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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Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
7753 | 24276^19961+19961^24276 | 104392 | Hans Havermann | 09/2020 |
7751 | 2^346780+121341 | 104392 | Stefano Morozzi | 11/2024 |
7752 | 2^346780+171943 | 104392 | Stefano Morozzi | 11/2024 |
7754 | 2^346777+28991 | 104391 | Stefano Morozzi | 11/2024 |
7755 | 2^346777+110021 | 104391 | Stefano Morozzi | 11/2024 |
7756 | 2^346778+53769 | 104391 | Stefano Morozzi | 11/2024 |
7757 | 2^346779+134115 | 104391 | Stefano Morozzi | 11/2024 |
7758 | 2^346779+172961 | 104391 | Stefano Morozzi | 11/2024 |
7759 | 2^346773+81797 | 104390 | Stefano Morozzi | 11/2024 |
7760 | 2^346774+164119 | 104390 | Stefano Morozzi | 11/2024 |
7761 | 2^346775+72063 | 104390 | Stefano Morozzi | 11/2024 |
7762 | 2^346775+197315 | 104390 | Stefano Morozzi | 11/2024 |
7763 | 2^346776+32233 | 104390 | Stefano Morozzi | 11/2024 |
7764 | 2^346776+187777 | 104390 | Stefano Morozzi | 11/2024 |
7765 | 2^346770+98719 | 104389 | Stefano Morozzi | 11/2024 |
7766 | 2^346770+110437 | 104389 | Stefano Morozzi | 11/2024 |
7767 | 2^346771+1205 | 104389 | Stefano Morozzi | 11/2024 |
7768 | 2^346771+3465 | 104389 | Stefano Morozzi | 11/2024 |
7769 | 2^346771+129543 | 104389 | Stefano Morozzi | 11/2024 |
7770 | 2^346772+41143 | 104389 | Stefano Morozzi | 11/2024 |
7771 | 2^346772+69865 | 104389 | Stefano Morozzi | 11/2024 |
7772 | 2^346767+168441 | 104388 | Stefano Morozzi | 11/2024 |
7773 | 2^346768+37897 | 104388 | Stefano Morozzi | 11/2024 |
7774 | 2^346768+80977 | 104388 | Stefano Morozzi | 11/2024 |
7775 | 2^346769+158745 | 104388 | Stefano Morozzi | 11/2024 |
7781 | 79^55009+78 | 104387 | Norbert Schneider | 02/2015 |
7776 | 2^346763+14723 | 104387 | Stefano Morozzi | 11/2024 |
7777 | 2^346763+90743 | 104387 | Stefano Morozzi | 11/2024 |
7778 | 2^346764+95503 | 104387 | Stefano Morozzi | 11/2024 |
7779 | 2^346766+31645 | 104387 | Stefano Morozzi | 11/2024 |
7780 | 2^346766+51115 | 104387 | Stefano Morozzi | 11/2024 |
7782 | 2^346760+90225 | 104386 | Stefano Morozzi | 11/2024 |
7783 | 2^346762+31825 | 104386 | Stefano Morozzi | 11/2024 |
7784 | 2^346762+192817 | 104386 | Stefano Morozzi | 11/2024 |
7785 | 2^346757+97691 | 104385 | Stefano Morozzi | 11/2024 |
7786 | 2^346758+111415 | 104385 | Stefano Morozzi | 11/2024 |
7787 | 2^346759+86331 | 104385 | Stefano Morozzi | 11/2024 |
7788 | 2^346755+22085 | 104384 | Stefano Morozzi | 11/2024 |
7789 | 2^346750+140967 | 104383 | Stefano Morozzi | 11/2024 |
