## 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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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 ? 3751 8*10^143361+17 143362 Robert Price 07/2021 3752 (2^475854+9)/73 143245 Lelio R Paula 08/2015 3753 2^475813-113239 143234 Enzo Doria 07/2014 3754 (19*10^143212+137)/3 143213 Robert Price 03/2022 3755 32218^27849+27849^32218 143203 Hans Havermann 04/2021 3756 580*33^94296+19 143193 Eric Chen 12/2023 3757 2^475624-114059 143178 Enzo Doria 11/2014 3758 (11*2^475553-7)/15 143156 Renaud Lifchitz 03/2011 3759 2^475480-2786129 143134 Enzo Doria 10/2015 3760 33912^16621+16621^33912 143131 Hans Havermann 05/2021 3761 (19*10^143129-43)/3 143130 Robert Price 05/2019 3762 31830^31373+31373^31830 143126 Hans Havermann 05/2021 3763 6*10^143105-53 143106 Robert Price 05/2021 3764 (14*10^143097+73)/3 143098 Robert Price 12/2018 3765 2^475299-111937 143080 Enzo Doria 05/2014 3766 35488^10753+10753^35488 143071 Hans Havermann 04/2021 3767 29695^31986-31986^29695 143064 Frank Doornink 06/2024 3768 2^475160-2797859 143038 Enzo Doria 04/2016 3769 (2^475069+3)/395 143008 Lelio R Paula 08/2015 3770 2^475027-461437 142998 Enzo Doria 07/2015 3771 (2^474958+78557)/3 142977 Lelio R Paula 07/2015 3772 (8*10^142932+43)/3 142933 Robert Price 06/2018 3773 35055^11942+11942^35055 142922 Hans Havermann 05/2021 3774 37650^6239+6239^37650 142887 Hans Havermann 05/2021 3775 (54^82471-1)/53 142871 Paul Bourdelais 09/2017 3776 31205^31784-31784^31205 142845 Frank Doornink 01/2024 3777 (11*2^474432-1)/95 142818 Lelio R Paula 09/2015 3778 2^474417-59923 142814 Enzo Doria 10/2015 3779 4*10^142810-21 142811 Robert Price 09/2018 3780 32287^26494+26494^32287 142811 Hans Havermann 06/2021 3781 37162^6965+6965^37162 142811 Hans Havermann 06/2021 3782 (34*10^142805-601)/9 142806 Robert Price 07/2022 3783 37456^6493+6493^37456 142799 Hans Havermann 05/2021 3784 35141^11572+11572^35141 142793 Hans Havermann 05/2021 3785 32231^26908+26908^32231 142780 Hans Havermann 05/2021 3786 (3*2^474166+1)/7 142738 Lelio R Paula 08/2015 3787 2^474053+2897 142705 Lelio R Paula 08/2012 3788 (10^142699+359)/9 142699 Serge Batalov 12/2014 3789 26073^32312-32312^26073 142696 Frank Doornink 03/2024 3790 898^48311-897^48311 142676 Jean-Louis Charton 12/2012 3791 2^473740-1856639 142610 Enzo Doria 09/2015 3792 (25*10^142573-403)/9 142574 Robert Price 12/2020 3793 2^473617-114223 142573 Enzo Doria 12/2014 3794 36115^8856+8856^36115 142555 Hans Havermann 05/2021 3795 fibonacci(682007)+4 142531 Jon Grantham 08/2023 3796 2^473257+1873217 142465 Enzo Doria 06/2016 3797 (19*2^473242+1)/11 142461 Lelio R Paula 09/2015 3798 32750^22371+22371^32750 142453 Hans Havermann 06/2021 3799 (61*10^142446-1)/3 142448 Robert Price 01/2020 3800 (14*10^142440+61)/3 142441 Robert Price 12/2018 3801 (10^142425+359)/9 142425 Serge Batalov 12/2014 3802 2^473101+773027 142418 Enzo Doria 05/2016 3803 (13*2^472838-1)/3 142340 Lelio R Paula 09/2015 3804 (17*2^472789-1)/187347 142320 Lelio R Paula 09/2015 3805 36915^7162+7162^36915 142309 Hans Havermann 05/2021 3806 2^472634-109511 142278 Enzo Doria 04/2014 3807 31870^28997+28997^31870 142216 Hans Havermann 06/2021 3808 (48^84589+1)/49 142213 Robert Price 01/2014 3809 7*10^142189+87 142190 Robert Price 07/2019 3810 2^472258+7 142164 Lelio R Paula 08/2015 3811 40135^3484+3484^40135 142162 Hans Havermann 05/2021 3812 