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 | 2^484743+1872923 | 145923 | Enzo Doria | 05/2016 |
| 4002 | 33140^25287+25287^33140 | 145913 | Hans Havermann | 01/2021 |
| 4003 | 37875^7112+7112^37875 | 145895 | Hans Havermann | 01/2021 |
| 4004 | 30542^32529-32529^30542 | 145890 | Frank Doornink | 06/2024 |
| 4005 | 32862^27473+27473^32862 | 145872 | Hans Havermann | 01/2021 |
| 4006 | V(1046652)/2093303 | 145817 | Serge Batalov | 07/2024 |
| 4007 | 32836^27587+27587^32836 | 145815 | Hans Havermann | 01/2021 |
| 4008 | 2^484341+1879157 | 145802 | Enzo Doria | 08/2016 |
| 4009 | 2*10^145784-91 | 145785 | Robert Price | 04/2020 |
| 4010 | 2^484271-51 | 145781 | Lelio R Paula | 11/2017 |
| 4011 | (188*10^145750-11)/3 | 145752 | Robert Price | 02/2022 |
| 4012 | 70^78989-69^78989 | 145743 | Robert Price | 01/2014 |
| 4013 | 51^85334+2 | 145714 | Robert Price | 07/2015 |
| 4014 | 10^2^72843+72843^2^10 | 145687 | Henri Lifchitz | 03/2025 |
| 4015 | 2^483886-1857101 | 145665 | Enzo Doria | 10/2015 |
| 4016 | 29312^32607-32607^29312 | 145657 | Frank Doornink | 06/2024 |
| 4017 | 33350^23307+23307^33350 | 145656 | Hans Havermann | 01/2021 |
| 4018 | (19*10^145585+131)/3 | 145586 | Robert Price | 06/2020 |
| 4019 | 31815^32332-32332^31815 | 145580 | Frank Doornink | 01/2024 |
| 4020 | 2^483563-1863457 | 145567 | Enzo Doria | 12/2015 |
| 4021 | 4*10^145563-69 | 145564 | Robert Price | 01/2022 |
| 4022 | 2^483516-1861409 | 145553 | Enzo Doria | 11/2015 |
| 4023 | 2^483384-115019 | 145514 | Enzo Doria | 06/2015 |
| 4024 | (259*10^145501-1)/3 | 145503 | Robert Price | 12/2020 |
| 4025 | (19*10^145499-61)/3 | 145500 | Robert Price | 05/2019 |
| 4026 | 2^483302-3221 | 145489 | Lelio R Paula | 12/2012 |
| 4027 | (23*10^145463+61)/3 | 145464 | Robert Price | 01/2022 |
| 4028 | 35523^12434+12434^35523 | 145453 | Hans Havermann | 01/2021 |
| 4029 | (29121^32761-1)/(29121^181-1) | 145444 | Ryan Propper | 11/2023 |
| 4030 | 2^483046+1874029 | 145412 | Enzo Doria | 06/2016 |
| 4031 | 2^482991-2789317 | 145395 | Enzo Doria | 12/2015 |
| 4032 | 2^482978-2789711 | 145391 | Enzo Doria | 12/2015 |
| 4033 | 2^482966-2789711 | 145388 | Enzo Doria | 12/2015 |
| 4034 | 2^482817-1858843 | 145343 | Enzo Doria | 10/2015 |
| 4035 | 2^482751-113635 | 145323 | Enzo Doria | 08/2014 |
| 4036 | 2^482705-459763 | 145309 | Enzo Doria | 05/2015 |
| 4037 | (4^241306+11)/3 | 145281 | Robert Price | 03/2017 |
| 4038 | (238*10^145276-1)/3 | 145278 | Robert Price | 04/2020 |
| 4039 | (19*2^482534+1)/7 | 145258 | Lelio R Paula | 09/2015 |
| 4040 | 53^84239-52^84239 | 145252 | Robert Price | 01/2013 |
| 4041 | U(1042497) | 145243 | Serge Batalov | 07/2024 |
| 4042 | 2^482386+212419 | 145213 | Enzo Doria | 08/2023 |
