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 | 2^338156+167053 | 101796 | Stefano Morozzi | 09/2022 |
8502 | 2^338158+69303 | 101796 | Stefano Morozzi | 09/2022 |
8503 | 2^338158+171189 | 101796 | Stefano Morozzi | 11/2022 |
8504 | 2^338157-188989 | 101796 | Stefano Morozzi | 12/2022 |
8505 | 2^338158-188711 | 101796 | Stefano Morozzi | 12/2022 |
8506 | 2^338155+132621 | 101795 | Stefano Morozzi | 02/2022 |
8507 | 2^338155-82605 | 101795 | Stefano Morozzi | 03/2022 |
8508 | 2^338155-182631 | 101795 | Stefano Morozzi | 03/2022 |
8509 | 2^338155+187755 | 101795 | Stefano Morozzi | 04/2022 |
8510 | 2^338154-83975 | 101795 | Stefano Morozzi | 04/2022 |
8511 | 2^338154+163759 | 101795 | Stefano Morozzi | 05/2022 |
8512 | 2^338152-25767 | 101794 | Stefano Morozzi | 12/2021 |
8513 | 2^338152+181927 | 101794 | Stefano Morozzi | 02/2022 |
8514 | 2^338151+60779 | 101794 | Stefano Morozzi | 03/2022 |
8515 | 2^338151+189149 | 101794 | Stefano Morozzi | 05/2022 |
8516 | 2^338152+45567 | 101794 | Stefano Morozzi | 11/2022 |
8517 | 2^338147+29343 | 101793 | Stefano Morozzi | 01/2022 |
8518 | 2^338148+130803 | 101793 | Stefano Morozzi | 01/2022 |
8519 | 2^338146+166167 | 101793 | Stefano Morozzi | 06/2022 |
8520 | 2^338149-185073 | 101793 | Stefano Morozzi | 06/2022 |
8521 | 2^338149+41757 | 101793 | Stefano Morozzi | 09/2022 |
8522 | 2^338149+125015 | 101793 | Stefano Morozzi | 02/2023 |
8523 | 2^338144+180697 | 101792 | Stefano Morozzi | 01/2022 |
8524 | 2^338143+8589 | 101792 | Stefano Morozzi | 02/2022 |
8525 | 2^338143-55611 | 101792 | Stefano Morozzi | 02/2022 |
8526 | 2^338143+60623 | 101792 | Stefano Morozzi | 03/2022 |
8527 | 2^338145-63609 | 101792 | Stefano Morozzi | 12/2022 |
8528 | 2^338141-77301 | 101791 | Stefano Morozzi | 12/2021 |
8529 | 2^338141+157145 | 101791 | Stefano Morozzi | 02/2022 |
8530 | 2^338140+84745 | 101791 | Stefano Morozzi | 03/2022 |
8531 | 2^338140+90073 | 101791 | Stefano Morozzi | 05/2022 |
8532 | 2^338142+96583 | 101791 | Stefano Morozzi | 11/2022 |
8533 | 2^338139-134719 | 101790 | Stefano Morozzi | 04/2022 |
8534 | 2^338138+95443 | 101790 | Stefano Morozzi | 11/2022 |
8535 | 2^338133+1445 | 101789 | Stefano Morozzi | 12/2021 |
8536 | 2^338133+172469 | 101789 | Stefano Morozzi | 11/2022 |
8537 | 2^338134+23235 | 101789 | Stefano Morozzi | 11/2022 |
8538 | 2^338132+105643 | 101788 | Stefano Morozzi | 01/2022 |
8539 | 2^338131+181871 | 101788 | Stefano Morozzi | 02/2022 |
8540 | 2^338132-184539 | 101788 | Stefano Morozzi | 04/2022 |
8541 | 2^338130+22383 | 101788 | Stefano Morozzi | 11/2022 |
