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) !!!
Submit your PRPs
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Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
3751 | 28302^23269+23269^28302 | 123589 | Hans Havermann | 03/2021 |
3752 | 2^410540-115079 | 123585 | Enzo Doria | 06/2015 |
3753 | (7*10^123563+107)/3 | 123564 | Robert Price | 02/2018 |
3754 | 9*10^123549+89 | 123550 | Robert Price | 11/2019 |
3755 | (197*10^123545+7)/3 | 123547 | Robert Price | 12/2020 |
3756 | (3*2^410392-1)/9229 | 123537 | Lelio R Paula | 05/2014 |
3757 | (29*10^123510+277)/9 | 123511 | Robert Price | 11/2021 |
3758 | 28118^24687+24687^28118 | 123508 | Hans Havermann | 03/2021 |
3759 | 39994^1225+1225^39994 | 123507 | Hans Havermann | 03/2021 |
3760 | 2^410206-113081 | 123485 | Enzo Doria | 07/2014 |
3761 | (25*2^410192+1)/10397 | 123478 | Lelio R Paula | 04/2014 |
3762 | 28974^18215+18215^28974 | 123442 | Hans Havermann | 03/2021 |
3763 | 28901^18618+18618^28901 | 123406 | Hans Havermann | 03/2021 |
3764 | 2^409909-189 | 123395 | Enzo Doria | 05/2014 |
3765 | 2^409896-109043 | 123391 | Enzo Doria | 04/2014 |
3766 | 2^409890+75409 | 123390 | Enzo Doria | 04/2016 |
3767 | 81254^33+33^81254 | 123386 | Hans Havermann | 03/2021 |
3768 | 33463^4854+4854^33463 | 123348 | Hans Havermann | 03/2021 |
3769 | 34061^4182+4182^34061 | 123348 | Hans Havermann | 03/2021 |
3770 | 133^58076-2 | 123345 | Lelio R Paula | 10/2017 |
3771 | F(590041) | 123311 | Henri Lifchitz | 01/2005 |
3772 | (82*10^123299+377)/9 | 123300 | Robert Price | 03/2022 |
3773 | 2^409566-113501 | 123292 | Enzo Doria | 08/2014 |
3774 | 2^409533+77747 | 123282 | Enzo Doria | 05/2016 |
3775 | 2^409436-112799 | 123253 | Enzo Doria | 06/2014 |
3776 | 28212^23321+23321^28212 | 123223 | Hans Havermann | 03/2021 |
3777 | 2^409225+1873787 | 123189 | Enzo Doria | 06/2016 |
3778 | 2^409174+73009 | 123174 | Enzo Doria | 04/2016 |
3779 | 2^409058-112685 | 123139 | Enzo Doria | 06/2014 |
3780 | (13*10^123137-61)/3 | 123138 | Robert Price | 11/2018 |
3781 | 4*10^123113+21 | 123114 | Robert Price | 12/2018 |
3782 | 2^408778+77689 | 123055 | Enzo Doria | 05/2016 |
3783 | 2^408690-75 | 123028 | Lelio R Paula | 11/2013 |
3784 | 28327^22032+22032^28327 | 123026 | Hans Havermann | 03/2021 |
3785 | (29*10^122996+673)/9 | 122997 | Robert Price | 12/2018 |
3786 | (65*10^122994-101)/9 | 122995 | Robert Price | 01/2022 |
3787 | 2^408574-2787341 | 122994 | Enzo Doria | 03/2016 |
3788 | 3*10^122977+37 | 122978 | Robert Price | 08/2018 |
3789 | (7*10^122976-67)/3 | 122977 | Robert Price | 10/2021 |
3790 | Phi(157825,10) | 122961 | Maksym Voznyy | 06/2015 |
