## PRP Records

### Probable Primes Top 10000

#### (295461 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 6*10^115211+79 115212 Robert Price 09/2020 5752 (2^382722+3598)/2 115211 Stefano Morozzi 09/2020 5753 27987^13078+13078^27987 115210 Hans Havermann 02/2021 5754 (2^382699+2090)/2 115204 Stefano Morozzi 09/2020 5755 (22*10^115188-193)/9 115189 Robert Price 07/2022 5756 2^382633+73697 115185 Enzo Doria 04/2016 5757 2^382509-113593 115147 Enzo Doria 08/2014 5758 2^382502-2791721 115145 Enzo Doria 03/2016 5759 (2^382495+1274)/2 115143 Stefano Morozzi 01/2021 5760 2^382464+22741 115134 Enzo Doria 09/2023 5761 26752^20065+20065^26752 115099 Hans Havermann 02/2021 5762 26383^23008+23008^26383 115080 Hans Havermann 02/2021 5763 9^120590-120590 115073 Robert Price 03/2014 5764 28203^12016+12016^28203 115062 Hans Havermann 02/2021 5765 2^382198+9 115054 Lelio R Paula 03/2013 5766 18268*31^77131+22839 115035 Eric Chen 05/2024 5767 30101^6630+6630^30101 115032 Hans Havermann 01/2021 5768 (89*10^115030-179)/9 115031 Robert Price 12/2019 5769 25554^26089-26089^25554 114987 Frank Doornink 02/2024 5770 25142^26129-26129^25142 114979 Frank Doornink 12/2023 5771 (2^381935+2774)/2 114974 Stefano Morozzi 02/2021 5772 27300^16271+16271^27300 114972 Hans Havermann 02/2021 5773 (23*10^114962+7)/3 114963 Robert Price 05/2023 5774 2^381883-59197 114959 Enzo Doria 10/2015 5775 27423^15542+15542^27423 114944 Hans Havermann 02/2021 5776 (2^381820+1626)/2 114939 Stefano Morozzi 09/2020 5778 2^381806-4481 114936 Yves Minet 07/2011 5777 2^381808-1851507 114936 Enzo Doria 08/2015 5779 (2^381792+2502)/2 114931 Stefano Morozzi 09/2020 5780 2^381774-112373 114926 Enzo Doria 06/2014 5781 26341^22980+22980^26341 114883 Hans Havermann 01/2021 5782 2^381555-109051 114860 Enzo Doria 04/2014 5783 2^381551+213683 114859 Enzo Doria 09/2023 5784 2^381546-113501 114857 Enzo Doria 08/2014 5785 (7*10^114845-19)/3 114846 Robert Price 10/2020 5786 26675^20178+20178^26675 114833 Hans Havermann 02/2021 5787 (2^381436+1182)/2 114824 Stefano Morozzi 09/2020 5788 3^240644+16 114817 Robert Price 04/2020 5789 2^381360-110429 114801 Enzo Doria 05/2014 5790 (17*10^114795+79)/3 114796 Robert Price 04/2019 5791 (66^63079+1)/67 114774 Paul Bourdelais 09/2017 5792 2^381252-115079 114769 Enzo Doria 06/2015 5793 (2^381251+3186)/2 114768 Stefano Morozzi 09/2020 5794 2^381209-29323 114756 Enzo Doria 07/2015 5795 2^381207-111546435 114755 Paul Bourdelais 10/2021 5796 569^41651-568^41651 114754 Jean-Louis Charton 11/2009 5797 2^381201+1873205 114753 Enzo Doria 06/2016 5798 (85*10^114737+293)/9 114738 Robert Price 12/2019 5799 (265*10^114736+17)/3 114738 Robert Price 03/2020 5800 (2^381062+2170)/2 114711 Stefano Morozzi 09/2020 5801 2^380974-112991 114685 Enzo Doria 07/2014 5802 37097^1234+1234^37097 114679 Hans Havermann 02/2021 5803 (26*10^114658-119)/3 114659 Robert Price 07/2023 5804 88^58949-87 114626 Norbert Schneider 11/2015 5805 (2^380773+662)/2 114624 Stefano Morozzi 09/2020 5806 Phi(155285,10)/242674820198201 114610 Makoto Kamada 02/2024 5807 29913^6782+6782^29913 114608 Hans Havermann 02/2021 5808 (331*10^114605-7)/9 114607 Robert Price 04/2022 5809 2^380700+91 114603 Lelio R Paula 03/2013 5810 (2^380632+2578)/2 114582 Stefano Morozzi 09/2020 5811 7*10^114577+27 114578 Robert Price 11/2020 5813 10^114575+3^114576 114576 