8542 | 2^338132+170143 | 101788 | Stefano Morozzi | 11/2022 |
8543 | 2^338131-62599 | 101788 | Stefano Morozzi | 12/2022 |
8544 | 2^338128+128953 | 101787 | Stefano Morozzi | 01/2022 |
8545 | 2^338127+11021 | 101787 | Stefano Morozzi | 03/2022 |
8546 | 2^338127+192935 | 101787 | Stefano Morozzi | 09/2022 |
8547 | 2^338127+98621 | 101787 | Stefano Morozzi | 11/2022 |
8548 | 2^338128+98853 | 101787 | Stefano Morozzi | 02/2023 |
8549 | 2^338123-25959 | 101786 | Stefano Morozzi | 12/2021 |
8550 | 2^338124-180765 | 101786 | Stefano Morozzi | 02/2022 |
8551 | 2^338125-7129 | 101786 | Stefano Morozzi | 03/2022 |
8552 | 2^338125-40071 | 101786 | Stefano Morozzi | 01/2023 |
8556 | 2^338122-20117 | 101785 | Enzo Doria | 06/2013 |
8557 | (2^338139+5)/905333 | 101785 | Lelio R Paula | 12/2013 |
8553 | 2^338122+32799 | 101785 | Stefano Morozzi | 02/2022 |
8554 | 2^338120+166411 | 101785 | Stefano Morozzi | 06/2022 |
8555 | 2^338122+90705 | 101785 | Stefano Morozzi | 06/2022 |
8558 | 2^338117+103761 | 101784 | Stefano Morozzi | 01/2022 |
8559 | 2^338118+53817 | 101784 | Stefano Morozzi | 01/2022 |
8560 | 2^338116+82585 | 101784 | Stefano Morozzi | 02/2022 |
8561 | 2^338118+39483 | 101784 | Stefano Morozzi | 05/2022 |
8562 | 2^338119+96659 | 101784 | Stefano Morozzi | 11/2022 |
8563 | 2^338115+61083 | 101783 | Stefano Morozzi | 03/2022 |
8564 | 2^338114+173287 | 101783 | Stefano Morozzi | 11/2022 |
8565 | 2^338113-139681 | 101783 | Stefano Morozzi | 01/2023 |
8566 | 2^338110-175365 | 101782 | Stefano Morozzi | 12/2021 |
8567 | 2^338110-3963 | 101782 | Stefano Morozzi | 01/2022 |
8568 | 2^338112+155061 | 101782 | Stefano Morozzi | 01/2022 |
8569 | 2^338112+137335 | 101782 | Stefano Morozzi | 04/2022 |
8570 | 2^338111-85627 | 101782 | Stefano Morozzi | 06/2022 |
8571 | 2^338111-90145 | 101782 | Stefano Morozzi | 01/2023 |
8580 | 35^65917-7092 | 101781 | Enzo Doria | 03/2013 |
8572 | 2^338107-1221 | 101781 | Stefano Morozzi | 12/2021 |
8573 | 2^338109+108539 | 101781 | Stefano Morozzi | 03/2022 |
8574 | 2^338109-7261 | 101781 | Stefano Morozzi | 03/2022 |
8575 | 2^338109-131961 | 101781 | Stefano Morozzi | 03/2022 |
8576 | 2^338108+39585 | 101781 | Stefano Morozzi | 05/2022 |
8577 | 2^338109+38147 | 101781 | Stefano Morozzi | 05/2022 |
8578 | 2^338108+17301 | 101781 | Stefano Morozzi | 09/2022 |
8579 | 2^338108-65859 | 101781 | Stefano Morozzi | 01/2023 |
8581 | 2^338105+79599 | 101780 | Stefano Morozzi | 01/2022 |
8582 | 2^338103-180675 | 101780 | Stefano Morozzi | 02/2022 |
8583 | 2^338103+19499 | 101780 | Stefano Morozzi | 09/2022 |
