PRP Records

Probable Primes Top 10000

(295756 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 28915^32438-32438^28915 144710 Frank Doornink 06/2024 3752 2^480678+1874239 144699 Enzo Doria 06/2016 3753 (8*10^144683+1)/9 144683 Serge Batalov 05/2010 3754 L(692147) 144651 Henri Lifchitz 10/2008 3755 (76*10^144648+77)/9 144649 Robert Price 10/2019 3756 32672^26721+26721^32672 144635 Hans Havermann 01/2021 3757 31478^32153-32153^31478 144625 Frank Doornink 01/2024 3758 2^480417+35 144620 Robert Price 11/2015 3759 2^480296-59879 144584 Enzo Doria 10/2015 3760 33157^22878+22878^33157 144546 Hans Havermann 12/2020 3761 27520^32541-32541^27520 144471 Frank Doornink 06/2024 3762 45494^1497+1497^45494 144454 Hans Havermann 12/2020 3763 2^479844+3 144448 Donovan Johnson 06/2006 3764 33442^20803+20803^33442 144407 Hans Havermann 01/2021 3765 (441*33^95095-3833)/32 144405 Eric Chen 12/2023 3766 31892^32061-32061^31892 144393 Norbert Schneider 01/2023 3767 (27*2^479642+1)/733 144386 Lelio R Paula 08/2015 3768 (56*10^144380+169)/9 144381 Robert Price 03/2022 3769 44917^1638+1638^44917 144378 Hans Havermann 12/2020 3770 (21*2^479605-1)/11 144376 Lelio R Paula 09/2015 3771 (56*10^144336+583)/9 144337 Robert Price 08/2021 3772 5*2^479430-3 144324 Jon Grantham 07/2023 3773 2^479348-2792219 144299 Enzo Doria 02/2016 3774 31134^32111-32111^31134 144283 Frank Doornink 01/2024 3775 3^302389-6242 144277 Enzo Doria 05/2014 3776 31665^32056-32056^31665 144271 Frank Doornink 01/2024 3777 33778^18641+18641^33778 144248 Hans Havermann 01/2021 3778 29083^32312-32312^29083 144230 Frank Doornink 06/2024 3779 2*10^144220-3 144221 Robert Price 07/2015 3780 25313^32750-32750^25313 144210 Frank Doornink 01/2024 3781 2^478904-109109 144165 Enzo Doria 04/2014 3782 43698^1987+1987^43698 144125 Hans Havermann 12/2020 3783 79^75948+75948 144121 Kellen Shenton 06/2023 3784 26941^32522-32522^26941 144086 Frank Doornink 06/2024 3785 36128^9723+9723^36128 144072 Hans Havermann 01/2021 3786 32817^24518+24518^32817 144050 Hans Havermann 12/2020 3787 (772*10^144036-7)/9 144038 Robert Price 06/2022 3788 34295^15828+15828^34295 144020 Hans Havermann 01/2021 3789 2^478337-115333 143994 Enzo Doria 07/2015 3790 (7*2^478330-1)/3 143993 Lelio R Paula 08/2015 3791 88^74047-87^74047 143984 Robert Price 05/2015 3792 33242^21441+21441^33242 143980 Hans Havermann 01/2021 3793 (19*10^143963+467)/9 143964 Robert Price 02/2018 3794 (71^77761+1)/72 143954 Paul Bourdelais 09/2017 3795 33490^19859+19859^33490 143939 Hans Havermann 01/2021 3796 (853*10^143931-7)/9 143933 Robert Price 07/2021 3797 2^478088+27 143919 Robert Price 11/2015 3798 (8*10^143898-137)/3 143899 Robert Price 03/2022 3799 7*10^143857-93 143858 Robert Price 08/2020 3800 3*10^143844+61 143845 Robert Price 09/2020 3801 41358^3005+3005^41358 143837 Hans Havermann 01/2021 3802 2^477475-22071 143735 Enzo Doria 07/2013 3803 2^477417-22123 143717 Enzo Doria 07/2013 3804 2^477359-3577 143700 Yves Minet 03/2017 3805 39435^4402+4402^39435 143688 Hans Havermann 01/2021 3806 (14*10^143662-71)/3 143663 Robert Price 12/2018 3807 6^184614+5 143658 Paul Bourdelais 01/2021 3808 46371^1252+1252^46371 143640 Hans Havermann 12/2020 3809 34975^12748+12748^34975 143588 Hans Havermann 01/2021 3810 2^476936-396765 143573 Enzo Doria 07/2013 3811 2^476888-2791229 143558 Enzo Doria 01/2016 3812 2^476868-1859939 143552 Enzo