| 4043 | 47952^1067+1067^47952 | 145207 | Hans Havermann | 01/2021 |
| 4044 | (2^482333+5)/9287 | 145193 | Lelio R Paula | 09/2015 |
| 4045 | 2^482087+72623 | 145123 | Enzo Doria | 04/2016 |
| 4046 | 2^482016-286565 | 145102 | Enzo Doria | 07/2015 |
| 4047 | (19*10^145093+101)/3 | 145094 | Robert Price | 09/2019 |
| 4048 | 2^481956+121 | 145084 | Stefano Morozzi | 04/2021 |
| 4049 | 27535^32676-32676^27535 | 145078 | Frank Doornink | 06/2024 |
| 4050 | 2^481840+15 | 145049 | Robert Price | 09/2015 |
| 4051 | (23*10^145040+7)/3 | 145041 | Robert Price | 05/2023 |
| 4052 | 2^481801-481801 | 145037 | Henri Lifchitz | 03/2005 |
| 4053 | 2^481775+1869083 | 145029 | Enzo Doria | 05/2016 |
| 4054 | 29^99167+2 | 145022 | Ray Chandler | 08/2011 |
| 4055 | 2^481663+1875653 | 144996 | Enzo Doria | 07/2016 |
| 4056 | 8*10^144977+27 | 144978 | Robert Price | 09/2021 |
| 4057 | 29840^32393-32393^29840 | 144953 | Frank Doornink | 06/2024 |
| 4058 | 36486^9379+9379^36486 | 144929 | Hans Havermann | 12/2020 |
| 4059 | 31580^32209-32209^31580 | 144922 | Frank Doornink | 01/2024 |
| 4060 | 35111^13378+13378^35111 | 144882 | Hans Havermann | 01/2021 |
| 4061 | 2^481149-459073 | 144841 | Enzo Doria | 05/2015 |
| 4062 | 2^481113+181419 | 144830 | Boyan Hu | 04/2024 |
| 4063 | 34619^15246+15246^34619 | 144817 | Hans Havermann | 01/2021 |
| 4064 | 2^481045-113215 | 144809 | Enzo Doria | 07/2014 |
| 4065 | (64*10^144797+287)/9 | 144798 | Robert Price | 04/2019 |
| 4066 | 27320^32629-32629^27320 | 144758 | Frank Doornink | 06/2024 |
| 4067 | 2^480859-113695 | 144753 | Enzo Doria | 09/2014 |
| 4068 | (106*10^144744+17)/3 | 144746 | Robert Price | 04/2021 |
| 4069 | 7*10^144742-27 | 144743 | Robert Price | 11/2022 |
| 4070 | 2^480766-2787191 | 144725 | Enzo Doria | 11/2015 |
| 4071 | (21*27^101106-151)/26 | 144720 | Curtis Bright | 05/2015 |
| 4072 | 28915^32438-32438^28915 | 144710 | Frank Doornink | 06/2024 |
| 4073 | 2^480678+1874239 | 144699 | Enzo Doria | 06/2016 |
| 4074 | (8*10^144683+1)/9 | 144683 | Serge Batalov | 05/2010 |
| 4075 | L(692147) | 144651 | Henri Lifchitz | 10/2008 |
| 4076 | (76*10^144648+77)/9 | 144649 | Robert Price | 10/2019 |
| 4077 | 32672^26721+26721^32672 | 144635 | Hans Havermann | 01/2021 |
| 4078 | 31478^32153-32153^31478 | 144625 | Frank Doornink | 01/2024 |
| 4079 | 2^480417+35 | 144620 | Robert Price | 11/2015 |
| 4080 | 2^480296-59879 | 144584 | Enzo Doria | 10/2015 |
| 4081 | 33157^22878+22878^33157 | 144546 | Hans Havermann | 12/2020 |
| 4082 | 27520^32541-32541^27520 | 144471 | Frank Doornink | 06/2024 |
| 4083 | 45494^1497+1497^45494 | 144454 | Hans Havermann | 12/2020 |
| 4084 | 2^479844+3 | 144448 | Donovan Johnson | 06/2006 |
