## PRP Records

### Probable Primes Top 10000

#### (253466 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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See the Latest PRPs
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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 ? 7751 V(340138) 67336 Serge Batalov 03/2015 7752 43125^14528-106 67334 Enzo Doria 07/2012 7753 15275^16086-16086^15275 67304 Norbert Schneider 09/2018 7754 8*10^67302-51 67303 Robert Price 10/2017 7755 17458^7153+7153^17458 67292 Hans Havermann 08/2016 7756 16366^12925+12925^16366 67288 Hans Havermann 08/2016 7757 37^42906-2 67286 Lelio R Paula 08/2013 7758 18^53592-13 67273 Lelio R Paula 08/2013 7759 V(396221) 67256 Serge Batalov 03/2015 7760 (34*10^67245-7)/9/3^4/193/1381537 67236 Makoto Morimoto 04/2016 7761 (14*10^67235-101)/3 67236 Robert Price 04/2017 7762 53^38993-52^38993 67235 Robert Price 01/2013 7763 (2^223349-7)/6485 67231 Lelio R Paula 04/2012 7764 2^223333+315 67230 Lelio R Paula 04/2012 7765 2^223278-111041 67214 Enzo Doria 05/2014 7766 (2347*2^223281+1)/(3*5*197*1213*1783) 67208 Jens K. Andersen 09/2007 7767 2^223256-45 67207 Lelio R Paula 02/2012 7768 2^223253-112111 67206 Enzo Doria 06/2014 7769 18407^4474+4474^18407 67199 Hans Havermann 08/2016 7770 47^40182+40182^47 67189 Norbert Schneider 11/2014 7771 13^60309+94 67181 Lelio R Paula 07/2013 7772 11^64503-84 67173 Lelio R Paula 07/2013 7773 3^140781+236 67170 Lelio R Paula 06/2013 7774 2^223107-865057 67162 Paul Bourdelais 03/2013 7775 2^223100-59 67160 Lelio R Paula 02/2012 7776 2^223087+71963 67156 Enzo Doria 04/2016 7777 18^53481-3779 67134 Enzo Doria 03/2013 7778 (326^26713-1)/325 67134 Eric Chen 09/2017 7779 4^111473-62573 67114 Mike Oakes 02/2011 7780 2^222943+29 67113 Henri Lifchitz 08/2005 7781 (2^222939-9)/103 67110 Lelio R Paula 04/2012 7782 2^222862-459161 67089 Enzo Doria 05/2015 7783 2^222828+8193 67078 Lelio R Paula 04/2012 7784 3^140570+2660 67069 Lelio R Paula 06/2013 7785 20731^1716+1716^20731 67055 Hans Havermann 08/2019 7786 2^222744+855 67053 Lelio R Paula 04/2012 7787 13^60189+84 67048 Lelio R Paula 07/2013 7788 2*10^67043-51 67044 Robert Price 11/2017 7789 22588^929+929^22588 67042 Hans Havermann 08/2019 7790 2^222701+577294575 67040 Lelio R Paula 02/2016 7791 (13*10^67038-31)/9 67039 Serge Batalov 11/2008 7792 (151*10^67027-7)/9 67029 Robert Price 07/2017 7793 (58695*2^222620-1)/61 67019 Lelio R Paula 04/2015 7794 2^222614-111041 67014 Enzo Doria 05/2014 7795 16255^13242+13242^16255 67003 Hans Havermann 08/2019 7796 16477^11650+11650^16477 67001 Hans Havermann 08/2019 7797 118^32333-117 66991 Norbert Schneider 08/2018 7798 2^222520-1907 66986 Yves Minet 03/2013 7799 (4^111231+23)/3 66968 Robert Price 02/2017 7800 16206^13549+13549^16206 66962 Hans Havermann 08/2019 7801 2^222408-111275 66952 Enzo Doria 05/2014 7802 10^66949-9^66949 66949 Jean-Louis Charton 12/2005 7803 2^222378-1005 66943 Lelio R Paula 04/2012 7804 (9*2^222366+1)/73 66938 Lelio R Paula 08/2012 7805 7^79202-6^(79202+1) 66934 Robert Price 06/2016 7806 2^222325-112255 66927 Enzo Doria 06/2014 7807 21789^1178+1178^21789 66918 Hans Havermann 08/2019 7808 20^51428+33 66910 Lelio R Paula 08/2013 7810 2^222224-18509 66897 Enzo Doria 05/2013 7809 (38*10^66896+187)/9 66897 