8584 | 2^338103-165319 | 101780 | Stefano Morozzi | 01/2023 |
8585 | 2^338100-100389 | 101779 | Stefano Morozzi | 12/2021 |
8586 | 2^338100+27595 | 101779 | Stefano Morozzi | 12/2021 |
8587 | 2^338101+101139 | 101779 | Stefano Morozzi | 12/2021 |
8588 | 2^338101+134985 | 101779 | Stefano Morozzi | 03/2022 |
8589 | 2^338102+186135 | 101779 | Stefano Morozzi | 03/2022 |
8590 | 2^338100+36885 | 101779 | Stefano Morozzi | 04/2022 |
8591 | 2^338102-8151 | 101779 | Stefano Morozzi | 04/2022 |
8592 | 2^338100+90637 | 101779 | Stefano Morozzi | 06/2022 |
8593 | 2^338101+68505 | 101779 | Stefano Morozzi | 09/2022 |
8594 | 2^338100-42867 | 101779 | Stefano Morozzi | 02/2023 |
8595 | 2^338097+100229 | 101778 | Stefano Morozzi | 11/2021 |
8596 | 2^338097-25695 | 101778 | Stefano Morozzi | 12/2021 |
8597 | 2^338098-110043 | 101778 | Stefano Morozzi | 06/2022 |
8598 | 2^338099-191389 | 101778 | Stefano Morozzi | 01/2023 |
8599 | 2^338093-128403 | 101777 | Stefano Morozzi | 01/2022 |
8600 | 2^338093+33051 | 101777 | Stefano Morozzi | 02/2022 |
8601 | 2^338094+135555 | 101777 | Stefano Morozzi | 03/2022 |
8602 | 2^338095-32395 | 101777 | Stefano Morozzi | 03/2022 |
8603 | 2^338090-175353 | 101776 | Stefano Morozzi | 12/2021 |
8604 | 2^338090+33277 | 101776 | Stefano Morozzi | 02/2022 |
8605 | 2^338091-105601 | 101776 | Stefano Morozzi | 02/2022 |
8606 | 2^338091-32127 | 101776 | Stefano Morozzi | 03/2022 |
8607 | 2^338092+12873 | 101776 | Stefano Morozzi | 04/2022 |
8608 | 2^338091-58485 | 101776 | Stefano Morozzi | 04/2022 |
8609 | 2^338086+177643 | 101775 | Stefano Morozzi | 12/2021 |
8610 | 2^338089+82905 | 101775 | Stefano Morozzi | 02/2022 |
8611 | 2^338088+87565 | 101775 | Stefano Morozzi | 04/2022 |
8612 | 2^338088-166205 | 101775 | Stefano Morozzi | 01/2023 |
8613 | 2^338089-140053 | 101775 | Stefano Morozzi | 01/2023 |
8614 | 2^338087+124935 | 101775 | Stefano Morozzi | 02/2023 |
8615 | 2^338085-3301 | 101774 | Stefano Morozzi | 01/2022 |
8616 | 2^338084+108691 | 101774 | Stefano Morozzi | 03/2022 |
8617 | 2^338083+164369 | 101774 | Stefano Morozzi | 05/2022 |
8618 | 2^338080+107521 | 101773 | Stefano Morozzi | 02/2022 |
8619 | 2^338080-156917 | 101773 | Stefano Morozzi | 03/2022 |
8620 | 2^338081+199775 | 101773 | Stefano Morozzi | 02/2023 |
8621 | 2^338076+62311 | 101772 | Stefano Morozzi | 04/2022 |
8622 | 2^338079+161745 | 101772 | Stefano Morozzi | 04/2022 |
8623 | 2^338078-60075 | 101772 | Stefano Morozzi | 06/2022 |
8624 | 2^338079+167079 | 101772 | Stefano Morozzi | 09/2022 |
8625 | 2^338076+122535 | 101772 | Stefano Morozzi | 11/2022 |
