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 | 2^338968+53461 | 102040 | Stefano Morozzi | 01/2022 |
8502 | 2^338969+160175 | 102040 | Stefano Morozzi | 03/2022 |
8503 | 2^338967+13409 | 102040 | Stefano Morozzi | 04/2022 |
8504 | 2^338969+67635 | 102040 | Stefano Morozzi | 09/2022 |
8505 | 2^338969-15913 | 102040 | Stefano Morozzi | 01/2023 |
8506 | 2^338963-127455 | 102039 | Stefano Morozzi | 12/2021 |
8507 | 2^338963+132195 | 102039 | Stefano Morozzi | 02/2022 |
8508 | 2^338966+137919 | 102039 | Stefano Morozzi | 04/2022 |
8509 | 2^338963-87529 | 102039 | Stefano Morozzi | 12/2022 |
8510 | 2^338963-116859 | 102039 | Stefano Morozzi | 02/2023 |
8517 | (2^338982-7)/1754517 | 102038 | Lelio R Paula | 12/2013 |
8511 | 2^338960+53935 | 102038 | Stefano Morozzi | 01/2022 |
8512 | 2^338962+83157 | 102038 | Stefano Morozzi | 02/2022 |
8513 | 2^338961+12341 | 102038 | Stefano Morozzi | 04/2022 |
8514 | 2^338960+63933 | 102038 | Stefano Morozzi | 05/2022 |
8515 | 2^338960+170791 | 102038 | Stefano Morozzi | 11/2022 |
8516 | 2^338962+21679 | 102038 | Stefano Morozzi | 11/2022 |
8518 | 2^338959-30919 | 102037 | Stefano Morozzi | 02/2022 |
8519 | 2^338959+164769 | 102037 | Stefano Morozzi | 05/2022 |
8520 | 2^338958-43161 | 102037 | Stefano Morozzi | 02/2023 |
8521 | 2^338954-177003 | 102036 | Stefano Morozzi | 12/2021 |
8522 | 2^338954+154207 | 102036 | Stefano Morozzi | 01/2022 |
8523 | 2^338956+182493 | 102036 | Stefano Morozzi | 02/2022 |
8524 | 2^338954+162715 | 102036 | Stefano Morozzi | 04/2022 |
8525 | 2^338955-158241 | 102036 | Stefano Morozzi | 04/2022 |
8526 | 2^338956-33395 | 102036 | Stefano Morozzi | 04/2022 |
8527 | 2^338954+190915 | 102036 | Stefano Morozzi | 06/2022 |
8528 | 2^338955+41643 | 102036 | Stefano Morozzi | 09/2022 |
8529 | 2^338954+194427 | 102036 | Stefano Morozzi | 09/2022 |
8530 | 2^338956+117967 | 102036 | Stefano Morozzi | 09/2022 |
8531 | 2^338956+195495 | 102036 | Stefano Morozzi | 11/2022 |
8532 | 2^338954-186371 | 102036 | Stefano Morozzi | 12/2022 |
8533 | 2^338950+175077 | 102035 | Stefano Morozzi | 12/2021 |
8534 | 2^338951-51687 | 102035 | Stefano Morozzi | 12/2021 |
8535 | 2^338951+66123 | 102035 | Stefano Morozzi | 06/2022 |
8536 | 2^338950+19317 | 102035 | Stefano Morozzi | 09/2022 |
8537 | 2^338951-161479 | 102035 | Stefano Morozzi | 12/2022 |
8538 | 2^338950-66335 | 102035 | Stefano Morozzi | 01/2023 |
8539 | 2^338951-41611 | 102035 | Stefano Morozzi | 02/2023 |
8540 | 2^338952-142887 | 102035 | Stefano Morozzi | 02/2023 |
8541 | 2^338949+85449 | 102034 | Stefano Morozzi | 03/2022 |
