## PRP Records

### Probable Primes Top 10000

#### (295149 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 ? 6751 2^350868-19725 105622 Enzo Doria 06/2013 6752 2^350858-59291 105619 Enzo Doria 10/2015 6753 2^350851+135 105617 Lelio R Paula 10/2011 6754 2^350841-741 105614 Lelio R Paula 01/2017 6755 3*10^105582+77 105583 Robert Price 09/2018 6756 24915^17284+17284^24915 105581 Hans Havermann 09/2020 6757 (5*10^105576-53)/3 105577 Robert Price 09/2020 6758 8*10^105571+3 105572 Robert Price 08/2015 6759 2^350674-78557 105564 Jorge Menendez 03/2018 6760 2*5^151026-3 105563 Lelio R Paula 11/2014 6761 (2^350702+5)/34264674063 105562 Lelio R Paula 12/2013 6762 6^135647-5^135647 105554 Jean-Louis Charton 02/2009 6763 3^221211+236 105545 Lelio R Paula 11/2016 6764 (32*10^105530-77)/9 105531 Robert Price 06/2018 6765 10^105515+33 105516 Lelio R Paula 11/2016 6766 24644^19125+19125^24644 105516 Hans Havermann 10/2020 6767 10^105515-41033 105515 Patrick De Geest 12/2016 6768 (29*2^350473-1)/267927 105499 Lelio R Paula 03/2014 6769 2^350455-430567 105498 Harrison Mesh 06/2022 6770 17^85732-72 105489 Lelio R Paula 01/2017 6771 (2^350399+3618)/2 105481 Stefano Morozzi 09/2020 6772 (2^350379+1010)/2 105475 Stefano Morozzi 09/2020 6773 2^350356+24241 105468 Enzo Doria 10/2023 6774 25233^15118+15118^25233 105462 Hans Havermann 09/2020 6775 26261^10366+10366^26261 105454 Hans Havermann 09/2020 6776 2^350307-110329 105453 Enzo Doria 05/2014 6777 2^350253-20365 105437 Enzo Doria 06/2013 6778 (3*29^72089-1075)/4 105423 Curtis Bright 05/2015 6779 (2^350187+2658)/2 105417 Stefano Morozzi 09/2020 6780 4*10^105415-69 105416 Robert Price 01/2022 6781 (22*10^105407+179)/3 105408 Robert Price 02/2022 6782 2^350139-109009 105403 Enzo Doria 04/2014 6783 (2^350129+3026)/2 105400 Stefano Morozzi 09/2020 6784 (2^350097+2070)/2 105390 Stefano Morozzi 09/2020 6785 3*5^150763+4 105380 Lelio R Paula 11/2014 6786 12^97643+91 105375 Lelio R Paula 02/2017 6787 6*5^150744-7 105367 Lelio R Paula 11/2014 6788 (2^350018+2074)/2 105366 Stefano Morozzi 09/2020 6789 4*10^105364-39 105365 Robert Price 09/2020 6791 2^349996-112169 105360 Enzo Doria 06/2014 6790 (2^349997+3702)/2 105360 Stefano Morozzi 09/2020 6792 (418*10^105343+23)/9 105345 Robert Price 02/2020 6793 25490^13563+13563^25490 105334 Hans Havermann 10/2020 6794 11^101142-1080 105329 Enzo Doria 12/2012 6795 (68*10^105320-41)/9 105321 Robert Price 10/2013 6796 24800^17649+17649^24800 105319 Hans Havermann 09/2020 6797 3^220712-9934 105307 Enzo Doria 05/2014 6798 7*10^105296+9 105297 Robert Price 09/2015 6799 89*10^105284-7 105286 Robert Price 04/2020 6800 2^349739+1873373 105282 Enzo Doria 06/2016 6801 7^124574+24 105278 Lelio R Paula 11/2016 6802 2^349708-20957 105273 Enzo Doria 06/2013 6803 34115^1218+1218^34115 105267 Hans Havermann 09/2020 6804 2^349649-20469 105255 Enzo Doria 06/2013 6805 2^349607-20109 105243 Enzo Doria 06/2013 6806 (85*10^105242+473)/9 105243 Robert Price 01/2020 6807 2^349594-19085 105239 Enzo Doria 05/2013 6808 2^349530+1874479 105220 Enzo Doria 06/2016 6809 (3^220528+8)/8081 105215 Lelio R Paula 12/2013 6810 (106*10^105199+17)/3 105201 Robert Price 04/2021 6811 (2^349452+3570)/2 105196 Stefano Morozzi 09/2020 6812 3^220464-112852 105189 Enzo Doria 