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 ? |
| 4751 | 28118^30097-30097^28118 | 133902 | Norbert Schneider | 01/2015 |
| 4752 | 2^444784-113859 | 133894 | Enzo Doria | 10/2014 |
| 4753 | (132^63127-1)/131 | 133864 | Anonymous | 06/2024 |
| 4754 | 32303^13914+13914^32303 | 133846 | Hans Havermann | 04/2021 |
| 4755 | (2276213*2^444444+1)/3 | 133797 | Alex_soldier | 11/2022 |
| 4756 | (1403559*2^444444+1)/5 | 133797 | Alex_soldier | 11/2022 |
| 4757 | (1209887*2^444444+1)/9 | 133797 | Alex_soldier | 11/2022 |
| 4758 | (608239*2^444444+1)/25 | 133796 | Alex_soldier | 11/2022 |
| 4759 | (1824587*2^444444+1)/27 | 133796 | Alex_soldier | 11/2022 |
| 4760 | (40795*2^444444+1)/7 | 133795 | Alex_soldier | 11/2022 |
| 4761 | 30739^22458+22458^30739 | 133757 | Hans Havermann | 04/2021 |
| 4762 | 34942^6721+6721^34942 | 133739 | Hans Havermann | 04/2021 |
| 4763 | (3^280229-1)/1120918 | 133698 | Aurel Gibier | 03/2025 |
| 4764 | (2^444046+100280245065) | 133672 | Paul Bourdelais | 05/2022 |
| 4765 | 34792^6935+6935^34792 | 133638 | Hans Havermann | 04/2021 |
| 4766 | (266*10^133603+1)/3 | 133605 | Robert Price | 04/2020 |
| 4767 | 32261^13842+13842^32261 | 133600 | Hans Havermann | 04/2021 |
| 4768 | (89*10^133580+1)/9 | 133581 | Serge Batalov | 05/2010 |
| 4769 | (134*10^133573-11)/3 | 133575 | Robert Price | 01/2022 |
| 4770 | 26726^30173-30173^26726 | 133574 | Frank Doornink | 03/2024 |
| 4771 | 2^443721+39527 | 133574 | Enzo Doria | 11/2024 |
| 4772 | 62^74521-61^74521 | 133571 | Robert Price | 05/2013 |
| 4773 | (182*10^133543+1)/3 | 133545 | Robert Price | 02/2020 |
| 4774 | (103*10^133535+11)/3 | 133537 | Robert Price | 01/2021 |
| 4775 | 32589^12520+12520^32589 | 133537 | Hans Havermann | 03/2021 |
| 4776 | L(638839)/274700771 | 133502 | Serge Batalov | 07/2024 |
| 4777 | 34516^7373+7373^34516 | 133496 | Hans Havermann | 04/2021 |
| 4778 | 8*10^133487-37 | 133488 | Robert Price | 03/2022 |
| 4779 | 30135^26882+26882^30135 | 133482 | Hans Havermann | 04/2021 |
| 4780 | 2^443198-1867301 | 133416 | Enzo Doria | 03/2016 |
| 4781 | 27^93192+26 | 133392 | Anonymous | 09/2024 |
| 4782 | (19*10^133390+101)/3 | 133391 | Robert Price | 09/2019 |
| 4783 | (71^72043-1)/70 | 133369 | Paul Bourdelais | 09/2017 |
| 4784 | 36117^4910+4910^36117 | 133311 | Hans Havermann | 04/2021 |
| 4785 | 2^442799+1874633 | 133296 | Enzo Doria | 06/2016 |
| 4786 | L(637751) | 133283 | Henri Lifchitz | 09/2008 |
| 4787 | 109^65410-2 | 133269 | Lelio R Paula | 10/2017 |
| 4788 | 2^442688-113489 | 133263 | Enzo Doria | 08/2014 |
| 4789 | (7*2^442640-1)/783 | 133246 | Lelio R Paula | 07/2015 |
| 4790 | (9*2^442463+1)/17441 | 133192 | Lelio R Paula | 07/2015 |
| 4791 | 2^442437-1849993 | 133187 | Enzo Doria | 08/2015 |
