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 ? |
8501 | 2^338284-104217 | 101834 | Stefano Morozzi | 02/2022 |
8502 | 2^338282-84533 | 101834 | Stefano Morozzi | 04/2022 |
8503 | 2^338283+67545 | 101834 | Stefano Morozzi | 09/2022 |
8504 | 2^338283-65439 | 101834 | Stefano Morozzi | 01/2023 |
8513 | 2^338280-19745 | 101833 | Enzo Doria | 06/2013 |
8505 | 2^338279-125947 | 101833 | Stefano Morozzi | 12/2021 |
8506 | 2^338280-50343 | 101833 | Stefano Morozzi | 12/2021 |
8507 | 2^338279+133331 | 101833 | Stefano Morozzi | 02/2022 |
8508 | 2^338281-54561 | 101833 | Stefano Morozzi | 02/2022 |
8509 | 2^338280+192063 | 101833 | Stefano Morozzi | 09/2022 |
8510 | 2^338281+18971 | 101833 | Stefano Morozzi | 09/2022 |
8511 | 2^338281-186711 | 101833 | Stefano Morozzi | 12/2022 |
8512 | 2^338281-91273 | 101833 | Stefano Morozzi | 01/2023 |
8514 | 2^338278+188215 | 101832 | Stefano Morozzi | 05/2022 |
8515 | 2^338273+181101 | 101831 | Stefano Morozzi | 01/2022 |
8516 | 2^338275+32909 | 101831 | Stefano Morozzi | 02/2022 |
8517 | 2^338272+166431 | 101831 | Stefano Morozzi | 06/2022 |
8518 | 2^338272+22011 | 101831 | Stefano Morozzi | 11/2022 |
8519 | 2^338275+148271 | 101831 | Stefano Morozzi | 11/2022 |
8520 | 2^338270-135725 | 101830 | Stefano Morozzi | 06/2022 |
8521 | 2^338269-136951 | 101830 | Stefano Morozzi | 12/2022 |
8522 | 2^338270-192701 | 101830 | Stefano Morozzi | 02/2023 |
8523 | 2^338271-42831 | 101830 | Stefano Morozzi | 02/2023 |
8524 | 2^338266+110665 | 101829 | Stefano Morozzi | 03/2022 |
8525 | 2^338267+110481 | 101829 | Stefano Morozzi | 03/2022 |
8526 | 2^338267-166035 | 101829 | Stefano Morozzi | 01/2023 |
8527 | 2^338265-154893 | 101828 | Stefano Morozzi | 02/2022 |
8528 | 2^338264+163611 | 101828 | Stefano Morozzi | 05/2022 |
8529 | 2^338263-62767 | 101828 | Stefano Morozzi | 12/2022 |
8530 | 2^338261-188119 | 101827 | Stefano Morozzi | 12/2022 |
8531 | 2^338259-40327 | 101827 | Stefano Morozzi | 01/2023 |
8532 | 2^338256+5223 | 101826 | Stefano Morozzi | 01/2022 |
8533 | 2^338257+178425 | 101826 | Stefano Morozzi | 01/2022 |
8534 | 2^338256-180569 | 101826 | Stefano Morozzi | 02/2022 |
8535 | 2^338257-5965 | 101826 | Stefano Morozzi | 02/2022 |
8536 | 2^338258-9225 | 101826 | Stefano Morozzi | 04/2022 |
8537 | 2^338255-127021 | 101825 | Stefano Morozzi | 12/2021 |
8538 | 2^338253+159005 | 101825 | Stefano Morozzi | 03/2022 |
8539 | 2^338253+64817 | 101825 | Stefano Morozzi | 05/2022 |
8540 | 2^338254-85403 | 101825 | Stefano Morozzi | 06/2022 |
8541 | 2^338254+142947 | 101825 | Stefano Morozzi | 09/2022 |