7790 | 2^346751+48515 | 104383 | Stefano Morozzi | 11/2024 |
7791 | 2^346751+74481 | 104383 | Stefano Morozzi | 11/2024 |
7792 | 2^346752+103497 | 104383 | Stefano Morozzi | 11/2024 |
7793 | 2^346747+4589 | 104382 | Stefano Morozzi | 11/2024 |
7794 | 2^346747+29969 | 104382 | Stefano Morozzi | 11/2024 |
7795 | 2^346747+130973 | 104382 | Stefano Morozzi | 11/2024 |
7796 | 2^346748+184387 | 104382 | Stefano Morozzi | 11/2024 |
7797 | 2^346743+39545 | 104381 | Stefano Morozzi | 11/2024 |
7798 | 2^346743+61335 | 104381 | Stefano Morozzi | 11/2024 |
7799 | 2^346746+99025 | 104381 | Stefano Morozzi | 11/2024 |
7800 | 2^346737+39431 | 104379 | Stefano Morozzi | 11/2024 |
7801 | 2^346733+96437 | 104378 | Stefano Morozzi | 11/2024 |
7802 | 2^346736+83025 | 104378 | Stefano Morozzi | 11/2024 |
7803 | 2^346736+196405 | 104378 | Stefano Morozzi | 11/2024 |
7804 | 2^346732+72685 | 104377 | Stefano Morozzi | 11/2024 |
7805 | 2^346727+86903 | 104376 | Stefano Morozzi | 11/2024 |
7806 | 2^346727+89829 | 104376 | Stefano Morozzi | 11/2024 |
7807 | 2^346729+199319 | 104376 | Stefano Morozzi | 11/2024 |
7808 | 2^346723+73521 | 104375 | Stefano Morozzi | 11/2024 |
7809 | 2^346724+91177 | 104375 | Stefano Morozzi | 11/2024 |
7810 | 2^346726+191527 | 104375 | Stefano Morozzi | 11/2024 |
7811 | 2^346720+235 | 104374 | Stefano Morozzi | 11/2024 |
7812 | 2^346720+189435 | 104374 | Stefano Morozzi | 11/2024 |
7813 | 2^346718+124833 | 104373 | Stefano Morozzi | 11/2024 |
7814 | 2^346718+127029 | 104373 | Stefano Morozzi | 11/2024 |
7815 | 2^346719+129291 | 104373 | Stefano Morozzi | 11/2024 |
7816 | 2^346719+183033 | 104373 | Stefano Morozzi | 11/2024 |
7817 | 2^346714+81909 | 104372 | Stefano Morozzi | 11/2024 |
7818 | 2^346714+174493 | 104372 | Stefano Morozzi | 11/2024 |
7819 | 2^346716+174123 | 104372 | Stefano Morozzi | 11/2024 |
7820 | 2^346711+160659 | 104371 | Stefano Morozzi | 11/2024 |
7821 | 2^346710+143649 | 104371 | Stefano Morozzi | 11/2024 |
7822 | 2^346712+52063 | 104371 | Stefano Morozzi | 11/2024 |
7823 | 2^346707+27099 | 104370 | Stefano Morozzi | 11/2024 |
7824 | 2^346708+26217 | 104370 | Stefano Morozzi | 11/2024 |
7825 | 2^346708+165715 | 104370 | Stefano Morozzi | 11/2024 |
7826 | 2^346705+6581 | 104369 | Stefano Morozzi | 11/2024 |
7827 | 2^346705+39851 | 104369 | Stefano Morozzi | 11/2024 |
7828 | 2^346706+172963 | 104369 | Stefano Morozzi | 11/2024 |
7831 | 3^218744+58 | 104368 | Lelio R Paula | 11/2016 |
7829 | 2^346700+191515 | 104368 | Stefano Morozzi | 11/2024 |
7830 | 2^346701+164841 | 104368 | Stefano Morozzi | 11/2024 |
7832 | 2^346694+20437 | 104366 | Stefano Morozzi | 11/2024 |