07/2014 6813 2^349419-17349 105186 Enzo Doria 05/2013 6814 2^349400-2579 105180 Yves Minet 07/2014 6815 8*5^150471+3 105176 Lelio R Paula 11/2014 6816 (2^349359+2298)/2 105168 Stefano Morozzi 02/2021 6817 655^37342+37342^655 105165 Norbert Schneider 08/2018 6818 13^94403+94 105160 Lelio R Paula 12/2016 6819 2^349301-112309 105151 Enzo Doria 06/2014 6820 30291^2960+2960^30291 105149 Hans Havermann 09/2020 6821 27350^6981+6981^27350 105132 Hans Havermann 09/2020 6823 9*2^349220+5 105127 Lelio R Paula 09/2014 6822 (2^349225+3122)/2 105127 Stefano Morozzi 09/2020 6824 7*3^220317+8 105119 Lelio R Paula 09/2014 6825 7^124386+88 105119 Lelio R Paula 11/2016 6826 (2^349197+570)/2 105119 Stefano Morozzi 09/2020 6827 2^349171-19657 105111 Enzo Doria 06/2013 6828 (2^349115+590)/2 105094 Stefano Morozzi 09/2020 6829 (2^(6*58185+1)-5)/3 105093 Kevin Acres 11/2013 6830 (2^349111-5)/3 105093 Lelio R Paula 12/2013 6831 675^37142+37142^675 105087 Norbert Schneider 08/2018 6832 2^348981-2797573 105054 Enzo Doria 04/2016 6833 (445^39667+1)/446 105050 Jinyuan Wang 05/2024 6834 2^348869-6555 105021 Lelio R Paula 01/2017 6835 5^150217+78 104998 Lelio R Paula 11/2016 6836 (88*10^104989-1)/3 104991 Robert Price 04/2020 6837 (28*10^104972+149)/3 104973 Robert Price 12/2019 6838 24927^16262+16262^24927 104972 Hans Havermann 10/2020 6839 2^348703-113005 104971 Enzo Doria 06/2014 6840 (191*10^104956-17)/3 104958 Robert Price 11/2021 6842 2^348612-809 104943 Yves Minet 05/2013 6841 (73*10^104942-1)/9 104943 Robert Price 01/2015 6843 2^348583-350407 104934 Enzo Doria 06/2015 6844 2^348531-949 104919 Yves Minet 05/2012 6845 20^80636-59 104910 Lelio R Paula 12/2016 6846 8*10^104893-13 104894 Robert Price 08/2019 6848 2^348437+35 104890 Lelio R Paula 09/2011 6847 25208^14487+14487^25208 104890 Hans Havermann 09/2020 6849 2^348348+135 104864 Lelio R Paula 09/2011 6850 (29*10^104858+349)/9 104859 Robert Price 06/2021 6851 6*10^104852-31 104853 Robert Price 07/2020 6853 (2^348284+9)/25 104843 Lelio R Paula 12/2013 6852 75^55914-74 104843 Norbert Schneider 01/2015 6854 2^348268+255255 104840 Lelio R Paula 01/2017 6855 35540^891+891^35540 104839 Hans Havermann 09/2020 6856 5^149985-52 104836 Lelio R Paula 11/2016 6857 2^348224-20249 104826 Enzo Doria 06/2013 6858 (2^348217+2522)/2 104824 Stefano Morozzi 09/2020 6859 2^348212-20105 104823 Enzo Doria 06/2013 6860 24647^17898+17898^24647 104819 Hans Havermann 10/2020 6861 20^80562+19 104814 Lelio R Paula 12/2016 6862 2*10^104811-87 104812 Robert Price 04/2018 6863 2^348149-20053 104804 Enzo Doria 06/2013 6864 2^348095-171 104788 Lelio R Paula 09/2011 6865 25383^13412+13412^25383 104769 Hans Havermann 09/2020 6866 2^348003-20377 104760 Enzo Doria 06/2013 6867 2^347994-741 104757 Lelio R Paula 12/2016 6868 (2^347993+2234)/2 104757 Stefano Morozzi 01/2021 6869 (2^347990+790)/2 104756 Stefano Morozzi 09/2020 6870 25137^14702+14702^25137 104756 Hans Havermann 09/2020 6871 (13*2^347972-1)/282309 104746 Lelio R Paula 03/2014 6872 12883^25484-25484^12883 104740 Norbert Schneider 08/2022 6873 2^347910-109937 104732 Enzo Doria 04/2014 6874 (88*10^104709-637)/9 104710 Robert Price 11/2020 6875 (13*10^104702+71)/3 104703 Robert Price 06/2021 6876 5^149794+28 104702 Lelio R Paula 11/2016 6877 105^51800-2 