8542 | 2^338949-184585 | 102034 | Stefano Morozzi | 04/2022 |
8543 | 2^338949-88555 | 102034 | Stefano Morozzi | 12/2022 |
8544 | 2^338948+49393 | 102034 | Stefano Morozzi | 02/2023 |
8545 | 2^338949-17601 | 102034 | Stefano Morozzi | 02/2023 |
8546 | 2^338943+127103 | 102033 | Stefano Morozzi | 12/2021 |
8547 | 2^338944-84003 | 102033 | Stefano Morozzi | 04/2022 |
8548 | 2^338945+138605 | 102033 | Stefano Morozzi | 05/2022 |
8549 | 2^338943+95133 | 102033 | Stefano Morozzi | 11/2022 |
8550 | 2^338943+147435 | 102033 | Stefano Morozzi | 11/2022 |
8551 | 2^338943-116067 | 102033 | Stefano Morozzi | 01/2023 |
8552 | 2^338940+78607 | 102032 | Stefano Morozzi | 01/2022 |
8553 | 2^338942-86687 | 102032 | Stefano Morozzi | 12/2022 |
8554 | 2^338939+151569 | 102031 | Stefano Morozzi | 12/2021 |
8555 | 2^338938+183975 | 102031 | Stefano Morozzi | 03/2022 |
8556 | 2^338937-33429 | 102031 | Stefano Morozzi | 04/2022 |
8557 | 2^338939-183259 | 102031 | Stefano Morozzi | 04/2022 |
8558 | 2^338937-139951 | 102031 | Stefano Morozzi | 01/2023 |
8559 | 2^338938-40151 | 102031 | Stefano Morozzi | 01/2023 |
8560 | 2^338938+74449 | 102031 | Stefano Morozzi | 02/2023 |
8561 | 2^338935+179999 | 102030 | Stefano Morozzi | 01/2022 |
8562 | 2^338936+84147 | 102030 | Stefano Morozzi | 03/2022 |
8563 | 2^338935+171261 | 102030 | Stefano Morozzi | 11/2022 |
8564 | 2^338936-41355 | 102030 | Stefano Morozzi | 01/2023 |
8565 | 2^338931+2349 | 102029 | Stefano Morozzi | 12/2021 |
8566 | 2^338933+79935 | 102029 | Stefano Morozzi | 01/2022 |
8567 | 2^338930+33819 | 102029 | Stefano Morozzi | 03/2022 |
8568 | 2^338931-31555 | 102029 | Stefano Morozzi | 03/2022 |
8569 | 2^338933+64169 | 102029 | Stefano Morozzi | 05/2022 |
8570 | 2^338932-184965 | 102029 | Stefano Morozzi | 06/2022 |
8571 | 2^338932+66943 | 102029 | Stefano Morozzi | 09/2022 |
8572 | 2^338932+92995 | 102029 | Stefano Morozzi | 09/2022 |
8573 | 2^338931+97001 | 102029 | Stefano Morozzi | 11/2022 |
8574 | 2^338932-165453 | 102029 | Stefano Morozzi | 01/2023 |
8575 | 2^338933-40899 | 102029 | Stefano Morozzi | 01/2023 |
8576 | 2^338928+2367 | 102028 | Stefano Morozzi | 12/2021 |
8577 | 2^338927+52779 | 102028 | Stefano Morozzi | 01/2022 |
8578 | 2^338927-79539 | 102028 | Stefano Morozzi | 02/2022 |
8579 | 2^338929+60819 | 102028 | Stefano Morozzi | 03/2022 |
8580 | 2^338928-156959 | 102028 | Stefano Morozzi | 03/2022 |
8581 | 2^338927-63919 | 102028 | Stefano Morozzi | 12/2022 |
8582 | 2^338925+106631 | 102027 | Stefano Morozzi | 01/2022 |
8583 | 2^338926+80235 | 102027 | Stefano Morozzi | 01/2022 |
