## PRP Records

### Probable Primes Top 10000

#### (295765 PRPs in the top)

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) !!!

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 1-250 251-500 501-750 751-1000 1001-1250 1251-1500 1501-1750 1751-2000 2001-2250 2251-2500 2501-2750 2751-3000 3001-3250 3251-3500 3501-3750 3751-4000 4001-4250 4251-4500 4501-4750 4751-5000 5001-5250 5251-5500 5501-5750 5751-6000 6001-6250 6251-6500 6501-6750 6751-7000 7001-7250 7251-7500 7501-7750 7751-8000 8001-8250 8251-8500 8501-8750 8751-9000 9001-9250 9251-9500 9501-9750 9751-10000

 Rank Probable prime Digits (> 50000) Who ? When ? 5751 (2^386087-5)/40959 116220 Lelio R Paula 03/2014 5752 (2^386054+714)/2 116214 Stefano Morozzi 09/2020 5753 (10^116201+7)/39623 116197 Alfred Reich 06/2021 5754 2^385969-823 116189 Yves Minet 05/2012 5755 57^66162+2 116173 Lelio R Paula 08/2013 5756 2^385854+75049 116154 Enzo Doria 04/2016 5757 (2^385832+2590)/2 116147 Stefano Morozzi 09/2020 5758 2^385775-109587 116130 Enzo Doria 04/2014 5759 (14*10^116112-101)/3 116113 Robert Price 02/2019 5760 Phi(236354,10)/24817171 116109 Makoto Kamada 08/2019 5761 3*10^116107+23 116108 Robert Price 03/2022 5762 28729^10990+10990^28729 116094 Hans Havermann 02/2021 5763 2^385622+71839 116084 Enzo Doria 04/2016 5765 2^385564+781 116067 Lelio R Paula 01/2012 5764 (2^385565+1562)/2 116067 Stefano Morozzi 09/2020 5766 (2^385563+378)/2 116066 Stefano Morozzi 02/2021 5767 (2^385557+2214)/2 116064 Stefano Morozzi 09/2020 5768 29431^8776+8776^29431 116056 Hans Havermann 01/2021 5769 (266*10^116024-17)/3 116026 Robert Price 07/2020 5770 30263^6820+6820^30263 116022 Hans Havermann 02/2021 5771 2^385410+71893 116020 Enzo Doria 04/2016 5772 38225^1084+1084^38225 116014 Hans Havermann 02/2021 5773 26548^23433+23433^26548 116011 Hans Havermann 02/2021 5774 12^107422-11 115928 Riley Fisher 12/2023 5775 (25*2^385091+1)/27 115924 Lelio R Paula 04/2014 5776 (11*10^115910-131)/3 115911 Robert Price 09/2018 5777 2^384953-111943 115883 Paul Bourdelais 02/2012 5778 43^70942-2 115882 Lelio R Paula 04/2014 5779 (94*10^115879-7)/3 115881 Robert Price 03/2020 5780 7*10^115863+3 115864 Robert Price 08/2015 5781 2^384834+93 115847 Donovan Johnson 07/2008 5782 2^384809+71297 115840 Enzo Doria 04/2016 5783 (55*10^115829+323)/9 115830 Robert Price 10/2021 5784 (7*2^384759-1)/5 115825 Lelio R Paula 04/2014 5785 31348^4951+4951^31348 115822 Hans Havermann 02/2021 5786 (793*10^115810+53)/9 115812 Robert Price 01/2022 5787 (71*10^115810-17)/9 115811 Ray Chandler 08/2011 5788 (97*10^115794-1)/3 115796 Serge Batalov 12/2014 5789 31115^5266+5266^31115 115794 Hans Havermann 02/2021 5790 2*10^115784-27 115785 Robert Price 05/2018 5791 10^115773+126739 115774 Patrick De Geest 04/2018 5793 