 2^481045-113215 | 144809 | Enzo Doria | 07/2014 |
| 4154 | (64*10^144797+287)/9 | 144798 | Robert Price | 04/2019 |
| 4155 | 27320^32629-32629^27320 | 144758 | Frank Doornink | 06/2024 |
| 4156 | 2^480859-113695 | 144753 | Enzo Doria | 09/2014 |
| 4157 | (106*10^144744+17)/3 | 144746 | Robert Price | 04/2021 |
| 4158 | 7*10^144742-27 | 144743 | Robert Price | 11/2022 |
| 4159 | 2^480766-2787191 | 144725 | Enzo Doria | 11/2015 |
| 4160 | (21*27^101106-151)/26 | 144720 | Curtis Bright | 05/2015 |
| 4161 | 28915^32438-32438^28915 | 144710 | Frank Doornink | 06/2024 |
| 4162 | 2^480678+1874239 | 144699 | Enzo Doria | 06/2016 |
| 4163 | (8*10^144683+1)/9 | 144683 | Serge Batalov | 05/2010 |
| 4164 | L(692147) | 144651 | Henri Lifchitz | 10/2008 |
| 4165 | (76*10^144648+77)/9 | 144649 | Robert Price | 10/2019 |
| 4166 | 32672^26721+26721^32672 | 144635 | Hans Havermann | 01/2021 |
| 4167 | 31478^32153-32153^31478 | 144625 | Frank Doornink | 01/2024 |
| 4168 | 2^480417+35 | 144620 | Robert Price | 11/2015 |
| 4169 | 2^480296-59879 | 144584 | Enzo Doria | 10/2015 |
| 4170 | 33157^22878+22878^33157 | 144546 | Hans Havermann | 12/2020 |
| 4171 | 27520^32541-32541^27520 | 144471 | Frank Doornink | 06/2024 |
| 4172 | 45494^1497+1497^45494 | 144454 | Hans Havermann | 12/2020 |
| 4173 | 2^479844+3 | 144448 | Donovan Johnson | 06/2006 |
| 4174 | 33442^20803+20803^33442 | 144407 | Hans Havermann | 01/2021 |
| 4175 | (441*33^95095-3833)/32 | 144405 | Eric Chen | 12/2023 |
| 4176 | 31892^32061-32061^31892 | 144393 | Norbert Schneider | 01/2023 |
| 4177 | (27*2^479642+1)/733 | 144386 | Lelio R Paula | 08/2015 |
| 4178 | (56*10^144380+169)/9 | 144381 | Robert Price | 03/2022 |
| 4179 | 44917^1638+1638^44917 | 144378 | Hans Havermann | 12/2020 |
| 4180 | (21*2^479605-1)/11 | 144376 | Lelio R Paula | 09/2015 |
| 4181 | (56*10^144336+583)/9 | 144337 | Robert Price | 08/2021 |
| 4182 | 5*2^479430-3 | 144324 | Jon Grantham | 07/2023 |
| 4183 | 2^479348-2792219 | 144299 | Enzo Doria | 02/2016 |
| 4184 | 31134^32111-32111^31134 | 144283 | Frank Doornink | 01/2024 |
| 4185 | 3^302389-6242 | 144277 | Enzo Doria | 05/2014 |
| 4186 | 31665^32056-32056^31665 | 144271 | Frank Doornink | 01/2024 |
| 4187 | 33778^18641+18641^33778 | 144248 | Hans Havermann | 01/2021 |
| 4188 | 29083^32312-32312^29083 | 144230 | Frank Doornink | 06/2024 |
| 4189 | 2*10^144220-3 | 144221 | Robert Price | 07/2015 |
| 4190 | 25313^32750-32750^25313 | 144210 | Frank Doornink | 01/2024 |
| 4191 | 2^478904-109109 | 144165 | Enzo Doria | 04/2014 |
| 4192 | 43698^1987+1987^43698 | 144125 | Hans Havermann | 12/2020 |
| 4193 | 79^75948+75948 | 144121 | Kellen Shenton | 06/2023 |
| 4194 | 26941^32522-32522^26941 | 144086 | Frank Doornink | 06/2024 |
| 4195 | 36128^9723+9723^36128 | 144072 | Hans Havermann | 01/2021 |
| 4196 | 32817^24518+24518^32817 | 144050 | Hans Havermann | 12/2020 |
| 4197 | (772*10^144036-7)/9 | 144038 | Robert Price | 06/2022 |
| 4198 | 34295^15828+15828^34295 | 144020 | Hans Havermann | 01/2021 |
| 4199 | 2^478337-115333 | 143994 | Enzo Doria | 07/2015 |
| 4200 | (7*2^478330-1)/3 | 143993 | Lelio R Paula | 08/2015 |
| 4201 | 88^74047-87^74047 | 143984 | Robert Price | 05/2015 |