8542 | 2^338253+121095 | 101825 | Stefano Morozzi | 11/2022 |
8543 | 2^338254+196725 | 101825 | Stefano Morozzi | 11/2022 |
8544 | 2^338254-91007 | 101825 | Stefano Morozzi | 01/2023 |
8545 | 2^338251+78975 | 101824 | Stefano Morozzi | 01/2022 |
8546 | 2^338252-178709 | 101824 | Stefano Morozzi | 01/2022 |
8547 | 2^338252+129703 | 101824 | Stefano Morozzi | 01/2022 |
8548 | 2^338252+132285 | 101824 | Stefano Morozzi | 02/2022 |
8549 | 2^338251-33381 | 101824 | Stefano Morozzi | 04/2022 |
8550 | 2^338252-13805 | 101824 | Stefano Morozzi | 12/2022 |
8551 | 2^338245-134755 | 101822 | Stefano Morozzi | 04/2022 |
8552 | 2^338244-59219 | 101822 | Stefano Morozzi | 04/2022 |
8553 | 2^338244-64703 | 101822 | Stefano Morozzi | 01/2023 |
8561 | (2^338242+2782)/2 | 101821 | Stefano Morozzi | 02/2021 |
8554 | 2^338241+1391 | 101821 | Stefano Morozzi | 12/2021 |
8555 | 2^338242+151195 | 101821 | Stefano Morozzi | 12/2021 |
8556 | 2^338240-152495 | 101821 | Stefano Morozzi | 12/2021 |
8557 | 2^338240+81745 | 101821 | Stefano Morozzi | 02/2022 |
8558 | 2^338241-155551 | 101821 | Stefano Morozzi | 02/2022 |
8559 | 2^338242-108237 | 101821 | Stefano Morozzi | 04/2022 |
8560 | 2^338242+43045 | 101821 | Stefano Morozzi | 09/2022 |
8562 | 2^338238-126735 | 101820 | Stefano Morozzi | 12/2021 |
8563 | 2^338238+183855 | 101820 | Stefano Morozzi | 03/2022 |
8564 | 2^338238+141013 | 101820 | Stefano Morozzi | 06/2022 |
8565 | 2^338237+97227 | 101820 | Stefano Morozzi | 11/2022 |
8566 | 2^338238+48429 | 101820 | Stefano Morozzi | 11/2022 |
8567 | 2^338234-80925 | 101819 | Stefano Morozzi | 02/2022 |
8568 | 2^338234-154593 | 101819 | Stefano Morozzi | 02/2022 |
8569 | 2^338235-131787 | 101819 | Stefano Morozzi | 03/2022 |
8570 | 2^338233+89781 | 101819 | Stefano Morozzi | 05/2022 |
8571 | 2^338235+169971 | 101819 | Stefano Morozzi | 11/2022 |
8572 | 2^338233-113875 | 101819 | Stefano Morozzi | 12/2022 |
8579 | (3*2^338236-1)/347 | 101818 | Lelio R Paula | 03/2014 |
8573 | 2^338232-175539 | 101818 | Stefano Morozzi | 12/2021 |
8574 | 2^338231+57345 | 101818 | Stefano Morozzi | 02/2022 |
8575 | 2^338232+36097 | 101818 | Stefano Morozzi | 03/2022 |
8576 | 2^338230+137403 | 101818 | Stefano Morozzi | 04/2022 |
8577 | 2^338231-59569 | 101818 | Stefano Morozzi | 04/2022 |
8578 | 2^338230-86633 | 101818 | Stefano Morozzi | 12/2022 |
8580 | 2^338228+159247 | 101817 | Stefano Morozzi | 03/2022 |
8581 | 2^338227-12631 | 101817 | Stefano Morozzi | 12/2022 |
8582 | (34*10^101815+191)/9 | 101816 | Robert Price | 08/2021 |
8583 | 2^338224+185461 | 101816 | Stefano Morozzi | 03/2022 |