10^115773-1000000001 115773 Robert Price 03/2018 5792 10^115773-396221 115773 Patrick De Geest 04/2018 5794 (2^384582+778)/2 115771 Stefano Morozzi 09/2020 5795 30537^6178+6178^30537 115762 Hans Havermann 01/2021 5796 2^384530+1874305 115756 Enzo Doria 06/2016 5797 (3*2^384524-1)/7631 115750 Lelio R Paula 03/2014 5798 28275^12406+12406^28275 115748 Hans Havermann 01/2021 5799 (44*10^115697-413)/9 115698 Robert Price 03/2019 5800 31408^4825+4825^31408 115692 Hans Havermann 02/2021 5801 (2^384317+1026)/2 115691 Stefano Morozzi 09/2020 5802 2^384312+81091 115690 Yves Minet 02/2010 5803 (2^384265+2150)/2 115675 Stefano Morozzi 09/2020 5804 (2^384246+2182)/2 115670 Stefano Morozzi 09/2020 5805 (4*10^115668-79)/3 115669 Robert Price 02/2018 5806 (2^384193+242)/2 115654 Stefano Morozzi 09/2020 5807 (266947#+1267)/(7^2*181) 115647 Makoto Morimoto 06/2019 5808 (266947#+273808)/(2*109*157) 115646 Makoto Morimoto 10/2017 5809 18^92125-92125^18 115642 Dylan Delgado 08/2019 5810 3^242337-4042 115625 Enzo Doria 05/2014 5811 (17699*31^77516-29)/30 115608 Eric Chen 05/2024 5812 (2^383931+674)/2 115575 Stefano Morozzi 09/2020 5813 7*10^115561+79 115562 Robert Price 07/2019 5814 (2^383872+3046)/2 115557 Stefano Morozzi 09/2020 5815 (11*2^383859-13)/15 115553 Renaud Lifchitz 03/2011 5816 2^383780-3149 115530 Yves Minet 10/2014 5817 (41*10^115523-383)/9 115524 Robert Price 11/2018 5818 27316^16923+16923^27316 115506 Hans Havermann 02/2021 5819 (2^383618+618)/2 115481 Stefano Morozzi 09/2020 5820 2^383560-455 115464 Yves Minet 03/2012 5821 (2^383544+5)/3 115458 Lelio R Paula 03/2014 5822 (22*10^115454+119)/3 115455 Robert Price 04/2021 5823 89^59221-88^59221 115445 Robert Price 06/2015 5824 (7^136559-5^136559)/2 115406 Jon Grantham 08/2023 5825 2^383347+1869413 115399 Enzo Doria 05/2016 5826 (103*10^115366+17)/3 115368 Robert Price 08/2020 5827 (2^383232+750)/2 115365 Stefano Morozzi 09/2020 5828 (2^383130-7)/131793 115329 Lelio R Paula 03/2014 5829 (12^106859+1)/13 115320 Paul Bourdelais 02/2010 5830 29961^7060+7060^29961 115315 Hans Havermann 01/2021 5832 2^383039+1869509 115307 Enzo Doria 05/2016 5831 32918^3183+3183^32918 115307 Hans Havermann 01/2021 5833 36964^1315+1315^36964 115288 Hans Havermann 02/2021 5834 (13*2^382968+1)/7 115286 Lelio R Paula 04/2014 5835 (22*10^115282+29)/3 115283 Robert Price 02/2021 5836 (2^382945+2046)/2 115278 Stefano Morozzi 09/2020 5837 (2^382789+3182)/2 115231 Stefano Morozzi 09/2020 5838 30416^6141+6141^30416 115224 Hans Havermann 02/2021 5839 6*10^115211+79 115212 Robert Price 09/2020 5840 (2^382722+3598)/2 115211 Stefano Morozzi 09/2020 5841 27987^13078+13078^27987 115210 Hans Havermann 02/2021 5842 (2^382699+2090)/2 115204 Stefano Morozzi 09/2020 5843 (22*10^115188-193)/9 115189 Robert Price 07/2022 5844 2^382633+73697 