| 4085 | 33442^20803+20803^33442 | 144407 | Hans Havermann | 01/2021 |
| 4086 | (441*33^95095-3833)/32 | 144405 | Eric Chen | 12/2023 |
| 4087 | 31892^32061-32061^31892 | 144393 | Norbert Schneider | 01/2023 |
| 4088 | (27*2^479642+1)/733 | 144386 | Lelio R Paula | 08/2015 |
| 4089 | (56*10^144380+169)/9 | 144381 | Robert Price | 03/2022 |
| 4090 | 44917^1638+1638^44917 | 144378 | Hans Havermann | 12/2020 |
| 4091 | (21*2^479605-1)/11 | 144376 | Lelio R Paula | 09/2015 |
| 4092 | (56*10^144336+583)/9 | 144337 | Robert Price | 08/2021 |
| 4093 | 5*2^479430-3 | 144324 | Jon Grantham | 07/2023 |
| 4094 | 2^479348-2792219 | 144299 | Enzo Doria | 02/2016 |
| 4095 | 31134^32111-32111^31134 | 144283 | Frank Doornink | 01/2024 |
| 4096 | 3^302389-6242 | 144277 | Enzo Doria | 05/2014 |
| 4097 | 31665^32056-32056^31665 | 144271 | Frank Doornink | 01/2024 |
| 4098 | 33778^18641+18641^33778 | 144248 | Hans Havermann | 01/2021 |
| 4099 | 29083^32312-32312^29083 | 144230 | Frank Doornink | 06/2024 |
| 4100 | 2*10^144220-3 | 144221 | Robert Price | 07/2015 |
| 4101 | 25313^32750-32750^25313 | 144210 | Frank Doornink | 01/2024 |
| 4102 | 2^478904-109109 | 144165 | Enzo Doria | 04/2014 |
| 4103 | 43698^1987+1987^43698 | 144125 | Hans Havermann | 12/2020 |
| 4104 | 79^75948+75948 | 144121 | Kellen Shenton | 06/2023 |
| 4105 | 26941^32522-32522^26941 | 144086 | Frank Doornink | 06/2024 |
| 4106 | 36128^9723+9723^36128 | 144072 | Hans Havermann | 01/2021 |
| 4107 | 32817^24518+24518^32817 | 144050 | Hans Havermann | 12/2020 |
| 4108 | (772*10^144036-7)/9 | 144038 | Robert Price | 06/2022 |
| 4109 | 34295^15828+15828^34295 | 144020 | Hans Havermann | 01/2021 |
| 4110 | 2^478337-115333 | 143994 | Enzo Doria | 07/2015 |
| 4111 | (7*2^478330-1)/3 | 143993 | Lelio R Paula | 08/2015 |
| 4112 | 88^74047-87^74047 | 143984 | Robert Price | 05/2015 |
| 4113 | 33242^21441+21441^33242 | 143980 | Hans Havermann | 01/2021 |
| 4114 | (19*10^143963+467)/9 | 143964 | Robert Price | 02/2018 |
| 4115 | (71^77761+1)/72 | 143954 | Paul Bourdelais | 09/2017 |
| 4116 | 33490^19859+19859^33490 | 143939 | Hans Havermann | 01/2021 |
| 4117 | (853*10^143931-7)/9 | 143933 | Robert Price | 07/2021 |
| 4118 | 2^478088+27 | 143919 | Robert Price | 11/2015 |
| 4119 | (8*10^143898-137)/3 | 143899 | Robert Price | 03/2022 |
| 4120 | 7*10^143857-93 | 143858 | Robert Price | 08/2020 |
| 4121 | 3*10^143844+61 | 143845 | Robert Price | 09/2020 |
| 4122 | 41358^3005+3005^41358 | 143837 | Hans Havermann | 01/2021 |
| 4123 | 2^477475-22071 | 143735 | Enzo Doria | 07/2013 |
| 4124 | 2^477417-22123 | 143717 | Enzo Doria | 07/2013 |
| 4125 | 2^477359-3577 | 143700 | Yves Minet | 03/2017 |
