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
Search by form
Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
5751 | (10^117059-71)/1 | 117059 | Serge Batalov | 12/2014 |
5752 | (2^388854+3630)/2 | 117057 | Stefano Morozzi | 09/2020 |
5753 | (2^388842+2098)/2 | 117053 | Stefano Morozzi | 09/2020 |
5754 | (2^388789+3150)/2 | 117037 | Stefano Morozzi | 09/2020 |
5755 | (2^388748+378)/2 | 117025 | Stefano Morozzi | 02/2021 |
5756 | (693^41189-1)/692 | 117005 | Michael Stocker | 05/2020 |
5757 | (26*10^116999-503)/9 | 117000 | Robert Price | 07/2018 |
5758 | 20^89917-21 | 116985 | Anonymous | 09/2024 |
5759 | (2^388609+1554)/2 | 116983 | Stefano Morozzi | 09/2020 |
5760 | 38496^1093+1093^38496 | 116975 | Hans Havermann | 02/2021 |
5761 | 3^245154-6256 | 116969 | Enzo Doria | 05/2014 |
5762 | 5*10^116966-43 | 116967 | Robert Price | 01/2019 |
5763 | 2^388536-113495 | 116961 | Enzo Doria | 08/2014 |
5764 | (2^388512+382)/2 | 116954 | Stefano Morozzi | 02/2021 |
5765 | (8*32^77701+271)/31 | 116952 | Eric Chen | 11/2023 |
5766 | 2^388469-43 | 116941 | Lelio R Paula | 03/2013 |
5767 | 27417^18416+18416^27417 | 116939 | Hans Havermann | 02/2021 |
5768 | (2^388438+1842)/2 | 116932 | Stefano Morozzi | 02/2021 |
5769 | (7*2^388372-1)/111 | 116911 | Lelio R Paula | 04/2014 |
5770 | (7*2^388335-1)/25 | 116900 | Lelio R Paula | 04/2014 |
5771 | 2^388180+93 | 116854 | Donovan Johnson | 07/2008 |
5772 | (2^388167+2510)/2 | 116850 | Stefano Morozzi | 09/2020 |
5773 | (85*10^116842+293)/9 | 116843 | Robert Price | 12/2019 |
5774 | 35296^2043+2043^35296 | 116840 | Hans Havermann | 02/2021 |
5775 | (2^388081+7)/1179 | 116821 | Lelio R Paula | 03/2014 |
5776 | 38633^1056+1056^38633 | 116814 | Hans Havermann | 02/2021 |
5777 | 2^387946-113261 | 116784 | Enzo Doria | 07/2014 |
5778 | 28*36^75009+305 | 116739 | Eric Chen | 12/2022 |
5779 | 28363^13056+13056^28363 | 116737 | Hans Havermann | 02/2021 |
5780 | 2^387745+75557 | 116723 | Enzo Doria | 04/2016 |
5781 | (29*10^116719+313)/9 | 116720 | Robert Price | 04/2021 |
5782 | 29622^8699+8699^29622 | 116695 | Hans Havermann | 02/2021 |
5783 | (206*10^116687-17)/9 | 116689 | Robert Price | 01/2020 |
5784 | (7*10^116684+179)/3 | 116685 | Robert Price | 09/2018 |
5785 | 2^387554+71455 | 116666 | Enzo Doria | 04/2016 |
5786 | (602*10^116647-71)/9 | 116649 | Robert Price | 12/2021 |
5787 | 3^244461-10 | 116638 | Tyler NeSmith | 09/2022 |
5788 | (2^387447+78557)/365 | 116631 | Lelio R Paula | 12/2014 |
5789 | (2*10^116620+43)/9 | 116620 | Serge Batalov | 11/2022 |
5790 | (19*10^116617+287)/9/12893 | 116614 | Alfred Reich | 11/2022 |