| 4202 | 33242^21441+21441^33242 | 143980 | Hans Havermann | 01/2021 |
| 4203 | (19*10^143963+467)/9 | 143964 | Robert Price | 02/2018 |
| 4204 | (71^77761+1)/72 | 143954 | Paul Bourdelais | 09/2017 |
| 4205 | 33490^19859+19859^33490 | 143939 | Hans Havermann | 01/2021 |
| 4206 | (853*10^143931-7)/9 | 143933 | Robert Price | 07/2021 |
| 4207 | 2^478088+27 | 143919 | Robert Price | 11/2015 |
| 4208 | (8*10^143898-137)/3 | 143899 | Robert Price | 03/2022 |
| 4209 | 7*10^143857-93 | 143858 | Robert Price | 08/2020 |
| 4210 | 3*10^143844+61 | 143845 | Robert Price | 09/2020 |
| 4211 | 41358^3005+3005^41358 | 143837 | Hans Havermann | 01/2021 |
| 4212 | 2^477475-22071 | 143735 | Enzo Doria | 07/2013 |
| 4213 | 2^477417-22123 | 143717 | Enzo Doria | 07/2013 |
| 4214 | 2^477359-3577 | 143700 | Yves Minet | 03/2017 |
| 4215 | 39435^4402+4402^39435 | 143688 | Hans Havermann | 01/2021 |
| 4216 | (14*10^143662-71)/3 | 143663 | Robert Price | 12/2018 |
| 4217 | 6^184614+5 | 143658 | Paul Bourdelais | 01/2021 |
| 4218 | 46371^1252+1252^46371 | 143640 | Hans Havermann | 12/2020 |
| 4219 | 34975^12748+12748^34975 | 143588 | Hans Havermann | 01/2021 |
| 4220 | 2^476936-396765 | 143573 | Enzo Doria | 07/2013 |
| 4221 | 2^476888-2791229 | 143558 | Enzo Doria | 01/2016 |
| 4222 | 2^476868-1859939 | 143552 | Enzo Doria | 11/2015 |
| 4223 | 40807^3294+3294^40807 | 143548 | Hans Havermann | 12/2020 |
| 4224 | 755^49878+49878^755 | 143547 | Norbert Schneider | 04/2019 |
| 4225 | (19^112247-4^112247)/15 | 143536 | Robert Price | 03/2021 |
| 4226 | 35561^10872+10872^35561 | 143536 | Hans Havermann | 06/2021 |
| 4227 | 37637^6492+6492^37637 | 143487 | Hans Havermann | 05/2021 |
| 4228 | 61567^214+214^61567 | 143477 | Hans Havermann | 05/2021 |
| 4229 | 25933^32504-32504^25933 | 143468 | Frank Doornink | 03/2024 |
| 4230 | 2^476558-113627 | 143459 | Enzo Doria | 08/2014 |
| 4231 | 2^476478-45 | 143435 | Lelio R Paula | 11/2017 |
| 4232 | 36380^8757+8757^36380 | 143423 | Hans Havermann | 06/2021 |
| 4233 | 32510^25707+25707^32510 | 143371 | Hans Havermann | 05/2021 |
| 4234 | 8*10^143361+17 | 143362 | Robert Price | 07/2021 |
| 4235 | (2^475854+9)/73 | 143245 | Lelio R Paula | 08/2015 |
| 4236 | 2^475813-113239 | 143234 | Enzo Doria | 07/2014 |
| 4237 | (19*10^143212+137)/3 | 143213 | Robert Price | 03/2022 |
| 4238 | 32218^27849+27849^32218 | 143203 | Hans Havermann | 04/2021 |
| 4239 | 580*33^94296+19 | 143193 | Eric Chen | 12/2023 |
| 4240 | 2^475624-114059 | 143178 | Enzo Doria | 11/2014 |
| 4241 | (11*2^475553-7)/15 | 143156 | Renaud Lifchitz | 03/2011 |
| 4242 | 2^475480-2786129 | 143134 | Enzo Doria | 10/2015 |
| 4243 | 33912^16621+16621^33912 | 143131 | Hans Havermann | 05/2021 |
| 4244 | (19*10^143129-43)/3 | 143130 | Robert Price | 05/2019 |
| 4245 | 31830^31373+31373^31830 | 143126 | Hans Havermann | 05/2021 |
| 4246 | 2^475392+1334025 | 143108 | Henri Lifchitz | 01/2025 |
| 4247 | 6*10^143105-53 | 143106 | Robert Price | 05/2021 |
| 4248 | (14*10^143097+73)/3 | 143098 | Robert Price | 12/2018 |
| 4249 | 2^475299-111937 | 143080 | Enzo Doria | 05/2014 |
| 4250 | 35488^10753+10753^35488 | 143071 | Hans Havermann | 04/2021 |