115185 Enzo Doria 04/2016 5845 2^382509-113593 115147 Enzo Doria 08/2014 5846 2^382502-2791721 115145 Enzo Doria 03/2016 5847 (2^382495+1274)/2 115143 Stefano Morozzi 01/2021 5848 2^382464+22741 115134 Enzo Doria 09/2023 5849 26752^20065+20065^26752 115099 Hans Havermann 02/2021 5850 26383^23008+23008^26383 115080 Hans Havermann 02/2021 5851 9^120590-120590 115073 Robert Price 03/2014 5852 28203^12016+12016^28203 115062 Hans Havermann 02/2021 5853 2^382198+9 115054 Lelio R Paula 03/2013 5854 18268*31^77131+22839 115035 Eric Chen 05/2024 5855 30101^6630+6630^30101 115032 Hans Havermann 01/2021 5856 (89*10^115030-179)/9 115031 Robert Price 12/2019 5857 25554^26089-26089^25554 114987 Frank Doornink 02/2024 5858 25142^26129-26129^25142 114979 Frank Doornink 12/2023 5859 (2^381935+2774)/2 114974 Stefano Morozzi 02/2021 5860 27300^16271+16271^27300 114972 Hans Havermann 02/2021 5861 (23*10^114962+7)/3 114963 Robert Price 05/2023 5862 2^381883-59197 114959 Enzo Doria 10/2015 5863 27423^15542+15542^27423 114944 Hans Havermann 02/2021 5864 (2^381820+1626)/2 114939 Stefano Morozzi 09/2020 5866 2^381806-4481 114936 Yves Minet 07/2011 5865 2^381808-1851507 114936 Enzo Doria 08/2015 5867 (2^381792+2502)/2 114931 Stefano Morozzi 09/2020 5868 2^381774-112373 114926 Enzo Doria 06/2014 5869 26341^22980+22980^26341 114883 Hans Havermann 01/2021 5870 2^381555-109051 114860 Enzo Doria 04/2014 5871 2^381551+213683 114859 Enzo Doria 09/2023 5872 2^381546-113501 114857 Enzo Doria 08/2014 5873 (7*10^114845-19)/3 114846 Robert Price 10/2020 5874 26675^20178+20178^26675 114833 Hans Havermann 02/2021 5875 (2^381436+1182)/2 114824 Stefano Morozzi 09/2020 5876 3^240644+16 114817 Robert Price 04/2020 5877 2^381360-110429 114801 Enzo Doria 05/2014 5878 (17*10^114795+79)/3 114796 Robert Price 04/2019 5879 (66^63079+1)/67 114774 Paul Bourdelais 09/2017 5880 2^381252-115079 114769 Enzo Doria 06/2015 5881 (2^381251+3186)/2 114768 Stefano Morozzi 09/2020 5882 2^381209-29323 114756 Enzo Doria 07/2015 5883 2^381207-111546435 114755 Paul Bourdelais 10/2021 5884 569^41651-568^41651 114754 Jean-Louis Charton 11/2009 5885 2^381201+1873205 114753 Enzo Doria 06/2016 5886 (85*10^114737+293)/9 114738 Robert Price 12/2019 5887 (265*10^114736+17)/3 114738 Robert Price 03/2020 5888 (2^381062+2170)/2 114711 Stefano Morozzi 09/2020 5889 2^380974-112991 114685 Enzo Doria 07/2014 5890 37097^1234+1234^37097 114679 Hans Havermann 02/2021 5891 (26*10^114658-119)/3 114659 Robert Price 07/2023 5892 88^58949-87 114626 Norbert Schneider 11/2015 5893 (2^380773+662)/2 114624 Stefano Morozzi 09/2020 5894 Phi(155285,10)/242674820198201 114610 Makoto Kamada 02/2024 5895 29913^6782+6782^29913 114608 Hans Havermann 02/2021 5896 (331*10^114605-7)/9 114607 Robert Price 04/2022 5897 