| 4792 | 2^442430-2791721 | 133185 | Enzo Doria | 03/2016 |
| 4793 | (13*2^442428-1)/309 | 133183 | Lelio R Paula | 07/2015 |
| 4794 | 29959^27870+27870^29959 | 133172 | Hans Havermann | 03/2021 |
| 4795 | (25*2^442379-1)/71 | 133169 | Lelio R Paula | 07/2015 |
| 4796 | 2^442368+213691 | 133167 | Enzo Doria | 09/2023 |
| 4797 | 34240^7737+7737^34240 | 133145 | Hans Havermann | 03/2021 |
| 4798 | 452^50145+50145^452 | 133142 | Norbert Schneider | 09/2020 |
| 4799 | (355^52201-1)/354 | 133122 | Tom Wu | 08/2024 |
| 4800 | 30659^21796+21796^30659 | 133011 | Hans Havermann | 04/2021 |
| 4801 | 33276^9935+9935^33276 | 133010 | Hans Havermann | 04/2021 |
| 4802 | 30111^26122+26122^30111 | 133001 | Hans Havermann | 04/2021 |
| 4803 | 30790^20869+20869^30790 | 132998 | Hans Havermann | 04/2021 |
| 4805 | (2^441799+78557)/5 | 132995 | Lelio R Paula | 07/2015 |
| 4804 | 8*10^132994-27 | 132995 | Robert Price | 10/2021 |
| 4806 | (109*10^132992+11)/3 | 132994 | Robert Price | 06/2022 |
| 4807 | 2^441781-2787883 | 132990 | Enzo Doria | 03/2016 |
| 4808 | fibonacci(636232)+4 | 132965 | Jon Grantham | 08/2023 |
| 4809 | (3*2^441685+1)/749 | 132959 | Lelio R Paula | 07/2015 |
| 4810 | 2^441618+37 | 132941 | Lelio R Paula | 08/2017 |
| 4811 | 34857^6514+6514^34857 | 132940 | Hans Havermann | 04/2021 |
| 4812 | 34065^7988+7988^34065 | 132937 | Hans Havermann | 04/2021 |
| 4813 | 35571^5452+5452^35571 | 132914 | Hans Havermann | 04/2021 |
| 4814 | 2^441521-113575 | 132912 | Enzo Doria | 08/2014 |
| 4815 | 7*10^132884-99 | 132885 | Robert Price | 06/2019 |
| 4816 | 26987^29988-29988^26987 | 132882 | Frank Doornink | 03/2024 |
| 4817 | (103*10^132879+17)/3 | 132881 | Robert Price | 08/2020 |
| 4818 | 2^441396-65 | 132874 | Lelio R Paula | 08/2017 |
| 4819 | 33350^9633+9633^33350 | 132859 | Hans Havermann | 04/2021 |
| 4820 | 2^441330+1871959 | 132854 | Enzo Doria | 05/2016 |
| 4821 | 25772^30111-30111^25772 | 132825 | Frank Doornink | 02/2024 |
| 4822 | 2^441063+383 | 132774 | Lelio R Paula | 06/2012 |
| 4823 | (10^132753+7)/17/19 | 132751 | Alfred Reich | 06/2021 |
| 4824 | (22*10^132746+53)/3 | 132747 | Robert Price | 07/2019 |
| 4825 | (77*10^132744-149)/9 | 132745 | Robert Price | 03/2022 |
| 4826 | (22*10^132732+119)/3 | 132733 | Robert Price | 04/2021 |
| 4827 | 2^440846+1870909 | 132708 | Enzo Doria | 05/2016 |
| 4828 | (948^44579-1)/947 | 132701 | Jinyuan Wang | 04/2023 |
| 4829 | 2^440656-113489 | 132651 | Enzo Doria | 08/2014 |
| 4830 | numbpart(14180123587) | 132646 | Serge Batalov | 04/2017 |
| 4831 | 32950^10591+10591^32950 | 132622 | Hans Havermann | 04/2021 |
| 4832 | 33302^9597+9597^33302 | 132614 | Hans Havermann | 04/2021 |
| 4833 | (19*10^132550+191)/3 | 132551 | Robert Price | 05/2019 |