5791 | (145*10^116610-1)/9 | 116612 | Serge Batalov | 12/2014 |
5792 | (25*10^116601-331)/9 | 116602 | Robert Price | 08/2018 |
5793 | 25791^26428-26428^25791 | 116587 | Frank Doornink | 03/2024 |
5795 | (17*2^387284-1)/59 | 116584 | Lelio R Paula | 04/2014 |
5794 | (2^387284+3726)/2 | 116584 | Stefano Morozzi | 09/2020 |
5796 | 2^387211+111546435 | 116563 | Paul Bourdelais | 10/2021 |
5797 | 10^116557+987654321 | 116558 | Robert Price | 12/2019 |
5798 | 10^116557+9141 | 116558 | Patrick De Geest | 02/2020 |
5799 | 10^116557-609431 | 116557 | Patrick De Geest | 02/2020 |
5800 | 209^50234-50234^209 | 116551 | Norman Luhn | 09/2024 |
5801 | (28*10^116546+41)/3 | 116547 | Robert Price | 07/2021 |
5802 | (2^387123+1814)/2 | 116536 | Stefano Morozzi | 02/2021 |
5803 | (2^387076+2046)/2 | 116522 | Stefano Morozzi | 09/2020 |
5804 | (2^387073+2570)/2 | 116521 | Stefano Morozzi | 09/2020 |
5805 | (7*10^116514-1)/3 | 116515 | Robert Price | 08/2022 |
5806 | (26*32^77406-390071011)/31 | 116508 | Eric Chen | 11/2023 |
5807 | 28846^10931+10931^28846 | 116500 | Hans Havermann | 02/2021 |
5808 | 10^116496+3593037 | 116497 | Paul Bourdelais | 10/2021 |
5809 | 272^47851-47851^272 | 116497 | Norman Luhn | 09/2024 |
5810 | (31*2^386968+1)/7 | 116490 | Lelio R Paula | 03/2014 |
5811 | 2^386947+1869143 | 116483 | Enzo Doria | 05/2016 |
5812 | (30^78857-1)/29 | 116480 | Robert Price | 12/2011 |
5813 | (2^386903-3)/5 | 116469 | Lelio R Paula | 03/2014 |
5814 | 28107^13892+13892^28107 | 116441 | Hans Havermann | 02/2021 |
5815 | 29110^9957+9957^29110 | 116386 | Hans Havermann | 02/2021 |
5816 | 26469^24838+24838^26469 | 116335 | Hans Havermann | 01/2021 |
5817 | 2^386389-1864783 | 116315 | Enzo Doria | 03/2016 |
5818 | (8*32^77250-163)/31 | 116273 | Eric Chen | 11/2023 |
5819 | (31*2^386231-1)/1711 | 116266 | Lelio R Paula | 03/2014 |
5820 | 297^47012+47012^297 | 116250 | Norbert Schneider | 07/2018 |
5821 | (35*10^116223-341)/9 | 116224 | Robert Price | 08/2021 |
5822 | (2^386087-5)/40959 | 116220 | Lelio R Paula | 03/2014 |
5823 | (2^386054+714)/2 | 116214 | Stefano Morozzi | 09/2020 |
5824 | (10^116201+7)/39623 | 116197 | Alfred Reich | 06/2021 |
5825 | 2^385969-823 | 116189 | Yves Minet | 05/2012 |
5826 | 57^66162+2 | 116173 | Lelio R Paula | 08/2013 |
5827 | 2^385854+75049 | 116154 | Enzo Doria | 04/2016 |
5828 | (2^385832+2590)/2 | 116147 | Stefano Morozzi | 09/2020 |
5829 | 2^385775-109587 | 116130 | Enzo Doria | 04/2014 |
5830 | (14*10^116112-101)/3 | 116113 | Robert Price | 02/2019 |
5831 | Phi(236354,10)/24817171 | 116109 | Makoto Kamada | 08/2019 |
5832 | 3*10^116107+23 | 116108 | Robert Price | 03/2022 |
