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 ? |
9501 | 2^338668+2583 | 101950 | Stefano Morozzi | 12/2021 |
9502 | 2^338670-157001 | 101950 | Stefano Morozzi | 03/2022 |
9503 | 2^338669-8353 | 101950 | Stefano Morozzi | 04/2022 |
9504 | 2^338670+40635 | 101950 | Stefano Morozzi | 06/2022 |
9512 | (2^338666+3154)/2 | 101949 | Stefano Morozzi | 09/2020 |
9505 | 2^338665+1577 | 101949 | Stefano Morozzi | 12/2021 |
9506 | 2^338665-51133 | 101949 | Stefano Morozzi | 12/2021 |
9507 | 2^338664+4345 | 101949 | Stefano Morozzi | 01/2022 |
9508 | 2^338666-128943 | 101949 | Stefano Morozzi | 01/2022 |
9509 | 2^338664+131535 | 101949 | Stefano Morozzi | 01/2022 |
9510 | 2^338667+14943 | 101949 | Stefano Morozzi | 05/2022 |
9511 | 2^338665+166637 | 101949 | Stefano Morozzi | 09/2022 |
9513 | 2^338662+31587 | 101948 | Stefano Morozzi | 02/2022 |
9514 | 2^338663-58375 | 101948 | Stefano Morozzi | 04/2022 |
9515 | 2^338663-107869 | 101948 | Stefano Morozzi | 04/2022 |
9516 | 2^338663+90435 | 101948 | Stefano Morozzi | 06/2022 |
9517 | 2^338661+70457 | 101948 | Stefano Morozzi | 11/2022 |
9518 | 2^338662+70519 | 101948 | Stefano Morozzi | 11/2022 |
9519 | 2^338663-39447 | 101948 | Stefano Morozzi | 01/2023 |
9520 | 2^338658-159191 | 101947 | Stefano Morozzi | 04/2022 |
9521 | 2^338659-159687 | 101947 | Stefano Morozzi | 04/2022 |
9522 | 2^338659+15543 | 101947 | Stefano Morozzi | 05/2022 |
9523 | 2^338658+44395 | 101947 | Stefano Morozzi | 09/2022 |
9524 | 2^338658+192537 | 101947 | Stefano Morozzi | 09/2022 |
9525 | 2^338659-90531 | 101947 | Stefano Morozzi | 01/2023 |
9526 | 2^338659-114759 | 101947 | Stefano Morozzi | 01/2023 |
9527 | 2^338659+124079 | 101947 | Stefano Morozzi | 02/2023 |
9528 | 2^338654+51027 | 101946 | Stefano Morozzi | 12/2021 |
9529 | 2^338656-152115 | 101946 | Stefano Morozzi | 12/2021 |
9530 | 2^338654+32415 | 101946 | Stefano Morozzi | 02/2022 |
9531 | 2^338654+39799 | 101946 | Stefano Morozzi | 05/2022 |
9532 | 2^338655+144579 | 101946 | Stefano Morozzi | 09/2022 |
9533 | 2^338657+97509 | 101946 | Stefano Morozzi | 11/2022 |
9534 | 2^338653+126629 | 101945 | Stefano Morozzi | 12/2021 |
9535 | 2^338653+33279 | 101945 | Stefano Morozzi | 02/2022 |
9536 | 2^338652-107097 | 101945 | Stefano Morozzi | 03/2022 |
9537 | 2^338653+94475 | 101945 | Stefano Morozzi | 09/2022 |
9538 | 2^338651+194073 | 101945 | Stefano Morozzi | 09/2022 |
9539 | 2^338652-89157 | 101945 | Stefano Morozzi | 01/2023 |
9540 | 2^338649-154663 | 101944 | Stefano Morozzi | 02/2022 |
9541 | 2^338650+61399 | 101944 | Stefano Morozzi | 04/2022 |