Robert Price 11/2017 7811 2^222192-869688105 66887 Lelio R Paula 02/2016 7812 (19*10^66878-43)/3 66879 Robert Price 10/2017 7813 11^64219-64 66878 Lelio R Paula 07/2013 7814 2^222151-17295 66875 Lelio R Paula 04/2012 7815 gcd(V(799885),5*F(159977)*(F(159977)+1)+1) 66867 Serge Batalov 04/2015 7816 2^222085-111031 66855 Enzo Doria 05/2014 7817 8*10^66848-13 66849 Robert Price 05/2017 7818 (3^140087+4)/13 66838 Lelio R Paula 04/2012 7819 (3^140102+4)/8843609437 66836 Lelio R Paula 04/2012 7820 19^52265+52 66835 Lelio R Paula 08/2013 7821 2*10^66826-27 66827 Robert Price 02/2017 7822 4*6^85867+5 66819 Lelio R Paula 09/2014 7823 11955^16384+2 66807 Matt Stath 12/2018 7824 15^56800+8 66802 Lelio R Paula 08/2013 7825 (2^221891-2^110946+1)/5 66796 11/2006 7826 10^66793+69441 66794 Patrick De Geest 05/2013 7827 10^66793-63 66793 Robert Price 05/2011 7828 35^43256-1704 66791 Enzo Doria 03/2013 7829 3^139976+2^(139976-1) 66786 Robert Price 05/2016 7830 88769!6-48 66786 Robert Price 08/2018 7831 7^79023-54 66783 Lelio R Paula 06/2013 7832 104^33109-103 66782 Norbert Schneider 11/2016 7833 (34*10^66778-7)/9/37/358901 66772 Makoto Morimoto 04/2016 7834 (-lucasV(1,2,443622)+2)/(7*281*487) 66766 Mike Oakes 04/2017 7836 2^221768+183 66759 Lelio R Paula 02/2012 7835 gcd(V(1197915),5*F(239583)*(F(239583)+1)+1) 66759 Serge Batalov 04/2015 7837 (154*10^66755-1)/9 66757 Serge Batalov 12/2014 7838 11^64097+48 66751 Lelio R Paula 07/2013 7839 (lucasV(1,2,443547)-2)/(7*13*79*1327*221773) 66749 Mike Oakes 04/2017 7840 (19*10^66748+413)/9 66749 Robert Price 10/2017 7841 (3*2^221696-1)/13 66737 Lelio R Paula 01/2014 7842 8*6^85758-7 66734 Lelio R Paula 09/2014 7843 135^31325+2 66733 Lelio R Paula 05/2013 7844 (49*10^66729+41)/9 66730 Robert Price 07/2015 7845 (349*10^66720-7)/9 66722 Robert Price 03/2017 7846 (-lucasV(1,2,443285)+2)/(3^2*307) 66718 Mike Oakes 04/2017 7847 (25*10^66714+71)/3 66715 Robert Price 01/2017 7848 11^64061-780 66713 Enzo Doria 11/2012 7849 7^78929+4 66703 Lelio R Paula 06/2013 7850 11^64048-930 66700 Enzo Doria 11/2012 7851 120^32079-119 66699 Norbert Schneider 09/2018 7852 2*7^78921+5 66697 Lelio R Paula 09/2014 7853 (25*2^221526+1)/409 66685 Lelio R Paula 08/2012 7854 16330^12117+12117^16330 66682 Hans Havermann 08/2019 7855 (2^221509-1)/292391881 66673 Jens K. Andersen 02/2009 7856 2^221479+72953 66672 Enzo Doria 04/2016 7857 10^66666+275403 66667 Patrick De Geest 03/2010 7858 16317^12182+12182^16317 66667 Hans Havermann 08/2019 7859 10^66666-115521 66666 Patrick De Geest 03/2010 7860 (18*10^66657-81)/99 66657 Ray Chandler 01/2011 7861 4*10^66653+21 66654 Robert Price 08/2016 7862 (10^66650+149)/3 66650 Serge Batalov 12/2014 7863 9^69842+3*8^69842-2*4^69842-3*2^69842 66647 Mike Oakes 12/2010 7864 2^221391-2145 66646 Lelio R Paula 04/2012 7865 22952^801+801^22952 66645 Hans Havermann 08/2019 7866 (5*10^66613-119)/3 66614 Robert Price 04/2016 7867 2^221273-113233 66610 Enzo Doria 07/2014 7868 3^139571-46 66593 Lelio R Paula 06/2013 7869 (4*10^(2*33295)-2*(10^33295)+1)/3 66591 Robert Price 04/2018 7870 2^221181-869688105 66583 Lelio R Paula 02/2016 7871 (61*10^66575-7)/9 66576 Ray Chandler 02/2012 7872 2^221126+133 66566 Lelio R Paula 02/2012 7873 12^61680+91 66564 Lelio R Paula 07/2013 7874 (lucasV(1,2,442258)+2)/103 