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 ? |
| 5751 | 29433^19676+19676^29433 | 126384 | Hans Havermann | 03/2021 |
| 5752 | F(604711) | 126377 | Henri Lifchitz | 02/2005 |
| 5753 | 2^419757+72707 | 126360 | Enzo Doria | 04/2016 |
| 5754 | 2^419720-21569 | 126349 | Enzo Doria | 07/2013 |
| 5755 | 2^419637+29 | 126324 | Henri Lifchitz | 02/2006 |
| 5756 | 31004^11865+11865^31004 | 126319 | Hans Havermann | 03/2021 |
| 5757 | 2^419612+1876741 | 126316 | Enzo Doria | 07/2016 |
| 5758 | 2^419520+2793271 | 126289 | Enzo Doria | 03/2016 |
| 5759 | (2^419447-5)/369 | 126264 | Lelio R Paula | 05/2014 |
| 5760 | 2^419328-1859939 | 126231 | Enzo Doria | 03/2016 |
| 5761 | 2^419282-1851507 | 126217 | Enzo Doria | 08/2015 |
| 5762 | (133*10^126212+17)/3 | 126214 | Robert Price | 11/2021 |
| 5763 | 2^419251+1866143 | 126208 | Enzo Doria | 03/2016 |
| 5764 | 11^121185+2 | 126202 | Robert Price | 05/2014 |
| 5765 | 28203^28352+28352^28203 | 126175 | Norbert Schneider | 01/2021 |
| 5766 | (23*2^419036-1)/1393 | 126141 | Lelio R Paula | 05/2014 |
| 5767 | 2^418851+23 | 126087 | Robert Price | 09/2015 |
| 5768 | (2^418849-9)/2681 | 126083 | Lelio R Paula | 05/2014 |
| 5769 | 2^418829+167 | 126081 | Lelio R Paula | 01/2012 |
| 5770 | 31037^11530+11530^31037 | 126067 | Hans Havermann | 03/2021 |
| 5771 | 4*10^126064-69 | 126065 | Robert Price | 01/2022 |
| 5772 | (31*2^418782-1)/75891 | 126063 | Lelio R Paula | 05/2014 |
| 5773 | (19*2^418754-1)/15 | 126058 | Lelio R Paula | 05/2014 |
| 5774 | (35*10^126048-323)/9 | 126049 | Robert Price | 10/2021 |
| 5775 | 33016^6551+6551^33016 | 126000 | Hans Havermann | 03/2021 |
| 5776 | 2^418548-111546435 | 125996 | Paul Bourdelais | 10/2021 |
| 5777 | 25134^28625-28625^25134 | 125958 | Frank Doornink | 12/2023 |
| 5778 | 34736^4227+4227^34736 | 125954 | Hans Havermann | 03/2021 |
| 5779 | (23*35^81566-144013)/34 | 125944 | Eric Chen | 05/2025 |
| 5780 | 26197^28502-28502^26197 | 125930 | Frank Doornink | 03/2024 |
| 5781 | 2^418319-109501 | 125927 | Enzo Doria | 04/2014 |
| 5782 | 2^418316-112373 | 125926 | Enzo Doria | 06/2014 |
| 5783 | 40398^1309+1309^40398 | 125919 | Hans Havermann | 03/2021 |
| 5784 | (8*10^125894-29)/3 | 125895 | Robert Price | 07/2018 |
| 5785 | (26*10^125886-413)/9 | 125887 | Robert Price | 05/2018 |
| 5786 | 10^(2*62938+1)-7*10^62938-1 | 125877 | Robert Price | 07/2023 |
| 5787 | 55*10^125847+9 | 125849 | Robert Price | 03/2022 |
| 5788 | 4*10^125832+57 | 125833 | Robert Price | 05/2022 |
| 5789 | 2^417968+1869811 | 125821 | Enzo Doria | 06/2016 |
| 5790 | 2^417902+63 | 125802 | Lelio R Paula | 09/2015 |
| 5791 | (10^125792-91)/9 | 125792 | Serge Batalov | 12/2014 |
| 5792 | 30438^13573+13573^30438 | 125791 | Hans Havermann | 03/2021 |