9542 | 2^338650-35655 | 101944 | Stefano Morozzi | 06/2022 |
9543 | 2^338650+169623 | 101944 | Stefano Morozzi | 09/2022 |
9544 | 2^338649-40743 | 101944 | Stefano Morozzi | 01/2023 |
9545 | 2^338645+150311 | 101943 | Stefano Morozzi | 11/2021 |
9546 | 2^338645+28481 | 101943 | Stefano Morozzi | 01/2022 |
9547 | 2^338647-77895 | 101943 | Stefano Morozzi | 01/2022 |
9548 | 2^338647-84607 | 101943 | Stefano Morozzi | 04/2022 |
9549 | 2^338647+164523 | 101943 | Stefano Morozzi | 05/2022 |
9550 | 2^338645+64845 | 101943 | Stefano Morozzi | 05/2022 |
9551 | 2^338644-35969 | 101943 | Stefano Morozzi | 12/2022 |
9552 | 2^338645-15715 | 101943 | Stefano Morozzi | 01/2023 |
9553 | 2^338641-152541 | 101942 | Stefano Morozzi | 12/2021 |
9554 | 2^338643-56487 | 101942 | Stefano Morozzi | 03/2022 |
9555 | 2^338642-186525 | 101942 | Stefano Morozzi | 12/2022 |
9556 | 2^338643-41715 | 101942 | Stefano Morozzi | 02/2023 |
9557 | 2^338638+100575 | 101941 | Stefano Morozzi | 12/2021 |
9558 | 2^338639-127461 | 101941 | Stefano Morozzi | 12/2021 |
9559 | 2^338640+187657 | 101941 | Stefano Morozzi | 04/2022 |
9560 | 2^338640+44431 | 101941 | Stefano Morozzi | 09/2022 |
9561 | 2^338635+1961 | 101940 | Stefano Morozzi | 12/2021 |
9562 | 2^338637+102125 | 101940 | Stefano Morozzi | 12/2021 |
9563 | 2^338636-135329 | 101940 | Stefano Morozzi | 06/2022 |
9564 | 2^338635+199485 | 101940 | Stefano Morozzi | 02/2023 |
9569 | 28594^3673+3673^28594 | 101939 | Hans Havermann | 02/2019 |
9565 | 2^338631+110741 | 101939 | Stefano Morozzi | 03/2022 |
9566 | 2^338631+112119 | 101939 | Stefano Morozzi | 04/2022 |
9567 | 2^338634-83097 | 101939 | Stefano Morozzi | 04/2022 |
9568 | 2^338633+139701 | 101939 | Stefano Morozzi | 05/2022 |
9570 | 2^338630-150341 | 101938 | Stefano Morozzi | 12/2021 |
9571 | 2^338630+12867 | 101938 | Stefano Morozzi | 04/2022 |
9572 | 2^338629+42147 | 101938 | Stefano Morozzi | 09/2022 |
9573 | 2^338628+121083 | 101938 | Stefano Morozzi | 11/2022 |
9574 | 2^338630+147235 | 101938 | Stefano Morozzi | 11/2022 |
9575 | 2^338628-37679 | 101938 | Stefano Morozzi | 12/2022 |
9576 | 2^338629-41383 | 101938 | Stefano Morozzi | 01/2023 |
9577 | 2^338628-91877 | 101938 | Stefano Morozzi | 02/2023 |
9578 | 2^338626-105875 | 101937 | Stefano Morozzi | 02/2022 |
9579 | 2^338625-111729 | 101937 | Stefano Morozzi | 12/2022 |
9580 | 2^338627+49299 | 101937 | Stefano Morozzi | 02/2023 |
9581 | 2^338621+33069 | 101936 | Stefano Morozzi | 02/2022 |
9582 | 2^338623-106405 | 101936 | Stefano Morozzi | 03/2022 |
9583 | 2^338621+61751 | 101936 | Stefano Morozzi | 04/2022 |
