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
See the Top discoverers
See the Latest PRPs
Search by form
| Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
| 7751 | 7*3^220317+8 | 105119 | Lelio R Paula | 09/2014 |
| 7752 | 7^124386+88 | 105119 | Lelio R Paula | 11/2016 |
| 7753 | (2^349197+570)/2 | 105119 | Stefano Morozzi | 09/2020 |
| 7754 | 2^349171-19657 | 105111 | Enzo Doria | 06/2013 |
| 7755 | (2^349115+590)/2 | 105094 | Stefano Morozzi | 09/2020 |
| 7756 | (2^(6*58185+1)-5)/3 | 105093 | Kevin Acres | 11/2013 |
| 7757 | (2^349111-5)/3 | 105093 | Lelio R Paula | 12/2013 |
| 7758 | 675^37142+37142^675 | 105087 | Norbert Schneider | 08/2018 |
| 7759 | 2^348981-2797573 | 105054 | Enzo Doria | 04/2016 |
| 7760 | (445^39667+1)/446 | 105050 | Jinyuan Wang | 05/2024 |
| 7761 | 2^348869-6555 | 105021 | Lelio R Paula | 01/2017 |
| 7762 | 10^105003-17319 | 105003 | Alfred Reich | 08/2024 |
| 7763 | 5^150217+78 | 104998 | Lelio R Paula | 11/2016 |
| 7764 | (88*10^104989-1)/3 | 104991 | Robert Price | 04/2020 |
| 7765 | (28*10^104972+149)/3 | 104973 | Robert Price | 12/2019 |
| 7766 | 24927^16262+16262^24927 | 104972 | Hans Havermann | 10/2020 |
| 7767 | 2^348703-113005 | 104971 | Enzo Doria | 06/2014 |
| 7768 | (191*10^104956-17)/3 | 104958 | Robert Price | 11/2021 |
| 7769 | 2^348612-809 | 104943 | Yves Minet | 05/2013 |
| 7770 | (73*10^104942-1)/9 | 104943 | Robert Price | 01/2015 |
| 7771 | 2^348583-350407 | 104934 | Enzo Doria | 06/2015 |
| 7772 | 2^348531-949 | 104919 | Yves Minet | 05/2012 |
| 7773 | 20^80636-59 | 104910 | Lelio R Paula | 12/2016 |
| 7774 | 8*10^104893-13 | 104894 | Robert Price | 08/2019 |
| 7776 | 2^348437+35 | 104890 | Lelio R Paula | 09/2011 |
| 7775 | 25208^14487+14487^25208 | 104890 | Hans Havermann | 09/2020 |
| 7777 | 2^348348+135 | 104864 | Lelio R Paula | 09/2011 |
| 7778 | (29*10^104858+349)/9 | 104859 | Robert Price | 06/2021 |
| 7779 | 6*10^104852-31 | 104853 | Robert Price | 07/2020 |
| 7781 | (2^348284+9)/25 | 104843 | Lelio R Paula | 12/2013 |
| 7780 | 75^55914-74 | 104843 | Norbert Schneider | 01/2015 |
| 7782 | 2^348268+255255 | 104840 | Lelio R Paula | 01/2017 |
| 7783 | 35540^891+891^35540 | 104839 | Hans Havermann | 09/2020 |
| 7784 | 5^149985-52 | 104836 | Lelio R Paula | 11/2016 |
| 7785 | 2^348224-20249 | 104826 | Enzo Doria | 06/2013 |
| 7786 | (2^348217+2522)/2 | 104824 | Stefano Morozzi | 09/2020 |
| 7787 | 2^348212-20105 | 104823 | Enzo Doria | 06/2013 |
| 7788 | 24647^17898+17898^24647 | 104819 | Hans Havermann | 10/2020 |
| 7789 | 20^80562+19 | 104814 | Lelio R Paula | 12/2016 |
| 7790 | 2*10^104811-87 | 104812 | Robert Price | 04/2018 |
