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) !!!
Submit your PRPs
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See the Latest PRPs
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Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
8704 | 25206!+p(4114) | 100001 | Henri Lifchitz | 09/2005 |
8705 | 25206!-p(5447) | 100001 | Henri Lifchitz | 10/2005 |
8706 | 25206!-p(12402) | 100001 | Henri Lifchitz | 04/2006 |
8707 | 25206!-p(16290) | 100001 | Henri Lifchitz | 09/2006 |
8708 | 25206!-p(19647) | 100001 | Henri Lifchitz | 02/2007 |
8709 | 2^332194+11473 | 100001 | Henri Lifchitz | 03/2007 |
8699 | 10^100000+342909 | 100001 | Milton L. Brown | 12/2007 |
8700 | 10^100000+346579 | 100001 | Robert Price | 04/2012 |
8701 | 10^100000+829767 | 100001 | Robert Price | 05/2012 |
8702 | 10^100000+871899 | 100001 | Robert Price | 05/2012 |
8703 | 10^100000+1475997 | 100001 | Robert Price | 07/2012 |
8692 | 10^100000+1751769 | 100001 | Robert Price | 08/2012 |
8693 | 10^100000+2155489 | 100001 | Robert Price | 10/2012 |
8694 | 10^100000+2483527 | 100001 | Robert Price | 12/2012 |
8695 | 10^100000+2503087 | 100001 | Robert Price | 12/2012 |
8696 | 10^100000+2686179 | 100001 | Robert Price | 12/2012 |
8697 | 10^100000+2688933 | 100001 | Robert Price | 12/2012 |
8698 | 10^100000+3667159 | 100001 | Robert Price | 08/2013 |
8501 | 2^332196-1-2*29696 | 100001 | Matt Stath | 11/2018 |
8502 | 10^100000+12363957 | 100001 | Robert Price | 11/2018 |
8503 | 2^332196+1+2*17152 | 100001 | Matt Stath | 12/2018 |
8504 | 10^100000+12778033 | 100001 | Robert Price | 02/2019 |
8505 | 10^100000+13581679 | 100001 | Robert Price | 05/2019 |
8506 | 10^100000+13613199 | 100001 | Robert Price | 05/2019 |
8507 | 10^100000+13752327 | 100001 | Robert Price | 05/2019 |
8508 | 10^100000+14139243 | 100001 | Robert Price | 06/2019 |
8509 | 10^100000+14151057 | 100001 | Robert Price | 06/2019 |
8510 | 10^100000+14218923 | 100001 | Robert Price | 06/2019 |
8672 | 10^100000+15136771 | 100001 | Robert Price | 09/2019 |
8673 | 10^100000+15219873 | 100001 | Robert Price | 10/2019 |
8674 | 10^100000+15274039 | 100001 | Robert Price | 10/2019 |
8675 | 10^100000+15394069 | 100001 | Robert Price | 10/2019 |
8676 | 10^100000+15547119 | 100001 | Robert Price | 10/2019 |
8677 | 10^100000+15932923 | 100001 | Robert Price | 11/2019 |
8678 | 10^100000+16345467 | 100001 | Robert Price | 12/2019 |
8679 | 10^100000+16672143 | 100001 | Robert Price | 01/2020 |
8680 | 10^100000+16731939 | 100001 | Robert Price | 02/2020 |
8681 | 10^100000+16907049 | 100001 | Robert Price | 03/2020 |
8682 | 10^100000+17652523 | 100001 | Robert Price | 05/2020 |
8683 | 10^100000+18047167 | 100001 | Robert Price | 05/2020 |
8684 | 10^100000+18471819 | 100001 | Robert Price | 06/2020 |
8685 | 10^100000+18494793 | 100001 | Robert Price | 07/2020 |
8686 | 10^100000+18762609 | 100001 | Robert Price | 07/2020 |
8687 | 10^100000+19204141 | 100001 | Robert Price | 08/2020 |
8688 | 10^100000+19349793 | 100001 | Robert Price | 08/2020 |
8689 | 10^100000+19495699 | 100001 | Robert Price | 09/2020 |