5833 | 28729^10990+10990^28729 | 116094 | Hans Havermann | 02/2021 |
5834 | 2^385622+71839 | 116084 | Enzo Doria | 04/2016 |
5836 | 2^385564+781 | 116067 | Lelio R Paula | 01/2012 |
5835 | (2^385565+1562)/2 | 116067 | Stefano Morozzi | 09/2020 |
5837 | (2^385563+378)/2 | 116066 | Stefano Morozzi | 02/2021 |
5838 | (2^385557+2214)/2 | 116064 | Stefano Morozzi | 09/2020 |
5839 | 29431^8776+8776^29431 | 116056 | Hans Havermann | 01/2021 |
5840 | (266*10^116024-17)/3 | 116026 | Robert Price | 07/2020 |
5841 | 30263^6820+6820^30263 | 116022 | Hans Havermann | 02/2021 |
5842 | 2^385410+71893 | 116020 | Enzo Doria | 04/2016 |
5843 | 38225^1084+1084^38225 | 116014 | Hans Havermann | 02/2021 |
5844 | 26548^23433+23433^26548 | 116011 | Hans Havermann | 02/2021 |
5845 | 12^107422-11 | 115928 | Riley Fisher | 12/2023 |
5846 | (25*2^385091+1)/27 | 115924 | Lelio R Paula | 04/2014 |
5847 | (11*10^115910-131)/3 | 115911 | Robert Price | 09/2018 |
5848 | 2^384953-111943 | 115883 | Paul Bourdelais | 02/2012 |
5849 | 43^70942-2 | 115882 | Lelio R Paula | 04/2014 |
5850 | (94*10^115879-7)/3 | 115881 | Robert Price | 03/2020 |
5851 | 7*10^115863+3 | 115864 | Robert Price | 08/2015 |
5852 | 2^384834+93 | 115847 | Donovan Johnson | 07/2008 |
5853 | 2^384809+71297 | 115840 | Enzo Doria | 04/2016 |
5854 | (55*10^115829+323)/9 | 115830 | Robert Price | 10/2021 |
5855 | (7*2^384759-1)/5 | 115825 | Lelio R Paula | 04/2014 |
5856 | 31348^4951+4951^31348 | 115822 | Hans Havermann | 02/2021 |
5857 | (793*10^115810+53)/9 | 115812 | Robert Price | 01/2022 |
5858 | (71*10^115810-17)/9 | 115811 | Ray Chandler | 08/2011 |
5859 | (97*10^115794-1)/3 | 115796 | Serge Batalov | 12/2014 |
5860 | 31115^5266+5266^31115 | 115794 | Hans Havermann | 02/2021 |
5861 | 2*10^115784-27 | 115785 | Robert Price | 05/2018 |
5862 | 10^115773+126739 | 115774 | Patrick De Geest | 04/2018 |
5864 | 10^115773-1000000001 | 115773 | Robert Price | 03/2018 |
5863 | 10^115773-396221 | 115773 | Patrick De Geest | 04/2018 |
5865 | (2^384582+778)/2 | 115771 | Stefano Morozzi | 09/2020 |
5866 | 30537^6178+6178^30537 | 115762 | Hans Havermann | 01/2021 |
5867 | 2^384530+1874305 | 115756 | Enzo Doria | 06/2016 |
5868 | (3*2^384524-1)/7631 | 115750 | Lelio R Paula | 03/2014 |
5869 | 28275^12406+12406^28275 | 115748 | Hans Havermann | 01/2021 |
5870 | (44*10^115697-413)/9 | 115698 | Robert Price | 03/2019 |
5871 | 31408^4825+4825^31408 | 115692 | Hans Havermann | 02/2021 |
5872 | (2^384317+1026)/2 | 115691 | Stefano Morozzi | 09/2020 |
5873 | 2^384312+81091 | 115690 | Yves Minet | 02/2010 |
5874 | (2^384265+2150)/2 | 115675 | Stefano Morozzi | 09/2020 |