8626 | 2^338077+95619 | 101772 | Stefano Morozzi | 11/2022 |
8627 | 2^338078+20539 | 101772 | Stefano Morozzi | 11/2022 |
8628 | 2^338076-36813 | 101772 | Stefano Morozzi | 12/2022 |
8629 | 2^338078-64911 | 101772 | Stefano Morozzi | 01/2023 |
8630 | 2^338073-77971 | 101771 | Stefano Morozzi | 01/2022 |
8631 | 2^338074+55579 | 101771 | Stefano Morozzi | 01/2022 |
8632 | 2^338073-81813 | 101771 | Stefano Morozzi | 03/2022 |
8633 | 2^338073+138645 | 101771 | Stefano Morozzi | 05/2022 |
8634 | 2^338075+148043 | 101771 | Stefano Morozzi | 11/2022 |
8635 | 2^338070-152607 | 101770 | Stefano Morozzi | 01/2022 |
8636 | 2^338070+138787 | 101770 | Stefano Morozzi | 05/2022 |
8637 | 2^338071+165249 | 101770 | Stefano Morozzi | 06/2022 |
8638 | 2^338070+70359 | 101770 | Stefano Morozzi | 11/2022 |
8639 | 2^338071+98573 | 101770 | Stefano Morozzi | 11/2022 |
8640 | 2^338069+79365 | 101769 | Stefano Morozzi | 01/2022 |
8641 | 2^338069+107571 | 101769 | Stefano Morozzi | 02/2022 |
8642 | 2^338068+73035 | 101769 | Stefano Morozzi | 11/2022 |
8643 | 2^338064+100087 | 101768 | Stefano Morozzi | 11/2021 |
8644 | 2^338064-83793 | 101768 | Stefano Morozzi | 04/2022 |
8645 | 2^338064+193701 | 101768 | Stefano Morozzi | 09/2022 |
8646 | 2^338065+199947 | 101768 | Stefano Morozzi | 02/2023 |
8647 | 2^338060-151047 | 101767 | Stefano Morozzi | 12/2021 |
8648 | 2^338060-130805 | 101767 | Stefano Morozzi | 02/2022 |
8649 | 2^338060-136593 | 101767 | Stefano Morozzi | 12/2022 |
8650 | 2^338062-15725 | 101767 | Stefano Morozzi | 01/2023 |
8651 | 2^338058-76415 | 101766 | Stefano Morozzi | 12/2021 |
8652 | 2^338057+83865 | 101766 | Stefano Morozzi | 03/2022 |
8653 | 2^338057+86997 | 101766 | Stefano Morozzi | 04/2022 |
8654 | 2^338058+188589 | 101766 | Stefano Morozzi | 05/2022 |
8655 | 2^338058+68089 | 101766 | Stefano Morozzi | 09/2022 |
8656 | 2^338059+121803 | 101766 | Stefano Morozzi | 11/2022 |
8657 | 2^338057-39021 | 101766 | Stefano Morozzi | 01/2023 |
8658 | 2^338056+50605 | 101765 | Stefano Morozzi | 11/2021 |
8659 | 2^338053+53231 | 101765 | Stefano Morozzi | 01/2022 |
8660 | 2^338054-180497 | 101765 | Stefano Morozzi | 02/2022 |
8661 | 2^338053+59891 | 101765 | Stefano Morozzi | 03/2022 |
8662 | 2^338056+33987 | 101765 | Stefano Morozzi | 03/2022 |
8663 | 2^338055-157779 | 101765 | Stefano Morozzi | 03/2022 |
8664 | 2^338056+90307 | 101765 | Stefano Morozzi | 06/2022 |
8665 | 2^338055+124443 | 101765 | Stefano Morozzi | 02/2023 |
8666 | 2^338052-55373 | 101764 | Stefano Morozzi | 02/2022 |