3791 | (68*10^122933-419)/9 | 122934 | Robert Price | 07/2019 |
3792 | 29712^13721+13721^29712 | 122931 | Hans Havermann | 03/2021 |
3793 | (13*2^408283+1)/1665 | 122904 | Lelio R Paula | 05/2014 |
3794 | (266*10^122872-17)/3 | 122874 | Robert Price | 07/2020 |
3795 | (16*10^122871+77)/3 | 122872 | Robert Price | 03/2019 |
3796 | 30395^11022+11022^30395 | 122865 | Hans Havermann | 03/2021 |
3797 | 4*10^122859-69 | 122860 | Robert Price | 01/2022 |
3798 | (10^122857+167)/3 | 122857 | Robert Price | 05/2021 |
3799 | 33331^4852+4852^33331 | 122856 | Hans Havermann | 03/2021 |
3800 | (11*2^408100-1)/35 | 122850 | Lelio R Paula | 04/2014 |
3801 | (19*10^122836-43)/3 | 122837 | Robert Price | 05/2019 |
3802 | 28420^20969+20969^28420 | 122820 | Hans Havermann | 03/2021 |
3803 | (16*10^122818+179)/3 | 122819 | Robert Price | 11/2021 |
3804 | 29865^12934+12934^29865 | 122797 | Hans Havermann | 03/2021 |
3805 | (2^407821-lucasV(1,2,407821)+1)/2 | 122767 | Mike Oakes | 11/2016 |
3806 | (32*10^122733-77)/9 | 122734 | Robert Price | 06/2018 |
3807 | (21*2^407604-1)/215 | 122701 | Lelio R Paula | 04/2014 |
3809 | (22*10^122681+161)/3 | 122682 | Robert Price | 05/2019 |
3808 | 29513^14350+14350^29513 | 122682 | Hans Havermann | 03/2021 |
3810 | (21*2^407433-1)/13 | 122650 | Lelio R Paula | 04/2014 |
3811 | (26*10^122625-131)/3 | 122626 | Robert Price | 10/2019 |
3812 | 27925^24562+24562^27925 | 122599 | Hans Havermann | 03/2021 |
3813 | (73*10^122592-1)/9 | 122593 | Robert Price | 01/2015 |
3814 | (5*10^122592+91)/3 | 122593 | Robert Price | 04/2018 |
3815 | 36751^2166+2166^36751 | 122589 | Hans Havermann | 03/2021 |
3816 | (85*10^122585-1)/3 | 122587 | Robert Price | 02/2020 |
3817 | 29368^14931+14931^29368 | 122585 | Hans Havermann | 03/2021 |
3818 | 2^407179-112075 | 122574 | Enzo Doria | 06/2014 |
3819 | (21*2^407131+1)/207517523 | 122552 | Lelio R Paula | 04/2014 |
3820 | (66^67349+1)/67 | 122543 | Paul Bourdelais | 09/2017 |
3821 | (646*10^122533+11)/9 | 122535 | Robert Price | 10/2021 |
3822 | 2^407008-1867919 | 122522 | Enzo Doria | 04/2016 |
3823 | 11^117642-300 | 122512 | Enzo Doria | 10/2012 |
3824 | (F(3*97700+1)^2+L(3*97700+1)^2)/2 | 122509 | Henri Lifchitz | 10/2017 |
3825 | 2^406949+72197 | 122504 | Enzo Doria | 04/2016 |
3826 | (19*10^122501+149)/3 | 122502 | Robert Price | 05/2019 |
3827 | 28632^18977+18977^28632 | 122495 | Hans Havermann | 03/2021 |
3828 | 31815^7076+7076^31815 | 122481 | Hans Havermann | 03/2021 |
3829 | 2^406826-65 | 122467 | Lelio R Paula | 11/2013 |
3830 | 2^406821-2797363 | 122466 | Enzo Doria | 04/2016 |
3831 | (7*10^122456-331)/9 | 122456 | Robert Price | 03/2022 |