8690 | 10^100000+19668927 | 100001 | Robert Price | 09/2020 |
8691 | 10^100000+19704313 | 100001 | Robert Price | 09/2020 |
8641 | 10^100000+19956229 | 100001 | Robert Price | 09/2020 |
8642 | 10^100000+3*(10^37093-1)/9*10^31454+1 | 100001 | Makoto Morimoto | 09/2020 |
8643 | 10^100000+4*(10^36149-1)/9*10^31926+1 | 100001 | Makoto Morimoto | 09/2020 |
8644 | 10^100000+6*(10^41029-1)/9*10^29486+1 | 100001 | Makoto Morimoto | 09/2020 |
8645 | 10^100000+7*(10^55505-1)/9*10^22248+1 | 100001 | Makoto Morimoto | 09/2020 |
8646 | 10^100000+20234607 | 100001 | Robert Price | 10/2020 |
8647 | 10^100000+20752303 | 100001 | Robert Price | 11/2020 |
8648 | 10^100000+20774041 | 100001 | Robert Price | 11/2020 |
8649 | 10^100000+20854741 | 100001 | Robert Price | 11/2020 |
8650 | 10^100000+20908917 | 100001 | Robert Price | 11/2020 |
8651 | 10^100000+20994793 | 100001 | Robert Price | 11/2020 |
8652 | 10^100000+21354249 | 100001 | Robert Price | 12/2020 |
8653 | 10^100000+21455559 | 100001 | Robert Price | 12/2020 |
8654 | 10^100000+21538873 | 100001 | Robert Price | 12/2020 |
8655 | 10^100000+21830901 | 100001 | Robert Price | 01/2021 |
8656 | 10^100000+21842629 | 100001 | Robert Price | 01/2021 |
8657 | 10^100000+21930861 | 100001 | Robert Price | 01/2021 |
8658 | 10^100000+22092943 | 100001 | Robert Price | 03/2021 |
8659 | 10^100000+22278417 | 100001 | Robert Price | 03/2021 |
8660 | 10^100000+22388581 | 100001 | Robert Price | 03/2021 |
8661 | 10^100000+22390933 | 100001 | Robert Price | 03/2021 |
8662 | 10^100000+22436169 | 100001 | Robert Price | 03/2021 |
8663 | 10^100000+22714557 | 100001 | Robert Price | 04/2021 |
8664 | 10^100000+22847671 | 100001 | Robert Price | 04/2021 |
8665 | 10^100000+23178567 | 100001 | Robert Price | 05/2021 |
8666 | 10^100000+23332003 | 100001 | Robert Price | 05/2021 |
8667 | 10^100000+23414571 | 100001 | Robert Price | 05/2021 |
8668 | 10^100000+23529979 | 100001 | Robert Price | 05/2021 |
8669 | 10^100000+23749243 | 100001 | Robert Price | 06/2021 |
8670 | 10^100000+23821771 | 100001 | Robert Price | 06/2021 |
8671 | 10^100000+24179307 | 100001 | Robert Price | 07/2021 |
8511 | 10^100000+24543147 | 100001 | Robert Price | 08/2021 |
8512 | 10^100000+24781659 | 100001 | Robert Price | 08/2021 |
8513 | 10^100000+24906153 | 100001 | Robert Price | 08/2021 |
8514 | 10^100000+25682679 | 100001 | Robert Price | 10/2021 |
8515 | 10^100000+25905301 | 100001 | Robert Price | 10/2021 |
8516 | 10^100000+25923967 | 100001 | Robert Price | 10/2021 |
8517 | 10^100000+26061691 | 100001 | Robert Price | 10/2021 |
8518 | 10^100000+26173351 | 100001 | Robert Price | 11/2021 |
8519 | 10^100000+26673487 | 100001 | Robert Price | 11/2021 |
8520 | 10^100000+26849359 | 100001 | Robert Price | 12/2021 |
8521 | 10^100000+26893887 | 100001 | Robert Price | 12/2021 |
8522 | 10^100000+26954551 | 100001 | Robert Price | 12/2021 |
8523 | 10^100000+27024543 | 100001 | Robert Price | 12/2021 |
8524 | 10^100000+27060877 | 100001 | Robert Price | 12/2021 |
8525 | 10^100000+27617577 | 100001 | Robert Price | 03/2022 |