| 7791 | 2^348149-20053 | 104804 | Enzo Doria | 06/2013 |
| 7792 | 2^348095-171 | 104788 | Lelio R Paula | 09/2011 |
| 7793 | 25383^13412+13412^25383 | 104769 | Hans Havermann | 09/2020 |
| 7794 | 2^348003-20377 | 104760 | Enzo Doria | 06/2013 |
| 7795 | 26^74036-27 | 104759 | Anonymous | 09/2024 |
| 7797 | 2^347994-741 | 104757 | Lelio R Paula | 12/2016 |
| 7796 | (2^347993+2234)/2 | 104757 | Stefano Morozzi | 01/2021 |
| 7798 | (2^347990+790)/2 | 104756 | Stefano Morozzi | 09/2020 |
| 7799 | 25137^14702+14702^25137 | 104756 | Hans Havermann | 09/2020 |
| 7800 | (13*2^347972-1)/282309 | 104746 | Lelio R Paula | 03/2014 |
| 7801 | 12883^25484-25484^12883 | 104740 | Norbert Schneider | 08/2022 |
| 7802 | 2^347910-109937 | 104732 | Enzo Doria | 04/2014 |
| 7803 | (88*10^104709-637)/9 | 104710 | Robert Price | 11/2020 |
| 7804 | (13*10^104702+71)/3 | 104703 | Robert Price | 06/2021 |
| 7805 | 5^149794+28 | 104702 | Lelio R Paula | 11/2016 |
| 7806 | 105^51800-2 | 104698 | Lelio R Paula | 10/2017 |
| 7807 | (16^86939+3^86939)/19 | 104684 | Robert Price | 06/2013 |
| 7808 | (15^89009-1)/14 | 104682 | Paul Bourdelais | 03/2010 |
| 7809 | 2^347731-18609 | 104678 | Enzo Doria | 05/2013 |
| 7810 | 4*6^134519+7 | 104677 | Lelio R Paula | 11/2014 |
| 7811 | (34*10^104672-259)/9 | 104673 | Robert Price | 12/2021 |
| 7812 | 25321^13588+13588^25321 | 104656 | Hans Havermann | 09/2020 |
| 7813 | 2^347625+5367 | 104646 | Riley Fisher | 04/2023 |
| 7814 | 2^347612-18545 | 104642 | Enzo Doria | 05/2013 |
| 7815 | 6^134465+95 | 104635 | Lelio R Paula | 11/2016 |
| 7816 | (2^347588+3718)/2 | 104635 | Stefano Morozzi | 09/2020 |
| 7817 | (166*10^104633-7)/3 | 104635 | Robert Price | 11/2020 |
| 7818 | V(750972)/15019441 | 104621 | Serge Batalov | 07/2024 |
| 7819 | 2^347517-17301 | 104614 | Enzo Doria | 05/2013 |
| 7820 | (2^347493+3186)/2 | 104606 | Stefano Morozzi | 09/2020 |
| 7821 | (2^347490+2574)/2 | 104605 | Stefano Morozzi | 09/2020 |
| 7822 | 3^219222-310 | 104596 | Lelio R Paula | 11/2016 |
| 7823 | 25993^10554+10554^25993 | 104581 | Hans Havermann | 09/2020 |
| 7824 | (15*2^347399-1)/13 | 104578 | Lelio R Paula | 03/2014 |
| 7825 | 2^347372-17853 | 104570 | Enzo Doria | 05/2013 |
| 7826 | 2^347314+99 | 104552 | Lelio R Paula | 09/2011 |
| 7827 | 2^347300-22233 | 104548 | Enzo Doria | 06/2013 |
| 7828 | 2^347287-19845 | 104544 | Enzo Doria | 06/2013 |
| 7829 | 2^347258-231191 | 104536 | Harrison Mesh | 06/2022 |
| 7830 | (31*2^347254-1)/891 | 104533 | Lelio R Paula | 03/2014 |
| 7831 | 5*F(250091)*(F(250091)-1)+1 | 104532 | Serge Batalov | 04/2015 |
| 7832 | 7*2^347239-3 | 104531 | Lelio R Paula | 09/2014 |