3832 | 2^406758-17 | 122447 | Lelio R Paula | 11/2013 |
3833 | 29941^12282+12282^29941 | 122437 | Hans Havermann | 03/2021 |
3834 | (30^82883-1)/29 | 122427 | Robert Price | 12/2011 |
3835 | 27496^27577+27577^27496 | 122422 | Norbert Schneider | 12/2020 |
3836 | 28732^18215+18215^28732 | 122411 | Hans Havermann | 03/2021 |
3837 | (2^406583-1)/813167 | 122388 | Jens K. Andersen | 02/2009 |
3838 | 4*10^122377+19 | 122378 | Robert Price | 10/2018 |
3839 | 28227^21634+21634^28227 | 122368 | Hans Havermann | 03/2021 |
3840 | Phi(246362,10) | 122365 | Makoto Kamada | 09/2019 |
3841 | 3*10^122345-97 | 122346 | Robert Price | 07/2018 |
3842 | 97^61575-2 | 122336 | Lelio R Paula | 12/2014 |
3843 | 2*10^122319+47 | 122320 | Robert Price | 12/2021 |
3844 | 208^52765+52765^208 | 122313 | Norbert Schneider | 11/2020 |
3845 | 2^406298+2799109 | 122308 | Enzo Doria | 04/2016 |
3846 | 7*10^122294+57 | 122295 | Robert Price | 06/2019 |
3847 | (27*2^406241-1)/10277 | 122289 | Lelio R Paula | 04/2014 |
3848 | 2^406229-1849993 | 122288 | Enzo Doria | 08/2015 |
3849 | 3*10^122274+7 | 122275 | Robert Price | 07/2015 |
3850 | 2^406117+1876577 | 122254 | Enzo Doria | 07/2016 |
3851 | 29308^14835+14835^29308 | 122253 | Hans Havermann | 03/2021 |
3852 | 28119^22268+22268^28119 | 122253 | Hans Havermann | 03/2021 |
3853 | 32167^6312+6312^32167 | 122240 | Hans Havermann | 03/2021 |
3854 | 3^256199-2^256199 | 122238 | Mike Oakes | 06/2005 |
3855 | 27678^26053+26053^27678 | 122223 | Hans Havermann | 03/2021 |
3856 | 2^405992-78557 | 122216 | Jorge Menendez | 03/2018 |
3857 | (8*10^122203+43)/3 | 122204 | Robert Price | 06/2018 |
3858 | (58*10^122170+329)/9 | 122171 | Robert Price | 05/2019 |
3859 | 2^405774+179149 | 122151 | Enzo Doria | 06/2016 |
3860 | (218*10^122109+7)/9 | 122111 | Robert Price | 06/2022 |
3861 | 29189^15246+15246^29189 | 122103 | Hans Havermann | 03/2021 |
3863 | 34*10^122082-9 | 122084 | Robert Price | 06/2020 |
3862 | 33442^4473+4473^33442 | 122084 | Hans Havermann | 03/2021 |
3864 | 5*10^122082+41 | 122083 | Robert Price | 03/2019 |
3865 | 31849^6808+6808^31849 | 122078 | Hans Havermann | 03/2021 |
3867 | 2^405514-3311 | 122072 | Yves Minet | 12/2014 |
3868 | 2^405514-115511 | 122072 | Enzo Doria | 07/2015 |
3866 | 23*10^122070-7 | 122072 | Robert Price | 02/2020 |
3869 | 2^405422-113261 | 122045 | Enzo Doria | 07/2014 |
3870 | 2^405173+71237 | 121970 | Enzo Doria | 04/2016 |
3871 | (154*10^121953+17)/9 | 121955 | Robert Price | 06/2022 |
3872 | (34*10^121924+191)/9 | 121925 | Robert Price | 08/2021 |
3873 | (2^405016+1)/257 | 121920 | Lelio R Paula | 04/2014 |
