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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See the Latest PRPs
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| Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
| 6751 | 9*10^118282+29 | 118283 | Robert Price | 03/2022 |
| 6752 | (9*35^76602+12877)/34 | 118279 | Eric Chen | 05/2025 |
| 6753 | (238*10^118265-1)/3 | 118267 | Robert Price | 04/2020 |
| 6755 | (53*10^118216+1)/9 | 118217 | Serge Batalov | 11/2010 |
| 6754 | (2^392707+1710)/2 | 118217 | Stefano Morozzi | 09/2020 |
| 6756 | (7*2^392697+1)/15 | 118214 | Renaud Lifchitz | 03/2011 |
| 6757 | Phi(89679,-100) | 118192 | Henri Lifchitz | 12/2025 |
| 6758 | (157^53819-1)/156 | 118179 | Alexander Zhirkov | 06/2016 |
| 6759 | (2^392567+2750)/2 | 118175 | Stefano Morozzi | 01/2021 |
| 6760 | 55*10^118172+3 | 118174 | Robert Price | 07/2022 |
| 6761 | (19*2^392551+1)/3 | 118171 | Lelio R Paula | 04/2014 |
| 6762 | 27185^22222+22222^27185 | 118168 | Hans Havermann | 01/2021 |
| 6763 | 2^392516-29219 | 118160 | Enzo Doria | 07/2015 |
| 6764 | 66*10^118155+7 | 118157 | Robert Price | 07/2020 |
| 6765 | Phi(177231,10) | 118152 | Maksym Voznyy | 09/2015 |
| 6766 | 2^392413-112123 | 118129 | Enzo Doria | 06/2014 |
| 6767 | 27491^19798+19798^27491 | 118119 | Hans Havermann | 02/2021 |
| 6768 | (49*10^118109-319)/9 | 118110 | Robert Price | 10/2021 |
| 6769 | (2^392342+5)/27 | 118106 | Lelio R Paula | 04/2014 |
| 6770 | (2^392333+1782)/2 | 118104 | Stefano Morozzi | 01/2021 |
| 6771 | 2^392300-1841429 | 118095 | Enzo Doria | 06/2015 |
| 6772 | 3*2^392260-5 | 118083 | Jon Grantham | 07/2023 |
| 6773 | 2^392220+75241 | 118070 | Enzo Doria | 04/2016 |
| 6774 | 27836^17409+17409^27836 | 118047 | Hans Havermann | 02/2021 |
| 6775 | (13^118026)%(10^118026) | 118026 | Henri Lifchitz | 05/2025 |
| 6776 | 10^118009+664447 | 118010 | Patrick De Geest | 07/2018 |
| 6777 | 10^118009-20001 | 118009 | Robert Price | 01/2018 |
| 6778 | (14*10^117991+61)/3 | 117992 | Robert Price | 12/2018 |
| 6779 | 2^391933+5897 | 117984 | Yves Minet | 02/2011 |
| 6780 | 2^391912-1849259 | 117978 | Enzo Doria | 08/2015 |
| 6781 | (2*34^77029+1043)/11 | 117968 | Eric Chen | 08/2023 |
| 6782 | 5*2^391836-3 | 117956 | Jon Grantham | 07/2023 |
| 6783 | 28357^14440+14440^28357 | 117953 | Hans Havermann | 02/2021 |
| 6784 | (2^391812+5)/14181 | 117944 | Lelio R Paula | 04/2014 |
| 6785 | 85^61124-61124^85 | 117934 | Norman Luhn | 09/2024 |
| 6786 | (7*10^117930-79)/9 | 117930 | Robert Price | 01/2021 |
| 6787 | 27531^19168+19168^27531 | 117904 | Hans Havermann | 02/2021 |
| 6788 | (46*10^117902+683)/9 | 117903 | Robert Price | 03/2019 |
| 6789 | 26349^26668-26668^26349 | 117893 | Frank Doornink | 03/2024 |