104698 Lelio R Paula 10/2017 6878 (16^86939+3^86939)/19 104684 Robert Price 06/2013 6879 (15^89009-1)/14 104682 Paul Bourdelais 03/2010 6880 2^347731-18609 104678 Enzo Doria 05/2013 6881 4*6^134519+7 104677 Lelio R Paula 11/2014 6882 (34*10^104672-259)/9 104673 Robert Price 12/2021 6883 25321^13588+13588^25321 104656 Hans Havermann 09/2020 6884 2^347625+5367 104646 Riley Fisher 04/2023 6885 2^347612-18545 104642 Enzo Doria 05/2013 6888 6^134465+95 104635 Lelio R Paula 11/2016 6887 (2^347588+3718)/2 104635 Stefano Morozzi 09/2020 6886 (166*10^104633-7)/3 104635 Robert Price 11/2020 6889 2^347517-17301 104614 Enzo Doria 05/2013 6890 (2^347493+3186)/2 104606 Stefano Morozzi 09/2020 6891 (2^347490+2574)/2 104605 Stefano Morozzi 09/2020 6892 3^219222-310 104596 Lelio R Paula 11/2016 6893 25993^10554+10554^25993 104581 Hans Havermann 09/2020 6894 (15*2^347399-1)/13 104578 Lelio R Paula 03/2014 6895 2^347372-17853 104570 Enzo Doria 05/2013 6896 2^347314+99 104552 Lelio R Paula 09/2011 6897 2^347300-22233 104548 Enzo Doria 06/2013 6898 2^347287-19845 104544 Enzo Doria 06/2013 6899 2^347258-231191 104536 Harrison Mesh 06/2022 6900 (31*2^347254-1)/891 104533 Lelio R Paula 03/2014 6901 5*F(250091)*(F(250091)-1)+1 104532 Serge Batalov 04/2015 6902 7*2^347239-3 104531 Lelio R Paula 09/2014 6903 (3^219098-8)/514147439969 104525 Lelio R Paula 12/2013 6904 5*3^219047+8 104513 Lelio R Paula 09/2014 6905 2^347148-109073 104502 Enzo Doria 04/2014 6906 2^347129-20145 104497 Enzo Doria 06/2013 6907 4*10^104461-57 104462 Robert Price 10/2018 6908 (7*10^(2*52227+1)+9*10^52227-7)/9 104455 Robert Price 10/2023 6909 (2^346989+590)/2 104454 Stefano Morozzi 09/2020 6910 2^346923-19585 104435 Enzo Doria 05/2013 6911 (11*2^346864-1)/175 104416 Lelio R Paula 03/2014 6912 2^346854+346854^2+1 104414 Robert Price 06/2014 6913 2^346834+11715 104408 Lelio R Paula 04/2015 6914 24276^19961+19961^24276 104392 Hans Havermann 09/2020 6915 79^55009+78 104387 Norbert Schneider 02/2015 6916 3^218744+58 104368 Lelio R Paula 11/2016 6917 9*10^104361+89 104362 Robert Price 11/2019 6918 25048^14665+14665^25048 104358 Hans Havermann 09/2020 6919 2^346649+65 104352 Lelio R Paula 09/2011 6920 (19*33^68718-600883)/32 104350 Eric Chen 05/2023 6921 2^346638-17265 104349 Enzo Doria 05/2013 6922 (2^346606+2082)/2 104339 Stefano Morozzi 09/2020 6923 (2^346607+2070)/2 104339 Stefano Morozzi 09/2020 6924 (2^346582+3202)/2 104332 Stefano Morozzi 09/2020 6925 26092^9967+9967^26092 104331 Hans Havermann 09/2020 6926 5*10^104326+77 104327 Robert Price 12/2018 6927 (2^346564+2026)/2 104326 Stefano Morozzi 09/2020 6928 (8925^26569-1)/(8925^163-1) 104320 Ryan Propper 11/2023 6931 2^346527-111817 104316 Enzo Doria 05/2014 6930 6^134055+101 104316 Lelio R Paula 11/2016 6929 fibonacci(499147)-4 104316 Jon Grantham 08/2023 6932 92105!4+8 104312 Robert Price 09/2019 6933 (7^123407-5^123407)/2 104291 Jon Grantham 08/2023 6934 6^134013+163 104283 Lelio R Paula 11/2016 6935 10^(2*52140+1)-10^52140-1 104281 Robert Price 07/2023 6936 (22*10^104272-61)/3 104273 Robert Price 03/2022 6937 (2^346318+862)/2 104252 Stefano Morozzi 02/2021 6939 18^83049-89 104250 Lelio R Paula 01/2017 6938 (2^346311+606)/2 104250 Stefano Morozzi 09/2020 6940 (166*10^104230+11)/3 104232 