3874 | 28557^18590+18590^28557 | 121918 | Hans Havermann | 03/2021 |
3875 | 28641^18002+18002^28641 | 121877 | Hans Havermann | 03/2021 |
3876 | 2^404858+71329 | 121875 | Enzo Doria | 04/2016 |
3877 | 2^404813-114703 | 121861 | Enzo Doria | 04/2015 |
3878 | 2^404764+77791 | 121847 | Enzo Doria | 05/2016 |
3879 | 28830^16841+16841^28830 | 121847 | Hans Havermann | 03/2021 |
3880 | (4*10^121825+89)/3 | 121826 | Robert Price | 08/2021 |
3881 | 317^48694+48694^317 | 121787 | Norbert Schneider | 08/2015 |
3882 | 2^404536-115259 | 121778 | Enzo Doria | 06/2015 |
3883 | 2^404501-631 | 121767 | Yves Minet | 07/2012 |
3884 | 5*10^121764-69 | 121765 | Robert Price | 02/2021 |
3885 | 28236^20485+20485^28236 | 121738 | Hans Havermann | 02/2021 |
3886 | (382*10^121694-31)/9 | 121696 | Robert Price | 06/2022 |
3887 | 63^67620+2 | 121672 | Lelio R Paula | 08/2015 |
3888 | (16*10^121633+167)/3 | 121634 | Robert Price | 06/2019 |
3889 | 29955^11494+11494^29955 | 121632 | Hans Havermann | 02/2021 |
3890 | (17*10^121621+1)/9 | 121622 | Serge Batalov | 05/2010 |
3891 | 31088^8163+8163^31088 | 121612 | Hans Havermann | 02/2021 |
3892 | (15*2^403912+1)/271 | 121589 | Lelio R Paula | 05/2014 |
3893 | (10^121543-79)/3 | 121543 | Robert Price | 01/2018 |
3894 | 2^403676+76831 | 121519 | Enzo Doria | 05/2016 |
3895 | (7*10^121487+143)/3 | 121488 | Robert Price | 03/2018 |
3896 | 27965^22086+22086^27965 | 121484 | Hans Havermann | 02/2021 |
3897 | (893*10^121470+7)/9 | 121472 | Robert Price | 06/2021 |
3898 | (206*10^121462-11)/3 | 121464 | Robert Price | 02/2022 |
3899 | (77*10^121455+67)/9 | 121456 | Robert Price | 12/2021 |
3900 | 2^403363-113635 | 121425 | Enzo Doria | 08/2014 |
3901 | (17*10^121418-113)/3 | 121419 | Robert Price | 06/2021 |
3902 | 2^403336-1861469 | 121417 | Enzo Doria | 03/2016 |
3903 | 27929^22186+22186^27929 | 121382 | Hans Havermann | 02/2021 |
3904 | p(24442)#/2-64 | 121381 | Robert Price | 04/2017 |
3905 | 11^116555-720 | 121380 | Enzo Doria | 11/2012 |
3906 | 2^403100-461267 | 121346 | Enzo Doria | 07/2015 |
3907 | 2^403093-112213 | 121344 | Enzo Doria | 06/2014 |
3908 | 29404^13385+13385^29404 | 121340 | Hans Havermann | 02/2021 |
3909 | 28106^20745+20745^28106 | 121332 | Hans Havermann | 02/2021 |
3910 | (316^48539+1)/317 | 121330 | Eric Chen | 10/2017 |
3911 | (23*10^121320-71)/3 | 121321 | Robert Price | 07/2020 |
3912 | 2^403004+1866361 | 121317 | Enzo Doria | 03/2016 |
3913 | 2^402953+89 | 121301 | Lelio R Paula | 10/2013 |
3914 | 2^402944-2788319 | 121299 | Enzo Doria | 03/2016 |
3915 | (44*10^121297-719)/9 | 121298 | Robert Price | 12/2018 |
3916 | (27*2^402865+1)/5 | 121276 | Lelio R Paula | 04/2014 |