8667 | 2^338050-138281 | 101764 | Stefano Morozzi | 12/2022 |
8668 | 2^338050+148959 | 101764 | Stefano Morozzi | 02/2023 |
8669 | 2^338051-118159 | 101764 | Stefano Morozzi | 02/2023 |
8670 | 2^338048+31185 | 101763 | Stefano Morozzi | 01/2022 |
8671 | 2^338047+31935 | 101763 | Stefano Morozzi | 02/2022 |
8672 | 2^338047+108011 | 101763 | Stefano Morozzi | 02/2022 |
8673 | 2^338049+56777 | 101763 | Stefano Morozzi | 02/2022 |
8674 | 2^338049-7531 | 101763 | Stefano Morozzi | 03/2022 |
8675 | 2^338048-304019 | 101763 | Harrison Mesh | 06/2022 |
8676 | 2^338049+191291 | 101763 | Stefano Morozzi | 06/2022 |
8677 | 2^338047-187699 | 101763 | Stefano Morozzi | 12/2022 |
8678 | 2^338047-66405 | 101763 | Stefano Morozzi | 01/2023 |
8679 | 2^338049-192633 | 101763 | Stefano Morozzi | 02/2023 |
8680 | 2^338046-25841 | 101762 | Stefano Morozzi | 12/2021 |
8681 | 2^338046-2285 | 101762 | Stefano Morozzi | 12/2021 |
8682 | 2^338046-177851 | 101762 | Stefano Morozzi | 01/2022 |
8683 | 2^338043+84045 | 101762 | Stefano Morozzi | 03/2022 |
8684 | 2^338046-57573 | 101762 | Stefano Morozzi | 03/2022 |
8685 | 2^338044-8177 | 101762 | Stefano Morozzi | 04/2022 |
8686 | 2^338045-58443 | 101762 | Stefano Morozzi | 04/2022 |
8687 | 2^338044+193497 | 101762 | Stefano Morozzi | 09/2022 |
8688 | 2^338043+45701 | 101762 | Stefano Morozzi | 11/2022 |
8689 | 2^338044-114197 | 101762 | Stefano Morozzi | 01/2023 |
8690 | 2^338042+194973 | 101761 | Stefano Morozzi | 11/2022 |
8691 | 2^338040-164483 | 101761 | Stefano Morozzi | 01/2023 |
8692 | 2^338038-57887 | 101760 | Stefano Morozzi | 04/2022 |
8693 | 2^338037+139169 | 101760 | Stefano Morozzi | 05/2022 |
8694 | 2^338037+188595 | 101760 | Stefano Morozzi | 05/2022 |
8695 | 2^338038-187241 | 101760 | Stefano Morozzi | 12/2022 |
8696 | 2^338039+124035 | 101760 | Stefano Morozzi | 02/2023 |
8697 | 2^338037-42523 | 101760 | Stefano Morozzi | 02/2023 |
8698 | 2^338034+125653 | 101759 | Stefano Morozzi | 11/2021 |
8699 | 2^338034-25211 | 101759 | Stefano Morozzi | 12/2021 |
8700 | 2^338033-154099 | 101759 | Stefano Morozzi | 02/2022 |
8701 | 2^338034-31803 | 101759 | Stefano Morozzi | 03/2022 |
8702 | 2^338033+162311 | 101759 | Stefano Morozzi | 04/2022 |
8703 | 2^338033-83071 | 101759 | Stefano Morozzi | 04/2022 |
8704 | 2^338035-158095 | 101759 | Stefano Morozzi | 04/2022 |
8705 | 2^338036-34193 | 101759 | Stefano Morozzi | 04/2022 |
8706 | 2^338036+42873 | 101759 | Stefano Morozzi | 09/2022 |
8707 | 2^338036+93373 | 101759 | Stefano Morozzi | 09/2022 |
8708 | 2^338035+146129 | 101759 | Stefano Morozzi | 11/2022 |
