## PRP Records

### Probable Primes Top 10000

#### (294613 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 ? 3751 2^464642+22189 139872 Enzo Doria 09/2023 3752 (16^116139+619)/5 139845 Anonymous 08/2022 3753 (2^464556+619)/5 139845 Eric Chen 10/2023 3754 4*10^139839-27 139840 Robert Price 08/2021 3755 33582^14573+14573^33582 139821 Hans Havermann 05/2021 3756 (17^113621+1)/18 139804 Paul Bourdelais 09/2011 3758 2*10^139800-21 139801 Robert Price 09/2020 3757 32628^19261+19261^32628 139801 Hans Havermann 04/2021 3759 (13*10^139782+191)/3 139783 Robert Price 11/2018 3760 (64*10^139776+791)/9 139777 Robert Price 01/2022 3761 (695*10^139772+7)/9 139774 Robert Price 12/2021 3762 (19*2^464312-1)/3 139773 Lelio R Paula 08/2015 3763 (74*10^139723+133)/9 139724 Robert Price 06/2019 3764 3*10^139722+13 139723 Robert Price 07/2018 3765 31577^26592+26592^31577 139721 Hans Havermann 05/2021 3766 77*10^139692+3 139694 Robert Price 06/2020 3767 (31*2^463970+1)/5 139670 Lelio R Paula 08/2015 3768 (18203^(2^15)+(18201)^(2^15))/2 139597 Robert Price 05/2018 3769 39640^3321+3321^39640 139584 Hans Havermann 05/2021 3770 36663^6410+6410^36663 139571 Hans Havermann 05/2021 3771 2^463633-2788423 139568 Enzo Doria 11/2015 3772 33659^13978+13978^33659 139532 Hans Havermann 05/2021 3773 31811^24318+24318^31811 139521 Hans Havermann 04/2021 3774 34149^12172+12172^34149 139512 Hans Havermann 04/2021 3775 (29*10^139476+313)/9 139477 Robert Price 04/2021 3776 31721^24940+24940^31721 139474 Hans Havermann 05/2021 3777 32833^17698+17698^32833 139473 Hans Havermann 05/2021 3778 2^463271-109501 139459 Enzo Doria 04/2014 3779 (5*10^139457+79)/3 139458 Robert Price 03/2018 3780 2^463237-99 139449 Lelio R Paula 09/2017 3781 (49*10^139442+383)/9 139443 Robert Price 04/2019 3782 31155^29902+29902^31155 139441 Hans Havermann 05/2021 3783 (7*10^139417-547)/9 139417 Robert Price 01/2018 3784 (10^139398+191)/3 139398 Robert Price 02/2018 3785 23*10^139386-3 139388 Robert Price 10/2021 3786 2^463019+79463 139383 Enzo Doria 06/2016 3787 3^292129-112756 139381 Enzo Doria 07/2014 3788 (15*2^462951+1)/527 139361 Lelio R Paula 08/2015 3789 31922^23205+23205^31922 139359 Hans Havermann 05/2021 3790 (19*10^139336+503)/9 139337 Alfred Reich 11/2023 3792 2^462855-1865707 139334 Enzo Doria 02/2016 3791 31237^28876+28876^31237 139334 Hans Havermann 05/2021 3793 (86*10^139315+121)/9 139316 Robert Price 08/2019 3794 2^462786-292043 139313 Enzo Doria 08/2015 3795 38915^3798+3798^38915 139299 Hans Havermann 05/2021 3797 (26*10^139289+1)/9 139290 Serge Batalov 05/2010 3796 (17*10^139289+7)/3 139290 Robert Price 06/2023 3798 34065^12248+12248^34065 139260 Hans Havermann 05/2021 3799 36425^6654+6654^36425 139256 Hans Havermann 05/2021 3800 39252^3527+3527^39252 139243 Hans Havermann 05/2021 3801 (17*10^139239+67)/3 139240 Robert Price 01/2019 3802 31887^23248+23248^31887 139231 Hans Havermann 05/2021 3803 (25*10^139210-97)/9 139211 Robert Price 01/2022 3804 2^462238-935 139148 Yves Minet 02/2014 3805 (29*10^139134-119)/9 139135 Robert Price 12/2021 3806 (109*10^139100-7)/3 139102 Robert Price 03/2021 3807 38744^3885+3885^38744 139068 Hans Havermann 05/2021 3808 31112^29499+29499^31112 139065 Hans Havermann 05/2021 3809 2*10^139043-63 139044 Robert Price 01/2022 3810 36390^6613+6613^36390 139025 Hans Havermann 04/2021 3811 2*10^138975+33 138976 Robert Price 11/2021 3812 42437^1882+1882^42437 138966 