8584 | 2^338926+41607 | 102027 | Stefano Morozzi | 09/2022 |
8585 | 2^338925+195435 | 102027 | Stefano Morozzi | 11/2022 |
8586 | 2^338924-92885 | 102027 | Stefano Morozzi | 02/2023 |
8587 | 2^338922-27291 | 102026 | Stefano Morozzi | 12/2021 |
8588 | 2^338919-103849 | 102025 | Stefano Morozzi | 01/2022 |
8589 | 2^338919+130221 | 102025 | Stefano Morozzi | 01/2022 |
8590 | 2^338918-91967 | 102025 | Stefano Morozzi | 02/2023 |
8591 | 2^338917+561057 | 102025 | Boyan Hu | 03/2024 |
8592 | 2^338914-79121 | 102024 | Stefano Morozzi | 02/2022 |
8593 | 2^338916+134047 | 102024 | Stefano Morozzi | 03/2022 |
8594 | 2^338914-11315 | 102024 | Stefano Morozzi | 12/2022 |
8595 | 2^338910+81027 | 102023 | Stefano Morozzi | 01/2022 |
8596 | 2^338912+179821 | 102023 | Stefano Morozzi | 01/2022 |
8597 | 2^338909+100769 | 102022 | Stefano Morozzi | 11/2021 |
8598 | 2^338908-100839 | 102022 | Stefano Morozzi | 12/2021 |
8599 | 2^338909-25951 | 102022 | Stefano Morozzi | 12/2021 |
8600 | 2^338909+66845 | 102022 | Stefano Morozzi | 09/2022 |
8601 | 2^338907+73509 | 102022 | Stefano Morozzi | 11/2022 |
8602 | 2^338906-25823 | 102021 | Stefano Morozzi | 12/2021 |
8603 | 2^338904+75951 | 102021 | Stefano Morozzi | 12/2021 |
8604 | 2^338906+6685 | 102021 | Stefano Morozzi | 01/2022 |
8605 | 2^338905+160365 | 102021 | Stefano Morozzi | 03/2022 |
8606 | 2^338906+92617 | 102021 | Stefano Morozzi | 09/2022 |
8607 | 2^338904+47065 | 102021 | Stefano Morozzi | 11/2022 |
8608 | 2^338905+70427 | 102021 | Stefano Morozzi | 11/2022 |
8609 | 2^338905-163975 | 102021 | Stefano Morozzi | 12/2022 |
8610 | 2^338903+4155 | 102020 | Stefano Morozzi | 01/2022 |
8611 | 2^338901+55571 | 102020 | Stefano Morozzi | 01/2022 |
8612 | 2^338901-55479 | 102020 | Stefano Morozzi | 02/2022 |
8613 | 2^338903+33555 | 102020 | Stefano Morozzi | 03/2022 |
8614 | 2^338901+39777 | 102020 | Stefano Morozzi | 05/2022 |
8615 | 2^338903+165981 | 102020 | Stefano Morozzi | 06/2022 |
8616 | 2^338901-34863 | 102020 | Stefano Morozzi | 06/2022 |
8617 | 2^338899-150051 | 102019 | Stefano Morozzi | 12/2021 |
8618 | 2^338899+125951 | 102019 | Stefano Morozzi | 12/2021 |
8619 | 2^338898+179623 | 102019 | Stefano Morozzi | 01/2022 |
8620 | 2^338899-154467 | 102019 | Stefano Morozzi | 02/2022 |
8621 | 2^338898-60753 | 102019 | Stefano Morozzi | 06/2022 |
8622 | 2^338898+68635 | 102019 | Stefano Morozzi | 09/2022 |
8623 | 2^338897-85963 | 102019 | Stefano Morozzi | 12/2022 |
8624 | 2^338898+174129 | 102019 | Stefano Morozzi | 02/2023 |
8625 | 2^338894-133295 | 102018 | Stefano Morozzi | 04/2022 |
