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 ? |
5001 | 2^446494-16485 | 134409 | Enzo Doria | 04/2013 |
5002 | 30042^29785+29785^30042 | 134408 | Hans Havermann | 12/2020 |
5003 | 29504^30069-30069^29504 | 134405 | Norbert Schneider | 12/2014 |
5004 | 2^446441+65 | 134393 | Lelio R Paula | 08/2017 |
5005 | (10^134385+719)/9 | 134385 | Serge Batalov | 12/2014 |
5006 | 30043^29688+29688^30043 | 134370 | Hans Havermann | 12/2020 |
5007 | (2*10^134364+529)/9 | 134364 | Robert Price | 01/2018 |
5008 | 34657^7512+7512^34657 | 134323 | Hans Havermann | 11/2020 |
5009 | (13*2^446187-1)/661 | 134314 | Lelio R Paula | 07/2015 |
5010 | 5^192103+3^192103+2^192103+1 | 134275 | Matthias Baur | 12/2019 |
5011 | 42035^1564+1564^42035 | 134270 | Hans Havermann | 12/2020 |
5013 | (2^446022-7)/339 | 134264 | Lelio R Paula | 07/2015 |
5012 | 30621^24248+24248^30621 | 134264 | Hans Havermann | 12/2020 |
5014 | 30341^26562+26562^30341 | 134237 | Hans Havermann | 11/2020 |
5015 | (189^58967-1)/188 | 134234 | Anonymous | 06/2024 |
5016 | 10^134209+99867 | 134210 | Patrick De Geest | 05/2021 |
5017 | 10^134209-80000001 | 134209 | Robert Price | 04/2021 |
5018 | 10^134209-323283 | 134209 | Patrick De Geest | 05/2021 |
5019 | 29976^29953+29953^29976 | 134186 | Hans Havermann | 12/2020 |
5020 | 35038^6755+6755^35038 | 134183 | Hans Havermann | 12/2020 |
5021 | 63^74568+2 | 134174 | Lelio R Paula | 06/2017 |
5022 | 2^445671-22071 | 134161 | Enzo Doria | 07/2013 |
5023 | 532^49205+49205^532 | 134129 | Norbert Schneider | 02/2019 |
5024 | 36453^4780+4780^36453 | 134127 | Hans Havermann | 04/2021 |
5025 | (28*10^134122-1)/9 | 134123 | Serge Batalov | 10/2014 |
5026 | 2^445515-113859 | 134114 | Enzo Doria | 10/2014 |
5028 | (22*10^134111-37)/3 | 134112 | Robert Price | 04/2019 |
5027 | 31083^20636+20636^31083 | 134112 | Hans Havermann | 04/2021 |
5029 | 3*2^445478+5 | 134103 | Jon Grantham | 07/2023 |
5030 | 31622^17379+17379^31622 | 134079 | Hans Havermann | 04/2021 |
5031 | 5*2^445380-3 | 134074 | Jon Grantham | 07/2023 |
5032 | (6*32^89076+4241)/31 | 134073 | Eric Chen | 11/2023 |
5033 | (277*10^134059-7)/9 | 134061 | Robert Price | 02/2022 |
5034 | 2^445328-216917 | 134058 | Enzo Doria | 05/2014 |
5035 | 2^445202+1874899 | 134020 | Enzo Doria | 06/2016 |
5036 | 5^191739-3^191739-1 | 134020 | Jon Grantham | 08/2023 |
5037 | (35*10^134003-89)/9 | 134004 | Robert Price | 02/2022 |
5038 | (13*2^445102+1)/17 | 133989 | Lelio R Paula | 07/2015 |
5039 | (35*10^133979-593)/9 | 133980 | Robert Price | 07/2018 |
5040 | 2*10^133955+51 | 133956 | Robert Price | 05/2018 |
5041 | (49*10^133952+437)/9 | 133953 | Robert Price | 09/2021 |