| 4834 | (2^440399-1)/(16210820281161978209*31518475633*880799) | 132538 | Dario Alpern | 01/2015 |
| 4835 | (38^83891+1)/39 | 132529 | Robert Price | 09/2013 |
| 4836 | 2*10^132493-43 | 132494 | Robert Price | 04/2018 |
| 4837 | 31352^16809+16809^31352 | 132480 | Hans Havermann | 04/2021 |
| 4838 | (418*10^132441+23)/9 | 132443 | Robert Price | 02/2020 |
| 4839 | 2^439931-21 | 132433 | Lelio R Paula | 08/2017 |
| 4840 | 47^79201-46^79201 | 132432 | Robert Price | 10/2012 |
| 4841 | 2^439897-113653 | 132423 | Enzo Doria | 08/2014 |
| 4842 | 35505^5362+5362^35505 | 132410 | Hans Havermann | 03/2021 |
| 4843 | 30079^25222+25222^30079 | 132402 | Hans Havermann | 04/2021 |
| 4844 | (5*2^439822+1)/9 | 132400 | Lelio R Paula | 06/2015 |
| 4845 | (695*10^132356+7)/9 | 132358 | Robert Price | 12/2021 |
| 4846 | (112*10^132337-1)/3 | 132339 | Serge Batalov | 12/2014 |
| 4847 | 2^439576-113247 | 132326 | Enzo Doria | 07/2014 |
| 4848 | 30059^25230+25230^30059 | 132318 | Hans Havermann | 04/2021 |
| 4849 | 2^439497-29143 | 132302 | Enzo Doria | 07/2015 |
| 4850 | 2^439409-114193 | 132276 | Enzo Doria | 12/2014 |
| 4851 | (39^83137+2^83137)/41 | 132275 | Robert Price | 12/2024 |
| 4852 | (44*10^132233-233)/9 | 132234 | Robert Price | 01/2019 |
| 4853 | 25507^30000-30000^25507 | 132200 | Frank Doornink | 02/2024 |
| 4854 | 9*10^132148-7 | 132149 | Robert Price | 09/2015 |
| 4855 | V(790390) | 132144 | Serge Batalov | 07/2024 |
| 4856 | (47*10^132125-119)/9 | 132126 | Robert Price | 05/2019 |
| 4857 | 2^438900+214051 | 132123 | Enzo Doria | 10/2023 |
| 4858 | 2^438845+1870217 | 132106 | Enzo Doria | 05/2016 |
| 4859 | 2^438789+87855 | 132089 | Lelio R Paula | 01/2016 |
| 4860 | 2^438774-2786411 | 132085 | Enzo Doria | 03/2016 |
| 4861 | 2^438755-1848205 | 132079 | Enzo Doria | 07/2015 |
| 4862 | 30502^21381+21381^30502 | 132075 | Hans Havermann | 04/2021 |
| 4863 | 2^438739-112087 | 132074 | Enzo Doria | 06/2014 |
| 4864 | (2^438438+100280245065) | 131983 | Paul Bourdelais | 05/2022 |
| 4865 | 35872^4777+4777^35872 | 131979 | Hans Havermann | 04/2021 |
| 4866 | 31198^16945+16945^31198 | 131938 | Hans Havermann | 03/2021 |
| 4867 | 13907#+(318259#)/(13907#) | 131923 | Makoto Morimoto | 10/2017 |
| 4868 | L(631181) | 131910 | Henri Lifchitz | 09/2008 |
| 4869 | (47*10^131886-119)/9 | 131887 | Robert Price | 05/2019 |
| 4870 | 5*2^438096-3 | 131881 | Jon Grantham | 07/2023 |
| 4871 | (3*2^438121+1)/4308193883 | 131879 | Lelio R Paula | 06/2015 |
| 4872 | 2^438079-1863877 | 131875 | Enzo Doria | 03/2016 |
| 4873 | (16*10^131872-37)/3 | 131873 | Robert Price | 05/2021 |
| 4874 | (2^438067+5)/329 | 131869 | Lelio R Paula | 06/2015 |
| 4875 | 2^437908-113855 | 131824 | Enzo Doria | 09/2014 |