Hans Havermann 05/2021 3813 32151^20990+20990^32151 138958 Hans Havermann 05/2021 3814 32154^20933+20933^32154 138933 Hans Havermann 04/2021 3815 31082^29499+29499^31082 138931 Hans Havermann 04/2021 3816 2^461228+1870441 138844 Enzo Doria 05/2016 3817 2^461204-113675 138837 Enzo Doria 08/2014 3818 (2^461139-7)/47 138815 Lelio R Paula 08/2015 3819 (17*10^138812-521)/9 138813 Robert Price 04/2018 3820 3*10^138811-11 138812 Robert Price 07/2018 3821 (28*10^138768+173)/3 138769 Robert Price 12/2019 3822 (17*2^460963+1)/124051613 138757 Lelio R Paula 08/2015 3823 (379*10^138737-1)/9 138739 Robert Price 02/2020 3824 (43*10^138648+101)/9 138649 Robert Price 11/2018 3825 2^460567-113541 138645 Enzo Doria 08/2014 3826 (10^138622+161)/9 138622 Robert Price 09/2021 3827 7*10^138604+3 138605 Robert Price 08/2015 3828 (133*10^138600+17)/3 138602 Robert Price 11/2021 3829 33912^12203+12203^33912 138581 Hans Havermann 05/2021 3830 2^460330+69 138574 Lelio R Paula 09/2017 3831 (17*10^138569-77)/3 138570 Robert Price 08/2019 3832 31186^27725+27725^31186 138556 Hans Havermann 05/2021 3833 (16*10^138545+89)/3 138546 Robert Price 03/2021 3834 39753^3056+3056^39753 138546 Hans Havermann 05/2021 3835 31282^26847+26847^31282 138545 Hans Havermann 05/2021 3836 6*10^138520-37 138521 Robert Price 02/2021 3838 2^460078-69581 138498 Enzo Doria 12/2015 3837 31830^22447+22447^31830 138498 Hans Havermann 05/2021 3839 37384^5065+5065^37384 138492 Hans Havermann 05/2021 3840 34774^9585+9585^34774 138456 Hans Havermann 05/2021 3841 10^138444-5001 138444 Robert Price 12/2021 3842 2^459768+1531 138404 Lelio R Paula 06/2012 3843 (266*10^138328-17)/3 138330 Robert Price 07/2020 3844 27200^31193-31193^27200 138328 Frank Doornink 01/2024 3845 32963^15696+15696^32963 138306 Hans Havermann 05/2021 3846 2^459343-113611 138277 Enzo Doria 08/2014 3847 (28*10^138240+113)/3 138241 Robert Price 03/2020 3848 2^459199+1874393 138233 Enzo Doria 06/2016 3849 33339^14002+14002^33339 138230 Hans Havermann 05/2021 3850 2^459063-345307 138192 Enzo Doria 06/2015 3851 2*10^138162-43 138163 Robert Price 04/2018 3852 2^458927-112747 138151 Enzo Doria 06/2014 3853 2^458927-69217 138151 Enzo Doria 11/2015 3854 30907^29458+29458^30907 138130 Hans Havermann 05/2021 3855 32882^15837+15837^32882 138094 Hans Havermann 05/2021 3856 39252^3295+3295^39252 138083 Hans Havermann 05/2021 3857 33789^12190+12190^33789 138062 Hans Havermann 06/2021 3858 555555*2^458524+1513 138036 Darren Bedwell 08/2009 3859 30931^29002+29002^30931 138028 Hans Havermann 05/2021 3860 2^458465+2^32+1 138012 T. D. Noe 06/2007 3861 32206^19275+19275^32206 138003 Hans Havermann 05/2021 3862 2^458321-113053 137969 Enzo Doria 07/2014 3863 6^177298+323 137965 Riley Fisher 03/2023 3864 2^458298+79459 137962 Enzo Doria 06/2016 3865 2^458248-21815 137947 Enzo Doria 07/2013 3866 2^458194+1876549 137931 Enzo Doria 07/2016 3867 (318259#+325270)/(2^2*5*11*2957) 137907 Makoto Morimoto 10/2017 3868 (318259#+2625)/(3^2*5*7^5*22965193) 137899 Makoto Morimoto 06/2019 3869 (793*10^137887+53)/9 137889 Robert Price 01/2022 3870 2^457937+57 137853 Lelio R Paula 09/2017 3871 (8*10^137845+13)/3 137846 Robert Price 06/2018 3872 2^457822+105 137819 Donovan Johnson 06/2006 3873 2^457754-113711 137798 Enzo Doria 09/2014 3874 11^132315-360 137792 Enzo Doria 09/2012 3875 32072^19689+19689^32072 137725 Hans Havermann 06/2021 3876 44592^1225+1225^44592 137707 Hans Havermann 