9*33^93598+26 142131 Eric Chen 12/2023 3813 (23*10^142105+91)/3 142106 Robert Price 08/2019 3814 tau(317^10330) 142098 Nik Lygeros / Olivier Rozier / LR team 10/2013 3815 (11*2^471913-1)/21 142060 Lelio R Paula 09/2015 3816 (16*10^142058+197)/3 142059 Robert Price 04/2019 3817 9*10^142037+91 142038 Robert Price 10/2020 3818 (4*10^142034+17)/3 142035 Tyler Busby 01/2023 3819 2^471792+1880881 142024 Enzo Doria 11/2016 3820 (509*10^142018+31)/9 142020 Robert Price 08/2022 3821 (31*2^471580-1)/135 141960 Lelio R Paula 08/2015 3822 (4*10^141926-79)/3 141927 Robert Price 02/2018 3823 2^471464-111546435 141925 Paul Bourdelais 10/2021 3824 (904*19^110984-1)/3 141924 Curtis Bright 05/2015 3825 (14*10^141853+37)/3 141854 Robert Price 12/2018 3826 (41*10^141836-59)/9 141837 Robert Price 10/2018 3827 4*5^202913-9 141831 Lelio R Paula 04/2015 3828 2*7^167812-3 141818 Lelio R Paula 12/2014 3829 2^471043+35 141799 Robert Price 11/2015 3830 (11*2^470956-1)/7945 141770 Lelio R Paula 08/2015 3831 43636^1773+1773^43636 141761 Hans Havermann 05/2021 3832 (2*10^141751-17)/3 141751 Serge Batalov 11/2022 3833 (53*10^141722-611)/9 141723 Robert Price 02/2022 3834 (11*10^141718-131)/3 141719 Robert Price 09/2018 3835 (61*10^141716+47)/9 141717 Robert Price 07/2022 3836 26057^32088-32088^26057 141699 Frank Doornink 03/2024 3837 2^470692+76771 141693 Enzo Doria 05/2016 3838 50160^667+667^50160 141659 Hans Havermann 05/2021 3839 31522^31181+31181^31522 141657 Hans Havermann 05/2021 3840 29487^31690-31690^29487 141643 Frank Doornink 06/2024 3841 33076^19135+19135^33076 141626 Hans Havermann 04/2021 3842 28237^31818-31818^28237 141617 Frank Doornink 06/2024 3843 (91*10^141610+71)/9 141612 Robert Price 01/2022 3844 (21*2^470391+1)/533 141601 Lelio R Paula 09/2015 3845 (5*10^141594-23)/9 141594 Serge Batalov 11/2022 3846 31932^27155+27155^31932 141582 Hans Havermann 05/2021 3847 36449^7660+7660^36449 141577 Hans Havermann 05/2021 3848 2^470305-459373 141576 Enzo Doria 05/2015 3849 32195^24936+24936^32195 141556 Hans Havermann 05/2021 3850 2^470183+72623 141540 Enzo Doria 04/2016 3851 2^470173-16465 141537 Enzo Doria 04/2013 3852 37297^6234+6234^37297 141534 Hans Havermann 05/2021 3853 (509*10^141479+13)/9 141481 Robert Price 05/2022 3854 44*10^141476+9 141478 Robert Price 10/2020 3855 2^469974-1841 141477 Enzo Doria 05/2014 3856 (23*2^469939+1)/25 141466 Lelio R Paula 08/2015 3857 312*33^93158+23 141465 Eric Chen 12/2023 3858 2*10^141448+63 141449 Robert Price 05/2018 3859 2^469824+43 141432 Lelio R Paula 09/2017 3860 2*10^141407-27 141408 Robert Price 05/2018 3861 (214*10^141385-1)/3 141387 Robert Price 01/2021 3862 2^469630-59711 141373 Enzo Doria 10/2015 3863 35277^10172+10172^35277 141370 Hans Havermann 04/2021 3864 33397^17100+17100^33397 141370 Hans Havermann 04/2021 3865 (25*10^141366-331)/9 141367 Robert Price 08/2018 3866 36986^6639+6639^36986 141365 Hans Havermann 06/2021 3867 34572^12271+12271^34572 141361 Hans Havermann 06/2021 3868 37179^6338+6338^37179 141353 Hans Havermann 05/2021 3869 (2^469564-3)/611 141351 Lelio R Paula 08/2015 3870 197^61601+2 141342 Lelio R Paula 08/2017 3871 33420^16951+16951^33420 141340 Hans Havermann 05/2021 3872 31623^29458+29458^31623 141330 Hans Havermann 05/2021 3873 48112^865+865^48112 141306 Hans Havermann 05/2021 3874 2^469372-112949 141296 Enzo Doria 07/2014 3875 5*10^141294-63 141295 Robert Price 04/2021 3876 