Doria 11/2015 3813 40807^3294+3294^40807 143548 Hans Havermann 12/2020 3814 755^49878+49878^755 143547 Norbert Schneider 04/2019 3815 (19^112247-4^112247)/15 143536 Robert Price 03/2021 3816 35561^10872+10872^35561 143536 Hans Havermann 06/2021 3817 37637^6492+6492^37637 143487 Hans Havermann 05/2021 3818 61567^214+214^61567 143477 Hans Havermann 05/2021 3819 25933^32504-32504^25933 143468 Frank Doornink 03/2024 3820 2^476558-113627 143459 Enzo Doria 08/2014 3821 2^476478-45 143435 Lelio R Paula 11/2017 3822 36380^8757+8757^36380 143423 Hans Havermann 06/2021 3823 32510^25707+25707^32510 143371 Hans Havermann 05/2021 3824 8*10^143361+17 143362 Robert Price 07/2021 3825 (2^475854+9)/73 143245 Lelio R Paula 08/2015 3826 2^475813-113239 143234 Enzo Doria 07/2014 3827 (19*10^143212+137)/3 143213 Robert Price 03/2022 3828 32218^27849+27849^32218 143203 Hans Havermann 04/2021 3829 580*33^94296+19 143193 Eric Chen 12/2023 3830 2^475624-114059 143178 Enzo Doria 11/2014 3831 (11*2^475553-7)/15 143156 Renaud Lifchitz 03/2011 3832 2^475480-2786129 143134 Enzo Doria 10/2015 3833 33912^16621+16621^33912 143131 Hans Havermann 05/2021 3834 (19*10^143129-43)/3 143130 Robert Price 05/2019 3835 31830^31373+31373^31830 143126 Hans Havermann 05/2021 3836 6*10^143105-53 143106 Robert Price 05/2021 3837 (14*10^143097+73)/3 143098 Robert Price 12/2018 3838 2^475299-111937 143080 Enzo Doria 05/2014 3839 35488^10753+10753^35488 143071 Hans Havermann 04/2021 3840 29695^31986-31986^29695 143064 Frank Doornink 06/2024 3841 2^475160-2797859 143038 Enzo Doria 04/2016 3842 (2^475069+3)/395 143008 Lelio R Paula 08/2015 3843 2^475027-461437 142998 Enzo Doria 07/2015 3844 (2^474958+78557)/3 142977 Lelio R Paula 07/2015 3845 (8*10^142932+43)/3 142933 Robert Price 06/2018 3846 35055^11942+11942^35055 142922 Hans Havermann 05/2021 3847 37650^6239+6239^37650 142887 Hans Havermann 05/2021 3848 (54^82471-1)/53 142871 Paul Bourdelais 09/2017 3849 31205^31784-31784^31205 142845 Frank Doornink 01/2024 3850 (11*2^474432-1)/95 142818 Lelio R Paula 09/2015 3851 2^474417-59923 142814 Enzo Doria 10/2015 3852 4*10^142810-21 142811 Robert Price 09/2018 3853 32287^26494+26494^32287 142811 Hans Havermann 06/2021 3854 37162^6965+6965^37162 142811 Hans Havermann 06/2021 3855 (34*10^142805-601)/9 142806 Robert Price 07/2022 3856 37456^6493+6493^37456 142799 Hans Havermann 05/2021 3857 35141^11572+11572^35141 142793 Hans Havermann 05/2021 3858 32231^26908+26908^32231 142780 Hans Havermann 05/2021 3859 (3*2^474166+1)/7 142738 Lelio R Paula 08/2015 3860 2^474053+2897 142705 Lelio R Paula 08/2012 3861 (10^142699+359)/9 142699 Serge Batalov 12/2014 3862 26073^32312-32312^26073 142696 Frank Doornink 03/2024 3863 898^48311-897^48311 142676 Jean-Louis Charton 12/2012 3864 2^473740-1856639 142610 Enzo Doria 09/2015 3865 (25*10^142573-403)/9 142574 Robert Price 12/2020 3866 2^473617-114223 142573 Enzo Doria 12/2014 3867 36115^8856+8856^36115 142555 Hans Havermann 05/2021 3868 fibonacci(682007)+4 142531 Jon Grantham 08/2023 3869 2^473257+1873217 142465 Enzo Doria 06/2016 3870 (19*2^473242+1)/11 142461 Lelio R Paula 09/2015 3871 32750^22371+22371^32750 142453 Hans Havermann 06/2021 3872 (61*10^142446-1)/3 142448 Robert Price 01/2020 3873 (14*10^142440+61)/3 142441 Robert Price 12/2018 3874 (10^142425+359)/9 142425 Serge Batalov 12/2014 3875 2^473101+773027 142418 Enzo Doria 