3917 | 2^402828-113183 | 121264 | Enzo Doria | 07/2014 |
3918 | (17*10^121242+1)/9 | 121243 | Serge Batalov | 05/2010 |
3919 | (15*2^402757+1)/101 | 121242 | Lelio R Paula | 05/2014 |
3921 | 2^402715+1874223 | 121230 | Enzo Doria | 06/2016 |
3920 | (35*10^121229-593)/9 | 121230 | Robert Price | 07/2018 |
3922 | (91^61879+1)/92 | 121222 | Paul Bourdelais | 09/2017 |
3923 | 28719^16568+16568^28719 | 121174 | Hans Havermann | 02/2021 |
3924 | 7*10^121144+9 | 121145 | Robert Price | 09/2015 |
3925 | 27490^25467+25467^27490 | 121121 | Hans Havermann | 02/2021 |
3926 | 34575^3182+3182^34575 | 121106 | Hans Havermann | 02/2021 |
3927 | 5*10^121100-37 | 121101 | Robert Price | 11/2021 |
3928 | 29954^10935+10935^29954 | 120979 | Hans Havermann | 02/2021 |
3929 | 33585^3992+3992^33585 | 120946 | Hans Havermann | 02/2021 |
3930 | 40296^1003+1003^40296 | 120941 | Hans Havermann | 02/2021 |
3931 | 2^401725-113251 | 120932 | Enzo Doria | 07/2014 |
3932 | (15*2^401677-1)/19 | 120917 | Lelio R Paula | 05/2014 |
3933 | 2^401652+73711 | 120910 | Enzo Doria | 04/2016 |
3934 | (2^401632+3)/79 | 120902 | Lelio R Paula | 04/2014 |
3935 | 40450^973+973^40450 | 120870 | Hans Havermann | 01/2021 |
3936 | 10^120841+88417 | 120842 | Patrick De Geest | 04/2020 |
3937 | 10^120841-123456789 | 120841 | Robert Price | 02/2020 |
3938 | 10^120841-176853 | 120841 | Patrick De Geest | 04/2020 |
3939 | 2^401406-2791331 | 120836 | Enzo Doria | 03/2016 |
3940 | (28^83497+1)/29 | 120832 | Robert Price | 07/2013 |
3941 | (22*10^120828+161)/3 | 120829 | Robert Price | 05/2019 |
3942 | 2^401369+1867367 | 120825 | Enzo Doria | 03/2016 |
3943 | (5*10^120821+43)/3 | 120822 | Robert Price | 12/2021 |
3944 | (10^120782+29)/3 | 120782 | Serge Batalov | 12/2014 |
3945 | 2^401215-1657 | 120778 | Yves Minet | 07/2014 |
3946 | 2^401159+53 | 120761 | Lelio R Paula | 10/2013 |
3947 | 27782^22179+22179^27782 | 120739 | Hans Havermann | 01/2021 |
3948 | 32974^4585+4585^32974 | 120730 | Hans Havermann | 02/2021 |
3949 | 2^401031-113047 | 120723 | Enzo Doria | 07/2014 |
3950 | 30598^8813+8813^30598 | 120713 | Hans Havermann | 02/2021 |
3951 | (71*10^120703-287)/9 | 120704 | Robert Price | 09/2019 |
3952 | (29*2^400909-1)/303 | 120685 | Lelio R Paula | 04/2014 |
3953 | 34793^2940+2940^34793 | 120675 | Hans Havermann | 02/2021 |
3954 | (2^400846+538)/2 | 120667 | Stefano Morozzi | 09/2020 |
3955 | (166*10^120654+11)/3 | 120656 | Robert Price | 03/2021 |
3956 | 34066^3481+3481^34066 | 120652 | Hans Havermann | 02/2021 |
3957 | 8*10^120637-27 | 120638 | Robert Price | 10/2021 |
3958 | (2^400709+3546)/2 | 120626 | Stefano Morozzi | 09/2020 |