66564 Mike Oakes 04/2017 7875 (13*10^66551-73)/3 66552 Robert Price 12/2016 7876 11^63901-1590 66547 Enzo Doria 12/2012 7877 11^63901-1500 66547 Enzo Doria 12/2012 7878 6^85517+23 66546 Lelio R Paula 07/2013 7879 17^54069-40 66530 Lelio R Paula 08/2013 7880 (2^110503+4725)^2+(2^110503+4725)+41 66530 Makoto Morimoto 05/2016 7881 (2^110503+8099)^2+(2^110503+8099)+41 66530 Makoto Morimoto 05/2016 7883 (2^221008-1017)/78533 66526 Lelio R Paula 04/2012 7882 3^139432+26 66526 Lelio R Paula 06/2013 7884 ((2^110503+5139)^2+(2^110503+5139)+41)/20865797 66523 Makoto Morimoto 05/2016 7885 ((2^110503+6647)^2+(2^110503+6647)+41)/197/17327 66523 Makoto Morimoto 05/2016 7886 6^85481+85481 66518 Henri Lifchitz 08/2014 7887 (9179*2^220913-1)/399 66503 Lelio R Paula 04/2015 7888 13^59687+66 66488 Lelio R Paula 07/2013 7889 (49*10^66485-31)/9 66486 Robert Price 07/2015 7890 (46*10^66469+17)/9 66470 Robert Price 06/2015 7891 2^220790+97 66465 Lelio R Paula 02/2012 7892 (23*2^220790+1)/807 66463 Lelio R Paula 06/2012 7893 40009^14441-102 66460 Enzo Doria 07/2012 7894 2^220736-143 66449 Lelio R Paula 02/2012 7895 (79*10^66447-97)/99 66447 Ray Chandler 01/2011 7896 21235^1344+1344^21235 66432 Hans Havermann 08/2019 7897 2^220675+69 66430 Lelio R Paula 02/2012 7898 19049^3070+3070^19049 66427 Hans Havermann 08/2019 7899 88323!6-16 66419 Robert Price 08/2018 7900 2^220633-111381 66418 Enzo Doria 05/2014 7901 (2^220625-509203)/4000321 66409 Lelio R Paula 05/2012 7902 2^220596-15813 66407 Enzo Doria 04/2013 7903 (5*10^66394-17)/3 66395 Serge Batalov 05/2009 7904 2^220549-1859173 66392 Enzo Doria 04/2016 7905 2^220478-161 66371 Lelio R Paula 02/2012 7906 5^94938-14636 66359 Enzo Doria 02/2013 7907 (F(67)^4861-F(66)^4861)/F(65) 66353 Wayne Halsdorf 03/2012 7908 15444^15839-15839^15444 66346 Norbert Schneider 08/2018 7909 2^220253-114871 66303 Enzo Doria 05/2015 7910 12^61432+95 66297 Lelio R Paula 07/2013 7911 2^220192-111563 66285 Enzo Doria 05/2014 7912 2^220188-111449 66284 Enzo Doria 05/2014 7913 (4*10^66284+23)/9 66284 Robert Price 11/2014 7914 32501!2+2 66266 Robert Price 01/2015 7915 (8*10^66261-101)/3 66262 Robert Price 10/2017 7916 1530*10^66254+R(66254) 66258 Patrick De Geest 05/2016 7917 (47^39623-1)/46 66252 Robert Price 06/2014 7918 2^220044-97305 66240 Lelio R Paula 04/2012 7919 (77*10^66237-257)/9 66238 Robert Price 10/2017 7920 29^45285+2 66225 Ray Chandler 08/2011 7921 16711^9178+9178^16711 66222 Hans Havermann 08/2019 7922 15^56289+38 66202 Lelio R Paula 08/2013 7923 3^138749+98 66201 Lelio R Paula 06/2013 7924 (21*2^219912-1)/5 66201 Lelio R Paula 01/2014 7926 2^219904-16995 66198 Lelio R Paula 10/2011 7925 2^219903-4615 66198 Yves Minet 05/2019 7927 (3^138712-2)/5297 66179 Lelio R Paula 04/2012 7928 Phi(198552,10) 66177 Ray Chandler 07/2010 7929 4*6^85041+7 66176 Lelio R Paula 09/2014 7930 2^219812-3149 66171 Yves Minet 10/2009 7931 2^219795-611167 66165 Paul Bourdelais 03/2013 7932 32455!2+512 66162 Robert Price 02/2015 7933 (27*2^219760-1)/227 66154 Lelio R Paula 01/2014 7935 (11^63521-4^63521)/7 66150 Robert Price 03/2013 7934 5*7^78274-6 66150 Lelio R Paula 09/2014 7936 15853^14872+14872^15853 66145 Hans Havermann 08/2019 7937 (-lucasV(1,2,439441)-2)/(3*11927*81359) 66134 Mike Oakes 04/2017 7938 2^219679-112015 