9584 | 2^338623-86577 | 101936 | Stefano Morozzi | 12/2022 |
9585 | 2^338620-150735 | 101935 | Stefano Morozzi | 12/2021 |
9586 | 2^338619-27765 | 101935 | Stefano Morozzi | 01/2022 |
9587 | 2^338619-77959 | 101935 | Stefano Morozzi | 01/2022 |
9588 | 2^338619-186367 | 101935 | Stefano Morozzi | 12/2022 |
9589 | 2^338618-64905 | 101935 | Stefano Morozzi | 01/2023 |
9590 | 2^338615+151655 | 101934 | Stefano Morozzi | 12/2021 |
9591 | 2^338616+5047 | 101934 | Stefano Morozzi | 01/2022 |
9592 | 2^338616+39705 | 101934 | Stefano Morozzi | 05/2022 |
9593 | 2^338617+149321 | 101934 | Stefano Morozzi | 02/2023 |
9594 | 2^338611+76659 | 101933 | Stefano Morozzi | 12/2021 |
9595 | 2^338613-109791 | 101933 | Stefano Morozzi | 04/2022 |
9596 | 2^338612+119583 | 101933 | Stefano Morozzi | 09/2022 |
9597 | 2^338611-140397 | 101933 | Stefano Morozzi | 01/2023 |
9598 | 2^338614-39653 | 101933 | Stefano Morozzi | 01/2023 |
9599 | 2^338609+130139 | 101932 | Stefano Morozzi | 01/2022 |
9600 | 2^338609+131327 | 101932 | Stefano Morozzi | 01/2022 |
9601 | 2^338608-155453 | 101932 | Stefano Morozzi | 02/2022 |
9602 | 2^338609+161721 | 101932 | Stefano Morozzi | 04/2022 |
9603 | 2^338609-10405 | 101932 | Stefano Morozzi | 06/2022 |
9604 | 2^338608+94017 | 101932 | Stefano Morozzi | 09/2022 |
9605 | 2^338610+170515 | 101932 | Stefano Morozzi | 11/2022 |
9606 | 2^338607+30611 | 101931 | Stefano Morozzi | 01/2022 |
9607 | 2^338607+106695 | 101931 | Stefano Morozzi | 02/2022 |
9608 | 2^338606-32291 | 101931 | Stefano Morozzi | 03/2022 |
9609 | 2^338606+15195 | 101931 | Stefano Morozzi | 05/2022 |
9610 | 2^338605+197789 | 101931 | Stefano Morozzi | 11/2022 |
9611 | 2^338607-90621 | 101931 | Stefano Morozzi | 01/2023 |
9612 | 2^338603-1195 | 101930 | Stefano Morozzi | 12/2021 |
9613 | 2^338601+108867 | 101930 | Stefano Morozzi | 03/2022 |
9614 | 2^338603+34311 | 101930 | Stefano Morozzi | 03/2022 |
9615 | 2^338598+57127 | 101929 | Stefano Morozzi | 02/2022 |
9616 | 2^338598+162645 | 101929 | Stefano Morozzi | 04/2022 |
9617 | 2^338599+43445 | 101929 | Stefano Morozzi | 09/2022 |
9618 | 2^338599+19485 | 101929 | Stefano Morozzi | 09/2022 |
9619 | 2^338598+46195 | 101929 | Stefano Morozzi | 11/2022 |
9620 | 2^338600-36393 | 101929 | Stefano Morozzi | 12/2022 |
9621 | 2^338596-1739 | 101928 | Stefano Morozzi | 12/2021 |
9622 | 2^338595-78687 | 101928 | Stefano Morozzi | 01/2022 |
9623 | 2^338595+181683 | 101928 | Stefano Morozzi | 02/2022 |
9624 | 2^338597-106045 | 101928 | Stefano Morozzi | 02/2022 |