7833 | 2^346694+131557 | 104366 | Stefano Morozzi | 11/2024 |
7834 | 2^346695+6795 | 104366 | Stefano Morozzi | 11/2024 |
7835 | 2^346691+158613 | 104365 | Stefano Morozzi | 11/2024 |
7836 | 2^346692+122623 | 104365 | Stefano Morozzi | 11/2024 |
7837 | 2^346687+188033 | 104364 | Stefano Morozzi | 11/2024 |
7838 | 2^346688+71005 | 104364 | Stefano Morozzi | 11/2024 |
7839 | 2^346688+89811 | 104364 | Stefano Morozzi | 11/2024 |
7840 | 2^346688+122115 | 104364 | Stefano Morozzi | 11/2024 |
7841 | 2^346689+100829 | 104364 | Stefano Morozzi | 11/2024 |
7842 | 2^346689+172847 | 104364 | Stefano Morozzi | 11/2024 |
7843 | 2^346685+136145 | 104363 | Stefano Morozzi | 11/2024 |
7846 | 9*10^104361+89 | 104362 | Robert Price | 11/2019 |
7844 | 2^346681+58601 | 104362 | Stefano Morozzi | 11/2024 |
7845 | 2^346681+186111 | 104362 | Stefano Morozzi | 11/2024 |
7847 | 2^346676+82285 | 104360 | Stefano Morozzi | 11/2024 |
7848 | 2^346670+69985 | 104359 | Stefano Morozzi | 11/2024 |
7849 | 2^346672+85371 | 104359 | Stefano Morozzi | 11/2024 |
7850 | 2^346673+47231 | 104359 | Stefano Morozzi | 11/2024 |
7856 | 25048^14665+14665^25048 | 104358 | Hans Havermann | 09/2020 |
7851 | 2^346667+84359 | 104358 | Stefano Morozzi | 11/2024 |
7852 | 2^346668+26391 | 104358 | Stefano Morozzi | 11/2024 |
7853 | 2^346668+138987 | 104358 | Stefano Morozzi | 11/2024 |
7854 | 2^346669+27735 | 104358 | Stefano Morozzi | 11/2024 |
7855 | 2^346669+33989 | 104358 | Stefano Morozzi | 11/2024 |
7857 | 2^346664+16377 | 104357 | Stefano Morozzi | 11/2024 |
7858 | 2^346666+29595 | 104357 | Stefano Morozzi | 11/2024 |
7859 | 2^346660+61095 | 104356 | Stefano Morozzi | 11/2024 |
7860 | 2^346661+114311 | 104356 | Stefano Morozzi | 11/2024 |
7861 | 2^346662+75745 | 104356 | Stefano Morozzi | 11/2024 |
7862 | 2^346663+123305 | 104356 | Stefano Morozzi | 11/2024 |
7863 | 2^346662+150475 | 104356 | Stefano Morozzi | 11/2024 |
7864 | 2^346658+28393 | 104355 | Stefano Morozzi | 11/2024 |
7865 | 2^346658+137619 | 104355 | Stefano Morozzi | 11/2024 |
7866 | 2^346659+86415 | 104355 | Stefano Morozzi | 11/2024 |
7867 | 2^346659+117849 | 104355 | Stefano Morozzi | 11/2024 |
7868 | 2^346655+199859 | 104354 | Stefano Morozzi | 11/2024 |
7869 | 2^346656+100627 | 104354 | Stefano Morozzi | 11/2024 |
7870 | 2^346651+88491 | 104353 | Stefano Morozzi | 11/2024 |
7871 | 2^346652+32971 | 104353 | Stefano Morozzi | 11/2024 |
7872 | 2^346652+85321 | 104353 | Stefano Morozzi | 11/2024 |
7873 | 2^346652+100627 | 104353 | Stefano Morozzi | 11/2024 |
7874 | 2^346652+190255 | 104353 | Stefano Morozzi | 11/2024 |