8584 | 2^338224+62295 | 101816 | Stefano Morozzi | 04/2022 |
8585 | 2^338225+162645 | 101816 | Stefano Morozzi | 04/2022 |
8586 | 2^338223+144209 | 101816 | Stefano Morozzi | 09/2022 |
8593 | 6^130841+103 | 101815 | Lelio R Paula | 10/2016 |
8587 | 2^338220+150405 | 101815 | Stefano Morozzi | 11/2021 |
8588 | 2^338219-4147 | 101815 | Stefano Morozzi | 01/2022 |
8589 | 2^338221+83391 | 101815 | Stefano Morozzi | 02/2022 |
8590 | 2^338221+62937 | 101815 | Stefano Morozzi | 04/2022 |
8591 | 2^338220-65697 | 101815 | Stefano Morozzi | 01/2023 |
8592 | 2^338220-139505 | 101815 | Stefano Morozzi | 01/2023 |
8594 | 2^338216+77473 | 101814 | Stefano Morozzi | 12/2021 |
8595 | 2^338218+155299 | 101814 | Stefano Morozzi | 01/2022 |
8596 | 2^338217-134745 | 101814 | Stefano Morozzi | 04/2022 |
8597 | 2^338218+73507 | 101814 | Stefano Morozzi | 11/2022 |
8598 | 2^338213-125631 | 101813 | Stefano Morozzi | 12/2021 |
8599 | 2^338215+25845 | 101813 | Stefano Morozzi | 12/2021 |
8600 | 2^338210-153537 | 101812 | Stefano Morozzi | 01/2022 |
8601 | 2^338209+60915 | 101812 | Stefano Morozzi | 03/2022 |
8602 | 2^338211-57297 | 101812 | Stefano Morozzi | 03/2022 |
8603 | 2^338211-110257 | 101812 | Stefano Morozzi | 06/2022 |
8604 | 2^338211+71549 | 101812 | Stefano Morozzi | 11/2022 |
8605 | 2^338208-178787 | 101811 | Stefano Morozzi | 01/2022 |
8606 | 2^338208+106153 | 101811 | Stefano Morozzi | 01/2022 |
8607 | 2^338207+16499 | 101811 | Stefano Morozzi | 06/2022 |
8608 | 2^338205+102471 | 101810 | Stefano Morozzi | 12/2021 |
8609 | 2^338199-176377 | 101809 | Stefano Morozzi | 12/2021 |
8610 | 2^338201-151233 | 101809 | Stefano Morozzi | 12/2021 |
8611 | 2^338202-152061 | 101809 | Stefano Morozzi | 12/2021 |
8612 | 2^338202+133785 | 101809 | Stefano Morozzi | 03/2022 |
8613 | 2^338200+135643 | 101809 | Stefano Morozzi | 03/2022 |
8614 | 2^338202+14169 | 101809 | Stefano Morozzi | 05/2022 |
8615 | 2^338202-85211 | 101809 | Stefano Morozzi | 06/2022 |
8616 | 2^338200+74265 | 101809 | Stefano Morozzi | 02/2023 |
8617 | 2^338196+121147 | 101808 | Stefano Morozzi | 11/2022 |
8618 | 2^338196+73551 | 101808 | Stefano Morozzi | 11/2022 |
8619 | 2^338194-175845 | 101807 | Stefano Morozzi | 12/2021 |
8620 | 2^338195+56771 | 101807 | Stefano Morozzi | 02/2022 |
8621 | 2^338195+162365 | 101807 | Stefano Morozzi | 04/2022 |
8622 | 2^338194+67497 | 101807 | Stefano Morozzi | 09/2022 |
8623 | 2^338193-116335 | 101807 | Stefano Morozzi | 01/2023 |
8624 | 2^338194-15585 | 101807 | Stefano Morozzi | 01/2023 |