| 6790 | 27670^18189+18189^27670 | 117869 | Hans Havermann | 02/2021 |
| 6791 | (7*2^391521+1)/285 | 117858 | Lelio R Paula | 04/2014 |
| 6792 | (56*10^117856+583)/9 | 117857 | Robert Price | 08/2021 |
| 6793 | 32169^4606+4606^32169 | 117846 | Hans Havermann | 02/2021 |
| 6794 | (71*10^117803-143)/9 | 117804 | Robert Price | 10/2021 |
| 6795 | 2^391324+90901 | 117801 | Yves Minet | 02/2011 |
| 6796 | 2^391301-1859923 | 117794 | Enzo Doria | 03/2016 |
| 6797 | 2^391261-4131 | 117782 | Yves Minet | 02/2018 |
| 6798 | (2^391211+554)/2 | 117766 | Stefano Morozzi | 09/2020 |
| 6799 | 816^40445-40445^816 | 117764 | Norman Luhn | 09/2024 |
| 6800 | 38434^1157+1157^38434 | 117737 | Hans Havermann | 01/2021 |
| 6801 | (2^391115-7)/11791 | 117734 | Lelio R Paula | 04/2014 |
| 6802 | (85*10^117719+473)/9 | 117720 | Robert Price | 01/2020 |
| 6803 | (2^391049+582)/2 | 117718 | Stefano Morozzi | 09/2020 |
| 6804 | (21*23^86445-197)/22 | 117715 | Eric Chen | 08/2023 |
| 6805 | 31083^6122+6122^31083 | 117709 | Hans Havermann | 02/2021 |
| 6806 | 2^390960+1880881 | 117691 | Enzo Doria | 11/2016 |
| 6807 | (71*10^117685+91)/9 | 117686 | Robert Price | 04/2022 |
| 6809 | 2^390897-1860553 | 117672 | Enzo Doria | 11/2015 |
| 6808 | (61*10^117671+47)/9 | 117672 | Robert Price | 07/2022 |
| 6810 | 2^390889-115003 | 117670 | Enzo Doria | 06/2015 |
| 6811 | 12^109010+35 | 117642 | Riley Fisher | 08/2023 |
| 6812 | 2^390779-30337 | 117637 | Paul Bourdelais | 02/2012 |
| 6813 | (2^390735+378)/2 | 117623 | Stefano Morozzi | 02/2021 |
| 6814 | 11^112916-780 | 117590 | Enzo Doria | 12/2012 |
| 6815 | 27641^17916+17916^27641 | 117564 | Hans Havermann | 02/2021 |
| 6816 | 27906^16321+16321^27906 | 117561 | Hans Havermann | 02/2021 |
| 6817 | 27294^20275+20275^27294 | 117555 | Hans Havermann | 02/2021 |
| 6818 | (2^390473+1002)/2 | 117544 | Stefano Morozzi | 09/2020 |
| 6819 | 35912^1875+1875^35912 | 117541 | Hans Havermann | 02/2021 |
| 6820 | (16^97613-5^97613)/11 | 117537 | Robert Price | 07/2013 |
| 6821 | (2^390438+1774)/2 | 117534 | Stefano Morozzi | 01/2021 |
| 6822 | (2^390418+1722)/2 | 117528 | Stefano Morozzi | 09/2020 |
| 6823 | (2^390403+654)/2 | 117523 | Stefano Morozzi | 09/2020 |
| 6824 | (2^390343+2246)/2 | 117505 | Stefano Morozzi | 01/2021 |
| 6825 | 28043^15478+15478^28043 | 117493 | Hans Havermann | 02/2021 |
| 6826 | Phi(247237,3) | 117487 | Henri Lifchitz | 12/2025 |
| 6827 | (17*2^390272+1)/1983 | 117482 | Lelio R Paula | 04/2014 |
| 6828 | 37077^1474+1474^37077 | 117479 | Hans Havermann | 01/2021 |
| 6829 | 31^78759-30 | 117459 | Theodore Burton | 02/2007 |
| 6830 | (2^390176+1222)/2 | 117455 | Stefano Morozzi | 09/2020 |
| 6831 | (2^390133+1242)/2 | 117442 | Stefano Morozzi | 09/2020 |