| 4876 | 2^437884-286349 | 131817 | Enzo Doria | 07/2015 |
| 4877 | 15^112072+14 | 131807 | Alfred Reich | 10/2023 |
| 4878 | 5^188558+4 | 131797 | Tyler NeSmith | 05/2021 |
| 4879 | (11*10^131784-17)/3 | 131785 | Robert Price | 06/2018 |
| 4880 | (166^59357-1)/165 | 131777 | Anonymous | 06/2024 |
| 4882 | 4*10^131719-93 | 131720 | Robert Price | 07/2020 |
| 4881 | 31629^14606+14606^31629 | 131720 | Hans Havermann | 04/2021 |
| 4883 | 3^276062-112292 | 131716 | Enzo Doria | 07/2014 |
| 4884 | 2^437539+2025 | 131713 | Henri Lifchitz | 01/2025 |
| 4885 | 11*31^88313+322688 | 131708 | Eric Chen | 05/2024 |
| 4886 | (7*10^131682+89)/3 | 131683 | Robert Price | 08/2020 |
| 4887 | 29512^28969+28969^29512 | 131681 | Hans Havermann | 03/2021 |
| 4888 | 2^437343+75953 | 131654 | Enzo Doria | 04/2016 |
| 4889 | 35^85243-34^85243 | 131621 | Robert Price | 05/2012 |
| 4890 | (28*10^131586+59)/3 | 131587 | Robert Price | 05/2021 |
| 4891 | (59*10^131575+391)/9 | 131576 | Robert Price | 03/2021 |
| 4892 | 39984^1945+1945^39984 | 131505 | Hans Havermann | 03/2021 |
| 4893 | 25842^29801-29801^25842 | 131492 | Frank Doornink | 03/2024 |
| 4894 | 28592^29505-29505^28592 | 131482 | Frank Doornink | 05/2024 |
| 4895 | 25647^29818-29818^25647 | 131469 | Frank Doornink | 02/2024 |
| 4896 | (203*10^131457+1)/3 | 131459 | Robert Price | 03/2020 |
| 4897 | 7*10^131421-41 | 131422 | Robert Price | 08/2021 |
| 4898 | 87309^32+32^87309 | 131414 | Hans Havermann | 03/2021 |
| 4899 | (68^71713+1)/69 | 131413 | Paul Bourdelais | 09/2017 |
| 4900 | 2^436521+224885 | 131406 | Enzo Doria | 07/2024 |
| 4901 | (650*10^131391+43)/9 | 131393 | Tyler Busby | 01/2023 |
| 4902 | 2^436451+1884713 | 131385 | Enzo Doria | 03/2017 |
| 4903 | 2^436365+35 | 131359 | Robert Price | 11/2015 |
| 4905 | 2^436300+1866871 | 131340 | Enzo Doria | 03/2016 |
| 4904 | (7*10^131339+179)/3 | 131340 | Robert Price | 09/2018 |
| 4906 | 14^114592-3 | 131338 | Paul Bourdelais | 12/2020 |
| 4907 | 36197^4236+4236^36197 | 131285 | Hans Havermann | 04/2021 |
| 4908 | (37*10^131270+341)/9 | 131271 | Robert Price | 08/2018 |
| 4909 | 29863^24790+24790^29863 | 131227 | Hans Havermann | 03/2021 |
| 4910 | (5*10^131223-29)/3 | 131224 | Robert Price | 03/2018 |
| 4911 | 29524^27825+27825^29524 | 131218 | Hans Havermann | 03/2021 |
| 4912 | (23*2^435891-1)/699 | 131215 | Lelio R Paula | 07/2015 |
| 4913 | (11*2^435879+1)/3337 | 131211 | Lelio R Paula | 06/2015 |
| 4914 | 30639^19136+19136^30639 | 131192 | Hans Havermann | 04/2021 |
| 4915 | (2^435808+1)/641/6700417 | 131182 | Lelio R Paula | 02/2012 |
| 4916 | (2^435808+1)/4294967297 | 131182 | Serge Batalov | 12/2016 |
| 4917 | 2^435773+1875557 | 131181 | Enzo Doria | 06/2016 |