| 5793 | 32867^6714+6714^32867 | 125782 | Hans Havermann | 03/2021 |
| 5794 | 31155^10892+10892^31155 | 125777 | Hans Havermann | 03/2021 |
| 5795 | (35*10^125754-593)/9 | 125755 | Robert Price | 07/2018 |
| 5796 | 30455^13464+13464^30455 | 125754 | Hans Havermann | 03/2021 |
| 5797 | (32*10^125751-77)/9 | 125752 | Robert Price | 06/2018 |
| 5798 | 2^417704+77011 | 125742 | Enzo Doria | 05/2016 |
| 5799 | 29755^16816+16816^29755 | 125737 | Hans Havermann | 03/2021 |
| 5800 | (22*10^125734+203)/9 | 125735 | Robert Price | 10/2021 |
| 5801 | 29918^15915+15915^29918 | 125710 | Hans Havermann | 03/2021 |
| 5802 | (10^125706+149)/3 | 125706 | Serge Batalov | 12/2014 |
| 5803 | 28531^25368+25368^28531 | 125659 | Hans Havermann | 03/2021 |
| 5804 | 2^417419-115309 | 125656 | Enzo Doria | 07/2015 |
| 5805 | (46*10^125642+593)/9 | 125643 | Robert Price | 04/2022 |
| 5806 | 2^417315+213953 | 125625 | Enzo Doria | 10/2023 |
| 5807 | 2^417300+77281 | 125620 | Enzo Doria | 05/2016 |
| 5808 | 30638^12537+12537^30638 | 125561 | Hans Havermann | 03/2021 |
| 5809 | 2^417095-1657 | 125559 | Yves Minet | 07/2014 |
| 5810 | 30162^14525+14525^30162 | 125538 | Hans Havermann | 03/2021 |
| 5811 | (56*10^125535+583)/9 | 125536 | Robert Price | 08/2021 |
| 5812 | (23*10^125517-179)/3 | 125518 | Robert Price | 06/2022 |
| 5813 | 9*10^125516+29 | 125517 | Robert Price | 03/2022 |
| 5814 | 404*35^81280+23 | 125505 | Eric Chen | 05/2025 |
| 5815 | (88*10^125492-637)/9 | 125493 | Robert Price | 11/2020 |
| 5816 | 28958^21525+21525^28958 | 125474 | Hans Havermann | 02/2021 |
| 5819 | 2^416773-25 | 125462 | Lelio R Paula | 09/2015 |
| 5817 | (10^125482+7)/162685667/1639829194459 | 125462 | Alfred Reich | 07/2021 |
| 5818 | 26078^28409-28409^26078 | 125462 | Frank Doornink | 03/2024 |
| 5820 | 33889^5032+5032^33889 | 125449 | Hans Havermann | 03/2021 |
| 5821 | (289511#+292834)/(2^3*146417) | 125444 | Makoto Morimoto | 10/2017 |
| 5822 | (2861^36481+1)/(2861^191+1) | 125438 | Martin Hopf | 12/2023 |
| 5823 | (11*2^416691+1)/43 | 125436 | Lelio R Paula | 05/2014 |
| 5824 | (289511#+1896)/(2*3^3*79*780193*9911849) | 125434 | Makoto Morimoto | 06/2019 |
| 5825 | 2^416641-2*416641+1 | 125422 | Robert Price | 05/2018 |
| 5826 | 33392^5697+5697^33392 | 125409 | Hans Havermann | 03/2021 |
| 5827 | (21*2^416566-1)/17 | 125399 | Lelio R Paula | 05/2014 |
| 5828 | 2^416530+1870429 | 125389 | Enzo Doria | 05/2016 |
| 5829 | (56*10^125385+691)/9 | 125386 | Robert Price | 05/2019 |
| 5830 | 27953^28198+28198^27953 | 125381 | Norbert Schneider | 01/2021 |
| 5831 | 31074^10837+10837^31074 | 125381 | Hans Havermann | 03/2021 |
| 5832 | 33745^5194+5194^33745 | 125380 | Hans Havermann | 03/2021 |