| 7833 | (3^219098-8)/514147439969 | 104525 | Lelio R Paula | 12/2013 |
| 7834 | 5*3^219047+8 | 104513 | Lelio R Paula | 09/2014 |
| 7835 | 2^347148-109073 | 104502 | Enzo Doria | 04/2014 |
| 7836 | 2^347129-20145 | 104497 | Enzo Doria | 06/2013 |
| 7837 | 4*10^104461-57 | 104462 | Robert Price | 10/2018 |
| 7838 | 2^346999+198831 | 104458 | Stefano Morozzi | 11/2024 |
| 7839 | 2^346996+166273 | 104457 | Stefano Morozzi | 11/2024 |
| 7840 | 2^346997+105755 | 104457 | Stefano Morozzi | 11/2024 |
| 7841 | 2^346997+115259 | 104457 | Stefano Morozzi | 11/2024 |
| 7842 | 2^346992+97515 | 104456 | Stefano Morozzi | 11/2024 |
| 7843 | 2^346992+169593 | 104456 | Stefano Morozzi | 11/2024 |
| 7844 | 2^346994+182215 | 104456 | Stefano Morozzi | 11/2024 |
| 7845 | 2^346994+187933 | 104456 | Stefano Morozzi | 11/2024 |
| 7846 | (7*10^(2*52227+1)+9*10^52227-7)/9 | 104455 | Robert Price | 10/2023 |
| 7849 | (2^346989+590)/2 | 104454 | Stefano Morozzi | 09/2020 |
| 7847 | 2^346988+295 | 104454 | Stefano Morozzi | 11/2024 |
| 7848 | 2^346988+47241 | 104454 | Stefano Morozzi | 11/2024 |
| 7850 | 2^346983+4203 | 104453 | Stefano Morozzi | 11/2024 |
| 7851 | 2^346983+119259 | 104453 | Stefano Morozzi | 11/2024 |
| 7852 | 2^346983+47729 | 104453 | Stefano Morozzi | 11/2024 |
| 7853 | 2^346985+124437 | 104453 | Stefano Morozzi | 11/2024 |
| 7854 | 2^346979+72443 | 104452 | Stefano Morozzi | 11/2024 |
| 7855 | 2^346980+167731 | 104452 | Stefano Morozzi | 11/2024 |
| 7856 | 2^346978+64933 | 104451 | Stefano Morozzi | 11/2024 |
| 7857 | 2^346974+105865 | 104450 | Stefano Morozzi | 11/2024 |
| 7858 | 2^346972+95343 | 104449 | Stefano Morozzi | 11/2024 |
| 7859 | 2^346966+63519 | 104448 | Stefano Morozzi | 11/2024 |
| 7860 | 2^346963+42825 | 104447 | Stefano Morozzi | 11/2024 |
| 7861 | 2^346963+140153 | 104447 | Stefano Morozzi | 11/2024 |
| 7862 | 2^346965+144537 | 104447 | Stefano Morozzi | 11/2024 |
| 7863 | 2^346962+128917 | 104446 | Stefano Morozzi | 11/2024 |
| 7864 | 2^346956+110455 | 104445 | Stefano Morozzi | 11/2024 |
| 7865 | 2^346956+72711 | 104445 | Stefano Morozzi | 11/2024 |
| 7866 | 2^346954+178093 | 104444 | Stefano Morozzi | 11/2024 |
| 7867 | 2^346955+46205 | 104444 | Stefano Morozzi | 11/2024 |
| 7868 | 2^346954+186043 | 104444 | Stefano Morozzi | 11/2024 |
| 7869 | 2^346949+140865 | 104443 | Stefano Morozzi | 11/2024 |
| 7870 | 2^346950+79857 | 104443 | Stefano Morozzi | 11/2024 |
| 7871 | 2^346951+161939 | 104443 | Stefano Morozzi | 11/2024 |
| 7872 | 2^346950+143647 | 104443 | Stefano Morozzi | 11/2024 |
| 7873 | 2^346950+103369 | 104443 | Stefano Morozzi | 11/2024 |
| 7874 | 2^346952+128895 | 104443 | Stefano Morozzi | 11/2024 |