5042 | 2^444964-113639 | 133948 | Enzo Doria | 08/2014 |
5043 | 31811^16240+16240^31811 | 133943 | Hans Havermann | 04/2021 |
5044 | 10^133902+167841 | 133903 | Patrick De Geest | 05/2021 |
5046 | 28118^30097-30097^28118 | 133902 | Norbert Schneider | 01/2015 |
5045 | 10^133902-100001 | 133902 | Robert Price | 07/2020 |
5047 | 2^444784-113859 | 133894 | Enzo Doria | 10/2014 |
5048 | (132^63127-1)/131 | 133864 | Anonymous | 06/2024 |
5049 | 32303^13914+13914^32303 | 133846 | Hans Havermann | 04/2021 |
5050 | (29^91493-3^91493)/26 | 133798 | Robert Price | 06/2025 |
5051 | (2276213*2^444444+1)/3 | 133797 | Alex_soldier | 11/2022 |
5052 | (1403559*2^444444+1)/5 | 133797 | Alex_soldier | 11/2022 |
5053 | (1209887*2^444444+1)/9 | 133797 | Alex_soldier | 11/2022 |
5054 | (608239*2^444444+1)/25 | 133796 | Alex_soldier | 11/2022 |
5055 | (1824587*2^444444+1)/27 | 133796 | Alex_soldier | 11/2022 |
5056 | (40795*2^444444+1)/7 | 133795 | Alex_soldier | 11/2022 |
5057 | 30739^22458+22458^30739 | 133757 | Hans Havermann | 04/2021 |
5058 | 34942^6721+6721^34942 | 133739 | Hans Havermann | 04/2021 |
5059 | (3^280229-1)/1120918 | 133698 | Aurel Gibier | 03/2025 |
5060 | (2^444046+100280245065) | 133672 | Paul Bourdelais | 05/2022 |
5061 | 34792^6935+6935^34792 | 133638 | Hans Havermann | 04/2021 |
5062 | (266*10^133603+1)/3 | 133605 | Robert Price | 04/2020 |
5063 | 32261^13842+13842^32261 | 133600 | Hans Havermann | 04/2021 |
5064 | (89*10^133580+1)/9 | 133581 | Serge Batalov | 05/2010 |
5065 | (134*10^133573-11)/3 | 133575 | Robert Price | 01/2022 |
5066 | 26726^30173-30173^26726 | 133574 | Frank Doornink | 03/2024 |
5067 | 2^443721+39527 | 133574 | Enzo Doria | 11/2024 |
5068 | 62^74521-61^74521 | 133571 | Robert Price | 05/2013 |
5069 | (182*10^133543+1)/3 | 133545 | Robert Price | 02/2020 |
5070 | (103*10^133535+11)/3 | 133537 | Robert Price | 01/2021 |
5071 | 32589^12520+12520^32589 | 133537 | Hans Havermann | 03/2021 |
5072 | L(638839)/274700771 | 133502 | Serge Batalov | 07/2024 |
5073 | 34516^7373+7373^34516 | 133496 | Hans Havermann | 04/2021 |
5074 | 8*10^133487-37 | 133488 | Robert Price | 03/2022 |
5075 | 30135^26882+26882^30135 | 133482 | Hans Havermann | 04/2021 |
5076 | 2^443198-1867301 | 133416 | Enzo Doria | 03/2016 |
5077 | 27^93192+26 | 133392 | Anonymous | 09/2024 |
5078 | (19*10^133390+101)/3 | 133391 | Robert Price | 09/2019 |
5079 | (71^72043-1)/70 | 133369 | Paul Bourdelais | 09/2017 |
5080 | 36117^4910+4910^36117 | 133311 | Hans Havermann | 04/2021 |
5081 | 2^442799+1874633 | 133296 | Enzo Doria | 06/2016 |
5082 | L(637751) | 133283 | Henri Lifchitz | 09/2008 |