| 4919 | (16*10^131180+167)/3 | 131181 | Robert Price | 06/2019 |
| 4918 | (26*10^131180-77)/3 | 131181 | Robert Price | 11/2019 |
| 4920 | (25*10^131144-7)/9 | 131145 | Robert Price | 05/2018 |
| 4921 | 29299^29358-29358^29299 | 131138 | Norbert Schneider | 03/2022 |
| 4922 | 2^435612-2789939 | 131133 | Enzo Doria | 12/2015 |
| 4923 | 33976^7231+7231^33976 | 131121 | Hans Havermann | 03/2021 |
| 4924 | 33715^7746+7746^33715 | 131121 | Hans Havermann | 03/2021 |
| 4925 | 66^72047-65^72047 | 131093 | Robert Price | 09/2013 |
| 4926 | (5*10^131090+37)/3 | 131091 | Robert Price | 03/2018 |
| 4927 | 2^435468+75631 | 131089 | Enzo Doria | 04/2016 |
| 4928 | 37^83588-2 | 131083 | Lelio R Paula | 08/2015 |
| 4929 | (4^217720+11)/3 | 131081 | Robert Price | 02/2017 |
| 4930 | 30407^20448+20448^30407 | 131074 | Hans Havermann | 04/2021 |
| 4931 | (22*10^131070+179)/3 | 131071 | Robert Price | 02/2022 |
| 4932 | 28831^29388-29388^28831 | 131067 | Frank Doornink | 05/2024 |
| 4933 | 29487^27836+27836^29487 | 131059 | Hans Havermann | 04/2021 |
| 4934 | 29962^23615+23615^29962 | 131030 | Hans Havermann | 03/2021 |
| 4935 | 2^435202-113193 | 131009 | Enzo Doria | 07/2014 |
| 4936 | 41705^1384+1384^41705 | 131002 | Hans Havermann | 04/2021 |
| 4937 | 9*10^130998-19 | 130999 | Robert Price | 07/2019 |
| 4938 | 36243^4108+4108^36243 | 130969 | Hans Havermann | 04/2021 |
| 4939 | (445^49433+1)/446 | 130914 | Jinyuan Wang | 05/2024 |
| 4940 | floor((sqrt(5)-1)/2*10^130911) | 130911 | Serge Batalov | 06/2017 |
| 4941 | 2^434835-111937 | 130899 | Enzo Doria | 05/2014 |
| 4942 | (62*10^130895-629)/9 | 130896 | Robert Price | 07/2021 |
| 4943 | 2^434807+225 | 130890 | Henri Lifchitz | 11/2024 |
| 4944 | 2^434685+72257 | 130854 | Enzo Doria | 04/2016 |
| 4945 | (7*10^130825+113)/3 | 130826 | Robert Price | 02/2018 |
| 4946 | 2^434539-29317 | 130810 | Enzo Doria | 07/2015 |
| 4947 | (74*10^130791+637)/9 | 130792 | Robert Price | 01/2022 |
| 4948 | 2^434469-114259 | 130789 | Enzo Doria | 01/2015 |
| 4949 | (5*10^130763+103)/9 | 130763 | Robert Price | 04/2022 |
| 4950 | 2^434246+33 | 130722 | Robert Price | 11/2015 |
| 4951 | 30156^21599+21599^30156 | 130710 | Hans Havermann | 04/2021 |
| 4952 | (17*10^130695-161)/9 | 130696 | Robert Price | 02/2021 |
| 4953 | 30513^19148+19148^30513 | 130661 | Hans Havermann | 03/2021 |
| 4954 | 29736^24761+24761^29736 | 130654 | Hans Havermann | 04/2021 |
| 4955 | 9*10^130638+41 | 130639 | Robert Price | 08/2020 |
| 4956 | 2^433911-91 | 130621 | Lelio R Paula | 06/2017 |
| 4957 | 30786^17449+17449^30786 | 130588 | Hans Havermann | 03/2021 |
| 4958 | 2^433744-114419 | 130570 | Enzo Doria | 02/2015 |
| 4960 | 2^433708+1869451 | 130560 | Enzo Doria | 05/2016 |