66130 Enzo Doria 05/2014 7939 2^219653+15015*219653 66123 Henri Lifchitz 04/2005 7940 15445^15782-15782^15445 66108 Norbert Schneider 08/2018 7941 2^219600+76561 66107 Enzo Doria 05/2016 7942 2^219594+255255 66105 Lelio R Paula 10/2011 7943 4*7^78210-3 66096 Lelio R Paula 09/2014 7944 (15185*2^219557-1)/63 66096 Lelio R Paula 04/2015 7945 (19*2^219499-1)/13 66076 Lelio R Paula 01/2014 7946 2^219496+66615 66075 Lelio R Paula 10/2011 7947 (F(79021)^5-F(79020)^5)/F(79019) 66057 Wayne Halsdorf 03/2012 7948 15871^14500+14500^15871 66046 Hans Havermann 08/2019 7949 (2^219414+7)/443657 66045 Lelio R Paula 04/2012 7950 (115*10^66043-1)/3 66045 Serge Batalov 12/2014 7951 10^66033+19 66034 Robert Price 01/2011 7952 10^66033-78309 66033 Patrick De Geest 05/2013 7953 (lucasV(1,2,438701)+2)/7599419 66025 Mike Oakes 04/2017 7954 2^219304+454245 66018 Henri Lifchitz 03/2007 7955 (27*2^219293+1)/9145 66012 Lelio R Paula 08/2012 7956 2^219273-112635 66008 Enzo Doria 06/2014 7957 17548^5771+5771^17548 66003 Hans Havermann 08/2019 7958 2^219250+25 66001 Lelio R Paula 08/2011 7959 132^31123+131 65999 Norbert Schneider 03/2015 7960 19327^2598+2598^19327 65995 Hans Havermann 08/2019 7961 18440^3789+3789^18440 65988 Hans Havermann 08/2019 7962 V(319871) 65987 Serge Batalov 03/2015 7963 2^219189-195 65983 Lelio R Paula 08/2011 7964 (7*2^219143-1)/55 65968 Lelio R Paula 01/2014 7965 (73^35401-1)/72 65962 Paul Bourdelais 08/2017 7966 2^219112-17009 65960 Enzo Doria 05/2013 7967 2^219093-111201 65954 Enzo Doria 05/2014 7968 2^219089-112099 65953 Enzo Doria 06/2014 7969 46714!3+81 65950 Robert Price 09/2014 7970 (11*10^65944-131)/3 65945 Robert Price 02/2017 7971 2^219021-3553 65932 Yves Minet 03/2017 7972 Pell-LucasQ(172243)/2 65931 Eric W. Weisstein 01/2007 7973 2^218990+73519 65923 Enzo Doria 04/2016 7974 58^37378-57 65914 Norbert Schneider 09/2014 7976 (2^218945-7)/1675 65906 Lelio R Paula 04/2012 7975 5*10^65905+81 65906 Robert Price 08/2017 7977 3*10^65899-13 65900 Robert Price 11/2017 7978 (-lucasV(1,2,437845)-2)/1679917 65896 Mike Oakes 04/2017 7979 127^31322-2 65896 Lelio R Paula 10/2017 7980 2^218897-111889 65895 Enzo Doria 05/2014 7981 2^218896+1869451 65895 Enzo Doria 05/2016 7982 63^36616+2 65885 Lelio R Paula 05/2013 7983 (3*2^218822-1)/11 65872 Lelio R Paula 01/2014 7984 2^218796-113297 65865 Enzo Doria 07/2014 7985 2^218797+73727 65865 Enzo Doria 04/2016 7986 3^138040-110 65862 Lelio R Paula 06/2013 7987 11^63240-1950 65858 Enzo Doria 12/2012 7988 2^218764-111873 65855 Enzo Doria 05/2014 7989 (34*10^65839-7)/9/37 65839 Makoto Morimoto 04/2016 7990 3^137988+26 65838 Lelio R Paula 06/2013 7991 2^218680-719 65830 Yves Minet 05/2012 7992 18^52424+17 65807 Lelio R Paula 08/2013 7993 19062^2827+2827^19062 65790 Hans Havermann 08/2019 7994 (2*15683^15683+1)/732384425 65789 David Broadhurst 09/2010 7995 (23*2^218517+1)/19003 65778 Lelio R Paula 07/2012 7996 (5*10^65773+1)/3 65774 Erik Branger 12/2013 7997 160^29839-159 65769 Norbert Schneider 12/2018 7998 2^218457-17329 65763 Enzo Doria 05/2013 7999 151703#+223381 65759 Nicolas PALAU 10/2016 8000 2^218436+40755 65756 Lelio R Paula 10/2011

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 20 2019 14:10 (Time in France)

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