| 7875 | 2^346946+106593 | 104442 | Stefano Morozzi | 11/2024 |
| 7876 | 2^346947+63431 | 104442 | Stefano Morozzi | 11/2024 |
| 7877 | 2^346947+75735 | 104442 | Stefano Morozzi | 11/2024 |
| 7878 | 2^346948+135547 | 104442 | Stefano Morozzi | 11/2024 |
| 7879 | 2^346944+20295 | 104441 | Stefano Morozzi | 11/2024 |
| 7880 | 2^346944+93783 | 104441 | Stefano Morozzi | 11/2024 |
| 7881 | 2^346939+116879 | 104440 | Stefano Morozzi | 11/2024 |
| 7882 | 2^346939+138489 | 104440 | Stefano Morozzi | 11/2024 |
| 7883 | 2^346940+40675 | 104440 | Stefano Morozzi | 11/2024 |
| 7884 | 2^346942+108495 | 104440 | Stefano Morozzi | 11/2024 |
| 7885 | 2^346942+137535 | 104440 | Stefano Morozzi | 11/2024 |
| 7886 | 2^346936+78235 | 104439 | Stefano Morozzi | 11/2024 |
| 7887 | 2^346936+156271 | 104439 | Stefano Morozzi | 11/2024 |
| 7888 | 2^346937+180909 | 104439 | Stefano Morozzi | 11/2024 |
| 7889 | 2^346938+159885 | 104439 | Stefano Morozzi | 11/2024 |
| 7890 | 2^346933+7865 | 104438 | Stefano Morozzi | 11/2024 |
| 7891 | 2^346933+119759 | 104438 | Stefano Morozzi | 11/2024 |
| 7892 | 2^346934+187797 | 104438 | Stefano Morozzi | 11/2024 |
| 7893 | 2^346935+198629 | 104438 | Stefano Morozzi | 11/2024 |
| 7894 | 2^346929+85449 | 104437 | Stefano Morozzi | 11/2024 |
| 7895 | 2^346929+155487 | 104437 | Stefano Morozzi | 11/2024 |
| 7896 | 2^346931+60719 | 104437 | Stefano Morozzi | 11/2024 |
| 7897 | 2^346932+49215 | 104437 | Stefano Morozzi | 11/2024 |
| 7898 | 2^346927+65709 | 104436 | Stefano Morozzi | 11/2024 |
| 7899 | 2^346928+126963 | 104436 | Stefano Morozzi | 11/2024 |
| 7900 | 2^346928+143721 | 104436 | Stefano Morozzi | 11/2024 |
| 7905 | 2^346923-19585 | 104435 | Enzo Doria | 05/2013 |
| 7901 | 2^346923+73001 | 104435 | Stefano Morozzi | 11/2024 |
| 7902 | 2^346924+28671 | 104435 | Stefano Morozzi | 11/2024 |
| 7903 | 2^346924+58657 | 104435 | Stefano Morozzi | 11/2024 |
| 7904 | 2^346924+173475 | 104435 | Stefano Morozzi | 11/2024 |
| 7906 | 2^346921+59357 | 104434 | Stefano Morozzi | 11/2024 |
| 7907 | 2^346916+18183 | 104433 | Stefano Morozzi | 11/2024 |
| 7908 | 2^346914+44625 | 104432 | Stefano Morozzi | 11/2024 |
| 7909 | 2^346912+26343 | 104431 | Stefano Morozzi | 11/2024 |
| 7910 | 2^346912+42367 | 104431 | Stefano Morozzi | 11/2024 |
| 7911 | 2^346908+123705 | 104430 | Stefano Morozzi | 11/2024 |
| 7912 | 2^346899+194015 | 104428 | Stefano Morozzi | 11/2024 |
| 7913 | 2^346900+63393 | 104428 | Stefano Morozzi | 11/2024 |
| 7914 | 2^346901+106215 | 104428 | Stefano Morozzi | 11/2024 |
| 7915 | 2^346901+119309 | 104428 | Stefano Morozzi | 11/2024 |
| 7916 | 2^346902+62587 | 104428 | Stefano Morozzi | 11/2024 |