| 5833 | 2^416490+1875109 | 125376 | Enzo Doria | 09/2016 |
| 5834 | 28360^26331+26331^28360 | 125365 | Hans Havermann | 03/2021 |
| 5835 | 2^416416-114929 | 125354 | Enzo Doria | 05/2015 |
| 5836 | 25805^28412-28412^25805 | 125346 | Frank Doornink | 03/2024 |
| 5837 | (77*10^125330-293)/9 | 125331 | Robert Price | 09/2019 |
| 5838 | (172*10^125292-1)/9 | 125294 | Serge Batalov | 12/2014 |
| 5839 | 2^416134+1865899 | 125269 | Enzo Doria | 03/2016 |
| 5840 | 153^57337-152 | 125264 | Norbert Schneider | 12/2018 |
| 5841 | (599*10^125224+13)/9 | 125226 | Robert Price | 02/2022 |
| 5842 | (9*2^415992+1)/13560845 | 125220 | Lelio R Paula | 05/2014 |
| 5843 | 30054^14657+14657^30054 | 125207 | Hans Havermann | 03/2021 |
| 5844 | (23^91943-1)/22 | 125201 | Robert Price | 01/2012 |
| 5845 | 2^415884-933075 | 125194 | Paul Bourdelais | 06/2021 |
| 5846 | 43125^27010-106 | 125185 | Enzo Doria | 08/2012 |
| 5847 | (38*10^125166+349)/9 | 125167 | Robert Price | 10/2018 |
| 5848 | 10^125166-5001 | 125166 | Robert Price | 12/2021 |
| 5849 | 2^415765-112603 | 125158 | Enzo Doria | 06/2014 |
| 5850 | 8*10^125088-13 | 125089 | Robert Price | 08/2019 |
| 5851 | (25*10^125076-13)/3 | 125077 | Robert Price | 09/2019 |
| 5852 | (11*10^125054+73)/3 | 125055 | Robert Price | 08/2021 |
| 5853 | (101^62383-1)/17542099700 | 125026 | Paul Vanderveen | 06/2025 |
| 5854 | (29*10^125021-113)/3 | 125022 | Robert Price | 10/2019 |
| 5855 | 2^415290-113591 | 125015 | Enzo Doria | 08/2014 |
| 5856 | 2^415276-460919 | 125011 | Enzo Doria | 06/2015 |
| 5857 | 2^415259+77243 | 125006 | Enzo Doria | 05/2016 |
| 5858 | (67*10^124990+77)/9 | 124991 | Robert Price | 10/2021 |
| 5859 | 2^415144-3683 | 124971 | Yves Minet | 10/2011 |
| 5860 | 2^415092+111546435 | 124956 | Paul Bourdelais | 10/2021 |
| 5861 | 31936^8173+8173^31936 | 124946 | Hans Havermann | 03/2021 |
| 5862 | 27458^28145-28145^27458 | 124927 | Frank Doornink | 03/2024 |
| 5863 | 5^178715-4 | 124917 | Tyler NeSmith | 07/2021 |
| 5864 | 29767^15700+15700^29767 | 124900 | Hans Havermann | 03/2021 |
| 5865 | (310^50131-1)/309 | 124892 | Tom Wu | 07/2024 |
| 5866 | 2^414874+79 | 124890 | Lelio R Paula | 01/2015 |
| 5867 | 25292^28361-28361^25292 | 124874 | Frank Doornink | 01/2024 |
| 5868 | (2^414765+7)/1389 | 124854 | Lelio R Paula | 05/2014 |
| 5869 | 2^414618+79459 | 124813 | Enzo Doria | 06/2016 |
| 5870 | (61*10^124809-1)/3 | 124811 | Robert Price | 01/2020 |
| 5871 | (235*29^85334+129)/28 | 124794 | Eric Chen | 06/2025 |
| 5872 | (29*10^124765-71)/3 | 124766 | Robert Price | 07/2021 |
| 5873 | 2^414432-1846709 | 124757 | Enzo Doria | 07/2015 |
| 5874 | 2*10^124751-51 | 124752 | Robert Price | 04/2018 |
| 5875 | (56*10^124735+367)/9 | 124736 | Robert Price | 06/2019 |