8625 | 2^338192+130387 | 101806 | Stefano Morozzi | 01/2022 |
8626 | 2^338190+89359 | 101806 | Stefano Morozzi | 05/2022 |
8627 | 2^338189+144605 | 101806 | Stefano Morozzi | 09/2022 |
8628 | 2^338190-113537 | 101806 | Stefano Morozzi | 12/2022 |
8629 | 2^338186+127245 | 101805 | Stefano Morozzi | 12/2021 |
8630 | 2^338186-130013 | 101805 | Stefano Morozzi | 02/2022 |
8631 | 2^338186+39235 | 101805 | Stefano Morozzi | 05/2022 |
8632 | 2^338185+77315 | 101804 | Stefano Morozzi | 12/2021 |
8633 | 2^338185+102519 | 101804 | Stefano Morozzi | 12/2021 |
8634 | 2^338183-76539 | 101804 | Stefano Morozzi | 12/2021 |
8635 | 2^338185+104489 | 101804 | Stefano Morozzi | 01/2022 |
8636 | 2^338179+35361 | 101803 | Stefano Morozzi | 03/2022 |
8637 | 2^338181+64235 | 101803 | Stefano Morozzi | 05/2022 |
8638 | 2^338181+94047 | 101803 | Stefano Morozzi | 09/2022 |
8639 | 2^338180+146131 | 101803 | Stefano Morozzi | 11/2022 |
8640 | 2^338179+123399 | 101803 | Stefano Morozzi | 11/2022 |
8641 | 2^338182-42425 | 101803 | Stefano Morozzi | 02/2023 |
8642 | 2^338177+51807 | 101802 | Stefano Morozzi | 12/2021 |
8643 | 2^338177+107385 | 101802 | Stefano Morozzi | 02/2022 |
8644 | 2^338178+34287 | 101802 | Stefano Morozzi | 03/2022 |
8645 | 2^338178+184207 | 101802 | Stefano Morozzi | 03/2022 |
8646 | 2^338177-108901 | 101802 | Stefano Morozzi | 04/2022 |
8647 | 2^338177+141569 | 101802 | Stefano Morozzi | 06/2022 |
8648 | 2^338176+46221 | 101802 | Stefano Morozzi | 11/2022 |
8649 | 2^338175+25161 | 101801 | Stefano Morozzi | 11/2021 |
8650 | 2^338173-27901 | 101801 | Stefano Morozzi | 01/2022 |
8651 | 2^338174+23217 | 101801 | Stefano Morozzi | 11/2022 |
8652 | 2^338174+23793 | 101801 | Stefano Morozzi | 11/2022 |
8653 | 2^338173-36183 | 101801 | Stefano Morozzi | 12/2022 |
8654 | 2^338173-137053 | 101801 | Stefano Morozzi | 12/2022 |
8655 | 2^338174-36797 | 101801 | Stefano Morozzi | 12/2022 |
8656 | 2^338175-166509 | 101801 | Stefano Morozzi | 01/2023 |
8657 | 2^338169-155965 | 101800 | Stefano Morozzi | 02/2022 |
8658 | 2^338172+95797 | 101800 | Stefano Morozzi | 11/2022 |
8659 | 2^338171-117987 | 101800 | Stefano Morozzi | 02/2023 |
8660 | 2^338166+183237 | 101799 | Stefano Morozzi | 02/2022 |
8661 | 2^338168-157835 | 101799 | Stefano Morozzi | 03/2022 |
8662 | 2^338166+137107 | 101799 | Stefano Morozzi | 04/2022 |
8663 | 2^338166+22897 | 101799 | Stefano Morozzi | 11/2022 |
8664 | 2^338166-161123 | 101799 | Stefano Morozzi | 12/2022 |
8665 | 2^338165-152139 | 101798 | Stefano Morozzi | 12/2021 |
8666 | 2^338163-178947 | 101798 | Stefano Morozzi | 02/2022 |