| 4126 | 39435^4402+4402^39435 | 143688 | Hans Havermann | 01/2021 |
| 4127 | (14*10^143662-71)/3 | 143663 | Robert Price | 12/2018 |
| 4128 | 6^184614+5 | 143658 | Paul Bourdelais | 01/2021 |
| 4129 | 46371^1252+1252^46371 | 143640 | Hans Havermann | 12/2020 |
| 4130 | 34975^12748+12748^34975 | 143588 | Hans Havermann | 01/2021 |
| 4131 | 2^476936-396765 | 143573 | Enzo Doria | 07/2013 |
| 4132 | 2^476888-2791229 | 143558 | Enzo Doria | 01/2016 |
| 4133 | 2^476868-1859939 | 143552 | Enzo Doria | 11/2015 |
| 4134 | 40807^3294+3294^40807 | 143548 | Hans Havermann | 12/2020 |
| 4135 | 755^49878+49878^755 | 143547 | Norbert Schneider | 04/2019 |
| 4136 | (19^112247-4^112247)/15 | 143536 | Robert Price | 03/2021 |
| 4137 | 35561^10872+10872^35561 | 143536 | Hans Havermann | 06/2021 |
| 4138 | 37637^6492+6492^37637 | 143487 | Hans Havermann | 05/2021 |
| 4139 | 61567^214+214^61567 | 143477 | Hans Havermann | 05/2021 |
| 4140 | 25933^32504-32504^25933 | 143468 | Frank Doornink | 03/2024 |
| 4141 | 2^476558-113627 | 143459 | Enzo Doria | 08/2014 |
| 4142 | 2^476478-45 | 143435 | Lelio R Paula | 11/2017 |
| 4143 | 36380^8757+8757^36380 | 143423 | Hans Havermann | 06/2021 |
| 4144 | 32510^25707+25707^32510 | 143371 | Hans Havermann | 05/2021 |
| 4145 | 8*10^143361+17 | 143362 | Robert Price | 07/2021 |
| 4146 | (2^475854+9)/73 | 143245 | Lelio R Paula | 08/2015 |
| 4147 | 2^475813-113239 | 143234 | Enzo Doria | 07/2014 |
| 4148 | (19*10^143212+137)/3 | 143213 | Robert Price | 03/2022 |
| 4149 | 32218^27849+27849^32218 | 143203 | Hans Havermann | 04/2021 |
| 4150 | 580*33^94296+19 | 143193 | Eric Chen | 12/2023 |
| 4151 | 2^475624-114059 | 143178 | Enzo Doria | 11/2014 |
| 4152 | (11*2^475553-7)/15 | 143156 | Renaud Lifchitz | 03/2011 |
| 4153 | 2^475480-2786129 | 143134 | Enzo Doria | 10/2015 |
| 4154 | 33912^16621+16621^33912 | 143131 | Hans Havermann | 05/2021 |
| 4155 | (19*10^143129-43)/3 | 143130 | Robert Price | 05/2019 |
| 4156 | 31830^31373+31373^31830 | 143126 | Hans Havermann | 05/2021 |
| 4157 | 2^475392+1334025 | 143108 | Henri Lifchitz | 01/2025 |
| 4158 | 6*10^143105-53 | 143106 | Robert Price | 05/2021 |
| 4159 | (14*10^143097+73)/3 | 143098 | Robert Price | 12/2018 |
| 4160 | 2^475299-111937 | 143080 | Enzo Doria | 05/2014 |
| 4161 | 35488^10753+10753^35488 | 143071 | Hans Havermann | 04/2021 |
| 4162 | 29695^31986-31986^29695 | 143064 | Frank Doornink | 06/2024 |
| 4163 | 2^475160-2797859 | 143038 | Enzo Doria | 04/2016 |
| 4164 | (2^475069+3)/395 | 143008 | Lelio R Paula | 08/2015 |
| 4165 | 2^475027-461437 | 142998 | Enzo Doria | 07/2015 |
| 4166 | (2^474958+78557)/3 | 142977 | Lelio R Paula | 07/2015 |
| 4167 | (8*10^142932+43)/3 | 142933 | Robert Price | 06/2018 |