2^380700+91 114603 Lelio R Paula 03/2013 5898 (2^380632+2578)/2 114582 Stefano Morozzi 09/2020 5899 7*10^114577+27 114578 Robert Price 11/2020 5901 10^114575+3^114576 114576 Mike Oakes 09/2010 5900 10^114575+66561 114576 Patrick De Geest 02/2017 5902 10^114575-581081 114575 Patrick De Geest 02/2017 5903 2^380587-115315 114569 Enzo Doria 06/2015 5904 31874^3927+3927^31874 114558 Hans Havermann 02/2021 5905 2^380513-216925 114546 Enzo Doria 05/2014 5906 2^380451-1840087 114528 Enzo Doria 06/2015 5907 (2^380426+1510)/2 114520 Stefano Morozzi 09/2020 5908 (15*2^380388-1)/539 114507 Lelio R Paula 04/2014 5909 2^380279-461347 114476 Enzo Doria 07/2015 5910 (331*10^114454-7)/9 114456 Robert Price 04/2022 5911 27121^16590+16590^27121 114447 Hans Havermann 01/2021 5912 25966^25555+25555^25966 114445 Hans Havermann 01/2021 5913 (611*32^76029-53)/31 114437 Eric Chen 11/2023 5914 (11*10^114400+529)/9 114401 Robert Price 09/2021 5915 2^380021+1871147 114398 Enzo Doria 05/2016 5916 2^380005+1869707 114393 Enzo Doria 05/2016 5917 2^379958-113297 114379 Enzo Doria 07/2014 5918 (2^379897+1274)/2 114361 Stefano Morozzi 01/2021 5919 2^379881-109105 114356 Enzo Doria 04/2014 5920 (21*2^379857-1)/13 114349 Lelio R Paula 03/2014 5921 (4*10^114340+83)/3 114341 Robert Price 02/2018 5922 (26*10^114317-77)/3 114318 Robert Price 11/2019 5923 (4*10^114296+149)/9 114296 Robert Price 04/2018 5924 88^58773-87 114284 Norbert Schneider 11/2015 5925 27764^13065+13065^27764 114280 Hans Havermann 01/2021 5926 (132^53891-1)/131 114278 Anonymous 06/2024 5927 2^379529-2790283 114250 Enzo Doria 03/2016 5928 2^379522+1869115 114248 Enzo Doria 05/2016 5929 (145*10^114226-1)/9 114228 Serge Batalov 12/2014 5930 2^379317-115033 114186 Enzo Doria 06/2015 5931 (22*10^114178+47)/3 114179 Robert Price 06/2021 5932 (17*2^379246-1)/17407 114162 Lelio R Paula 03/2014 5933 (2^379192+226)/2 114148 Stefano Morozzi 09/2020 5934 (228^48407-1)/227 114139 Alexander Zhirkov 03/2023 5935 6*10^114091+23 114092 Robert Price 09/2020 5936 (4*10^114076+143)/3 114077 Robert Price 03/2018 5937 332*25^81584+12357 114053 Eric Chen 10/2023 5938 (2^378820+3226)/2 114036 Stefano Morozzi 01/2021 5939 (2^378754+2058)/2 114017 Stefano Morozzi 09/2020 5940 13643^27572-27572^13643 114008 Norbert Schneider 12/2022 5942 (46*10^113969+683)/9 113970 Robert Price 03/2019 5941 (83*10^113969+133)/9 113970 Robert Price 08/2021 5943 32226^3439+3439^32226 113966 Hans Havermann 02/2021 5944 (77*10^113963-149)/9 113964 Robert Price 03/2022 5945 78*10^113954-7 113956 Robert Price 10/2020 5946 2*10^113941+9 113942 Dmitry Domanov 11/2010 5947 10^113933+145897 113934 Patrick De Geest 02/2021 5950 (2^378478+1642)/2 113933 Stefano Morozzi 09/2020 5948 10^113933-8000000001 113933 Robert Price 11/2020 5949 10^113933-66167 