| 6832 | (2^390013+2634)/2 | 117406 | Stefano Morozzi | 09/2020 |
| 6833 | 3*10^117402+61 | 117403 | Robert Price | 09/2020 |
| 6834 | 2^389998+37 | 117402 | Lelio R Paula | 03/2013 |
| 6835 | (2^389977+314)/2 | 117395 | Stefano Morozzi | 09/2020 |
| 6836 | (2^389921+342)/2 | 117378 | Stefano Morozzi | 01/2021 |
| 6837 | 71830^43+43^71830 | 117333 | Hans Havermann | 01/2021 |
| 6838 | (2^389768+1582)/2 | 117332 | Stefano Morozzi | 09/2020 |
| 6839 | 33802^2951+2951^33802 | 117292 | Hans Havermann | 02/2021 |
| 6840 | (2^561185)%L(561185) | 117281 | Henri Lifchitz | 05/2025 |
| 6841 | 26789^23866+23866^26789 | 117277 | Hans Havermann | 02/2021 |
| 6842 | 29^80192-1*80192^29 | 117273 | Dylan Delgado | 12/2019 |
| 6843 | (101*10^117260+7)/9 | 117262 | Robert Price | 02/2022 |
| 6844 | (13*10^117249+161)/3 | 117250 | Robert Price | 11/2018 |
| 6845 | 2^389478+43 | 117245 | Lelio R Paula | 03/2013 |
| 6846 | (298*10^117229-7)/3 | 117231 | Robert Price | 06/2020 |
| 6847 | (2^389416+342)/2 | 117226 | Stefano Morozzi | 01/2021 |
| 6848 | (29*2^389351-1)/9 | 117207 | Lelio R Paula | 04/2014 |
| 6849 | 5*10^117205+23 | 117206 | Robert Price | 03/2019 |
| 6850 | (2^389341-7)/3865 | 117200 | Lelio R Paula | 03/2014 |
| 6851 | 27272^19827+19827^27272 | 117195 | Hans Havermann | 01/2021 |
| 6852 | (2^389276+2650)/2 | 117184 | Stefano Morozzi | 09/2020 |
| 6853 | (844*10^117175-7)/9 | 117177 | Robert Price | 05/2021 |
| 6854 | 10^117142+209223 | 117143 | Patrick De Geest | 04/2018 |
| 6856 | 10^117142-1000000001 | 117142 | Robert Price | 03/2018 |
| 6855 | 10^117142-966057 | 117142 | Patrick De Geest | 04/2018 |
| 6857 | 10^117135+360577 | 117136 | Patrick De Geest | 07/2018 |
| 6858 | 10^117135-401 | 117135 | Robert Price | 01/2018 |
| 6859 | 26415^26488-26488^26415 | 117126 | Norbert Schneider | 05/2021 |
| 6860 | 4*10^117123+79 | 117124 | Robert Price | 08/2018 |
| 6861 | 2^389033-12797413 | 117111 | Enzo Doria | 04/2016 |
| 6862 | (2^388987+2634)/2 | 117097 | Stefano Morozzi | 09/2020 |
| 6863 | 2^388960-109505 | 117089 | Enzo Doria | 04/2014 |
| 6864 | 7*10^117082-57 | 117083 | Robert Price | 06/2020 |
| 6865 | 791^40398-40398^791 | 117081 | Norman Luhn | 09/2024 |
| 6866 | (2^388928-5)/569 | 117077 | Lelio R Paula | 03/2014 |
| 6867 | 2^388888-1529 | 117067 | Yves Minet | 01/2013 |
| 6868 | 10^117059+28879 | 117060 | Patrick De Geest | 05/2016 |
| 6869 | (10^117059-71)/1 | 117059 | Serge Batalov | 12/2014 |
| 6870 | (2^388854+3630)/2 | 117057 | Stefano Morozzi | 09/2020 |
| 6871 | (2^388842+2098)/2 | 117053 | Stefano Morozzi | 09/2020 |
| 6872 | (2^388789+3150)/2 | 117037 | Stefano Morozzi | 09/2020 |
| 6873 | (2^388748+378)/2 | 117025 | Stefano Morozzi | 02/2021 |