| 7917 | 2^346897+120207 | 104427 | Stefano Morozzi | 11/2024 |
| 7918 | 2^346897+121107 | 104427 | Stefano Morozzi | 11/2024 |
| 7919 | 2^346897+134289 | 104427 | Stefano Morozzi | 11/2024 |
| 7920 | 2^346898+57429 | 104427 | Stefano Morozzi | 11/2024 |
| 7921 | 2^346898+162267 | 104427 | Stefano Morozzi | 11/2024 |
| 7922 | 2^346890+148989 | 104425 | Stefano Morozzi | 11/2024 |
| 7923 | 2^346891+46313 | 104425 | Stefano Morozzi | 11/2024 |
| 7924 | 2^346892+121191 | 104425 | Stefano Morozzi | 11/2024 |
| 7925 | 2^346888+39211 | 104424 | Stefano Morozzi | 11/2024 |
| 7926 | 2^346883+100949 | 104423 | Stefano Morozzi | 11/2024 |
| 7927 | 2^346883+138341 | 104423 | Stefano Morozzi | 11/2024 |
| 7928 | 2^346885+78357 | 104423 | Stefano Morozzi | 11/2024 |
| 7929 | 2^346882+167169 | 104422 | Stefano Morozzi | 11/2024 |
| 7930 | 2^346877+43587 | 104421 | Stefano Morozzi | 11/2024 |
| 7931 | 2^346879+69983 | 104421 | Stefano Morozzi | 11/2024 |
| 7932 | 2^346875+24885 | 104420 | Stefano Morozzi | 11/2024 |
| 7933 | 2^346875+131835 | 104420 | Stefano Morozzi | 11/2024 |
| 7934 | 2^346875+161301 | 104420 | Stefano Morozzi | 11/2024 |
| 7935 | 2^346871+85491 | 104419 | Stefano Morozzi | 11/2024 |
| 7936 | 2^346866+135849 | 104418 | Stefano Morozzi | 11/2024 |
| 7937 | 2^346868+445 | 104418 | Stefano Morozzi | 11/2024 |
| 7938 | 2^346868+111637 | 104418 | Stefano Morozzi | 11/2024 |
| 7939 | 2^346864+104917 | 104417 | Stefano Morozzi | 11/2024 |
| 7941 | (11*2^346864-1)/175 | 104416 | Lelio R Paula | 03/2014 |
| 7940 | 2^346862+60109 | 104416 | Stefano Morozzi | 11/2024 |
| 7942 | 2^346857+43607 | 104415 | Stefano Morozzi | 11/2024 |
| 7943 | 2^346857+142719 | 104415 | Stefano Morozzi | 11/2024 |
| 7947 | 2^346854+346854^2+1 | 104414 | Robert Price | 06/2014 |
| 7944 | 2^346853+29051 | 104414 | Stefano Morozzi | 11/2024 |
| 7945 | 2^346855+3549 | 104414 | Stefano Morozzi | 11/2024 |
| 7946 | 2^346855+194849 | 104414 | Stefano Morozzi | 11/2024 |
| 7948 | 2^346850+34423 | 104413 | Stefano Morozzi | 11/2024 |
| 7949 | 2^346851+95235 | 104413 | Stefano Morozzi | 11/2024 |
| 7950 | 2^346846+99883 | 104412 | Stefano Morozzi | 11/2024 |
| 7951 | 2^346846+146089 | 104412 | Stefano Morozzi | 11/2024 |
| 7952 | 2^346848+14577 | 104412 | Stefano Morozzi | 11/2024 |
| 7953 | 2^346848+38901 | 104412 | Stefano Morozzi | 11/2024 |
| 7954 | 2^346849+94107 | 104412 | Stefano Morozzi | 11/2024 |
| 7955 | 2^346843+112473 | 104411 | Stefano Morozzi | 11/2024 |
| 7956 | 2^346845+186035 | 104411 | Stefano Morozzi | 11/2024 |
| 7957 | 2^346841+146711 | 104410 | Stefano Morozzi | 11/2024 |
| 7958 | 2^346839+59931 | 104409 | Stefano Morozzi | 11/2024 |