8667 | 2^338164-64329 | 101798 | Stefano Morozzi | 01/2023 |
8668 | 2^338159-127575 | 101797 | Stefano Morozzi | 12/2021 |
8669 | 2^338161+154259 | 101797 | Stefano Morozzi | 01/2022 |
8670 | 2^338160+139947 | 101797 | Stefano Morozzi | 05/2022 |
8671 | 2^338160+191815 | 101797 | Stefano Morozzi | 09/2022 |
8672 | 2^338160+22207 | 101797 | Stefano Morozzi | 11/2022 |
8673 | 2^338161+196157 | 101797 | Stefano Morozzi | 11/2022 |
8674 | 2^338162-138635 | 101797 | Stefano Morozzi | 12/2022 |
8675 | 2^338156-75269 | 101796 | Stefano Morozzi | 12/2021 |
8676 | 2^338156-151247 | 101796 | Stefano Morozzi | 12/2021 |
8677 | 2^338156+103273 | 101796 | Stefano Morozzi | 01/2022 |
8678 | 2^338156+167053 | 101796 | Stefano Morozzi | 09/2022 |
8679 | 2^338158+69303 | 101796 | Stefano Morozzi | 09/2022 |
8680 | 2^338158+171189 | 101796 | Stefano Morozzi | 11/2022 |
8681 | 2^338157-188989 | 101796 | Stefano Morozzi | 12/2022 |
8682 | 2^338158-188711 | 101796 | Stefano Morozzi | 12/2022 |
8683 | 2^338155+132621 | 101795 | Stefano Morozzi | 02/2022 |
8684 | 2^338155-82605 | 101795 | Stefano Morozzi | 03/2022 |
8685 | 2^338155-182631 | 101795 | Stefano Morozzi | 03/2022 |
8686 | 2^338155+187755 | 101795 | Stefano Morozzi | 04/2022 |
8687 | 2^338154-83975 | 101795 | Stefano Morozzi | 04/2022 |
8688 | 2^338154+163759 | 101795 | Stefano Morozzi | 05/2022 |
8689 | 2^338152-25767 | 101794 | Stefano Morozzi | 12/2021 |
8690 | 2^338152+181927 | 101794 | Stefano Morozzi | 02/2022 |
8691 | 2^338151+60779 | 101794 | Stefano Morozzi | 03/2022 |
8692 | 2^338151+189149 | 101794 | Stefano Morozzi | 05/2022 |
8693 | 2^338152+45567 | 101794 | Stefano Morozzi | 11/2022 |
8694 | 2^338147+29343 | 101793 | Stefano Morozzi | 01/2022 |
8695 | 2^338148+130803 | 101793 | Stefano Morozzi | 01/2022 |
8696 | 2^338146+166167 | 101793 | Stefano Morozzi | 06/2022 |
8697 | 2^338149-185073 | 101793 | Stefano Morozzi | 06/2022 |
8698 | 2^338149+41757 | 101793 | Stefano Morozzi | 09/2022 |
8699 | 2^338149+125015 | 101793 | Stefano Morozzi | 02/2023 |
8700 | 2^338144+180697 | 101792 | Stefano Morozzi | 01/2022 |
8701 | 2^338143+8589 | 101792 | Stefano Morozzi | 02/2022 |
8702 | 2^338143-55611 | 101792 | Stefano Morozzi | 02/2022 |
8703 | 2^338143+60623 | 101792 | Stefano Morozzi | 03/2022 |
8704 | 2^338145-63609 | 101792 | Stefano Morozzi | 12/2022 |
8705 | 2^338141-77301 | 101791 | Stefano Morozzi | 12/2021 |
8706 | 2^338141+157145 | 101791 | Stefano Morozzi | 02/2022 |
8707 | 2^338140+84745 | 101791 | Stefano Morozzi | 03/2022 |
8708 | 2^338140+90073 | 101791 | Stefano Morozzi | 05/2022 |