Mike Oakes 09/2010 5812 10^114575+66561 114576 Patrick De Geest 02/2017 5814 10^114575-581081 114575 Patrick De Geest 02/2017 5815 2^380587-115315 114569 Enzo Doria 06/2015 5816 31874^3927+3927^31874 114558 Hans Havermann 02/2021 5817 2^380513-216925 114546 Enzo Doria 05/2014 5818 2^380451-1840087 114528 Enzo Doria 06/2015 5819 (2^380426+1510)/2 114520 Stefano Morozzi 09/2020 5820 (15*2^380388-1)/539 114507 Lelio R Paula 04/2014 5821 2^380279-461347 114476 Enzo Doria 07/2015 5822 (331*10^114454-7)/9 114456 Robert Price 04/2022 5823 27121^16590+16590^27121 114447 Hans Havermann 01/2021 5824 25966^25555+25555^25966 114445 Hans Havermann 01/2021 5825 (611*32^76029-53)/31 114437 Eric Chen 11/2023 5826 (11*10^114400+529)/9 114401 Robert Price 09/2021 5827 2^380021+1871147 114398 Enzo Doria 05/2016 5828 2^380005+1869707 114393 Enzo Doria 05/2016 5829 2^379958-113297 114379 Enzo Doria 07/2014 5830 (2^379897+1274)/2 114361 Stefano Morozzi 01/2021 5831 2^379881-109105 114356 Enzo Doria 04/2014 5832 (21*2^379857-1)/13 114349 Lelio R Paula 03/2014 5833 (4*10^114340+83)/3 114341 Robert Price 02/2018 5834 (26*10^114317-77)/3 114318 Robert Price 11/2019 5835 (4*10^114296+149)/9 114296 Robert Price 04/2018 5836 88^58773-87 114284 Norbert Schneider 11/2015 5837 27764^13065+13065^27764 114280 Hans Havermann 01/2021 5838 (132^53891-1)/131 114278 Anonymous 06/2024 5839 2^379529-2790283 114250 Enzo Doria 03/2016 5840 2^379522+1869115 114248 Enzo Doria 05/2016 5841 (145*10^114226-1)/9 114228 Serge Batalov 12/2014 5842 2^379317-115033 114186 Enzo Doria 06/2015 5843 (22*10^114178+47)/3 114179 Robert Price 06/2021 5844 (17*2^379246-1)/17407 114162 Lelio R Paula 03/2014 5845 (2^379192+226)/2 114148 Stefano Morozzi 09/2020 5846 (228^48407-1)/227 114139 Alexander Zhirkov 03/2023 5847 6*10^114091+23 114092 Robert Price 09/2020 5848 (4*10^114076+143)/3 114077 Robert Price 03/2018 5849 332*25^81584+12357 114053 Eric Chen 10/2023 5850 (2^378820+3226)/2 114036 Stefano Morozzi 01/2021 5851 (2^378754+2058)/2 114017 Stefano Morozzi 09/2020 5852 13643^27572-27572^13643 114008 Norbert Schneider 12/2022 5854 (46*10^113969+683)/9 113970 Robert Price 03/2019 5853 (83*10^113969+133)/9 113970 Robert Price 08/2021 5855 32226^3439+3439^32226 113966 Hans Havermann 02/2021 5856 (77*10^113963-149)/9 113964 Robert Price 03/2022 5857 78*10^113954-7 113956 Robert Price 10/2020 5858 2*10^113941+9 113942 Dmitry Domanov 11/2010 5859 10^113933+145897 113934 Patrick De Geest 02/2021 5862 (2^378478+1642)/2 113933 Stefano Morozzi 09/2020 5860 10^113933-8000000001 113933 Robert Price 11/2020 5861 10^113933-66167 113933 Patrick De Geest 02/2021 5863 2339662057597*10^113903+9 113916 Robert Price 03/2021 5864 4*10^113905+91 113906 Robert Price 08/2018 5865 10^113894+76609 113895 Patrick De Geest 02/2021 5867 10^113894-10000001 113894 Robert Price 09/2020 5866 10^113894-373947 113894 Patrick De Geest 02/2021 5868 33933^2270+2270^33933 113881 Hans Havermann 02/2021 5869 4*10^113874-21 113875 Robert Price 09/2018 5870 2^378272-16565 113872 Enzo Doria 04/2013 5871 2^378217-109075 113855 Enzo Doria 04/2014 5872 2^378198+67 113849 Lelio R Paula 03/2013 5873 2^378173-3249 113842 Yves Minet 12/2014 5874 (2^378155-5)/6597 113833 Lelio R Paula 03/2014 5875 92941#+(355049#)/(92941#) 113830 Makoto Morimoto 10/2017 5876 30030^6173+6173^30030 