| 6874 | (693^41189-1)/692 | 117005 | Michael Stocker | 05/2020 |
| 6875 | (26*10^116999-503)/9 | 117000 | Robert Price | 07/2018 |
| 6876 | 20^89917-21 | 116985 | Anonymous | 09/2024 |
| 6877 | (2^388609+1554)/2 | 116983 | Stefano Morozzi | 09/2020 |
| 6878 | 38496^1093+1093^38496 | 116975 | Hans Havermann | 02/2021 |
| 6879 | 3^245154-6256 | 116969 | Enzo Doria | 05/2014 |
| 6880 | 5*10^116966-43 | 116967 | Robert Price | 01/2019 |
| 6881 | (748^40699-1)/747 | 116963 | Tom Wu | 08/2025 |
| 6882 | 2^388536-113495 | 116961 | Enzo Doria | 08/2014 |
| 6883 | (2^388512+382)/2 | 116954 | Stefano Morozzi | 02/2021 |
| 6884 | (8*32^77701+271)/31 | 116952 | Eric Chen | 11/2023 |
| 6885 | 2^388469-43 | 116941 | Lelio R Paula | 03/2013 |
| 6886 | 27417^18416+18416^27417 | 116939 | Hans Havermann | 02/2021 |
| 6887 | (2^388438+1842)/2 | 116932 | Stefano Morozzi | 02/2021 |
| 6888 | (7*2^388372-1)/111 | 116911 | Lelio R Paula | 04/2014 |
| 6889 | (7*2^388335-1)/25 | 116900 | Lelio R Paula | 04/2014 |
| 6890 | 2^388180+93 | 116854 | Donovan Johnson | 07/2008 |
| 6891 | (2^388167+2510)/2 | 116850 | Stefano Morozzi | 09/2020 |
| 6892 | (85*10^116842+293)/9 | 116843 | Robert Price | 12/2019 |
| 6893 | 35296^2043+2043^35296 | 116840 | Hans Havermann | 02/2021 |
| 6894 | (2^388081+7)/1179 | 116821 | Lelio R Paula | 03/2014 |
| 6895 | 38633^1056+1056^38633 | 116814 | Hans Havermann | 02/2021 |
| 6896 | 2^387946-113261 | 116784 | Enzo Doria | 07/2014 |
| 6897 | 28*36^75009+305 | 116739 | Eric Chen | 12/2022 |
| 6898 | 28363^13056+13056^28363 | 116737 | Hans Havermann | 02/2021 |
| 6899 | 2^387745+75557 | 116723 | Enzo Doria | 04/2016 |
| 6900 | (29*10^116719+313)/9 | 116720 | Robert Price | 04/2021 |
| 6901 | 29622^8699+8699^29622 | 116695 | Hans Havermann | 02/2021 |
| 6902 | (206*10^116687-17)/9 | 116689 | Robert Price | 01/2020 |
| 6903 | (7*10^116684+179)/3 | 116685 | Robert Price | 09/2018 |
| 6904 | 2^387554+71455 | 116666 | Enzo Doria | 04/2016 |
| 6905 | (602*10^116647-71)/9 | 116649 | Robert Price | 12/2021 |
| 6906 | 3^244461-10 | 116638 | Tyler NeSmith | 09/2022 |
| 6907 | (2^387447+78557)/365 | 116631 | Lelio R Paula | 12/2014 |
| 6908 | (2*10^116620+43)/9 | 116620 | Serge Batalov | 11/2022 |
| 6909 | (19*10^116617+287)/9/12893 | 116614 | Alfred Reich | 11/2022 |
| 6910 | (145*10^116610-1)/9 | 116612 | Serge Batalov | 12/2014 |
| 6911 | (25*10^116601-331)/9 | 116602 | Robert Price | 08/2018 |
| 6912 | 25791^26428-26428^25791 | 116587 | Frank Doornink | 03/2024 |
| 6914 | (17*2^387284-1)/59 | 116584 | Lelio R Paula | 04/2014 |
| 6913 | (2^387284+3726)/2 | 116584 | Stefano Morozzi | 09/2020 |
| 6915 | 2^387211+111546435 | 116563 | Paul Bourdelais | 10/2021 |