8709 | 2^338036+23983 | 101759 | Stefano Morozzi | 11/2022 |
8710 | 2^338036+170433 | 101759 | Stefano Morozzi | 11/2022 |
8711 | 2^338031+79989 | 101758 | Stefano Morozzi | 01/2022 |
8712 | 2^338032+158073 | 101758 | Stefano Morozzi | 02/2022 |
8713 | 2^338030-54371 | 101758 | Stefano Morozzi | 02/2022 |
8714 | 2^338032-180747 | 101758 | Stefano Morozzi | 02/2022 |
8715 | 2^338029-27909 | 101757 | Stefano Morozzi | 01/2022 |
8716 | 2^338027+70475 | 101757 | Stefano Morozzi | 11/2022 |
8717 | 2^338028-38705 | 101757 | Stefano Morozzi | 12/2022 |
8718 | 2^338028-140459 | 101757 | Stefano Morozzi | 01/2023 |
8719 | 2^338024-128495 | 101756 | Stefano Morozzi | 01/2022 |
8720 | 2^338025+34785 | 101756 | Stefano Morozzi | 03/2022 |
8721 | 2^338025-181765 | 101756 | Stefano Morozzi | 03/2022 |
8722 | 2^338024+63765 | 101756 | Stefano Morozzi | 05/2022 |
8723 | 2^338023-160621 | 101756 | Stefano Morozzi | 06/2022 |
8724 | 2^338026+117553 | 101756 | Stefano Morozzi | 09/2022 |
8725 | 2^338020-52437 | 101755 | Stefano Morozzi | 12/2021 |
8726 | 2^338021+160241 | 101755 | Stefano Morozzi | 03/2022 |
8727 | 2^338022+185845 | 101755 | Stefano Morozzi | 03/2022 |
8728 | 2^338021+189587 | 101755 | Stefano Morozzi | 05/2022 |
8729 | 2^338021-85891 | 101755 | Stefano Morozzi | 06/2022 |
8730 | 2^338020-87797 | 101755 | Stefano Morozzi | 12/2022 |
8731 | 2^338018-102741 | 101754 | Stefano Morozzi | 01/2022 |
8732 | 2^338018+29937 | 101754 | Stefano Morozzi | 01/2022 |
8733 | 2^338017-29505 | 101754 | Stefano Morozzi | 02/2022 |
8734 | 2^338018-30873 | 101754 | Stefano Morozzi | 02/2022 |
8735 | 2^338018-157013 | 101754 | Stefano Morozzi | 03/2022 |
8736 | 2^338019+168929 | 101754 | Stefano Morozzi | 09/2022 |
8737 | 2^338017+172721 | 101754 | Stefano Morozzi | 11/2022 |
8738 | 2^338018-136131 | 101754 | Stefano Morozzi | 12/2022 |
8739 | 2^338016+50797 | 101753 | Stefano Morozzi | 11/2021 |
8740 | 2^338016+26707 | 101753 | Stefano Morozzi | 12/2021 |
8741 | 2^338014+104677 | 101753 | Stefano Morozzi | 01/2022 |
8742 | 2^338013+145091 | 101753 | Stefano Morozzi | 11/2022 |
8743 | 2^338016-16335 | 101753 | Stefano Morozzi | 01/2023 |
8746 | 2^338010-19833 | 101752 | Enzo Doria | 06/2013 |
8744 | 2^338011+28665 | 101752 | Stefano Morozzi | 01/2022 |
8745 | 2^338010+89505 | 101752 | Stefano Morozzi | 05/2022 |
8747 | 2^338007+58985 | 101751 | Stefano Morozzi | 03/2022 |
8748 | 2^338008+109741 | 101751 | Stefano Morozzi | 03/2022 |
8749 | 2^338009+9527 | 101751 | Stefano Morozzi | 03/2022 |
8750 | 2^338007+14511 | 101751 | Stefano Morozzi | 05/2022 |