9625 | 2^338595+119565 | 101928 | Stefano Morozzi | 09/2022 |
9626 | 2^338595+19623 | 101928 | Stefano Morozzi | 09/2022 |
9627 | 2^338595+21711 | 101928 | Stefano Morozzi | 11/2022 |
9628 | 2^338596-111129 | 101928 | Stefano Morozzi | 12/2022 |
9629 | 2^338591+53769 | 101927 | Stefano Morozzi | 01/2022 |
9630 | 2^338593+156989 | 101927 | Stefano Morozzi | 02/2022 |
9631 | 2^338592+36157 | 101927 | Stefano Morozzi | 03/2022 |
9632 | 2^338593+42099 | 101927 | Stefano Morozzi | 09/2022 |
9633 | 2^338591+46685 | 101927 | Stefano Morozzi | 11/2022 |
9634 | 2^338593+120437 | 101927 | Stefano Morozzi | 11/2022 |
9635 | 2^338591-165517 | 101927 | Stefano Morozzi | 01/2023 |
9636 | 2^338592-166107 | 101927 | Stefano Morozzi | 01/2023 |
9637 | 2^338592-189249 | 101927 | Stefano Morozzi | 01/2023 |
9638 | 2^338594-40493 | 101927 | Stefano Morozzi | 01/2023 |
9639 | 2^338590+182007 | 101926 | Stefano Morozzi | 02/2022 |
9640 | 2^338590+60747 | 101926 | Stefano Morozzi | 03/2022 |
9641 | 2^338588+62397 | 101926 | Stefano Morozzi | 04/2022 |
9642 | 2^338589-9685 | 101926 | Stefano Morozzi | 04/2022 |
9643 | 2^338588+73765 | 101926 | Stefano Morozzi | 02/2023 |
9644 | 2^338589-16915 | 101926 | Stefano Morozzi | 02/2023 |
9651 | (2^338587+2306)/2 | 101925 | Stefano Morozzi | 02/2021 |
9645 | 2^338586+1153 | 101925 | Stefano Morozzi | 12/2021 |
9646 | 2^338587-51709 | 101925 | Stefano Morozzi | 12/2021 |
9647 | 2^338586+105303 | 101925 | Stefano Morozzi | 01/2022 |
9648 | 2^338585-131773 | 101925 | Stefano Morozzi | 03/2022 |
9649 | 2^338587+168039 | 101925 | Stefano Morozzi | 09/2022 |
9650 | 2^338585-140719 | 101925 | Stefano Morozzi | 01/2023 |
9652 | 2^338584+100771 | 101924 | Stefano Morozzi | 11/2021 |
9653 | 2^338581-150415 | 101924 | Stefano Morozzi | 12/2021 |
9654 | 2^338581-2349 | 101924 | Stefano Morozzi | 12/2021 |
9655 | 2^338582+42933 | 101924 | Stefano Morozzi | 09/2022 |
9656 | 2^338584+93267 | 101924 | Stefano Morozzi | 09/2022 |
9657 | 2^338582-86697 | 101924 | Stefano Morozzi | 12/2022 |
9658 | 2^338582-138035 | 101924 | Stefano Morozzi | 12/2022 |
9659 | 2^338584-115569 | 101924 | Stefano Morozzi | 01/2023 |
9660 | 2^338581-92793 | 101924 | Stefano Morozzi | 02/2023 |
9661 | 2^338578+67593 | 101923 | Stefano Morozzi | 09/2022 |
9662 | 2^338580+142201 | 101923 | Stefano Morozzi | 09/2022 |
9663 | 2^338579-14635 | 101923 | Stefano Morozzi | 01/2023 |
9664 | 2^338579-164985 | 101923 | Stefano Morozzi | 01/2023 |
9665 | 2^338575-28815 | 101922 | Stefano Morozzi | 01/2022 |
9666 | 2^338575-33645 | 101922 | Stefano Morozzi | 04/2022 |