8526 | 10^100000+27869671 | 100001 | Robert Price | 03/2022 |
8527 | 10^100000+27956481 | 100001 | Robert Price | 03/2022 |
8528 | 10^100000+28078261 | 100001 | Robert Price | 03/2022 |
8529 | 10^100000+28150203 | 100001 | Robert Price | 03/2022 |
8530 | 10^100000+28626021 | 100001 | Robert Price | 05/2022 |
8531 | 10^100000+28649299 | 100001 | Robert Price | 05/2022 |
8532 | 10^100000+29409799 | 100001 | Robert Price | 06/2022 |
8533 | 10^100000+29415577 | 100001 | Robert Price | 06/2022 |
8534 | 10^100000+29424201 | 100001 | Robert Price | 06/2022 |
8535 | 10^100000+29610153 | 100001 | Robert Price | 07/2022 |
8536 | 10^100000+30166789 | 100001 | Robert Price | 07/2022 |
8537 | 10^100000+30338259 | 100001 | Robert Price | 07/2022 |
8538 | 10^100000+30540031 | 100001 | Robert Price | 07/2022 |
8539 | 10^100000+30635157 | 100001 | Robert Price | 07/2022 |
8540 | 10^100000+30762711 | 100001 | Robert Price | 07/2022 |
8541 | 10^100000+30862057 | 100001 | Robert Price | 07/2022 |
8542 | 10^100000+30998953 | 100001 | Robert Price | 07/2022 |
8543 | 10^100000+31405203 | 100001 | Robert Price | 07/2022 |
8544 | 10^100000+40159119 | 100001 | Robert Price | 07/2022 |
8545 | 10^100000+40181863 | 100001 | Robert Price | 07/2022 |
8546 | 10^100000+40277131 | 100001 | Robert Price | 07/2022 |
8547 | 10^100000+40326061 | 100001 | Robert Price | 07/2022 |
8548 | 10^100000+40417411 | 100001 | Robert Price | 07/2022 |
8549 | 10^100000+50049909 | 100001 | Robert Price | 07/2022 |
8550 | 10^100000+50510163 | 100001 | Robert Price | 07/2022 |
8551 | 10^100000+50591583 | 100001 | Robert Price | 07/2022 |
8552 | 10^100000+50850357 | 100001 | Robert Price | 07/2022 |
8553 | 10^100000+50974641 | 100001 | Robert Price | 07/2022 |
8554 | 10^100000+51046671 | 100001 | Robert Price | 07/2022 |
8555 | 10^100000+51459657 | 100001 | Robert Price | 07/2022 |
8556 | 10^100000+70081471 | 100001 | Robert Price | 07/2022 |
8557 | 10^100000+70159557 | 100001 | Robert Price | 07/2022 |
8558 | 10^100000+70262479 | 100001 | Robert Price | 07/2022 |
8559 | 10^100000+70417521 | 100001 | Robert Price | 07/2022 |
8560 | 10^100000+70476531 | 100001 | Robert Price | 07/2022 |
8561 | 10^100000+70534627 | 100001 | Robert Price | 07/2022 |
8562 | 10^100000+70873077 | 100001 | Robert Price | 07/2022 |
8563 | 10^100000+71114643 | 100001 | Robert Price | 07/2022 |
8564 | 10^100000+71272539 | 100001 | Robert Price | 07/2022 |
8565 | 10^100000+80025337 | 100001 | Robert Price | 07/2022 |
8566 | 10^100000+71580817 | 100001 | Robert Price | 07/2022 |
8567 | 10^100000+80270349 | 100001 | Robert Price | 07/2022 |
8568 | 10^100000+29831551 | 100001 | Robert Price | 07/2022 |
8569 | 10^100000+29955417 | 100001 | Robert Price | 08/2022 |
8570 | 479072067*10^99992+1+2*1779 | 100001 | Matt Stath | 12/2022 |
8571 | 10^100000+90000000+851439 | 100001 | Robert Price | 04/2023 |
8572 | 10^100000+90000000+1088017 | 100001 | Robert Price | 04/2023 |
8573 | 10^100000+90000000+1288173 | 100001 | Robert Price | 04/2023 |
8574 | 10^100000+90000000+1324549 | 100001 | Robert Price | 04/2023 |