| 7959 | 2^346834+11715 | 104408 | Lelio R Paula | 04/2015 |
| 7960 | 2^346830+73129 | 104407 | Stefano Morozzi | 11/2024 |
| 7961 | 2^346832+168607 | 104407 | Stefano Morozzi | 11/2024 |
| 7962 | 2^346832+179253 | 104407 | Stefano Morozzi | 11/2024 |
| 7963 | 2^346826+73969 | 104406 | Stefano Morozzi | 11/2024 |
| 7964 | 2^346827+122901 | 104406 | Stefano Morozzi | 11/2024 |
| 7965 | 2^346823+36191 | 104405 | Stefano Morozzi | 11/2024 |
| 7966 | 2^346823+185955 | 104405 | Stefano Morozzi | 11/2024 |
| 7967 | 2^346825+3297 | 104405 | Stefano Morozzi | 11/2024 |
| 7968 | 2^346822+74757 | 104404 | Stefano Morozzi | 11/2024 |
| 7969 | 2^346822+160495 | 104404 | Stefano Morozzi | 11/2024 |
| 7970 | 2^346816+146085 | 104403 | Stefano Morozzi | 11/2024 |
| 7971 | 2^346816+158707 | 104403 | Stefano Morozzi | 11/2024 |
| 7972 | 2^346818+26689 | 104403 | Stefano Morozzi | 11/2024 |
| 7973 | 2^346818+69805 | 104403 | Stefano Morozzi | 11/2024 |
| 7974 | 2^346818+83899 | 104403 | Stefano Morozzi | 11/2024 |
| 7975 | 2^346818+110299 | 104403 | Stefano Morozzi | 11/2024 |
| 7976 | 2^346818+182793 | 104403 | Stefano Morozzi | 11/2024 |
| 7977 | 2^346819+95351 | 104403 | Stefano Morozzi | 11/2024 |
| 7978 | 2^346814+136243 | 104402 | Stefano Morozzi | 11/2024 |
| 7979 | 2^346814+188649 | 104402 | Stefano Morozzi | 11/2024 |
| 7980 | 2^346810+106309 | 104401 | Stefano Morozzi | 11/2024 |
| 7981 | 2^346807+86769 | 104400 | Stefano Morozzi | 11/2024 |
| 7982 | 2^346808+114975 | 104400 | Stefano Morozzi | 11/2024 |
| 7983 | 2^346809+61035 | 104400 | Stefano Morozzi | 11/2024 |
| 7984 | 2^346803+10845 | 104399 | Stefano Morozzi | 11/2024 |
| 7985 | 2^346803+110705 | 104399 | Stefano Morozzi | 11/2024 |
| 7986 | 2^346804+134761 | 104399 | Stefano Morozzi | 11/2024 |
| 7987 | 2^346800+137791 | 104398 | Stefano Morozzi | 11/2024 |
| 7988 | 2^346797+109589 | 104397 | Stefano Morozzi | 11/2024 |
| 7989 | 2^346798+91909 | 104397 | Stefano Morozzi | 11/2024 |
| 7990 | 2^346798+163029 | 104397 | Stefano Morozzi | 11/2024 |
| 7991 | 2^346793+62669 | 104396 | Stefano Morozzi | 11/2024 |
| 7992 | 2^346793+189081 | 104396 | Stefano Morozzi | 11/2024 |
| 7993 | 2^346794+109095 | 104396 | Stefano Morozzi | 11/2024 |
| 7994 | 2^346796+57285 | 104396 | Stefano Morozzi | 11/2024 |
| 7995 | 2^346791+184833 | 104395 | Stefano Morozzi | 11/2024 |
| 7996 | 2^346787+81005 | 104394 | Stefano Morozzi | 11/2024 |
| 7997 | 2^346787+81605 | 104394 | Stefano Morozzi | 11/2024 |
| 7998 | 2^346789+2015 | 104394 | Stefano Morozzi | 11/2024 |
| 7999 | 2^346789+19595 | 104394 | Stefano Morozzi | 11/2024 |
| 8000 | 2^346784+84771 | 104393 | Stefano Morozzi | 11/2024 |