3^296115+4 141283 Tyler NeSmith 01/2021 3877 (64*10^141256+161)/9 141257 Robert Price 08/2022 3879 143^(2^16)+106^(2^16) 141253 Valeryi Kuryshev 02/2011 3878 143^65536+106^65536 141253 Serge Batalov 03/2018 3880 (11*10^141243-23)/3 141244 Robert Price 09/2021 3882 2^469198+782569 141243 Enzo Doria 10/2016 3881 38129^5062+5062^38129 141243 Hans Havermann 05/2021 3883 2^469076-2786939 141206 Enzo Doria 11/2015 3884 38630^4521+4521^38630 141202 Hans Havermann 05/2021 3885 31755^27836+27836^31755 141139 Hans Havermann 05/2021 3886 35554^9325+9325^35554 141137 Hans Havermann 05/2021 3887 2^468804+1874941 141125 Enzo Doria 06/2016 3888 2^468787+81353 141119 Enzo Doria 08/2016 3889 30204^31493-31493^30204 141091 Frank Doornink 06/2024 3890 2^468595-350407 141062 Enzo Doria 06/2015 3891 2^468564+87855 141052 Lelio R Paula 01/2016 3892 2^468551-21987 141048 Enzo Doria 07/2013 3893 2^468523-7 141040 Lelio R Paula 08/2015 3894 (25*10^141019-13)/3 141020 Robert Price 09/2019 3895 2^468405+87855 141004 Lelio R Paula 01/2016 3896 39338^3831+3831^39338 140961 Hans Havermann 05/2021 3897 31458^30239+30239^31458 140950 Hans Havermann 05/2021 3898 8*10^140932+29 140933 Robert Price 11/2021 3899 33166^17691+17691^33166 140881 Hans Havermann 06/2021 3900 2^467978-113051 140876 Enzo Doria 07/2014 3901 2^467780-344429 140816 Enzo Doria 07/2015 3902 9*10^140802-89 140803 Robert Price 04/2020 3903 2^467605-1855603 140764 Enzo Doria 09/2015 3904 (9^147503-5^147503)/4 140754 Jon Grantham 07/2023 3905 5*10^140744-7 140745 Robert Price 09/2015 3906 (5^201359-1)/4 140744 Paul Bourdelais 12/2008 3907 2^467401-1850023 140702 Enzo Doria 08/2015 3908 (14*10^140693+13)/9 140694 Tyler Busby 02/2023 3909 (266*10^140681-17)/3 140683 Robert Price 07/2020 3910 (2^467270+78557)/23247 140658 Lelio R Paula 07/2015 3911 32138^23781+23781^32138 140644 Hans Havermann 05/2021 3912 31654^27735+27735^31654 140640 Hans Havermann 05/2021 3913 (29*2^467205+1)/2780517107 140635 Lelio R Paula 08/2015 3914 2^467166-1854941 140631 Enzo Doria 09/2015 3915 (203*10^140615-11)/3 140617 Robert Price 12/2020 3916 (85*10^140609+473)/9 140610 Robert Price 01/2020 3917 39231^3836+3836^39231 140600 Hans Havermann 06/2021 3918 5*3^294676+2^294676 140597 Jon Grantham 08/2023 3919 2^466866-1840571 140541 Enzo Doria 06/2015 3920 2^466829-459523 140530 Enzo Doria 05/2015 3921 2^466692-113213 140489 Enzo Doria 07/2014 3922 23*10^140464-3 140466 Robert Price 10/2021 3923 (2*10^140461-17)/3 140461 Serge Batalov 11/2022 3924 31335^30364+30364^31335 140455 Hans Havermann 05/2021 3925 28511^31524-31524^28511 140440 Frank Doornink 06/2024 3926 32795^19126+19126^32795 140416 Hans Havermann 05/2021 3927 (44*10^140410-503)/9 140411 Robert Price 12/2018 3928 28332^31535-31535^28332 140403 Frank Doornink 06/2024 3929 153^64265-2 140400 Lelio R Paula 11/2017 3930 30323^31322-31322^30323 140379 Frank Doornink 06/2024 3931 (112*10^140357-1)/3 140359 Serge Batalov 12/2014 3932 (29*10^140337-17)/3 140338 Robert Price 09/2019 3933 2^466181-112735 140335 Enzo Doria 07/2014 3934 (16*10^140290-37)/3 140291 Robert Price 05/2021 3935 (5*10^140281-119)/3 140282 Robert Price 03/2018 3936 34568^11415+11415^34568 140259 Hans Havermann 05/2021 3937 (27*2^465872+1)/691 140241 Lelio R Paula 08/2015 3938 33632^14781+14781^33632 140236 Hans Havermann 05/2021 3939 31803^25670+25670^31803 140233 Hans Havermann 05/2021 3940 2^465803-114817 