8626 | 2^338894+165573 | 102018 | Stefano Morozzi | 06/2022 |
8627 | 2^338894-60957 | 102018 | Stefano Morozzi | 06/2022 |
8628 | 2^338894-89463 | 102018 | Stefano Morozzi | 01/2023 |
8638 | 2^338891-18885 | 102017 | Enzo Doria | 05/2013 |
8629 | 2^338891+26499 | 102017 | Stefano Morozzi | 12/2021 |
8630 | 2^338891-2625 | 102017 | Stefano Morozzi | 12/2021 |
8631 | 2^338893+128727 | 102017 | Stefano Morozzi | 01/2022 |
8632 | 2^338890-52965 | 102017 | Stefano Morozzi | 01/2022 |
8633 | 2^338892-55467 | 102017 | Stefano Morozzi | 02/2022 |
8634 | 2^338892-83393 | 102017 | Stefano Morozzi | 04/2022 |
8635 | 2^338893+13649 | 102017 | Stefano Morozzi | 05/2022 |
8636 | 2^338892+117957 | 102017 | Stefano Morozzi | 09/2022 |
8637 | 2^338892-14643 | 102017 | Stefano Morozzi | 01/2023 |
8639 | 2^338887+154029 | 102016 | Stefano Morozzi | 01/2022 |
8640 | 2^338889-104293 | 102016 | Stefano Morozzi | 02/2022 |
8641 | 2^338887+147741 | 102016 | Stefano Morozzi | 11/2022 |
8642 | 2^338889+195975 | 102016 | Stefano Morozzi | 11/2022 |
8643 | 2^338889-117873 | 102016 | Stefano Morozzi | 02/2023 |
8644 | 2^338886+177159 | 102015 | Stefano Morozzi | 12/2021 |
8645 | 2^338885+40425 | 102015 | Stefano Morozzi | 06/2022 |
8646 | 2^338884-13053 | 102015 | Stefano Morozzi | 12/2022 |
8647 | 2^338885-112569 | 102015 | Stefano Morozzi | 12/2022 |
8648 | 2^338880+11341 | 102014 | Stefano Morozzi | 03/2022 |
8649 | 2^338880-160383 | 102014 | Stefano Morozzi | 06/2022 |
8650 | 2^338880-161627 | 102014 | Stefano Morozzi | 12/2022 |
8651 | 2^338879-1059 | 102013 | Stefano Morozzi | 12/2021 |
8652 | 2^338879-54525 | 102013 | Stefano Morozzi | 02/2022 |
8653 | 2^338877-82813 | 102013 | Stefano Morozzi | 03/2022 |
8654 | 2^338878-185883 | 102013 | Stefano Morozzi | 06/2022 |
8655 | 2^338879-60355 | 102013 | Stefano Morozzi | 06/2022 |
8656 | 2^338878+43719 | 102013 | Stefano Morozzi | 09/2022 |
8657 | 2^338879+122049 | 102013 | Stefano Morozzi | 11/2022 |
8658 | 2^338874-15063 | 102012 | Stefano Morozzi | 01/2023 |
8659 | 2^338874+148993 | 102012 | Stefano Morozzi | 02/2023 |
8660 | 2^338871+7679 | 102011 | Stefano Morozzi | 02/2022 |
8661 | 2^338872+61141 | 102011 | Stefano Morozzi | 03/2022 |
8662 | 2^338872-183923 | 102011 | Stefano Morozzi | 04/2022 |
8663 | 2^338873+19527 | 102011 | Stefano Morozzi | 09/2022 |
8664 | 2^338870+70719 | 102011 | Stefano Morozzi | 11/2022 |
8665 | (19*10^102011+287)/9/3 | 102011 | Alfred Reich | 11/2022 |
8666 | 2^338870-37571 | 102011 | Stefano Morozzi | 12/2022 |