113933 Patrick De Geest 02/2021 5951 2339662057597*10^113903+9 113916 Robert Price 03/2021 5952 4*10^113905+91 113906 Robert Price 08/2018 5953 10^113894+76609 113895 Patrick De Geest 02/2021 5955 10^113894-10000001 113894 Robert Price 09/2020 5954 10^113894-373947 113894 Patrick De Geest 02/2021 5956 33933^2270+2270^33933 113881 Hans Havermann 02/2021 5957 4*10^113874-21 113875 Robert Price 09/2018 5958 2^378272-16565 113872 Enzo Doria 04/2013 5959 2^378217-109075 113855 Enzo Doria 04/2014 5960 2^378198+67 113849 Lelio R Paula 03/2013 5961 2^378173-3249 113842 Yves Minet 12/2014 5962 (2^378155-5)/6597 113833 Lelio R Paula 03/2014 5963 92941#+(355049#)/(92941#) 113830 Makoto Morimoto 10/2017 5964 30030^6173+6173^30030 113829 Hans Havermann 01/2021 5965 2^378128-262977 113828 Enzo Doria 05/2014 5966 2^378123-113215 113827 Enzo Doria 07/2014 5967 6^146274-18893 113824 Enzo Doria 03/2013 5968 34596^1949+1949^34596 113815 Hans Havermann 02/2021 5969 2^378078+75 113813 Lelio R Paula 03/2013 5970 (28*10^113810+449)/9 113811 Robert Price 11/2021 5971 26273^21448+21448^26273 113799 Hans Havermann 02/2021 5972 2^377966+255255 113780 Paul Bourdelais 10/2021 5973 2^377940+63 113772 Lelio R Paula 03/2013 5974 2^377941-2785843 113772 Enzo Doria 04/2016 5975 (7*10^113757+11)/9 113757 Tyler Busby 01/2023 5976 2^377810+1875109 113733 Enzo Doria 09/2016 5977 2^377803-1838635 113731 Enzo Doria 05/2015 5978 2^377799+52223 113729 Yves Minet 08/2010 5979 (2^377791+3258)/2 113727 Stefano Morozzi 02/2021 5980 11^109190-270 113710 Enzo Doria 12/2012 5981 28206^10739+10739^28206 113698 Hans Havermann 01/2021 5982 7*10^113693+9 113694 Robert Price 09/2015 5983 13899^27442+27442^13899 113692 Norbert Schneider 12/2020 5984 (82*10^113681+161)/9 113682 Robert Price 10/2019 5985 26121^22478+22478^26121 113673 Hans Havermann 01/2021 5986 4*10^113658+49 113659 Robert Price 01/2019 5987 (10^113656+7)/40231/6439001 113645 Alfred Reich 06/2021 5988 (2*10^113631+529)/9 113631 Robert Price 01/2018 5989 2^377408-2798279 113612 Enzo Doria 04/2016 5990 (292^46336+1)/(292^256+1) 113605 Martin Hopf 12/2023 5991 13706^27459+27459^13706 113596 Norbert Schneider 12/2020 5992 5*10^113586+57 113587 Robert Price 12/2018 5993 (2^377242+2794)/2 113561 Stefano Morozzi 02/2021 5994 2^377222+93679 113556 Yves Minet 02/2011 5996 262147#+316847 113552 Makoto Morimoto 02/2016 5995 27172^15101+15101^27172 113552 Hans Havermann 01/2021 5997 (2^377131+2018)/2 113528 Stefano Morozzi 09/2020 5998 2^377026-458903 113497 Enzo Doria 04/2015 5999 (2^377014+2202)/2 113493 Stefano Morozzi 09/2020 6000 34791^1828+1828^34791 113488 Hans Havermann 02/2021

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 13 2024 17:43 (Time in France)

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