05/2016 3876 (13*2^472838-1)/3 142340 Lelio R Paula 09/2015 3877 (17*2^472789-1)/187347 142320 Lelio R Paula 09/2015 3878 36915^7162+7162^36915 142309 Hans Havermann 05/2021 3879 2^472634-109511 142278 Enzo Doria 04/2014 3880 31870^28997+28997^31870 142216 Hans Havermann 06/2021 3881 (48^84589+1)/49 142213 Robert Price 01/2014 3882 7*10^142189+87 142190 Robert Price 07/2019 3883 2^472258+7 142164 Lelio R Paula 08/2015 3884 40135^3484+3484^40135 142162 Hans Havermann 05/2021 3885 9*33^93598+26 142131 Eric Chen 12/2023 3886 (23*10^142105+91)/3 142106 Robert Price 08/2019 3887 tau(317^10330) 142098 Nik Lygeros / Olivier Rozier / LR team 10/2013 3888 (11*2^471913-1)/21 142060 Lelio R Paula 09/2015 3889 (16*10^142058+197)/3 142059 Robert Price 04/2019 3890 9*10^142037+91 142038 Robert Price 10/2020 3891 (4*10^142034+17)/3 142035 Tyler Busby 01/2023 3892 2^471792+1880881 142024 Enzo Doria 11/2016 3893 (509*10^142018+31)/9 142020 Robert Price 08/2022 3894 (31*2^471580-1)/135 141960 Lelio R Paula 08/2015 3895 (4*10^141926-79)/3 141927 Robert Price 02/2018 3896 2^471464-111546435 141925 Paul Bourdelais 10/2021 3897 (904*19^110984-1)/3 141924 Curtis Bright 05/2015 3898 (14*10^141853+37)/3 141854 Robert Price 12/2018 3899 (41*10^141836-59)/9 141837 Robert Price 10/2018 3900 4*5^202913-9 141831 Lelio R Paula 04/2015 3901 2*7^167812-3 141818 Lelio R Paula 12/2014 3902 2^471043+35 141799 Robert Price 11/2015 3903 (11*2^470956-1)/7945 141770 Lelio R Paula 08/2015 3904 43636^1773+1773^43636 141761 Hans Havermann 05/2021 3905 (2*10^141751-17)/3 141751 Serge Batalov 11/2022 3906 (53*10^141722-611)/9 141723 Robert Price 02/2022 3907 (11*10^141718-131)/3 141719 Robert Price 09/2018 3908 (61*10^141716+47)/9 141717 Robert Price 07/2022 3909 26057^32088-32088^26057 141699 Frank Doornink 03/2024 3910 2^470692+76771 141693 Enzo Doria 05/2016 3911 50160^667+667^50160 141659 Hans Havermann 05/2021 3912 31522^31181+31181^31522 141657 Hans Havermann 05/2021 3913 29487^31690-31690^29487 141643 Frank Doornink 06/2024 3914 33076^19135+19135^33076 141626 Hans Havermann 04/2021 3915 28237^31818-31818^28237 141617 Frank Doornink 06/2024 3916 (91*10^141610+71)/9 141612 Robert Price 01/2022 3917 (21*2^470391+1)/533 141601 Lelio R Paula 09/2015 3918 (5*10^141594-23)/9 141594 Serge Batalov 11/2022 3919 31932^27155+27155^31932 141582 Hans Havermann 05/2021 3920 36449^7660+7660^36449 141577 Hans Havermann 05/2021 3921 2^470305-459373 141576 Enzo Doria 05/2015 3922 32195^24936+24936^32195 141556 Hans Havermann 05/2021 3923 2^470183+72623 141540 Enzo Doria 04/2016 3924 2^470173-16465 141537 Enzo Doria 04/2013 3925 37297^6234+6234^37297 141534 Hans Havermann 05/2021 3926 (509*10^141479+13)/9 141481 Robert Price 05/2022 3927 44*10^141476+9 141478 Robert Price 10/2020 3928 2^469974-1841 141477 Enzo Doria 05/2014 3929 (23*2^469939+1)/25 141466 Lelio R Paula 08/2015 3930 312*33^93158+23 141465 Eric Chen 12/2023 3931 2*10^141448+63 141449 Robert Price 05/2018 3932 2^469824+43 141432 Lelio R Paula 09/2017 3933 2*10^141407-27 141408 Robert Price 05/2018 3934 (214*10^141385-1)/3 141387 Robert Price 01/2021 3935 2^469630-59711 141373 Enzo Doria 10/2015 3936 35277^10172+10172^35277 141370 Hans Havermann 04/2021 3937 33397^17100+17100^33397 141370 Hans Havermann 04/2021 3938 (25*10^141366-331)/9 141367 Robert Price 08/2018 3939 36986^6639+6639^36986 141365 Hans