113829 Hans Havermann 01/2021 5877 2^378128-262977 113828 Enzo Doria 05/2014 5878 2^378123-113215 113827 Enzo Doria 07/2014 5879 6^146274-18893 113824 Enzo Doria 03/2013 5880 34596^1949+1949^34596 113815 Hans Havermann 02/2021 5881 2^378078+75 113813 Lelio R Paula 03/2013 5882 (28*10^113810+449)/9 113811 Robert Price 11/2021 5883 26273^21448+21448^26273 113799 Hans Havermann 02/2021 5884 2^377966+255255 113780 Paul Bourdelais 10/2021 5885 2^377940+63 113772 Lelio R Paula 03/2013 5886 2^377941-2785843 113772 Enzo Doria 04/2016 5887 (7*10^113757+11)/9 113757 Tyler Busby 01/2023 5888 2^377810+1875109 113733 Enzo Doria 09/2016 5889 2^377803-1838635 113731 Enzo Doria 05/2015 5890 2^377799+52223 113729 Yves Minet 08/2010 5891 (2^377791+3258)/2 113727 Stefano Morozzi 02/2021 5892 11^109190-270 113710 Enzo Doria 12/2012 5893 28206^10739+10739^28206 113698 Hans Havermann 01/2021 5894 7*10^113693+9 113694 Robert Price 09/2015 5895 13899^27442+27442^13899 113692 Norbert Schneider 12/2020 5896 (82*10^113681+161)/9 113682 Robert Price 10/2019 5897 26121^22478+22478^26121 113673 Hans Havermann 01/2021 5898 4*10^113658+49 113659 Robert Price 01/2019 5899 (10^113656+7)/40231/6439001 113645 Alfred Reich 06/2021 5900 (2*10^113631+529)/9 113631 Robert Price 01/2018 5901 2^377408-2798279 113612 Enzo Doria 04/2016 5902 (292^46336+1)/(292^256+1) 113605 Martin Hopf 12/2023 5903 13706^27459+27459^13706 113596 Norbert Schneider 12/2020 5904 5*10^113586+57 113587 Robert Price 12/2018 5905 (2^377242+2794)/2 113561 Stefano Morozzi 02/2021 5906 2^377222+93679 113556 Yves Minet 02/2011 5908 262147#+316847 113552 Makoto Morimoto 02/2016 5907 27172^15101+15101^27172 113552 Hans Havermann 01/2021 5909 (2^377131+2018)/2 113528 Stefano Morozzi 09/2020 5910 2^377026-458903 113497 Enzo Doria 04/2015 5911 (2^377014+2202)/2 113493 Stefano Morozzi 09/2020 5912 34791^1828+1828^34791 113488 Hans Havermann 02/2021 5913 (2^376967+258)/2 113479 Stefano Morozzi 09/2020 5914 (29*10^113468-17)/3 113469 Robert Price 09/2019 5915 35^73477-34^73477 113454 Robert Price 05/2012 5916 (14*10^113451-89)/3 113452 Robert Price 05/2020 5917 2^376790+27 113426 Lelio R Paula 03/2013 5918 2^376786-112701 113424 Enzo Doria 06/2014 5919 2^376731+21 113408 Lelio R Paula 03/2013 5920 9*10^113394-73 113395 Robert Price 01/2021 5921 29660^6651+6651^29660 113387 Hans Havermann 01/2021 5923 2^376634+1871245 113379 Enzo Doria 05/2016 5922 (4^188318+17)/3 113379 Robert Price 02/2017 5924 E(29532)/492842728006750534663978950979381235 113367 Thomas Ritschel 01/2021 5925 2^376576-344369 113361 Enzo Doria 07/2015 5926 2^376549-4543 113353 Yves Minet 03/2019 5927 (17*2^376526-1)/223 113345 Lelio R Paula 03/2014 5928 (27*2^376441-1)/811 113319 Lelio R Paula 03/2014 5929 (2^376350+3538)/2 113293 Stefano Morozzi 09/2020 5930 27265^14272+14272^27265 113273 Hans Havermann 02/2021 5931 32174^3315+3315^32174 113269 Hans Havermann 02/2021 5932 (2*10^113248+73)/3 113248 Robert Price 09/2020 5933 2^376128-21237 113226 Enzo Doria 06/2013 5934 5*10^113224-81 113225 Robert Price 01/2019 5935 10^113220+51409 113221 Patrick De Geest 02/2021 5937 10^113220-1000001 113220 Robert Price 08/2020 5936 10^113220-61779 113220 Patrick De Geest 02/2021 5938 (2^376102+1578)/2 113218 Stefano Morozzi 09/2020 5939 (2^375996+3102)/2 113186 Stefano Morozzi 09/2020 5940 37258^1091+1091^37258 