140221 Enzo Doria 05/2015 3941 floor(Pi*10^140344)%10^140165 140165 Serge Batalov 08/2012 3942 2^465503-112735 140131 Enzo Doria 07/2014 3943 (16*10^140091+167)/3 140092 Robert Price 06/2019 3944 (8*10^140087-137)/3 140088 Robert Price 03/2022 3945 6^179964+179964^6-1 140040 Robert Price 04/2014 3946 (89*10^140008-179)/9 140009 Robert Price 12/2019 3947 (29*2^465077-1)/9 140003 Lelio R Paula 08/2015 3948 2^465072-344789 140001 Enzo Doria 07/2015 3949 34742^10683+10683^34742 139965 Hans Havermann 05/2021 3950 5*10^139945+81 139946 Robert Price 03/2019 3951 32648^19335+19335^32648 139941 Hans Havermann 05/2021 3952 2^464864-17 139939 Lelio R Paula 09/2017 3953 8*10^139920+51 139921 Robert Price 08/2019 3954 (85*10^139913-1)/3 139915 Robert Price 02/2020 3955 31203^30436+30436^31203 139896 Hans Havermann 04/2021 3956 2^464642+22189 139872 Enzo Doria 09/2023 3957 26138^31663-31663^26138 139865 Frank Doornink 03/2024 3958 (16^116139+619)/5 139845 Anonymous 08/2022 3959 (2^464556+619)/5 139845 Eric Chen 10/2023 3960 4*10^139839-27 139840 Robert Price 08/2021 3961 33582^14573+14573^33582 139821 Hans Havermann 05/2021 3962 (17^113621+1)/18 139804 Paul Bourdelais 09/2011 3964 2*10^139800-21 139801 Robert Price 09/2020 3963 32628^19261+19261^32628 139801 Hans Havermann 04/2021 3965 (13*10^139782+191)/3 139783 Robert Price 11/2018 3966 (64*10^139776+791)/9 139777 Robert Price 01/2022 3967 (695*10^139772+7)/9 139774 Robert Price 12/2021 3968 (19*2^464312-1)/3 139773 Lelio R Paula 08/2015 3969 (74*10^139723+133)/9 139724 Robert Price 06/2019 3970 3*10^139722+13 139723 Robert Price 07/2018 3971 31577^26592+26592^31577 139721 Hans Havermann 05/2021 3972 77*10^139692+3 139694 Robert Price 06/2020 3973 (31*2^463970+1)/5 139670 Lelio R Paula 08/2015 3974 (18203^(2^15)+(18201)^(2^15))/2 139597 Robert Price 05/2018 3975 39640^3321+3321^39640 139584 Hans Havermann 05/2021 3976 36663^6410+6410^36663 139571 Hans Havermann 05/2021 3977 2^463633-2788423 139568 Enzo Doria 11/2015 3978 33659^13978+13978^33659 139532 Hans Havermann 05/2021 3979 31811^24318+24318^31811 139521 Hans Havermann 04/2021 3980 34149^12172+12172^34149 139512 Hans Havermann 04/2021 3981 (29*10^139476+313)/9 139477 Robert Price 04/2021 3982 31721^24940+24940^31721 139474 Hans Havermann 05/2021 3983 32833^17698+17698^32833 139473 Hans Havermann 05/2021 3984 2^463271-109501 139459 Enzo Doria 04/2014 3985 (5*10^139457+79)/3 139458 Robert Price 03/2018 3986 2^463237-99 139449 Lelio R Paula 09/2017 3987 (49*10^139442+383)/9 139443 Robert Price 04/2019 3988 31155^29902+29902^31155 139441 Hans Havermann 05/2021 3989 (7*10^139417-547)/9 139417 Robert Price 01/2018 3990 29636^31175-31175^29636 139409 Frank Doornink 05/2024 3991 (10^139398+191)/3 139398 Robert Price 02/2018 3992 23*10^139386-3 139388 Robert Price 10/2021 3993 2^463019+79463 139383 Enzo Doria 06/2016 3994 3^292129-112756 139381 Enzo Doria 07/2014 3995 (15*2^462951+1)/527 139361 Lelio R Paula 08/2015 3996 31922^23205+23205^31922 139359 Hans Havermann 05/2021 3997 (19*10^139336+503)/9 139337 Alfred Reich 11/2023 3999 2^462855-1865707 139334 Enzo Doria 02/2016 3998 31237^28876+28876^31237 139334 Hans Havermann 05/2021 4000 (86*10^139315+121)/9 139316 Robert Price 08/2019

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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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