5083 | 109^65410-2 | 133269 | Lelio R Paula | 10/2017 |
5084 | 2^442688-113489 | 133263 | Enzo Doria | 08/2014 |
5085 | (7*2^442640-1)/783 | 133246 | Lelio R Paula | 07/2015 |
5086 | (9*2^442463+1)/17441 | 133192 | Lelio R Paula | 07/2015 |
5087 | 2^442437-1849993 | 133187 | Enzo Doria | 08/2015 |
5088 | 2^442430-2791721 | 133185 | Enzo Doria | 03/2016 |
5089 | (13*2^442428-1)/309 | 133183 | Lelio R Paula | 07/2015 |
5090 | 29959^27870+27870^29959 | 133172 | Hans Havermann | 03/2021 |
5091 | (25*2^442379-1)/71 | 133169 | Lelio R Paula | 07/2015 |
5092 | 2^442368+213691 | 133167 | Enzo Doria | 09/2023 |
5093 | 34240^7737+7737^34240 | 133145 | Hans Havermann | 03/2021 |
5094 | 452^50145+50145^452 | 133142 | Norbert Schneider | 09/2020 |
5095 | (355^52201-1)/354 | 133122 | Tom Wu | 08/2024 |
5096 | (3^278981-1)/14507014 | 133101 | Paul Vanderveen | 05/2025 |
5097 | 30659^21796+21796^30659 | 133011 | Hans Havermann | 04/2021 |
5098 | 33276^9935+9935^33276 | 133010 | Hans Havermann | 04/2021 |
5099 | 30111^26122+26122^30111 | 133001 | Hans Havermann | 04/2021 |
5100 | 30790^20869+20869^30790 | 132998 | Hans Havermann | 04/2021 |
5102 | (2^441799+78557)/5 | 132995 | Lelio R Paula | 07/2015 |
5101 | 8*10^132994-27 | 132995 | Robert Price | 10/2021 |
5103 | (109*10^132992+11)/3 | 132994 | Robert Price | 06/2022 |
5104 | 2^441781-2787883 | 132990 | Enzo Doria | 03/2016 |
5105 | fibonacci(636232)+4 | 132965 | Jon Grantham | 08/2023 |
5106 | (3*2^441685+1)/749 | 132959 | Lelio R Paula | 07/2015 |
5107 | 2^441618+37 | 132941 | Lelio R Paula | 08/2017 |
5108 | 34857^6514+6514^34857 | 132940 | Hans Havermann | 04/2021 |
5109 | 34065^7988+7988^34065 | 132937 | Hans Havermann | 04/2021 |
5110 | 35571^5452+5452^35571 | 132914 | Hans Havermann | 04/2021 |
5111 | 2^441521-113575 | 132912 | Enzo Doria | 08/2014 |
5112 | 7*10^132884-99 | 132885 | Robert Price | 06/2019 |
5113 | 26987^29988-29988^26987 | 132882 | Frank Doornink | 03/2024 |
5114 | (103*10^132879+17)/3 | 132881 | Robert Price | 08/2020 |
5115 | 2^441396-65 | 132874 | Lelio R Paula | 08/2017 |
5116 | 33350^9633+9633^33350 | 132859 | Hans Havermann | 04/2021 |
5117 | 2^441330+1871959 | 132854 | Enzo Doria | 05/2016 |
5118 | 25772^30111-30111^25772 | 132825 | Frank Doornink | 02/2024 |
5119 | 2^441063+383 | 132774 | Lelio R Paula | 06/2012 |
5120 | (10^132753+7)/17/19 | 132751 | Alfred Reich | 06/2021 |
5121 | (22*10^132746+53)/3 | 132747 | Robert Price | 07/2019 |
5122 | (77*10^132744-149)/9 | 132745 | Robert Price | 03/2022 |
5123 | (22*10^132732+119)/3 | 132733 | Robert Price | 04/2021 |
5124 | 2^440846+1870909 | 132708 | Enzo Doria | 05/2016 |