7875 | 2^346652+194667 | 104353 | Stefano Morozzi | 11/2024 |
7876 | 2^346652+197073 | 104353 | Stefano Morozzi | 11/2024 |
7880 | 2^346649+65 | 104352 | Lelio R Paula | 09/2011 |
7877 | 2^346647+128475 | 104352 | Stefano Morozzi | 11/2024 |
7878 | 2^346647+181169 | 104352 | Stefano Morozzi | 11/2024 |
7879 | 2^346648+97381 | 104352 | Stefano Morozzi | 11/2024 |
7881 | (19*33^68718-600883)/32 | 104350 | Eric Chen | 05/2023 |
7882 | 2^346640+73723 | 104350 | Stefano Morozzi | 11/2024 |
7883 | 2^346641+169667 | 104350 | Stefano Morozzi | 11/2024 |
7884 | 2^346642+100395 | 104350 | Stefano Morozzi | 11/2024 |
7885 | 2^346643+61025 | 104350 | Stefano Morozzi | 11/2024 |
7886 | 2^346643+160785 | 104350 | Stefano Morozzi | 11/2024 |
7888 | 2^346638-17265 | 104349 | Enzo Doria | 05/2013 |
7887 | 2^346637+34139 | 104349 | Stefano Morozzi | 11/2024 |
7889 | 2^346635+13071 | 104348 | Stefano Morozzi | 11/2024 |
7890 | 2^346630+66003 | 104347 | Stefano Morozzi | 11/2024 |
7891 | 2^346630+187137 | 104347 | Stefano Morozzi | 11/2024 |
7892 | 2^346631+27393 | 104347 | Stefano Morozzi | 11/2024 |
7893 | 2^346632+21883 | 104347 | Stefano Morozzi | 11/2024 |
7894 | 2^346632+136015 | 104347 | Stefano Morozzi | 11/2024 |
7895 | 2^346628+87907 | 104346 | Stefano Morozzi | 11/2024 |
7896 | 2^346624+174075 | 104345 | Stefano Morozzi | 11/2024 |
7897 | 2^346620+87451 | 104344 | Stefano Morozzi | 11/2024 |
7898 | 2^346622+12247 | 104344 | Stefano Morozzi | 11/2024 |
7899 | 2^346623+69161 | 104344 | Stefano Morozzi | 11/2024 |
7900 | 2^346614+85737 | 104342 | Stefano Morozzi | 11/2024 |
7901 | 2^346611+183923 | 104341 | Stefano Morozzi | 11/2024 |
7902 | 2^346607+36209 | 104340 | Stefano Morozzi | 11/2024 |
7903 | 2^346607+65291 | 104340 | Stefano Morozzi | 11/2024 |
7904 | 2^346609+47471 | 104340 | Stefano Morozzi | 11/2024 |
7909 | (2^346606+2082)/2 | 104339 | Stefano Morozzi | 09/2020 |
7910 | (2^346607+2070)/2 | 104339 | Stefano Morozzi | 09/2020 |
7905 | 2^346605+1041 | 104339 | Stefano Morozzi | 11/2024 |
7906 | 2^346605+181167 | 104339 | Stefano Morozzi | 11/2024 |
7907 | 2^346606+1035 | 104339 | Stefano Morozzi | 11/2024 |
7908 | 2^346606+103863 | 104339 | Stefano Morozzi | 11/2024 |
7911 | 2^346601+26529 | 104338 | Stefano Morozzi | 11/2024 |
7912 | 2^346603+133431 | 104338 | Stefano Morozzi | 11/2024 |
7913 | 2^346597+97661 | 104337 | Stefano Morozzi | 11/2024 |
7914 | 2^346597+186809 | 104337 | Stefano Morozzi | 11/2024 |
7915 | 2^346598+31719 | 104337 | Stefano Morozzi | 11/2024 |
7916 | 2^346598+162513 | 104337 | Stefano Morozzi | 11/2024 |