| 6916 | 10^116557+987654321 | 116558 | Robert Price | 12/2019 |
| 6917 | 10^116557+9141 | 116558 | Patrick De Geest | 02/2020 |
| 6918 | 10^116557-609431 | 116557 | Patrick De Geest | 02/2020 |
| 6919 | 209^50234-50234^209 | 116551 | Norman Luhn | 09/2024 |
| 6920 | (28*10^116546+41)/3 | 116547 | Robert Price | 07/2021 |
| 6921 | (2^387123+1814)/2 | 116536 | Stefano Morozzi | 02/2021 |
| 6922 | (2^387076+2046)/2 | 116522 | Stefano Morozzi | 09/2020 |
| 6923 | (2^387073+2570)/2 | 116521 | Stefano Morozzi | 09/2020 |
| 6924 | (7*10^116514-1)/3 | 116515 | Robert Price | 08/2022 |
| 6925 | (26*32^77406-390071011)/31 | 116508 | Eric Chen | 11/2023 |
| 6926 | 28846^10931+10931^28846 | 116500 | Hans Havermann | 02/2021 |
| 6927 | 10^116496+3593037 | 116497 | Paul Bourdelais | 10/2021 |
| 6928 | 272^47851-47851^272 | 116497 | Norman Luhn | 09/2024 |
| 6929 | (31*2^386968+1)/7 | 116490 | Lelio R Paula | 03/2014 |
| 6930 | (944^39157+1)/945 | 116489 | Jinyuan Wang | 12/2024 |
| 6931 | 998^38840+997 | 116487 | Alfred Reich | 03/2026 |
| 6932 | 2^386947+1869143 | 116483 | Enzo Doria | 05/2016 |
| 6934 | (30^78857-1)/29 | 116480 | Robert Price | 12/2011 |
| 6933 | Phi(78857,5#) | 116480 | Henri Lifchitz | 12/2025 |
| 6935 | (2^386903-3)/5 | 116469 | Lelio R Paula | 03/2014 |
| 6936 | 28107^13892+13892^28107 | 116441 | Hans Havermann | 02/2021 |
| 6937 | 29110^9957+9957^29110 | 116386 | Hans Havermann | 02/2021 |
| 6938 | 26469^24838+24838^26469 | 116335 | Hans Havermann | 01/2021 |
| 6939 | 2^386389-1864783 | 116315 | Enzo Doria | 03/2016 |
| 6940 | 993^38799+992 | 116279 | Alfred Reich | 03/2026 |
| 6941 | (8*32^77250-163)/31 | 116273 | Eric Chen | 11/2023 |
| 6942 | (31*2^386231-1)/1711 | 116266 | Lelio R Paula | 03/2014 |
| 6943 | 297^47012+47012^297 | 116250 | Norbert Schneider | 07/2018 |
| 6944 | (35*10^116223-341)/9 | 116224 | Robert Price | 08/2021 |
| 6945 | (2^386087-5)/40959 | 116220 | Lelio R Paula | 03/2014 |
| 6946 | (2^386054+714)/2 | 116214 | Stefano Morozzi | 09/2020 |
| 6947 | (10^116201+7)/39623 | 116197 | Alfred Reich | 06/2021 |
| 6948 | 2^385969-823 | 116189 | Yves Minet | 05/2012 |
| 6949 | 57^66162+2 | 116173 | Lelio R Paula | 08/2013 |
| 6950 | 2^385854+75049 | 116154 | Enzo Doria | 04/2016 |
| 6951 | (2^385832+2590)/2 | 116147 | Stefano Morozzi | 09/2020 |
| 6952 | 2^385775-109587 | 116130 | Enzo Doria | 04/2014 |
| 6953 | (14*10^116112-101)/3 | 116113 | Robert Price | 02/2019 |
| 6954 | Phi(236354,10)/24817171 | 116109 | Makoto Kamada | 08/2019 |
| 6955 | 3*10^116107+23 | 116108 | Robert Price | 03/2022 |
| 6956 | 28729^10990+10990^28729 | 116094 | Hans Havermann | 02/2021 |
| 6957 | 2^385622+71839 | 116084 | Enzo Doria | 04/2016 |
| 6959 | 2^385564+781 | 116067 | Lelio R Paula | 01/2012 |