5125 | (948^44579-1)/947 | 132701 | Jinyuan Wang | 04/2023 |
5126 | 2^440656-113489 | 132651 | Enzo Doria | 08/2014 |
5127 | numbpart(14180123587) | 132646 | Serge Batalov | 04/2017 |
5128 | 32950^10591+10591^32950 | 132622 | Hans Havermann | 04/2021 |
5129 | 33302^9597+9597^33302 | 132614 | Hans Havermann | 04/2021 |
5130 | (19*10^132550+191)/3 | 132551 | Robert Price | 05/2019 |
5131 | (2^440399-1)/(16210820281161978209*31518475633*880799) | 132538 | Dario Alpern | 01/2015 |
5132 | (38^83891+1)/39 | 132529 | Robert Price | 09/2013 |
5133 | 2*10^132493-43 | 132494 | Robert Price | 04/2018 |
5134 | 31352^16809+16809^31352 | 132480 | Hans Havermann | 04/2021 |
5135 | (418*10^132441+23)/9 | 132443 | Robert Price | 02/2020 |
5136 | 2^439931-21 | 132433 | Lelio R Paula | 08/2017 |
5137 | 47^79201-46^79201 | 132432 | Robert Price | 10/2012 |
5138 | 2^439897-113653 | 132423 | Enzo Doria | 08/2014 |
5139 | 35505^5362+5362^35505 | 132410 | Hans Havermann | 03/2021 |
5140 | 30079^25222+25222^30079 | 132402 | Hans Havermann | 04/2021 |
5141 | (5*2^439822+1)/9 | 132400 | Lelio R Paula | 06/2015 |
5142 | (695*10^132356+7)/9 | 132358 | Robert Price | 12/2021 |
5143 | (112*10^132337-1)/3 | 132339 | Serge Batalov | 12/2014 |
5144 | 2^439576-113247 | 132326 | Enzo Doria | 07/2014 |
5145 | (7^156589-1)/65346468774 | 132323 | Paul Vanderveen | 05/2025 |
5146 | 30059^25230+25230^30059 | 132318 | Hans Havermann | 04/2021 |
5147 | 2^439497-29143 | 132302 | Enzo Doria | 07/2015 |
5148 | 2^439409-114193 | 132276 | Enzo Doria | 12/2014 |
5149 | (39^83137+2^83137)/41 | 132275 | Robert Price | 12/2024 |
5150 | (44*10^132233-233)/9 | 132234 | Robert Price | 01/2019 |
5151 | 25507^30000-30000^25507 | 132200 | Frank Doornink | 02/2024 |
5152 | 9*10^132148-7 | 132149 | Robert Price | 09/2015 |
5153 | V(790390) | 132144 | Serge Batalov | 07/2024 |
5154 | (47*10^132125-119)/9 | 132126 | Robert Price | 05/2019 |
5155 | 2^438900+214051 | 132123 | Enzo Doria | 10/2023 |
5156 | 2^438845+1870217 | 132106 | Enzo Doria | 05/2016 |
5157 | 2^438789+87855 | 132089 | Lelio R Paula | 01/2016 |
5158 | 2^438774-2786411 | 132085 | Enzo Doria | 03/2016 |
5159 | 2^438755-1848205 | 132079 | Enzo Doria | 07/2015 |
5160 | 30502^21381+21381^30502 | 132075 | Hans Havermann | 04/2021 |
5161 | 2^438739-112087 | 132074 | Enzo Doria | 06/2014 |
5162 | (588859*29^90289-19)/28 | 132043 | Eric Chen | 06/2025 |
5163 | (2^438438+100280245065) | 131983 | Paul Bourdelais | 05/2022 |
5164 | 35872^4777+4777^35872 | 131979 | Hans Havermann | 04/2021 |
5165 | 31198^16945+16945^31198 | 131938 | Hans Havermann | 03/2021 |
5166 | 13907#+(318259#)/(13907#) | 131923 | Makoto Morimoto | 10/2017 |