5875 | (2^384246+2182)/2 | 115670 | Stefano Morozzi | 09/2020 |
5876 | (4*10^115668-79)/3 | 115669 | Robert Price | 02/2018 |
5877 | (2^384193+242)/2 | 115654 | Stefano Morozzi | 09/2020 |
5878 | (266947#+1267)/(7^2*181) | 115647 | Makoto Morimoto | 06/2019 |
5879 | (266947#+273808)/(2*109*157) | 115646 | Makoto Morimoto | 10/2017 |
5880 | 18^92125-92125^18 | 115642 | Dylan Delgado | 08/2019 |
5881 | 3^242337-4042 | 115625 | Enzo Doria | 05/2014 |
5882 | (17699*31^77516-29)/30 | 115608 | Eric Chen | 05/2024 |
5883 | (2^383931+674)/2 | 115575 | Stefano Morozzi | 09/2020 |
5884 | 7*10^115561+79 | 115562 | Robert Price | 07/2019 |
5885 | (2^383872+3046)/2 | 115557 | Stefano Morozzi | 09/2020 |
5886 | (11*2^383859-13)/15 | 115553 | Renaud Lifchitz | 03/2011 |
5887 | 2^383780-3149 | 115530 | Yves Minet | 10/2014 |
5888 | (41*10^115523-383)/9 | 115524 | Robert Price | 11/2018 |
5889 | 27316^16923+16923^27316 | 115506 | Hans Havermann | 02/2021 |
5890 | (2^383618+618)/2 | 115481 | Stefano Morozzi | 09/2020 |
5891 | 2^383560-455 | 115464 | Yves Minet | 03/2012 |
5892 | (2^383544+5)/3 | 115458 | Lelio R Paula | 03/2014 |
5893 | (22*10^115454+119)/3 | 115455 | Robert Price | 04/2021 |
5894 | 89^59221-88^59221 | 115445 | Robert Price | 06/2015 |
5895 | (7^136559-5^136559)/2 | 115406 | Jon Grantham | 08/2023 |
5896 | 2^383347+1869413 | 115399 | Enzo Doria | 05/2016 |
5897 | (103*10^115366+17)/3 | 115368 | Robert Price | 08/2020 |
5898 | (2^383232+750)/2 | 115365 | Stefano Morozzi | 09/2020 |
5899 | (2^383130-7)/131793 | 115329 | Lelio R Paula | 03/2014 |
5900 | (12^106859+1)/13 | 115320 | Paul Bourdelais | 02/2010 |
5901 | 29961^7060+7060^29961 | 115315 | Hans Havermann | 01/2021 |
5903 | 2^383039+1869509 | 115307 | Enzo Doria | 05/2016 |
5902 | 32918^3183+3183^32918 | 115307 | Hans Havermann | 01/2021 |
5904 | 36964^1315+1315^36964 | 115288 | Hans Havermann | 02/2021 |
5905 | (13*2^382968+1)/7 | 115286 | Lelio R Paula | 04/2014 |
5906 | (22*10^115282+29)/3 | 115283 | Robert Price | 02/2021 |
5907 | (2^382945+2046)/2 | 115278 | Stefano Morozzi | 09/2020 |
5908 | (2^382789+3182)/2 | 115231 | Stefano Morozzi | 09/2020 |
5909 | 30416^6141+6141^30416 | 115224 | Hans Havermann | 02/2021 |
5910 | 6*10^115211+79 | 115212 | Robert Price | 09/2020 |
5911 | (2^382722+3598)/2 | 115211 | Stefano Morozzi | 09/2020 |
5912 | 27987^13078+13078^27987 | 115210 | Hans Havermann | 02/2021 |
5913 | (2^382699+2090)/2 | 115204 | Stefano Morozzi | 09/2020 |
5914 | (22*10^115188-193)/9 | 115189 | Robert Price | 07/2022 |
5915 | 2^382633+73697 | 115185 | Enzo Doria | 04/2016 |
5916 | 2^382509-113593 | 115147 | Enzo Doria | 08/2014 |