| 4168 | 35055^11942+11942^35055 | 142922 | Hans Havermann | 05/2021 |
| 4169 | 37650^6239+6239^37650 | 142887 | Hans Havermann | 05/2021 |
| 4170 | (54^82471-1)/53 | 142871 | Paul Bourdelais | 09/2017 |
| 4171 | 31205^31784-31784^31205 | 142845 | Frank Doornink | 01/2024 |
| 4172 | (11*2^474432-1)/95 | 142818 | Lelio R Paula | 09/2015 |
| 4173 | 2^474417-59923 | 142814 | Enzo Doria | 10/2015 |
| 4174 | 4*10^142810-21 | 142811 | Robert Price | 09/2018 |
| 4175 | 32287^26494+26494^32287 | 142811 | Hans Havermann | 06/2021 |
| 4176 | 37162^6965+6965^37162 | 142811 | Hans Havermann | 06/2021 |
| 4177 | (34*10^142805-601)/9 | 142806 | Robert Price | 07/2022 |
| 4178 | 37456^6493+6493^37456 | 142799 | Hans Havermann | 05/2021 |
| 4179 | 35141^11572+11572^35141 | 142793 | Hans Havermann | 05/2021 |
| 4180 | 32231^26908+26908^32231 | 142780 | Hans Havermann | 05/2021 |
| 4181 | (3*2^474166+1)/7 | 142738 | Lelio R Paula | 08/2015 |
| 4182 | 2^474053+2897 | 142705 | Lelio R Paula | 08/2012 |
| 4183 | (10^142699+359)/9 | 142699 | Serge Batalov | 12/2014 |
| 4184 | 26073^32312-32312^26073 | 142696 | Frank Doornink | 03/2024 |
| 4185 | 898^48311-897^48311 | 142676 | Jean-Louis Charton | 12/2012 |
| 4186 | 2^473740-1856639 | 142610 | Enzo Doria | 09/2015 |
| 4187 | (25*10^142573-403)/9 | 142574 | Robert Price | 12/2020 |
| 4188 | 2^473617-114223 | 142573 | Enzo Doria | 12/2014 |
| 4189 | 36115^8856+8856^36115 | 142555 | Hans Havermann | 05/2021 |
| 4190 | fibonacci(682007)+4 | 142531 | Jon Grantham | 08/2023 |
| 4191 | 2^473257+1873217 | 142465 | Enzo Doria | 06/2016 |
| 4192 | (19*2^473242+1)/11 | 142461 | Lelio R Paula | 09/2015 |
| 4193 | 32750^22371+22371^32750 | 142453 | Hans Havermann | 06/2021 |
| 4194 | (61*10^142446-1)/3 | 142448 | Robert Price | 01/2020 |
| 4195 | (14*10^142440+61)/3 | 142441 | Robert Price | 12/2018 |
| 4196 | (10^142425+359)/9 | 142425 | Serge Batalov | 12/2014 |
| 4197 | 2^473101+773027 | 142418 | Enzo Doria | 05/2016 |
| 4198 | (13*2^472838-1)/3 | 142340 | Lelio R Paula | 09/2015 |
| 4199 | (17*2^472789-1)/187347 | 142320 | Lelio R Paula | 09/2015 |
| 4200 | 36915^7162+7162^36915 | 142309 | Hans Havermann | 05/2021 |
| 4201 | 2^472634-109511 | 142278 | Enzo Doria | 04/2014 |
| 4202 | 31870^28997+28997^31870 | 142216 | Hans Havermann | 06/2021 |
| 4203 | (48^84589+1)/49 | 142213 | Robert Price | 01/2014 |
| 4204 | 7*10^142189+87 | 142190 | Robert Price | 07/2019 |
| 4205 | 2^472258+7 | 142164 | Lelio R Paula | 08/2015 |
| 4206 | 40135^3484+3484^40135 | 142162 | Hans Havermann | 05/2021 |
| 4207 | 9*33^93598+26 | 142131 | Eric Chen | 12/2023 |
| 4208 | (23*10^142105+91)/3 | 142106 | Robert Price | 08/2019 |
| 4209 | tau(317^10330) | 142098 | Nik Lygeros / Olivier Rozier / LR team | 10/2013 |