05/2021 3877 2^457347-37 137676 Lelio R Paula 09/2017 3878 2^457322-2786393 137668 Enzo Doria 10/2015 3879 gcd(Phi(699340,10),(10^34967+1)^3*(10^34967+1+10^17484)-(10^69934+10^34967)*(10^17484-1)+10^104901) 137664 Serge Batalov 04/2015 3880 34015^11134+11134^34015 137647 Hans Havermann 06/2021 3881 2^457240-59939 137643 Enzo Doria 10/2015 3882 (856*10^137633-1)/9 137635 Robert Price 03/2020 3883 36232^6289+6289^36232 137631 Hans Havermann 05/2021 3884 2^457120-21575 137607 Enzo Doria 07/2013 3885 (11*2^456978+1)/15 137564 Lelio R Paula 07/2015 3886 30963^27722+27722^30963 137564 Hans Havermann 04/2021 3887 33722^12003+12003^33722 137562 Hans Havermann 06/2021 3888 (7*25^98399+10613)/12 137556 Curtis Bright 05/2015 3889 41901^1918+1918^41901 137555 Hans Havermann 06/2021 3890 (7*10^137551-1)/3 137552 Robert Price 08/2022 3891 32930^15021+15021^32930 137539 Hans Havermann 05/2021 3892 31178^25785+25785^31178 137538 Hans Havermann 05/2021 3893 419^52446+52446^419 137525 Norbert Schneider 11/2020 3894 2^456813+214175 137515 Enzo Doria 10/2023 3895 2^456796-113513 137510 Enzo Doria 08/2014 3896 31788^21137+21137^31788 137485 Hans Havermann 04/2021 3897 (7*2^456655+1)/39 137467 Lelio R Paula 07/2015 3898 27151^31004-31004^27151 137466 Frank Doornink 01/2024 3899 2^456503-114361 137422 Enzo Doria 01/2015 3900 (11*2^456387+1)/19 137386 Lelio R Paula 07/2015 3901 36248^6147+6147^36248 137332 Hans Havermann 05/2021 3902 31986^19651+19651^31986 137329 Hans Havermann 05/2021 3903 2^456167+22313 137320 Enzo Doria 09/2023 3904 31817^20656+20656^31817 137292 Hans Havermann 05/2021 3905 (71*10^137250+1)/9 137251 Serge Batalov 05/2010 3906 2^455922+76249 137247 Enzo Doria 05/2016 3907 31310^24171+24171^31310 137241 Hans Havermann 05/2021 3908 14^119741-119741^14 137239 Serge Batalov 04/2016 3909 35014^8297+8297^35014 137218 Hans Havermann 05/2021 3910 (19*2^455760+1)/3455 137196 Lelio R Paula 07/2015 3912 124^(2^16)+57^(2^16) 137195 Valeryi Kuryshev 02/2011 3911 124^65536+57^65536 137195 Serge Batalov 03/2018 3913 2^455689+72677 137177 Enzo Doria 04/2016 3914 (17948!)^2+Prime(17948) 137118 Robert Price 08/2014 3915 31287^24128+24128^31287 137116 Hans Havermann 05/2021 3916 (37^87421-1)/36 137093 Robert Price 03/2012 3917 36233^6070+6070^36233 137077 Hans Havermann 05/2021 3918 (8*10^137073-17)/9 137073 Serge Batalov 11/2022 3919 38418^3697+3697^38418 137070 Hans Havermann 04/2021 3920 2^455323-57 137066 Lelio R Paula 09/2017 3921 (56*10^137019+583)/9 137020 Robert Price 08/2021 3922 25017^31148-31148^25017 136997 Frank Doornink 12/2023 3923 (73*17^111333-9)/16 136991 Curtis Bright 05/2015 3924 2^455025-112723 136977 Enzo Doria 06/2014 3925 33876^11039+11039^33876 136959 Hans Havermann 05/2021 3926 (19860^32041-1)/(19860^179-1) 136943 Ryan Propper 11/2023 3927 35142^7873+7873^35142 136919 Hans Havermann 05/2021 3928 66*10^136894+7 136896 Robert Price 07/2020 3929 2^454675-1777 136871 Yves Minet 10/2011 3930 31676^20931+20931^31676 136866 Hans Havermann 05/2021 3931 3*10^136829+29 136830 Robert Price 05/2018 3932 4*10^136813-57 136814 Robert Price 10/2018 3933 (6092*28^94536-143)/9 136812 Curtis Bright 05/2015 3934 fibonacci(654572)-2 136798 Jon Grantham 08/2023 3935 37359^4588+4588^37359 136795 Hans Havermann 05/2021 3936 2^454348-53 136773 Lelio R Paula 09/2017 3937 31^91680-2 136729 Lelio R Paula 05/2017 3938 2^454199-113697 136728 Enzo Doria 09/2014 3939 