| 5876 | 27362^28111-28111^27362 | 124733 | Frank Doornink | 03/2024 |
| 5877 | (13*2^414274-1)/153 | 124708 | Lelio R Paula | 05/2014 |
| 5878 | (23*10^124690+37)/3 | 124691 | Robert Price | 02/2022 |
| 5879 | p(25046)#-p(25046+1) | 124675 | Henri Lifchitz | 11/2024 |
| 5880 | 56*10^124656-3 | 124658 | Robert Price | 03/2020 |
| 5881 | (7*10^124648+197)/3 | 124649 | Robert Price | 07/2018 |
| 5883 | 2^414032-5 | 124637 | Henri Lifchitz | 07/2006 |
| 5882 | 2^414032+1872331 | 124637 | Enzo Doria | 05/2016 |
| 5884 | 37373^2158+2158^37373 | 124604 | Hans Havermann | 03/2021 |
| 5885 | 29811^15112+15112^29811 | 124590 | Hans Havermann | 03/2021 |
| 5886 | (22^92791-3^92791)/19 | 124564 | Robert Price | 02/2025 |
| 5887 | F(596093)/36870605281541 | 124563 | Serge Batalov | 07/2024 |
| 5888 | 2^413781-2023 | 124561 | Riley Fisher | 09/2023 |
| 5889 | 14120^30009-30009^14120 | 124533 | Norbert Schneider | 02/2015 |
| 5890 | 29757^15296+15296^29757 | 124521 | Hans Havermann | 03/2021 |
| 5891 | 35056^3561+3561^35056 | 124504 | Hans Havermann | 03/2021 |
| 5892 | 40588^1167+1167^40588 | 124487 | Hans Havermann | 02/2021 |
| 5893 | (85*10^124485-49)/9 | 124486 | Robert Price | 12/2020 |
| 5894 | 64^68909-63^68909 | 124463 | Robert Price | 07/2013 |
| 5895 | 35016^3581+3581^35016 | 124448 | Hans Havermann | 03/2021 |
| 5896 | 2^413387+76253 | 124442 | Enzo Doria | 04/2016 |
| 5897 | 28749^21298+21298^28749 | 124436 | Hans Havermann | 03/2021 |
| 5898 | 2^413352+524287 | 124432 | Paul Underwood | 09/2018 |
| 5899 | 287117#+391613 | 124424 | Nicolas PALAU | 01/2017 |
| 5900 | (4*10^124420+83)/3 | 124421 | Robert Price | 02/2018 |
| 5901 | 34578^3965+3965^34578 | 124421 | Hans Havermann | 03/2021 |
| 5902 | (68*10^124392-329)/9 | 124393 | Robert Price | 03/2021 |
| 5903 | (27*2^413207-1)/108335 | 124385 | Lelio R Paula | 05/2014 |
| 5904 | 10^124383+58407 | 124384 | Patrick De Geest | 08/2021 |
| 5906 | 10^124383-8000001 | 124383 | Robert Price | 04/2021 |
| 5905 | 10^124383-5801 | 124383 | Patrick De Geest | 08/2021 |
| 5907 | 26091^28154-28154^26091 | 124342 | Frank Doornink | 03/2024 |
| 5908 | (41*10^124335-383)/9 | 124336 | Robert Price | 11/2018 |
| 5909 | (304*10^124329-43)/9 | 124331 | Robert Price | 02/2020 |
| 5910 | 34716^3811+3811^34716 | 124320 | Hans Havermann | 03/2021 |
| 5911 | 26892^28063-28063^26892 | 124309 | Frank Doornink | 03/2024 |
| 5912 | 2^412868-120599 | 124286 | Paul Bourdelais | 02/2012 |
| 5913 | 10^124248+899089 | 124249 | Patrick De Geest | 05/2021 |
| 5915 | 10^124248-1000001 | 124248 | Robert Price | 08/2020 |
| 5914 | 10^124248-501903 | 124248 | Patrick De Geest | 05/2021 |
| 5916 | 45^75145-2 | 124231 | Lelio R Paula | 08/2015 |