8667 | 2^338872-138573 | 102011 | Stefano Morozzi | 12/2022 |
8668 | 2^338873-63843 | 102011 | Stefano Morozzi | 12/2022 |
8669 | 2^338868-5985 | 102010 | Stefano Morozzi | 02/2022 |
8670 | 2^338867+38079 | 102010 | Stefano Morozzi | 05/2022 |
8671 | 2^338868+140437 | 102010 | Stefano Morozzi | 06/2022 |
8672 | 2^338868-110175 | 102010 | Stefano Morozzi | 06/2022 |
8673 | 2^338868+123337 | 102010 | Stefano Morozzi | 11/2022 |
8674 | 2^338867-13327 | 102010 | Stefano Morozzi | 12/2022 |
8675 | 2^338868-11279 | 102010 | Stefano Morozzi | 12/2022 |
8676 | 2^338868-115685 | 102010 | Stefano Morozzi | 01/2023 |
8677 | 2^338864+158191 | 102009 | Stefano Morozzi | 02/2022 |
8678 | 2^338865-39699 | 102009 | Stefano Morozzi | 01/2023 |
8679 | 2^338865-40789 | 102009 | Stefano Morozzi | 01/2023 |
8680 | 2^338862+60433 | 102008 | Stefano Morozzi | 03/2022 |
8681 | 2^338861-9453 | 102008 | Stefano Morozzi | 04/2022 |
8682 | 2^338861+98067 | 102008 | Stefano Morozzi | 11/2022 |
8683 | 2^338862+146545 | 102008 | Stefano Morozzi | 11/2022 |
8684 | 2^338863-186207 | 102008 | Stefano Morozzi | 12/2022 |
8685 | 2^338860-41429 | 102008 | Stefano Morozzi | 01/2023 |
8686 | 2^338862-115833 | 102008 | Stefano Morozzi | 01/2023 |
8687 | 2^338863+74259 | 102008 | Stefano Morozzi | 02/2023 |
8688 | 2^338863-193017 | 102008 | Stefano Morozzi | 02/2023 |
8689 | 2^338858-190185 | 102007 | Stefano Morozzi | 01/2023 |
8690 | 2^338855+102141 | 102006 | Stefano Morozzi | 12/2021 |
8691 | 2^338856-27173 | 102006 | Stefano Morozzi | 12/2021 |
8692 | 2^338856-102839 | 102006 | Stefano Morozzi | 01/2022 |
8693 | 2^338855+79629 | 102006 | Stefano Morozzi | 01/2022 |
8694 | 2^338856+47755 | 102006 | Stefano Morozzi | 11/2022 |
8695 | 2^338850+27987 | 102005 | Stefano Morozzi | 01/2022 |
8696 | 2^338853+111791 | 102005 | Stefano Morozzi | 04/2022 |
8697 | 2^338852+145797 | 102005 | Stefano Morozzi | 11/2022 |
8698 | 2^338852-88497 | 102005 | Stefano Morozzi | 12/2022 |
8699 | 2^338850+124843 | 102005 | Stefano Morozzi | 02/2023 |
8700 | 2^338853-167695 | 102005 | Stefano Morozzi | 02/2023 |
8701 | 2^338847+176013 | 102004 | Stefano Morozzi | 12/2021 |
8702 | 2^338847-2365 | 102004 | Stefano Morozzi | 12/2021 |
8703 | 2^338848+158941 | 102004 | Stefano Morozzi | 03/2022 |
8704 | 2^338848+16671 | 102004 | Stefano Morozzi | 06/2022 |
8705 | 2^338847-35061 | 102004 | Stefano Morozzi | 06/2022 |
8706 | 2^338848+145063 | 102004 | Stefano Morozzi | 11/2022 |
8707 | 2^338847-61885 | 102004 | Stefano Morozzi | 12/2022 |
8708 | 2^338845+135831 | 102003 | Stefano Morozzi | 03/2022 |