30785^27622+27622^30785 136725 Hans Havermann 05/2021 3940 32973^14014+14014^32973 136725 Hans Havermann 05/2021 3942 7*10^136716+69 136717 Robert Price 07/2019 3941 36002^6273+6273^36002 136717 Hans Havermann 05/2021 3943 6*10^136692+53 136693 Robert Price 05/2020 3944 (13*10^136687+47)/3 136688 Robert Price 10/2018 3945 2^453935-2791357 136649 Enzo Doria 01/2016 3946 2^453906-69131 136640 Enzo Doria 11/2015 3947 33232^12915+12915^33232 136620 Hans Havermann 05/2021 3948 2^453791+1873913 136605 Enzo Doria 06/2016 3949 34166^9951+9951^34166 136592 Hans Havermann 05/2021 3950 (21*2^453740-1)/2735 136588 Lelio R Paula 07/2015 3951 31102^24635+24635^31102 136587 Hans Havermann 05/2021 3952 580^49413+49413^580 136550 Norbert Schneider 02/2019 3953 2^453503-2788297 136519 Enzo Doria 11/2015 3954 34989^7958+7958^34989 136486 Hans Havermann 12/2020 3955 (2*10^136484+187)/9 136484 Robert Price 06/2022 3956 31007^25158+25158^31007 136452 Hans Havermann 11/2020 3957 2^453267-113827 136447 Enzo Doria 09/2014 3958 32234^17085+17085^32234 136435 Hans Havermann 12/2020 3959 2^453102+1877629 136398 Enzo Doria 08/2016 3960 31016^24981+24981^31016 136397 Hans Havermann 12/2020 3961 (62*10^136384-791)/9 136385 Robert Price 06/2019 3962 34171^9798+9798^34171 136382 Hans Havermann 12/2020 3963 (17*10^136354-113)/3 136355 Robert Price 06/2021 3964 32756^14541+14541^32756 136350 Hans Havermann 11/2020 3965 32205^17086+17086^32205 136313 Hans Havermann 12/2020 3966 (25*10^136303+161)/3 136304 Robert Price 09/2019 3967 35337^7196+7196^35337 136299 Hans Havermann 12/2020 3968 (182*10^136291+1)/3 136293 Robert Price 02/2020 3969 (88*10^136234+83)/9 136235 Robert Price 03/2022 3970 23*10^136225-7 136227 Robert Price 02/2020 3971 L(651821) 136223 Henri Lifchitz 09/2008 3972 25519^30908-30908^25519 136208 Frank Doornink 02/2024 3973 2^452460+77701 136205 Enzo Doria 05/2016 3974 2^452440-114755 136199 Enzo Doria 04/2015 3975 32286^16489+16489^32286 136157 Hans Havermann 11/2020 3976 (47*10^136141+493)/9 136142 Robert Price 03/2019 3977 27140^30699-30699^27140 136108 Frank Doornink 01/2024 3978 40392^2339+2339^40392 136082 Hans Havermann 12/2020 3979 2*10^136057-43 136058 Robert Price 04/2018 3980 2^451971+21563 136057 Enzo Doria 08/2023 3981 (2^451956-5)/181 136051 Lelio R Paula 07/2015 3982 2^451947-22165 136050 Enzo Doria 07/2013 3983 2^451787-21805 136002 Enzo Doria 07/2013 3984 2^451734-112817 135986 Enzo Doria 06/2014 3985 (11*2^451714+1)/75 135979 Lelio R Paula 07/2015 3986 2^451705-21879 135977 Enzo Doria 07/2013 3987 (4666^37249-1)/(4666^193-1) 135957 Ryan Propper 11/2023 3988 2^451560-112349 135934 Enzo Doria 06/2014 3989 2^451530+45 135925 Lelio R Paula 08/2017 3990 31622^19875+19875^31622 135922 Hans Havermann 11/2020 3991 (25*10^135906-73)/3 135907 Robert Price 09/2019 3992 2^451450-21743 135900 Enzo Doria 07/2013 3993 (7*10^135879+11)/9 135879 Tyler Busby 01/2023 3994 35218^7199+7199^35218 135846 Hans Havermann 11/2020 3995 35661^6446+6446^35661 135844 Hans Havermann 11/2020 3996 (7*33^89453-4743239)/32 135835 Eric Chen 12/2023 3997 31869^18248+18248^31869 135801 Hans Havermann 12/2020 3998 (77*10^135789+157)/9 135790 Robert Price 05/2022 3999 2^450958+60529 135752 Enzo Doria 08/2023 4000 2^450805+65 135706 Lelio R Paula 08/2017

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 04 2024 15:31 (Time in France)

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