9667 | 2^338577-92239 | 101922 | Stefano Morozzi | 02/2023 |
9668 | 2^338573-156693 | 101921 | Stefano Morozzi | 03/2022 |
9669 | 2^338572+193305 | 101921 | Stefano Morozzi | 09/2022 |
9670 | 2^338573+173751 | 101921 | Stefano Morozzi | 02/2023 |
9671 | 2^338574+73707 | 101921 | Stefano Morozzi | 02/2023 |
9676 | 2^338568+37 | 101920 | Lelio R Paula | 07/2011 |
9672 | 2^338570-53933 | 101920 | Stefano Morozzi | 02/2022 |
9673 | 2^338569+87201 | 101920 | Stefano Morozzi | 04/2022 |
9674 | 2^338570-36897 | 101920 | Stefano Morozzi | 12/2022 |
9675 | 2^338570-61157 | 101920 | Stefano Morozzi | 12/2022 |
9677 | 2^338567-9619 | 101919 | Stefano Morozzi | 04/2022 |
9678 | 2^338565-141589 | 101919 | Stefano Morozzi | 01/2023 |
9679 | 2^338565+148821 | 101919 | Stefano Morozzi | 02/2023 |
9680 | 2^338564-56763 | 101918 | Stefano Morozzi | 03/2022 |
9681 | 2^338561+112007 | 101918 | Stefano Morozzi | 04/2022 |
9682 | 2^338561-9315 | 101918 | Stefano Morozzi | 04/2022 |
9683 | 2^338564+41965 | 101918 | Stefano Morozzi | 09/2022 |
9684 | 2^338561+121139 | 101918 | Stefano Morozzi | 11/2022 |
9685 | 2^338562+21799 | 101918 | Stefano Morozzi | 11/2022 |
9693 | 2^338559-1858777 | 101917 | Enzo Doria | 04/2016 |
9686 | 2^338558+4825 | 101917 | Stefano Morozzi | 01/2022 |
9687 | 2^338559-127935 | 101917 | Stefano Morozzi | 01/2022 |
9688 | 2^338560+154891 | 101917 | Stefano Morozzi | 01/2022 |
9689 | 2^338559+131885 | 101917 | Stefano Morozzi | 02/2022 |
9690 | 2^338558+93735 | 101917 | Stefano Morozzi | 09/2022 |
9691 | 2^338559-90957 | 101917 | Stefano Morozzi | 01/2023 |
9692 | 2^338559-190761 | 101917 | Stefano Morozzi | 01/2023 |
9694 | 2^338555+189981 | 101916 | Stefano Morozzi | 05/2022 |
9695 | 2^338553-125383 | 101915 | Stefano Morozzi | 12/2021 |
9696 | 2^338554-82821 | 101915 | Stefano Morozzi | 03/2022 |
9697 | 2^338548+76923 | 101914 | Stefano Morozzi | 12/2021 |
9698 | 2^338549+158517 | 101914 | Stefano Morozzi | 03/2022 |
9699 | 2^338549+85397 | 101914 | Stefano Morozzi | 03/2022 |
9700 | 2^338548+138121 | 101914 | Stefano Morozzi | 05/2022 |
9701 | 2^338550-110301 | 101914 | Stefano Morozzi | 06/2022 |
9702 | 2^338547+129321 | 101913 | Stefano Morozzi | 01/2022 |
9703 | 2^338547-153481 | 101913 | Stefano Morozzi | 01/2022 |
9704 | 2^338545-11059 | 101913 | Stefano Morozzi | 12/2022 |
9705 | 2^338544+107853 | 101912 | Stefano Morozzi | 02/2022 |
9706 | 2^338542+172813 | 101912 | Stefano Morozzi | 11/2022 |
9707 | 2^338544-12687 | 101912 | Stefano Morozzi | 12/2022 |
9708 | 2^338543-140677 | 101912 | Stefano Morozzi | 01/2023 |