113184 Hans Havermann 02/2021 5941 (94*10^113176+11)/3 113178 Robert Price 04/2020 5942 (46*10^113162+521)/9 113163 Robert Price 02/2019 5943 (2^375885+3614)/2 113153 Stefano Morozzi 09/2020 5944 (2^375873+2006)/2 113149 Stefano Morozzi 09/2020 5945 3*10^113137+23 113138 Robert Price 03/2022 5946 (8*10^113135-269)/9 113135 Robert Price 09/2021 5947 (2^375726+694)/2 113105 Stefano Morozzi 09/2020 5948 26050^21959+21959^26050 113100 Hans Havermann 02/2021 5949 2^375638-1787171 113079 Enzo Doria 03/2016 5950 (2^375563+2178)/2 113056 Stefano Morozzi 09/2020 5951 2^375537+4847 113048 Yves Minet 02/2011 5952 (17^91837+16^91837)/33 113000 Robert Price 08/2013 5953 5*F(270343)*(F(270343)+1)+1 112997 Serge Batalov 04/2015 5954 2^375350-3221 112992 Yves Minet 07/2011 5955 (13*2^375306+1)/7 112979 Lelio R Paula 03/2014 5956 2^375305+76757 112979 Enzo Doria 05/2016 5957 2^375258+1874989 112964 Enzo Doria 07/2016 5958 (29^77237-1)/28 112950 Robert Price 04/2012 5959 26620^17483+17483^26620 112939 Hans Havermann 01/2021 5960 2^375154+74959 112933 Enzo Doria 04/2016 5961 (266*10^112930-17)/3 112932 Robert Price 07/2020 5962 (2^375134+778)/2 112927 Stefano Morozzi 09/2020 5963 (85*10^112919+293)/9 112920 Robert Price 12/2019 5964 29412^6899+6899^29412 112907 Hans Havermann 02/2021 5965 (191*10^112903-17)/3 112905 Robert Price 11/2021 5966 (2^375022+1210)/2 112893 Stefano Morozzi 09/2020 5967 25992^22039+22039^25992 112889 Hans Havermann 02/2021 5968 2^374993-2787163 112885 Enzo Doria 11/2015 5969 (697*10^112869+23)/9 112871 Robert Price 04/2021 5970 (19*10^112851+377)/9 112852 Alfred Reich 11/2022 5971 30420^5111+5111^30420 112813 Hans Havermann 02/2021 5972 13699^27268+27268^13699 112800 Norbert Schneider 12/2020 5973 123^53970+2 112793 Lelio R Paula 06/2013 5974 12308*27^78796+23 112790 Eric Chen 07/2023 5975 28942^7887+7887^28942 112785 Hans Havermann 01/2021 5976 2^374640-4685 112778 Yves Minet 05/2019 5977 12^104501-11 112776 Riley Fisher 12/2023 5978 57290^93+93^57290 112775 Hans Havermann 01/2021 5979 13608^27277-27277^13608 112758 Norbert Schneider 12/2022 5980 (2^374556+682)/2 112753 Stefano Morozzi 09/2020 5981 p(22852)#/2+512 112745 Robert Price 05/2017 5982 (11*10^112742-131)/3 112743 Robert Price 09/2018 5983 2^374441-21049 112718 Enzo Doria 06/2013 5984 4*10^112706-93 112707 Robert Price 07/2020 5985 (2^374321+1)/3 112682 H.&R. Lifchitz 12/2000 5986 (2^374213+1766)/2 112650 Stefano Morozzi 09/2020 5987 (2^374094+2674)/2 112614 Stefano Morozzi 09/2020 5988 (13^101089-1)/12 112607 Paul Bourdelais 03/2010 5989 3^236011-8828 112606 Enzo Doria 05/2014 5990 31854^3427+3427^31854 112602 Hans Havermann 02/2021 5991 (85*10^112530-373)/9 112531 Robert Price 05/2021 5992 (2^373748+1090)/2 112510 Stefano Morozzi 09/2020 5993 (2^373727+1806)/2 112503 Stefano Morozzi 01/2021 5994 27618^11821+11821^27618 112479 Hans Havermann 01/2021 5995 26343^18580+18580^26343 112460 Hans Havermann 01/2021 5996 39^70666+2 112435 Lelio R Paula 11/2013 5997 (134*10^112400+7)/3 112402 Robert Price 02/2020 5998 (2^373365+326)/2 112394 Stefano Morozzi 09/2020 5999 (2^373350-7)/3 112390 Lelio R Paula 03/2014 6000 2^373306-1840931 112377 Enzo Doria 06/2015

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: July, 19 2024 15:29 (Time in France)

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