5167 | L(631181) | 131910 | Henri Lifchitz | 09/2008 |
5168 | (47*10^131886-119)/9 | 131887 | Robert Price | 05/2019 |
5169 | 5*2^438096-3 | 131881 | Jon Grantham | 07/2023 |
5170 | (3*2^438121+1)/4308193883 | 131879 | Lelio R Paula | 06/2015 |
5171 | 2^438079-1863877 | 131875 | Enzo Doria | 03/2016 |
5172 | (16*10^131872-37)/3 | 131873 | Robert Price | 05/2021 |
5173 | (2^438067+5)/329 | 131869 | Lelio R Paula | 06/2015 |
5174 | 2^437908-113855 | 131824 | Enzo Doria | 09/2014 |
5175 | 2^437884-286349 | 131817 | Enzo Doria | 07/2015 |
5176 | 15^112072+14 | 131807 | Alfred Reich | 10/2023 |
5177 | 5^188558+4 | 131797 | Tyler NeSmith | 05/2021 |
5178 | (11*10^131784-17)/3 | 131785 | Robert Price | 06/2018 |
5179 | (166^59357-1)/165 | 131777 | Anonymous | 06/2024 |
5181 | 4*10^131719-93 | 131720 | Robert Price | 07/2020 |
5180 | 31629^14606+14606^31629 | 131720 | Hans Havermann | 04/2021 |
5182 | 3^276062-112292 | 131716 | Enzo Doria | 07/2014 |
5183 | 2^437539+2025 | 131713 | Henri Lifchitz | 01/2025 |
5184 | 11*31^88313+322688 | 131708 | Eric Chen | 05/2024 |
5185 | (7*10^131682+89)/3 | 131683 | Robert Price | 08/2020 |
5186 | 29512^28969+28969^29512 | 131681 | Hans Havermann | 03/2021 |
5187 | 2^437343+75953 | 131654 | Enzo Doria | 04/2016 |
5188 | 35^85243-34^85243 | 131621 | Robert Price | 05/2012 |
5189 | (28*10^131586+59)/3 | 131587 | Robert Price | 05/2021 |
5190 | (59*10^131575+391)/9 | 131576 | Robert Price | 03/2021 |
5191 | 39984^1945+1945^39984 | 131505 | Hans Havermann | 03/2021 |
5192 | 25842^29801-29801^25842 | 131492 | Frank Doornink | 03/2024 |
5193 | 28592^29505-29505^28592 | 131482 | Frank Doornink | 05/2024 |
5194 | 25647^29818-29818^25647 | 131469 | Frank Doornink | 02/2024 |
5195 | (203*10^131457+1)/3 | 131459 | Robert Price | 03/2020 |
5196 | 7*10^131421-41 | 131422 | Robert Price | 08/2021 |
5197 | 87309^32+32^87309 | 131414 | Hans Havermann | 03/2021 |
5198 | (68^71713+1)/69 | 131413 | Paul Bourdelais | 09/2017 |
5199 | 2^436521+224885 | 131406 | Enzo Doria | 07/2024 |
5200 | (650*10^131391+43)/9 | 131393 | Tyler Busby | 01/2023 |
5201 | 2^436451+1884713 | 131385 | Enzo Doria | 03/2017 |
5202 | 2^436365+35 | 131359 | Robert Price | 11/2015 |
5204 | 2^436300+1866871 | 131340 | Enzo Doria | 03/2016 |
5203 | (7*10^131339+179)/3 | 131340 | Robert Price | 09/2018 |
5205 | 14^114592-3 | 131338 | Paul Bourdelais | 12/2020 |
5206 | 36197^4236+4236^36197 | 131285 | Hans Havermann | 04/2021 |
5207 | (37*10^131270+341)/9 | 131271 | Robert Price | 08/2018 |
5208 | 29863^24790+24790^29863 | 131227 | Hans Havermann | 03/2021 |