9709 | 2^338541+152721 | 101911 | Stefano Morozzi | 01/2022 |
9710 | 2^338539+60825 | 101911 | Stefano Morozzi | 03/2022 |
9711 | 2^338539+160881 | 101911 | Stefano Morozzi | 03/2022 |
9712 | 2^338541-182523 | 101911 | Stefano Morozzi | 03/2022 |
9713 | 2^338540+87645 | 101911 | Stefano Morozzi | 04/2022 |
9714 | 2^338541+148305 | 101911 | Stefano Morozzi | 11/2022 |
9715 | 2^338541-163075 | 101911 | Stefano Morozzi | 12/2022 |
9716 | 2^338536-100785 | 101910 | Stefano Morozzi | 12/2021 |
9717 | 2^338535-51837 | 101910 | Stefano Morozzi | 12/2021 |
9718 | 2^338535-158745 | 101910 | Stefano Morozzi | 04/2022 |
9719 | 2^338536-189977 | 101910 | Stefano Morozzi | 01/2023 |
9720 | 2^338537-65623 | 101910 | Stefano Morozzi | 01/2023 |
9721 | 2^338532+39445 | 101909 | Stefano Morozzi | 05/2022 |
9722 | 2^338532+141415 | 101909 | Stefano Morozzi | 06/2022 |
9723 | 2^338532-136037 | 101909 | Stefano Morozzi | 06/2022 |
9724 | 2^338531+81081 | 101908 | Stefano Morozzi | 01/2022 |
9725 | 2^338530+59835 | 101908 | Stefano Morozzi | 03/2022 |
9726 | 2^338529+186551 | 101908 | Stefano Morozzi | 04/2022 |
9727 | 2^338531+61313 | 101908 | Stefano Morozzi | 04/2022 |
9728 | 2^338531-9277 | 101908 | Stefano Morozzi | 04/2022 |
9729 | 2^338528-92727 | 101908 | Stefano Morozzi | 02/2023 |
9730 | 2^338527+191205 | 101907 | Stefano Morozzi | 06/2022 |
9731 | 2^338525+99621 | 101907 | Stefano Morozzi | 02/2023 |
9732 | 2^338524+54421 | 101906 | Stefano Morozzi | 01/2022 |
9733 | 2^338522-155811 | 101906 | Stefano Morozzi | 02/2022 |
9734 | 2^338523-16291 | 101906 | Stefano Morozzi | 01/2023 |
9735 | 2^338522-142137 | 101906 | Stefano Morozzi | 02/2023 |
9736 | 2^338521+183131 | 101905 | Stefano Morozzi | 02/2022 |
9737 | 2^338520+34945 | 101905 | Stefano Morozzi | 03/2022 |
9738 | 2^338518-182885 | 101905 | Stefano Morozzi | 04/2022 |
9739 | 2^338518+114633 | 101905 | Stefano Morozzi | 05/2022 |
9740 | 2^338518-12621 | 101905 | Stefano Morozzi | 12/2022 |
9741 | 2^338518-187325 | 101905 | Stefano Morozzi | 12/2022 |
9749 | (9*2^338520+1)/365 | 101904 | Lelio R Paula | 12/2013 |
9742 | 2^338517-125955 | 101904 | Stefano Morozzi | 12/2021 |
9743 | 2^338517+126437 | 101904 | Stefano Morozzi | 12/2021 |
9744 | 2^338517-53499 | 101904 | Stefano Morozzi | 01/2022 |
9745 | 2^338515+30369 | 101904 | Stefano Morozzi | 01/2022 |
9746 | 2^338517-184623 | 101904 | Stefano Morozzi | 04/2022 |
9747 | 2^338515+89333 | 101904 | Stefano Morozzi | 05/2022 |
9748 | 2^338515+198813 | 101904 | Stefano Morozzi | 02/2023 |
9750 | 2^338512-827 | 101903 | Stefano Morozzi | 12/2021 |