Havermann 06/2021 3940 34572^12271+12271^34572 141361 Hans Havermann 06/2021 3941 37179^6338+6338^37179 141353 Hans Havermann 05/2021 3942 (2^469564-3)/611 141351 Lelio R Paula 08/2015 3943 197^61601+2 141342 Lelio R Paula 08/2017 3944 33420^16951+16951^33420 141340 Hans Havermann 05/2021 3945 31623^29458+29458^31623 141330 Hans Havermann 05/2021 3946 48112^865+865^48112 141306 Hans Havermann 05/2021 3947 2^469372-112949 141296 Enzo Doria 07/2014 3948 5*10^141294-63 141295 Robert Price 04/2021 3949 3^296115+4 141283 Tyler NeSmith 01/2021 3950 (64*10^141256+161)/9 141257 Robert Price 08/2022 3951 143^(2^16)+106^(2^16) 141253 Valeryi Kuryshev 02/2011 3952 143^65536+106^65536 141253 Serge Batalov 03/2018 3953 (11*10^141243-23)/3 141244 Robert Price 09/2021 3955 2^469198+782569 141243 Enzo Doria 10/2016 3954 38129^5062+5062^38129 141243 Hans Havermann 05/2021 3956 2^469076-2786939 141206 Enzo Doria 11/2015 3957 38630^4521+4521^38630 141202 Hans Havermann 05/2021 3958 31755^27836+27836^31755 141139 Hans Havermann 05/2021 3959 35554^9325+9325^35554 141137 Hans Havermann 05/2021 3960 2^468804+1874941 141125 Enzo Doria 06/2016 3961 2^468787+81353 141119 Enzo Doria 08/2016 3962 30204^31493-31493^30204 141091 Frank Doornink 06/2024 3963 2^468595-350407 141062 Enzo Doria 06/2015 3964 2^468564+87855 141052 Lelio R Paula 01/2016 3965 2^468551-21987 141048 Enzo Doria 07/2013 3966 2^468523-7 141040 Lelio R Paula 08/2015 3967 (25*10^141019-13)/3 141020 Robert Price 09/2019 3968 2^468405+87855 141004 Lelio R Paula 01/2016 3969 39338^3831+3831^39338 140961 Hans Havermann 05/2021 3970 31458^30239+30239^31458 140950 Hans Havermann 05/2021 3971 8*10^140932+29 140933 Robert Price 11/2021 3972 33166^17691+17691^33166 140881 Hans Havermann 06/2021 3973 2^467978-113051 140876 Enzo Doria 07/2014 3974 2^467780-344429 140816 Enzo Doria 07/2015 3975 9*10^140802-89 140803 Robert Price 04/2020 3976 2^467605-1855603 140764 Enzo Doria 09/2015 3977 (9^147503-5^147503)/4 140754 Jon Grantham 07/2023 3978 5*10^140744-7 140745 Robert Price 09/2015 3979 (5^201359-1)/4 140744 Paul Bourdelais 12/2008 3980 2^467401-1850023 140702 Enzo Doria 08/2015 3981 (14*10^140693+13)/9 140694 Tyler Busby 02/2023 3982 (266*10^140681-17)/3 140683 Robert Price 07/2020 3983 (2^467270+78557)/23247 140658 Lelio R Paula 07/2015 3984 32138^23781+23781^32138 140644 Hans Havermann 05/2021 3985 31654^27735+27735^31654 140640 Hans Havermann 05/2021 3986 (29*2^467205+1)/2780517107 140635 Lelio R Paula 08/2015 3987 2^467166-1854941 140631 Enzo Doria 09/2015 3988 (203*10^140615-11)/3 140617 Robert Price 12/2020 3989 (85*10^140609+473)/9 140610 Robert Price 01/2020 3990 39231^3836+3836^39231 140600 Hans Havermann 06/2021 3991 5*3^294676+2^294676 140597 Jon Grantham 08/2023 3992 2^466866-1840571 140541 Enzo Doria 06/2015 3993 2^466829-459523 140530 Enzo Doria 05/2015 3994 2^466692-113213 140489 Enzo Doria 07/2014 3995 23*10^140464-3 140466 Robert Price 10/2021 3996 (2*10^140461-17)/3 140461 Serge Batalov 11/2022 3997 31335^30364+30364^31335 140455 Hans Havermann 05/2021 3998 28511^31524-31524^28511 140440 Frank Doornink 06/2024 3999 32795^19126+19126^32795 140416 Hans Havermann 05/2021 4000 (44*10^140410-503)/9 140411 Robert Price 12/2018

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 12 2024 08:27 (Time in France)

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