5917 | 2^382502-2791721 | 115145 | Enzo Doria | 03/2016 |
5918 | (2^382495+1274)/2 | 115143 | Stefano Morozzi | 01/2021 |
5919 | 2^382464+22741 | 115134 | Enzo Doria | 09/2023 |
5920 | 26752^20065+20065^26752 | 115099 | Hans Havermann | 02/2021 |
5921 | 26383^23008+23008^26383 | 115080 | Hans Havermann | 02/2021 |
5922 | 9^120590-120590 | 115073 | Robert Price | 03/2014 |
5923 | 28203^12016+12016^28203 | 115062 | Hans Havermann | 02/2021 |
5924 | 2^382198+9 | 115054 | Lelio R Paula | 03/2013 |
5925 | 18268*31^77131+22839 | 115035 | Eric Chen | 05/2024 |
5926 | 30101^6630+6630^30101 | 115032 | Hans Havermann | 01/2021 |
5927 | (89*10^115030-179)/9 | 115031 | Robert Price | 12/2019 |
5928 | 25554^26089-26089^25554 | 114987 | Frank Doornink | 02/2024 |
5929 | 25142^26129-26129^25142 | 114979 | Frank Doornink | 12/2023 |
5930 | (2^381935+2774)/2 | 114974 | Stefano Morozzi | 02/2021 |
5931 | 27300^16271+16271^27300 | 114972 | Hans Havermann | 02/2021 |
5932 | (23*10^114962+7)/3 | 114963 | Robert Price | 05/2023 |
5933 | 2^381883-59197 | 114959 | Enzo Doria | 10/2015 |
5934 | 27423^15542+15542^27423 | 114944 | Hans Havermann | 02/2021 |
5935 | (2^381820+1626)/2 | 114939 | Stefano Morozzi | 09/2020 |
5937 | 2^381806-4481 | 114936 | Yves Minet | 07/2011 |
5936 | 2^381808-1851507 | 114936 | Enzo Doria | 08/2015 |
5938 | (2^381792+2502)/2 | 114931 | Stefano Morozzi | 09/2020 |
5939 | 2^381774-112373 | 114926 | Enzo Doria | 06/2014 |
5940 | 26341^22980+22980^26341 | 114883 | Hans Havermann | 01/2021 |
5941 | 2^381555-109051 | 114860 | Enzo Doria | 04/2014 |
5942 | 2^381551+213683 | 114859 | Enzo Doria | 09/2023 |
5943 | 2^381546-113501 | 114857 | Enzo Doria | 08/2014 |
5944 | (7*10^114845-19)/3 | 114846 | Robert Price | 10/2020 |
5945 | 26675^20178+20178^26675 | 114833 | Hans Havermann | 02/2021 |
5946 | (2^381436+1182)/2 | 114824 | Stefano Morozzi | 09/2020 |
5947 | 3^240644+16 | 114817 | Robert Price | 04/2020 |
5948 | 2^381360-110429 | 114801 | Enzo Doria | 05/2014 |
5949 | (17*10^114795+79)/3 | 114796 | Robert Price | 04/2019 |
5950 | (66^63079+1)/67 | 114774 | Paul Bourdelais | 09/2017 |
5951 | 2^381252-115079 | 114769 | Enzo Doria | 06/2015 |
5952 | (2^381251+3186)/2 | 114768 | Stefano Morozzi | 09/2020 |
5953 | 2^381209-29323 | 114756 | Enzo Doria | 07/2015 |
5954 | 2^381207-111546435 | 114755 | Paul Bourdelais | 10/2021 |
5955 | 569^41651-568^41651 | 114754 | Jean-Louis Charton | 11/2009 |
5956 | 2^381201+1873205 | 114753 | Enzo Doria | 06/2016 |
5957 | (85*10^114737+293)/9 | 114738 | Robert Price | 12/2019 |
5958 | (265*10^114736+17)/3 | 114738 | Robert Price | 03/2020 |