| 4210 | (11*2^471913-1)/21 | 142060 | Lelio R Paula | 09/2015 |
| 4211 | (16*10^142058+197)/3 | 142059 | Robert Price | 04/2019 |
| 4212 | 9*10^142037+91 | 142038 | Robert Price | 10/2020 |
| 4213 | (4*10^142034+17)/3 | 142035 | Tyler Busby | 01/2023 |
| 4214 | 2^471792+1880881 | 142024 | Enzo Doria | 11/2016 |
| 4215 | (509*10^142018+31)/9 | 142020 | Robert Price | 08/2022 |
| 4216 | (31*2^471580-1)/135 | 141960 | Lelio R Paula | 08/2015 |
| 4217 | (4*10^141926-79)/3 | 141927 | Robert Price | 02/2018 |
| 4218 | 2^471464-111546435 | 141925 | Paul Bourdelais | 10/2021 |
| 4219 | (904*19^110984-1)/3 | 141924 | Curtis Bright | 05/2015 |
| 4220 | (14*10^141853+37)/3 | 141854 | Robert Price | 12/2018 |
| 4221 | (41*10^141836-59)/9 | 141837 | Robert Price | 10/2018 |
| 4222 | 4*5^202913-9 | 141831 | Lelio R Paula | 04/2015 |
| 4223 | 2*7^167812-3 | 141818 | Lelio R Paula | 12/2014 |
| 4224 | 2^471043+35 | 141799 | Robert Price | 11/2015 |
| 4225 | (11*2^470956-1)/7945 | 141770 | Lelio R Paula | 08/2015 |
| 4226 | 43636^1773+1773^43636 | 141761 | Hans Havermann | 05/2021 |
| 4227 | (2*10^141751-17)/3 | 141751 | Serge Batalov | 11/2022 |
| 4228 | (53*10^141722-611)/9 | 141723 | Robert Price | 02/2022 |
| 4229 | (11*10^141718-131)/3 | 141719 | Robert Price | 09/2018 |
| 4230 | (61*10^141716+47)/9 | 141717 | Robert Price | 07/2022 |
| 4231 | 26057^32088-32088^26057 | 141699 | Frank Doornink | 03/2024 |
| 4232 | 2^470692+76771 | 141693 | Enzo Doria | 05/2016 |
| 4233 | 50160^667+667^50160 | 141659 | Hans Havermann | 05/2021 |
| 4234 | 31522^31181+31181^31522 | 141657 | Hans Havermann | 05/2021 |
| 4235 | 29487^31690-31690^29487 | 141643 | Frank Doornink | 06/2024 |
| 4236 | 33076^19135+19135^33076 | 141626 | Hans Havermann | 04/2021 |
| 4237 | 28237^31818-31818^28237 | 141617 | Frank Doornink | 06/2024 |
| 4238 | (91*10^141610+71)/9 | 141612 | Robert Price | 01/2022 |
| 4239 | (21*2^470391+1)/533 | 141601 | Lelio R Paula | 09/2015 |
| 4240 | (5*10^141594-23)/9 | 141594 | Serge Batalov | 11/2022 |
| 4241 | 31932^27155+27155^31932 | 141582 | Hans Havermann | 05/2021 |
| 4242 | 36449^7660+7660^36449 | 141577 | Hans Havermann | 05/2021 |
| 4243 | 2^470305-459373 | 141576 | Enzo Doria | 05/2015 |
| 4244 | 32195^24936+24936^32195 | 141556 | Hans Havermann | 05/2021 |
| 4245 | 2^470183+72623 | 141540 | Enzo Doria | 04/2016 |
| 4246 | 2^470173-16465 | 141537 | Enzo Doria | 04/2013 |
| 4247 | 37297^6234+6234^37297 | 141534 | Hans Havermann | 05/2021 |
| 4248 | 2^4^117533+117533^4^2 | 141524 | Henri Lifchitz | 03/2025 |
| 4249 | (509*10^141479+13)/9 | 141481 | Robert Price | 05/2022 |
| 4250 | 44*10^141476+9 | 141478 | Robert Price | 10/2020 |