3959 | (2^400700+3126)/2 | 120623 | Stefano Morozzi | 09/2020 |
3960 | (2^400693+2634)/2 | 120621 | Stefano Morozzi | 09/2020 |
3961 | 9*10^120617-61 | 120618 | Robert Price | 06/2021 |
3962 | (29*10^120590-71)/3 | 120591 | Robert Price | 07/2021 |
3963 | 2^400571-15 | 120584 | Lelio R Paula | 10/2013 |
3964 | (10^120574+359)/9 | 120574 | Serge Batalov | 12/2014 |
3965 | 27431^24810+24810^27431 | 120550 | Hans Havermann | 02/2021 |
3966 | 2^400424-216413 | 120540 | Enzo Doria | 04/2013 |
3967 | 29090^13911+13911^29090 | 120531 | Hans Havermann | 02/2021 |
3968 | (2^400346+1722)/2 | 120516 | Stefano Morozzi | 09/2020 |
3969 | 27899^20868+20868^27899 | 120510 | Hans Havermann | 02/2021 |
3970 | 33740^3729+3729^33740 | 120506 | Hans Havermann | 02/2021 |
3971 | (17*2^400200-1)/587 | 120471 | Lelio R Paula | 05/2014 |
3972 | 2^400166+1874899 | 120462 | Enzo Doria | 06/2016 |
3973 | (2^400165+1602)/2 | 120462 | Stefano Morozzi | 09/2020 |
3974 | 37078^1771+1771^37078 | 120438 | Hans Havermann | 02/2021 |
3975 | (2^400084+1638)/2 | 120437 | Stefano Morozzi | 09/2020 |
3976 | (3*2^400045-1)/865 | 120424 | Lelio R Paula | 04/2014 |
3977 | (2^399974+2790)/2 | 120404 | Stefano Morozzi | 02/2021 |
3978 | 2^399966+73759 | 120402 | Enzo Doria | 04/2016 |
3979 | (2^399961+2306)/2 | 120400 | Stefano Morozzi | 02/2021 |
3980 | (112*10^120395-1)/3 | 120397 | Serge Batalov | 12/2014 |
3981 | 2^399918-95 | 120388 | Lelio R Paula | 04/2013 |
3982 | (28*10^120381-67)/3 | 120382 | Robert Price | 10/2020 |
3983 | (49*10^120380-139)/9 | 120381 | Robert Price | 03/2019 |
3984 | (2^399874+2194)/2 | 120374 | Stefano Morozzi | 09/2020 |
3985 | 2^399792-1849259 | 120350 | Enzo Doria | 08/2015 |
3986 | 9*10^120342-7 | 120343 | Robert Price | 09/2015 |
3987 | (2^399751+786)/2 | 120337 | Stefano Morozzi | 09/2020 |
3988 | (331*10^120332-7)/9 | 120334 | Robert Price | 04/2022 |
3989 | (13*10^120306-37)/3 | 120307 | Robert Price | 01/2019 |
3990 | (23*10^120299+37)/3 | 120300 | Robert Price | 02/2022 |
3991 | (2^399604+3070)/2 | 120293 | Stefano Morozzi | 09/2020 |
3992 | (2^399549+1062)/2 | 120276 | Stefano Morozzi | 09/2020 |
3993 | 2^399526-1861721 | 120270 | Enzo Doria | 11/2015 |
3994 | (10^(2*60126+1)+36*10^60126-1)/9 | 120253 | Robert Price | 10/2015 |
3995 | 32016^5687+5687^32016 | 120217 | Hans Havermann | 01/2021 |
3996 | (205*10^120212-1)/3 | 120214 | Robert Price | 11/2021 |
3997 | 2^399322-2798111 | 120208 | Enzo Doria | 04/2016 |
3998 | 30438^8867+8867^30438 | 120163 | Hans Havermann | 02/2021 |
4000 | 72^64693-71^64693 | 120157 | Robert Price | 03/2014 |
3999 | (17*10^120156-161)/9 | 120157 | Robert Price | 02/2021 |