Robert Price 03/2021 6941 2^346213+484049 104221 Enzo Doria 04/2017 6942 18^83021-91 104214 Lelio R Paula 01/2017 6943 10^104212+128779 104213 Patrick De Geest 05/2016 6944 10^104212+237447 104213 Patrick De Geest 05/2016 6945 10^104212+242139 104213 Patrick De Geest 05/2016 6946 10^104212+269199 104213 Patrick De Geest 05/2016 6947 24254^19803+19803^24254 104213 Hans Havermann 09/2020 6948 (10^104212-71)/1 104212 Serge Batalov 12/2014 6949 23678^23821-23821^23678 104202 Norbert Schneider 01/2020 6950 (13*31^69863+12407)/30 104191 Eric Chen 04/2024 6951 2^346078+7695 104180 Lelio R Paula 12/2016 6952 2^346055-19537 104173 Enzo Doria 05/2013 6953 (3*2^346057+1)/77 104173 Lelio R Paula 12/2013 6954 2^346037-20125 104168 Enzo Doria 06/2013 6955 (34*10^104168-7)/9/13/551179 104162 Makoto Morimoto 05/2016 6956 6^133854-17993 104159 Enzo Doria 03/2013 6957 2^345990+1874239 104154 Enzo Doria 06/2016 6958 2^345988-20373 104153 Enzo Doria 06/2013 6959 (2^345965+2214)/2 104146 Stefano Morozzi 09/2020 6960 (26*10^104132-503)/9 104133 Robert Price 07/2018 6961 3*5^148968+8 104125 Lelio R Paula 11/2014 6962 (7*10^104113+53)/3 104114 Robert Price 05/2018 6963 p(21253)#/2+8 104113 Robert Price 01/2017 6964 33582^1259+1259^33582 104106 Hans Havermann 09/2020 6965 32958^1441+1441^32958 104104 Hans Havermann 09/2020 6966 29127^3748+3748^29127 104095 Hans Havermann 09/2020 6967 322^41507+41507^322 104094 Norbert Schneider 12/2014 6968 6^133768-17423 104092 Enzo Doria 03/2013 6969 2^345786-19557 104092 Enzo Doria 05/2013 6970 171^46606-2 104072 Lelio R Paula 10/2017 6971 (29*10^104071+91)/3 104072 Robert Price 04/2020 6972 norm(Mod(x,x^3-x-1)^852167-1) 104070 Paul Vanderveen 09/2022 6973 2^345704-149 104068 Lelio R Paula 09/2011 6974 25821^10712+10712^25821 104056 Hans Havermann 09/2020 6975 (2^345662+2038)/2 104055 Stefano Morozzi 09/2020 6976 6^133704-17273 104042 Enzo Doria 02/2013 6977 (3*2^345590-1)/23 104033 Lelio R Paula 03/2014 6978 (19*2^345590+1)/33859 104030 Lelio R Paula 12/2013 6979 2^345547+11 104021 Lelio R Paula 09/2011 6980 (19*10^104014-49)/3 104015 Robert Price 05/2019 6981 (2^345519+1794)/2 104012 Stefano Morozzi 01/2021 6982 2^345504+723 104008 Lelio R Paula 09/2011 6983 2^345498-20037 104006 Enzo Doria 06/2013 6985 18^82854-37 104005 Lelio R Paula 01/2017 6984 (2^345497+2070)/2 104005 Stefano Morozzi 09/2020 6986 2^345486-109065 104002 Enzo Doria 04/2014 6987 2^345487-1851507 104002 Enzo Doria 08/2015 6988 2^345476+777 103999 Lelio R Paula 09/2011 6989 (2^345477+1554)/2 103999 Stefano Morozzi 09/2020 6990 4*10^103981-83 103982 Robert Price 10/2018 6991 (2^345327+3206)/2 103954 Stefano Morozzi 09/2020 6992 (5*2^345321-1)/3 103953 Lelio R Paula 03/2014 6993 (2^345267-9)/539049127 103927 Lelio R Paula 12/2013 6994 (19*10^103907+77)/3 103908 Robert Price 05/2019 6995 (78557*2^345163+1)/78589 103905 Lelio R Paula 07/2014 6996 2^345106-112181 103888 Enzo Doria 06/2014 6997 (2^345105+1326)/2 103887 Stefano Morozzi 02/2021 6998 2^345079+99 103880 Lelio R Paula 09/2011 6999 (2^345034+1198)/2 103866 Stefano Morozzi 09/2020 7000 11^99736-1500 103865 Enzo Doria 12/2012

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 22 2024 21:19 (Time in France)

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