7917 | 2^346599+45731 | 104337 | Stefano Morozzi | 11/2024 |
7918 | 2^346599+187061 | 104337 | Stefano Morozzi | 11/2024 |
7919 | 2^346600+175993 | 104337 | Stefano Morozzi | 11/2024 |
7920 | 2^346595+89753 | 104336 | Stefano Morozzi | 11/2024 |
7921 | 2^346595+114491 | 104336 | Stefano Morozzi | 11/2024 |
7922 | 2^346596+120183 | 104336 | Stefano Morozzi | 11/2024 |
7923 | 2^346591+183651 | 104335 | Stefano Morozzi | 11/2024 |
7924 | 2^346591+192149 | 104335 | Stefano Morozzi | 11/2024 |
7925 | 2^346592+77347 | 104335 | Stefano Morozzi | 11/2024 |
7926 | 2^346592+178161 | 104335 | Stefano Morozzi | 11/2024 |
7927 | 2^346592+195985 | 104335 | Stefano Morozzi | 11/2024 |
7928 | 2^346589+40607 | 104334 | Stefano Morozzi | 11/2024 |
7929 | 2^346590+151533 | 104334 | Stefano Morozzi | 11/2024 |
7930 | 2^346584+105103 | 104333 | Stefano Morozzi | 11/2024 |
7931 | 2^346585+56861 | 104333 | Stefano Morozzi | 11/2024 |
7937 | (2^346582+3202)/2 | 104332 | Stefano Morozzi | 09/2020 |
7932 | 2^346581+1601 | 104332 | Stefano Morozzi | 11/2024 |
7933 | 2^346581+82115 | 104332 | Stefano Morozzi | 11/2024 |
7934 | 2^346581+193979 | 104332 | Stefano Morozzi | 11/2024 |
7935 | 2^346582+197767 | 104332 | Stefano Morozzi | 11/2024 |
7936 | 2^346583+116579 | 104332 | Stefano Morozzi | 11/2024 |
7938 | 26092^9967+9967^26092 | 104331 | Hans Havermann | 09/2020 |
7939 | 2^346577+47501 | 104331 | Stefano Morozzi | 11/2024 |
7940 | 2^346578+163287 | 104331 | Stefano Morozzi | 11/2024 |
7941 | 2^346579+37019 | 104331 | Stefano Morozzi | 11/2024 |
7942 | 2^346579+119645 | 104331 | Stefano Morozzi | 11/2024 |
7943 | 2^346579+157611 | 104331 | Stefano Morozzi | 11/2024 |
7944 | 2^346576+100803 | 104330 | Stefano Morozzi | 11/2024 |
7945 | 2^346576+144495 | 104330 | Stefano Morozzi | 11/2024 |
7946 | 2^346573+13859 | 104329 | Stefano Morozzi | 11/2024 |
7947 | 2^346568+110181 | 104328 | Stefano Morozzi | 11/2024 |
7949 | 5*10^104326+77 | 104327 | Robert Price | 12/2018 |
7948 | 2^346564+151101 | 104327 | Stefano Morozzi | 11/2024 |
7955 | (2^346564+2026)/2 | 104326 | Stefano Morozzi | 09/2020 |
7950 | 2^346561+53385 | 104326 | Stefano Morozzi | 11/2024 |
7951 | 2^346561+139791 | 104326 | Stefano Morozzi | 11/2024 |
7952 | 2^346562+110383 | 104326 | Stefano Morozzi | 11/2024 |
7953 | 2^346563+1013 | 104326 | Stefano Morozzi | 11/2024 |
7954 | 2^346563+9305 | 104326 | Stefano Morozzi | 11/2024 |
7956 | 2^346558+97033 | 104325 | Stefano Morozzi | 11/2024 |
7957 | 2^346556+101283 | 104324 | Stefano Morozzi | 11/2024 |
7958 | 2^346551+55043 | 104323 | Stefano Morozzi | 11/2024 |