5959 | (2^381062+2170)/2 | 114711 | Stefano Morozzi | 09/2020 |
5960 | 2^380974-112991 | 114685 | Enzo Doria | 07/2014 |
5961 | 37097^1234+1234^37097 | 114679 | Hans Havermann | 02/2021 |
5962 | (26*10^114658-119)/3 | 114659 | Robert Price | 07/2023 |
5963 | 88^58949-87 | 114626 | Norbert Schneider | 11/2015 |
5964 | (2^380773+662)/2 | 114624 | Stefano Morozzi | 09/2020 |
5965 | Phi(155285,10)/242674820198201 | 114610 | Makoto Kamada | 02/2024 |
5966 | 29913^6782+6782^29913 | 114608 | Hans Havermann | 02/2021 |
5967 | (331*10^114605-7)/9 | 114607 | Robert Price | 04/2022 |
5968 | 2^380700+91 | 114603 | Lelio R Paula | 03/2013 |
5969 | (2^380632+2578)/2 | 114582 | Stefano Morozzi | 09/2020 |
5970 | 7*10^114577+27 | 114578 | Robert Price | 11/2020 |
5972 | 10^114575+3^114576 | 114576 | Mike Oakes | 09/2010 |
5971 | 10^114575+66561 | 114576 | Patrick De Geest | 02/2017 |
5973 | 10^114575-581081 | 114575 | Patrick De Geest | 02/2017 |
5974 | 2^380587-115315 | 114569 | Enzo Doria | 06/2015 |
5975 | 31874^3927+3927^31874 | 114558 | Hans Havermann | 02/2021 |
5976 | 2^380513-216925 | 114546 | Enzo Doria | 05/2014 |
5977 | 2^380451-1840087 | 114528 | Enzo Doria | 06/2015 |
5978 | (2^380426+1510)/2 | 114520 | Stefano Morozzi | 09/2020 |
5979 | (15*2^380388-1)/539 | 114507 | Lelio R Paula | 04/2014 |
5980 | 2^380279-461347 | 114476 | Enzo Doria | 07/2015 |
5981 | (331*10^114454-7)/9 | 114456 | Robert Price | 04/2022 |
5982 | 27121^16590+16590^27121 | 114447 | Hans Havermann | 01/2021 |
5983 | 25966^25555+25555^25966 | 114445 | Hans Havermann | 01/2021 |
5984 | (611*32^76029-53)/31 | 114437 | Eric Chen | 11/2023 |
5985 | (11*10^114400+529)/9 | 114401 | Robert Price | 09/2021 |
5986 | 2^380021+1871147 | 114398 | Enzo Doria | 05/2016 |
5987 | 2^380005+1869707 | 114393 | Enzo Doria | 05/2016 |
5988 | 2^379958-113297 | 114379 | Enzo Doria | 07/2014 |
5989 | (2^379897+1274)/2 | 114361 | Stefano Morozzi | 01/2021 |
5990 | 2^379881-109105 | 114356 | Enzo Doria | 04/2014 |
5991 | (21*2^379857-1)/13 | 114349 | Lelio R Paula | 03/2014 |
5992 | (4*10^114340+83)/3 | 114341 | Robert Price | 02/2018 |
5993 | (26*10^114317-77)/3 | 114318 | Robert Price | 11/2019 |
5994 | (4*10^114296+149)/9 | 114296 | Robert Price | 04/2018 |
5995 | 88^58773-87 | 114284 | Norbert Schneider | 11/2015 |
5996 | 27764^13065+13065^27764 | 114280 | Hans Havermann | 01/2021 |
5997 | (132^53891-1)/131 | 114278 | Anonymous | 06/2024 |
5998 | 2^379529-2790283 | 114250 | Enzo Doria | 03/2016 |
5999 | 2^379522+1869115 | 114248 | Enzo Doria | 05/2016 |
6000 | (145*10^114226-1)/9 | 114228 | Serge Batalov | 12/2014 |