| 6958 | (2^385565+1562)/2 | 116067 | Stefano Morozzi | 09/2020 |
| 6960 | (2^385563+378)/2 | 116066 | Stefano Morozzi | 02/2021 |
| 6961 | (2^385557+2214)/2 | 116064 | Stefano Morozzi | 09/2020 |
| 6962 | 29431^8776+8776^29431 | 116056 | Hans Havermann | 01/2021 |
| 6963 | (266*10^116024-17)/3 | 116026 | Robert Price | 07/2020 |
| 6964 | 30263^6820+6820^30263 | 116022 | Hans Havermann | 02/2021 |
| 6965 | 2^385410+71893 | 116020 | Enzo Doria | 04/2016 |
| 6966 | 38225^1084+1084^38225 | 116014 | Hans Havermann | 02/2021 |
| 6967 | 26548^23433+23433^26548 | 116011 | Hans Havermann | 02/2021 |
| 6968 | Phi(183801,-9) | 115960 | Henri Lifchitz | 12/2025 |
| 6969 | 12^107422-11 | 115928 | Riley Fisher | 12/2023 |
| 6970 | (25*2^385091+1)/27 | 115924 | Lelio R Paula | 04/2014 |
| 6971 | (11*10^115910-131)/3 | 115911 | Robert Price | 09/2018 |
| 6972 | 2^384953-111943 | 115883 | Paul Bourdelais | 02/2012 |
| 6973 | 43^70942-2 | 115882 | Lelio R Paula | 04/2014 |
| 6974 | (94*10^115879-7)/3 | 115881 | Robert Price | 03/2020 |
| 6975 | 7*10^115863+3 | 115864 | Robert Price | 08/2015 |
| 6976 | 2^384834+93 | 115847 | Donovan Johnson | 07/2008 |
| 6977 | 2^384809+71297 | 115840 | Enzo Doria | 04/2016 |
| 6978 | (55*10^115829+323)/9 | 115830 | Robert Price | 10/2021 |
| 6979 | (7*2^384759-1)/5 | 115825 | Lelio R Paula | 04/2014 |
| 6980 | 31348^4951+4951^31348 | 115822 | Hans Havermann | 02/2021 |
| 6981 | (793*10^115810+53)/9 | 115812 | Robert Price | 01/2022 |
| 6982 | (71*10^115810-17)/9 | 115811 | Ray Chandler | 08/2011 |
| 6983 | (97*10^115794-1)/3 | 115796 | Serge Batalov | 12/2014 |
| 6984 | 31115^5266+5266^31115 | 115794 | Hans Havermann | 02/2021 |
| 6985 | 2*10^115784-27 | 115785 | Robert Price | 05/2018 |
| 6986 | 10^115773+126739 | 115774 | Patrick De Geest | 04/2018 |
| 6988 | 10^115773-1000000001 | 115773 | Robert Price | 03/2018 |
| 6987 | 10^115773-396221 | 115773 | Patrick De Geest | 04/2018 |
| 6989 | (2^384582+778)/2 | 115771 | Stefano Morozzi | 09/2020 |
| 6990 | 30537^6178+6178^30537 | 115762 | Hans Havermann | 01/2021 |
| 6991 | 2^384530+1874305 | 115756 | Enzo Doria | 06/2016 |
| 6992 | (3*2^384524-1)/7631 | 115750 | Lelio R Paula | 03/2014 |
| 6993 | 28275^12406+12406^28275 | 115748 | Hans Havermann | 01/2021 |
| 6994 | (44*10^115697-413)/9 | 115698 | Robert Price | 03/2019 |
| 6995 | 31408^4825+4825^31408 | 115692 | Hans Havermann | 02/2021 |
| 6996 | (2^384317+1026)/2 | 115691 | Stefano Morozzi | 09/2020 |
| 6997 | 2^384312+81091 | 115690 | Yves Minet | 02/2010 |
| 6998 | (2^384265+2150)/2 | 115675 | Stefano Morozzi | 09/2020 |
| 6999 | (2^384246+2182)/2 | 115670 | Stefano Morozzi | 09/2020 |
| 7000 | (4*10^115668-79)/3 | 115669 | Robert Price | 02/2018 |