7959 | 2^346547+71855 | 104322 | Stefano Morozzi | 11/2024 |
7960 | 2^346548+119695 | 104322 | Stefano Morozzi | 11/2024 |
7961 | 2^346550+55249 | 104322 | Stefano Morozzi | 11/2024 |
7962 | 2^346550+158655 | 104322 | Stefano Morozzi | 11/2024 |
7963 | 2^346545+87885 | 104321 | Stefano Morozzi | 11/2024 |
7964 | 2^346545+95105 | 104321 | Stefano Morozzi | 11/2024 |
7965 | 2^346546+126763 | 104321 | Stefano Morozzi | 11/2024 |
7966 | 2^346546+149397 | 104321 | Stefano Morozzi | 11/2024 |
7967 | (8925^26569-1)/(8925^163-1) | 104320 | Ryan Propper | 11/2023 |
7968 | 2^346542+128005 | 104320 | Stefano Morozzi | 11/2024 |
7969 | 2^346538+123507 | 104319 | Stefano Morozzi | 11/2024 |
7970 | 2^346540+118251 | 104319 | Stefano Morozzi | 11/2024 |
7971 | 2^346540+128965 | 104319 | Stefano Morozzi | 11/2024 |
7972 | 2^346535+138485 | 104318 | Stefano Morozzi | 11/2024 |
7973 | 2^346536+149013 | 104318 | Stefano Morozzi | 11/2024 |
7974 | 2^346531+98801 | 104317 | Stefano Morozzi | 11/2024 |
7975 | 2^346533+12035 | 104317 | Stefano Morozzi | 11/2024 |
7979 | 2^346527-111817 | 104316 | Enzo Doria | 05/2014 |
7978 | 6^134055+101 | 104316 | Lelio R Paula | 11/2016 |
7976 | fibonacci(499147)-4 | 104316 | Jon Grantham | 08/2023 |
7977 | 2^346529+101351 | 104316 | Stefano Morozzi | 11/2024 |
7980 | 2^346524+81585 | 104315 | Stefano Morozzi | 11/2024 |
7981 | 2^346524+184821 | 104315 | Stefano Morozzi | 11/2024 |
7982 | 2^346525+41051 | 104315 | Stefano Morozzi | 11/2024 |
7983 | 2^346525+61845 | 104315 | Stefano Morozzi | 11/2024 |
7984 | 2^346521+47439 | 104314 | Stefano Morozzi | 11/2024 |
7985 | 2^346522+34689 | 104314 | Stefano Morozzi | 11/2024 |
7986 | 2^346519+24543 | 104313 | Stefano Morozzi | 11/2024 |
7987 | 2^346519+75119 | 104313 | Stefano Morozzi | 11/2024 |
7991 | 92105!4+8 | 104312 | Robert Price | 09/2019 |
7988 | 2^346514+11023 | 104312 | Stefano Morozzi | 11/2024 |
7989 | 2^346514+22009 | 104312 | Stefano Morozzi | 11/2024 |
7990 | 2^346516+107031 | 104312 | Stefano Morozzi | 11/2024 |
7992 | 2^346511+65675 | 104311 | Stefano Morozzi | 11/2024 |
7993 | 2^346512+105345 | 104311 | Stefano Morozzi | 11/2024 |
7994 | 2^346513+80387 | 104311 | Stefano Morozzi | 11/2024 |
7995 | 2^346510+104955 | 104310 | Stefano Morozzi | 11/2024 |
7996 | 2^346510+145347 | 104310 | Stefano Morozzi | 11/2024 |
7997 | 2^346506+105537 | 104309 | Stefano Morozzi | 11/2024 |
7998 | 2^346506+145353 | 104309 | Stefano Morozzi | 11/2024 |
7999 | 2^346503+160109 | 104308 | Stefano Morozzi | 11/2024 |
8000 | 2^346494+155215 | 104306 | Stefano Morozzi | 11/2024 |