| 5917 | 29901^14272+14272^29901 | 124224 | Hans Havermann | 03/2021 |
| 5918 | 2^412645-112213 | 124219 | Enzo Doria | 06/2014 |
| 5919 | 29837^14500+14500^29837 | 124163 | Hans Havermann | 03/2021 |
| 5920 | 28074^26455+26455^28074 | 124158 | Hans Havermann | 03/2021 |
| 5921 | 954^41669-41669^954 | 124155 | Norman Luhn | 10/2024 |
| 5922 | 432^47093-47093^432 | 124113 | Norman Luhn | 10/2024 |
| 5923 | 2^412285+213317 | 124111 | Enzo Doria | 09/2023 |
| 5924 | (12^115001-1)/2530033 | 124101 | Paul Vanderveen | 06/2025 |
| 5925 | 2^412248+74611 | 124100 | Enzo Doria | 04/2016 |
| 5926 | (22*10^124096-13)/9 | 124097 | Robert Price | 06/2018 |
| 5927 | (455*10^124093+31)/9 | 124095 | Robert Price | 06/2021 |
| 5928 | 2^412192-3329 | 124083 | Yves Minet | 12/2014 |
| 5929 | (25*2^412191-1)/23 | 124082 | Lelio R Paula | 05/2014 |
| 5931 | (25*10^124076-67)/3 | 124077 | Robert Price | 06/2019 |
| 5930 | 28132^25735+25735^28132 | 124077 | Hans Havermann | 03/2021 |
| 5932 | F(593689) | 124074 | Henri Lifchitz | 01/2005 |
| 5933 | (11*2^412161+1)/19 | 124073 | Lelio R Paula | 05/2014 |
| 5934 | 1232^40143-40143^1232 | 124067 | Norman Luhn | 10/2024 |
| 5935 | 26372^28057-28057^26372 | 124045 | Frank Doornink | 03/2024 |
| 5936 | 27528^27937-27937^27528 | 124034 | Frank Doornink | 03/2024 |
| 5937 | 35364^3215+3215^35364 | 124028 | Hans Havermann | 03/2021 |
| 5939 | (266*10^124022-11)/3 | 124024 | Robert Price | 04/2020 |
| 5938 | 29987^13674+13674^29987 | 124024 | Hans Havermann | 03/2021 |
| 5940 | 2^411932-111546435 | 124004 | Paul Bourdelais | 10/2021 |
| 5941 | 2^411884-113279 | 123990 | Enzo Doria | 07/2014 |
| 5942 | (2^411832+1)/257 | 123972 | Lelio R Paula | 05/2014 |
| 5943 | (2^411833+2)/514 | 123972 | Stefano Morozzi | 03/2020 |
| 5944 | (26*10^123970-89)/9 | 123971 | Robert Price | 06/2018 |
| 5945 | 2^411790-1853531 | 123962 | Enzo Doria | 08/2015 |
| 5946 | (5^177337+1)/6 | 123953 | Paul Bourdelais | 11/2008 |
| 5947 | (101*10^123950+7)/9 | 123952 | Robert Price | 02/2022 |
| 5948 | 2^411711-113257 | 123938 | Enzo Doria | 07/2014 |
| 5949 | (23*2^411675-1)/3 | 123928 | Lelio R Paula | 05/2014 |
| 5950 | 36289^2598+2598^36289 | 123914 | Hans Havermann | 03/2021 |
| 5951 | (11*10^123899-179)/3 | 123900 | Robert Price | 09/2018 |
| 5952 | 32276^6879+6879^32276 | 123860 | Hans Havermann | 02/2021 |
| 5953 | 2^411325-351103 | 123822 | Enzo Doria | 06/2015 |
| 5954 | (646*10^123817+11)/9 | 123819 | Robert Price | 10/2021 |
| 5955 | 30738^10643+10643^30738 | 123784 | Hans Havermann | 03/2021 |
| 5956 | 31074^9607+9607^31074 | 123755 | Hans Havermann | 03/2021 |
| 5957 | 2^411052+1872481 | 123739 | Enzo Doria | 05/2016 |
| 5958 | 34365^3986+3986^34365 | 123733 | Hans Havermann | 03/2021 |