5209 | (5*10^131223-29)/3 | 131224 | Robert Price | 03/2018 |
5210 | 29524^27825+27825^29524 | 131218 | Hans Havermann | 03/2021 |
5211 | (23*2^435891-1)/699 | 131215 | Lelio R Paula | 07/2015 |
5212 | (11*2^435879+1)/3337 | 131211 | Lelio R Paula | 06/2015 |
5213 | 30639^19136+19136^30639 | 131192 | Hans Havermann | 04/2021 |
5214 | (2^435808+1)/641/6700417 | 131182 | Lelio R Paula | 02/2012 |
5215 | (2^435808+1)/4294967297 | 131182 | Serge Batalov | 12/2016 |
5216 | 2^435773+1875557 | 131181 | Enzo Doria | 06/2016 |
5218 | (16*10^131180+167)/3 | 131181 | Robert Price | 06/2019 |
5217 | (26*10^131180-77)/3 | 131181 | Robert Price | 11/2019 |
5219 | (25*10^131144-7)/9 | 131145 | Robert Price | 05/2018 |
5220 | 29299^29358-29358^29299 | 131138 | Norbert Schneider | 03/2022 |
5221 | 2^435612-2789939 | 131133 | Enzo Doria | 12/2015 |
5222 | 33976^7231+7231^33976 | 131121 | Hans Havermann | 03/2021 |
5223 | 33715^7746+7746^33715 | 131121 | Hans Havermann | 03/2021 |
5224 | 66^72047-65^72047 | 131093 | Robert Price | 09/2013 |
5225 | (5*10^131090+37)/3 | 131091 | Robert Price | 03/2018 |
5226 | 2^435468+75631 | 131089 | Enzo Doria | 04/2016 |
5227 | 37^83588-2 | 131083 | Lelio R Paula | 08/2015 |
5228 | (4^217720+11)/3 | 131081 | Robert Price | 02/2017 |
5229 | 30407^20448+20448^30407 | 131074 | Hans Havermann | 04/2021 |
5230 | (22*10^131070+179)/3 | 131071 | Robert Price | 02/2022 |
5231 | 28831^29388-29388^28831 | 131067 | Frank Doornink | 05/2024 |
5232 | 29487^27836+27836^29487 | 131059 | Hans Havermann | 04/2021 |
5233 | 29962^23615+23615^29962 | 131030 | Hans Havermann | 03/2021 |
5234 | 2^435202-113193 | 131009 | Enzo Doria | 07/2014 |
5235 | 41705^1384+1384^41705 | 131002 | Hans Havermann | 04/2021 |
5236 | 9*10^130998-19 | 130999 | Robert Price | 07/2019 |
5237 | 36243^4108+4108^36243 | 130969 | Hans Havermann | 04/2021 |
5238 | (445^49433+1)/446 | 130914 | Jinyuan Wang | 05/2024 |
5239 | floor((sqrt(5)-1)/2*10^130911) | 130911 | Serge Batalov | 06/2017 |
5240 | 2^434835-111937 | 130899 | Enzo Doria | 05/2014 |
5241 | (62*10^130895-629)/9 | 130896 | Robert Price | 07/2021 |
5242 | 2^434807+225 | 130890 | Henri Lifchitz | 11/2024 |
5243 | 2^434685+72257 | 130854 | Enzo Doria | 04/2016 |
5244 | (7*10^130825+113)/3 | 130826 | Robert Price | 02/2018 |
5245 | 2^434539-29317 | 130810 | Enzo Doria | 07/2015 |
5246 | (74*10^130791+637)/9 | 130792 | Robert Price | 01/2022 |
5247 | 2^434469-114259 | 130789 | Enzo Doria | 01/2015 |
5248 | (5*10^130763+103)/9 | 130763 | Robert Price | 04/2022 |
5249 | 2^434246+33 | 130722 | Robert Price | 11/2015 |
5250 | 30156^21599+21599^30156 | 130710 | Hans Havermann | 04/2021 |