8709 | 2^338846+85695 | 102003 | Stefano Morozzi | 03/2022 |
8710 | 2^338845+186525 | 102003 | Stefano Morozzi | 04/2022 |
8711 | 2^338846-163473 | 102003 | Stefano Morozzi | 12/2022 |
8712 | 2^338844-16077 | 102003 | Stefano Morozzi | 01/2023 |
8713 | 2^338844-165143 | 102003 | Stefano Morozzi | 01/2023 |
8714 | 2^338843-127261 | 102002 | Stefano Morozzi | 12/2021 |
8715 | 2^338843+107205 | 102002 | Stefano Morozzi | 02/2022 |
8716 | 2^338842-33185 | 102002 | Stefano Morozzi | 04/2022 |
8717 | 2^338842+14227 | 102002 | Stefano Morozzi | 05/2022 |
8718 | 2^338842+147973 | 102002 | Stefano Morozzi | 11/2022 |
8726 | 8*10^102000+51 | 102001 | Robert Price | 08/2019 |
8719 | 2^338838+150837 | 102001 | Stefano Morozzi | 11/2021 |
8720 | 2^338838+141397 | 102001 | Stefano Morozzi | 06/2022 |
8721 | 2^338839+194363 | 102001 | Stefano Morozzi | 09/2022 |
8722 | 2^338838+95637 | 102001 | Stefano Morozzi | 11/2022 |
8723 | 2^338839+171545 | 102001 | Stefano Morozzi | 11/2022 |
8724 | 2^338837-40071 | 102001 | Stefano Morozzi | 01/2023 |
8725 | 2^338838-90251 | 102001 | Stefano Morozzi | 01/2023 |
8727 | 2^338835-150625 | 102000 | Stefano Morozzi | 12/2021 |
8728 | 2^338834-32877 | 102000 | Stefano Morozzi | 04/2022 |
8732 | (2^338832+642)/2 | 101999 | Stefano Morozzi | 09/2020 |
8729 | 2^338833-100905 | 101999 | Stefano Morozzi | 12/2021 |
8730 | 2^338831+54419 | 101999 | Stefano Morozzi | 01/2022 |
8731 | 2^338831-63687 | 101999 | Stefano Morozzi | 12/2022 |
8740 | 2^338829-113239 | 101998 | Enzo Doria | 07/2014 |
8741 | 2^338828-113297 | 101998 | Enzo Doria | 07/2014 |
8733 | 2^338830+25017 | 101998 | Stefano Morozzi | 11/2021 |
8734 | 2^338831+321 | 101998 | Stefano Morozzi | 11/2021 |
8735 | 2^338827-26197 | 101998 | Stefano Morozzi | 12/2021 |
8736 | 2^338829+52727 | 101998 | Stefano Morozzi | 01/2022 |
8737 | 2^338827-55461 | 101998 | Stefano Morozzi | 02/2022 |
8738 | 2^338828-65859 | 101998 | Stefano Morozzi | 01/2023 |
8739 | 2^338829+99365 | 101998 | Stefano Morozzi | 02/2023 |
8742 | 2^338825-27453 | 101997 | Stefano Morozzi | 12/2021 |
8743 | 2^338824+89355 | 101997 | Stefano Morozzi | 05/2022 |
8744 | 2^338825-10995 | 101997 | Stefano Morozzi | 06/2022 |
8745 | 2^338824+149865 | 101997 | Stefano Morozzi | 02/2023 |
8746 | 2^338822+111175 | 101996 | Stefano Morozzi | 03/2022 |
8747 | 2^338822+187819 | 101996 | Stefano Morozzi | 04/2022 |
8748 | 2^338823+139545 | 101996 | Stefano Morozzi | 05/2022 |
8749 | 2^338823-184905 | 101996 | Stefano Morozzi | 06/2022 |
8750 | 2^338821-38919 | 101996 | Stefano Morozzi | 12/2022 |