| 5959 | 2^410997+39 | 123723 | Lelio R Paula | 05/2014 |
| 5960 | (649^43987-1)/648 | 123700 | Michael Stocker | 05/2020 |
| 5961 | (148*10^123688-1)/3 | 123690 | Robert Price | 03/2020 |
| 5962 | 36825^2284+2284^36825 | 123684 | Hans Havermann | 03/2021 |
| 5963 | 29582^15171+15171^29582 | 123683 | Hans Havermann | 03/2021 |
| 5964 | 10^123671+3593037 | 123672 | Paul Bourdelais | 10/2021 |
| 5965 | 8*10^123657+87 | 123658 | Robert Price | 10/2019 |
| 5966 | 30505^11302+11302^30505 | 123642 | Hans Havermann | 03/2021 |
| 5967 | 29956^13401+13401^29956 | 123633 | Hans Havermann | 03/2021 |
| 5968 | 19*35^80065+19442 | 123628 | Eric Chen | 05/2025 |
| 5969 | 155^56438+154 | 123618 | Norbert Schneider | 01/2019 |
| 5970 | 2^410596-39 | 123602 | Lelio R Paula | 05/2014 |
| 5971 | (41*10^123600-221)/9 | 123601 | Robert Price | 10/2021 |
| 5972 | 28995^18302+18302^28995 | 123592 | Hans Havermann | 03/2021 |
| 5973 | 28302^23269+23269^28302 | 123589 | Hans Havermann | 03/2021 |
| 5974 | (41^76630+40)/37 | 123587 | Alfred Reich | 06/2024 |
| 5975 | 2^410540-115079 | 123585 | Enzo Doria | 06/2015 |
| 5976 | (7*10^123563+107)/3 | 123564 | Robert Price | 02/2018 |
| 5977 | 9*10^123549+89 | 123550 | Robert Price | 11/2019 |
| 5978 | (197*10^123545+7)/3 | 123547 | Robert Price | 12/2020 |
| 5979 | (3*2^410392-1)/9229 | 123537 | Lelio R Paula | 05/2014 |
| 5980 | 2^410342+212449 | 123526 | Enzo Doria | 08/2023 |
| 5981 | (29*10^123510+277)/9 | 123511 | Robert Price | 11/2021 |
| 5982 | 28118^24687+24687^28118 | 123508 | Hans Havermann | 03/2021 |
| 5983 | 39994^1225+1225^39994 | 123507 | Hans Havermann | 03/2021 |
| 5984 | 2^410206-113081 | 123485 | Enzo Doria | 07/2014 |
| 5985 | (25*2^410192+1)/10397 | 123478 | Lelio R Paula | 04/2014 |
| 5986 | 28974^18215+18215^28974 | 123442 | Hans Havermann | 03/2021 |
| 5987 | 28901^18618+18618^28901 | 123406 | Hans Havermann | 03/2021 |
| 5988 | 2^409909-189 | 123395 | Enzo Doria | 05/2014 |
| 5989 | 135^57922-57922^135 | 123394 | Norman Luhn | 10/2024 |
| 5990 | 2^409896-109043 | 123391 | Enzo Doria | 04/2014 |
| 5991 | 2^409890+75409 | 123390 | Enzo Doria | 04/2016 |
| 5992 | 81254^33+33^81254 | 123386 | Hans Havermann | 03/2021 |
| 5993 | 33463^4854+4854^33463 | 123348 | Hans Havermann | 03/2021 |
| 5994 | 34061^4182+4182^34061 | 123348 | Hans Havermann | 03/2021 |
| 5995 | 133^58076-2 | 123345 | Lelio R Paula | 10/2017 |
| 5996 | L(2*409661)%(2^409661) | 123320 | Henri Lifchitz | 06/2025 |
| 5997 | F(590041) | 123311 | Henri Lifchitz | 01/2005 |
| 5998 | (82*10^123299+377)/9 | 123300 | Robert Price | 03/2022 |
| 5999 | 2^409566-113501 | 123292 | Enzo Doria | 08/2014 |
| 6000 | 2^409533+77747 | 123282 | Enzo Doria | 05/2016 |