8709 | 2^338142+96583 | 101791 | Stefano Morozzi | 11/2022 |
8710 | 2^338139-134719 | 101790 | Stefano Morozzi | 04/2022 |
8711 | 2^338138+95443 | 101790 | Stefano Morozzi | 11/2022 |
8712 | 2^338133+1445 | 101789 | Stefano Morozzi | 12/2021 |
8713 | 2^338133+172469 | 101789 | Stefano Morozzi | 11/2022 |
8714 | 2^338134+23235 | 101789 | Stefano Morozzi | 11/2022 |
8715 | 2^338132+105643 | 101788 | Stefano Morozzi | 01/2022 |
8716 | 2^338131+181871 | 101788 | Stefano Morozzi | 02/2022 |
8717 | 2^338132-184539 | 101788 | Stefano Morozzi | 04/2022 |
8718 | 2^338130+22383 | 101788 | Stefano Morozzi | 11/2022 |
8719 | 2^338132+170143 | 101788 | Stefano Morozzi | 11/2022 |
8720 | 2^338131-62599 | 101788 | Stefano Morozzi | 12/2022 |
8721 | 2^338128+128953 | 101787 | Stefano Morozzi | 01/2022 |
8722 | 2^338127+11021 | 101787 | Stefano Morozzi | 03/2022 |
8723 | 2^338127+192935 | 101787 | Stefano Morozzi | 09/2022 |
8724 | 2^338127+98621 | 101787 | Stefano Morozzi | 11/2022 |
8725 | 2^338128+98853 | 101787 | Stefano Morozzi | 02/2023 |
8726 | 2^338123-25959 | 101786 | Stefano Morozzi | 12/2021 |
8727 | 2^338124-180765 | 101786 | Stefano Morozzi | 02/2022 |
8728 | 2^338125-7129 | 101786 | Stefano Morozzi | 03/2022 |
8729 | 2^338125-40071 | 101786 | Stefano Morozzi | 01/2023 |
8733 | 2^338122-20117 | 101785 | Enzo Doria | 06/2013 |
8734 | (2^338139+5)/905333 | 101785 | Lelio R Paula | 12/2013 |
8730 | 2^338122+32799 | 101785 | Stefano Morozzi | 02/2022 |
8731 | 2^338120+166411 | 101785 | Stefano Morozzi | 06/2022 |
8732 | 2^338122+90705 | 101785 | Stefano Morozzi | 06/2022 |
8735 | 2^338117+103761 | 101784 | Stefano Morozzi | 01/2022 |
8736 | 2^338118+53817 | 101784 | Stefano Morozzi | 01/2022 |
8737 | 2^338116+82585 | 101784 | Stefano Morozzi | 02/2022 |
8738 | 2^338118+39483 | 101784 | Stefano Morozzi | 05/2022 |
8739 | 2^338119+96659 | 101784 | Stefano Morozzi | 11/2022 |
8740 | 2^338115+61083 | 101783 | Stefano Morozzi | 03/2022 |
8741 | 2^338114+173287 | 101783 | Stefano Morozzi | 11/2022 |
8742 | 2^338113-139681 | 101783 | Stefano Morozzi | 01/2023 |
8743 | 2^338110-175365 | 101782 | Stefano Morozzi | 12/2021 |
8744 | 2^338110-3963 | 101782 | Stefano Morozzi | 01/2022 |
8745 | 2^338112+155061 | 101782 | Stefano Morozzi | 01/2022 |
8746 | 2^338112+137335 | 101782 | Stefano Morozzi | 04/2022 |
8747 | 2^338111-85627 | 101782 | Stefano Morozzi | 06/2022 |
8748 | 2^338111-90145 | 101782 | Stefano Morozzi | 01/2023 |
8749 | 2^338107-1221 | 101781 | Stefano Morozzi | 12/2021 |
8750 | 2^338109+108539 | 101781 | Stefano Morozzi | 03/2022 |