| 4959 | 2^433710+93 | 130560 | Lelio R Paula | 06/2017 |
| 4961 | 7*10^130535-27 | 130536 | Robert Price | 11/2022 |
| 4962 | (9629^32768+1)/120501441265666 | 130520 | Kellen Shenton | 05/2021 |
| 4963 | 804*34^85220+713 | 130516 | Eric Chen | 08/2023 |
| 4964 | (29*2^433547-1)/27 | 130511 | Lelio R Paula | 06/2015 |
| 4965 | 3^273521+10 | 130503 | Tyler NeSmith | 01/2021 |
| 4966 | 41659^1356+1356^41659 | 130487 | Hans Havermann | 03/2021 |
| 4967 | 4*10^130480+9 | 130481 | Robert Price | 05/2015 |
| 4968 | (23*2^433449-1)/75 | 130481 | Lelio R Paula | 06/2015 |
| 4969 | 3*2^433422+5 | 130474 | Jon Grantham | 07/2023 |
| 4970 | (23*2^433334-1)/3731 | 130445 | Lelio R Paula | 06/2015 |
| 4971 | (31*10^130414-49)/9 | 130415 | Robert Price | 11/2021 |
| 4972 | 26462^29485-29485^26462 | 130402 | Frank Doornink | 03/2024 |
| 4973 | 33481^7848+7848^33481 | 130401 | Hans Havermann | 03/2021 |
| 4974 | (17*10^130393+7)/3 | 130394 | Robert Price | 06/2023 |
| 4975 | (22*10^130392+203)/9 | 130393 | Robert Price | 10/2021 |
| 4976 | 29773^23950+23950^29773 | 130386 | Hans Havermann | 04/2021 |
| 4977 | 2^433023-113497 | 130353 | Enzo Doria | 08/2014 |
| 4978 | 31175^15178+15178^31175 | 130350 | Hans Havermann | 04/2021 |
| 4979 | 2^433002+1179379 | 130347 | Enzo Doria | 06/2016 |
| 4980 | 2^432974+19 | 130339 | Robert Price | 08/2015 |
| 4981 | 31903^12168+12168^31903 | 130331 | Hans Havermann | 04/2021 |
| 4982 | 2^432917+22217 | 130322 | Enzo Doria | 09/2023 |
| 4983 | 29387^27112+27112^29387 | 130278 | Hans Havermann | 04/2021 |
| 4984 | 2^432768+213181 | 130277 | Enzo Doria | 09/2023 |
| 4985 | 29577^25370+25370^29577 | 130267 | Hans Havermann | 04/2021 |
| 4986 | 31738^12685+12685^31738 | 130231 | Hans Havermann | 03/2021 |
| 4987 | 44235^878+878^44235 | 130206 | Hans Havermann | 04/2021 |
| 4988 | 32160^11171+11171^32160 | 130187 | Hans Havermann | 04/2021 |
| 4989 | 29489^25956+25956^29489 | 130172 | Hans Havermann | 04/2021 |
| 4990 | (2^432457-1)/1672739247834685086279697 | 130159 | Tony Prest / Never Odd Or Even | 09/2013 |
| 4991 | 33005^8766+8766^33005 | 130133 | Hans Havermann | 04/2021 |
| 4992 | (35*10^130132-611)/9 | 130133 | Robert Price | 02/2022 |
| 4993 | (444^49408+1)/(444^256+1) | 130125 | Martin Hopf | 12/2023 |
| 4994 | 2^432217+41 | 130111 | Lelio R Paula | 06/2017 |
| 4995 | (2^216089*(2^216091-1)-339)/25 | 130098 | Makoto Morimoto | 03/2017 |
| 4996 | ((2^216091+1066)^2+(2^216091+1066)+41)/47/2069 | 130095 | Makoto Morimoto | 05/2016 |
| 4997 | 97^65480-2 | 130094 | Lelio R Paula | 05/2017 |
| 4998 | 36007^4102+4102^36007 | 130094 | Hans Havermann | 04/2021 |
| 4999 | 4*10^130088-89 | 130089 | Robert Price | 11/2018 |
| 5000 | 2^432117-113215 | 130081 | Enzo Doria | 07/2014 |