8575 | 10^100000+90000000+3643869 | 100001 | Robert Price | 04/2023 |
8576 | 10^100000+110000000+60221 | 100001 | Robert Price | 04/2023 |
8577 | 10^100000+110000000+373261 | 100001 | Robert Price | 04/2023 |
8578 | 10^100000+110000000+497513 | 100001 | Robert Price | 04/2023 |
8579 | 10^100000+120000000+33823 | 100001 | Robert Price | 04/2023 |
8580 | 10^100000+120000000+419053 | 100001 | Robert Price | 04/2023 |
8581 | 10^100000+32110183 | 100001 | Robert Price | 09/2023 |
8582 | 10^100000+32401957 | 100001 | Robert Price | 09/2023 |
8583 | 10^100000+32301613 | 100001 | Robert Price | 09/2023 |
8584 | 10^100000+32784673 | 100001 | Robert Price | 09/2023 |
8585 | 10^100000+32896891 | 100001 | Robert Price | 09/2023 |
8586 | 10^100000+33279769 | 100001 | Robert Price | 09/2023 |
8587 | 10^100000+33648571 | 100001 | Robert Price | 09/2023 |
8588 | 10^100000+35157571 | 100001 | Robert Price | 09/2023 |
8589 | 10^100000+35226249 | 100001 | Robert Price | 09/2023 |
8590 | 10^100000+35282473 | 100001 | Robert Price | 09/2023 |
8591 | 10^100000+35948761 | 100001 | Robert Price | 09/2023 |
8592 | 10^100000+36443959 | 100001 | Robert Price | 09/2023 |
8593 | 10^100000+36497599 | 100001 | Robert Price | 09/2023 |
8594 | 10^100000+36558403 | 100001 | Robert Price | 09/2023 |
8595 | 10^100000+36812521 | 100001 | Robert Price | 09/2023 |
8596 | 10^100000+36858877 | 100001 | Robert Price | 09/2023 |
8597 | 10^100000+37230043 | 100001 | Robert Price | 09/2023 |
8598 | 10^100000+37449007 | 100001 | Robert Price | 09/2023 |
8599 | 10^100000+37329319 | 100001 | Robert Price | 09/2023 |
8600 | 10^100000+37677673 | 100001 | Robert Price | 09/2023 |
8601 | 10^100000+37696443 | 100001 | Robert Price | 09/2023 |
8602 | 10^100000+37782939 | 100001 | Robert Price | 09/2023 |
8603 | 10^100000+37952341 | 100001 | Robert Price | 09/2023 |
8604 | 10^100000+37954359 | 100001 | Robert Price | 09/2023 |
8605 | 10^100000+37962607 | 100001 | Robert Price | 09/2023 |
8606 | 10^100000+38385177 | 100001 | Robert Price | 09/2023 |
8607 | 10^100000+38497629 | 100001 | Robert Price | 09/2023 |
8608 | 10^100000+38506677 | 100001 | Robert Price | 09/2023 |
8609 | 10^100000+38707363 | 100001 | Robert Price | 09/2023 |
8610 | 10^100000+38769241 | 100001 | Robert Price | 09/2023 |
8611 | 10^100000+38974447 | 100001 | Robert Price | 09/2023 |
8612 | 10^100000+39124453 | 100001 | Robert Price | 09/2023 |
8613 | 10^100000+39127687 | 100001 | Robert Price | 09/2023 |
8614 | 10^100000+39197317 | 100001 | Robert Price | 09/2023 |
8615 | 10^100000+39465897 | 100001 | Robert Price | 09/2023 |
8616 | 10^100000+40588669 | 100001 | Robert Price | 09/2023 |
8617 | 10^100000+40944997 | 100001 | Robert Price | 09/2023 |
8618 | 10^100000+40948201 | 100001 | Robert Price | 09/2023 |
8619 | 10^100000+41456151 | 100001 | Robert Price | 09/2023 |
8620 | 10^100000+41492707 | 100001 | Robert Price | 09/2023 |
8621 | 10^100000+41653389 | 100001 | Robert Price | 09/2023 |
8622 | 10^100000+41853379 | 100001 | Robert Price | 09/2023 |
8623 | 10^100000+41983459 | 100001 | Robert Price | 09/2023 |
8624 | 10^100000+42043387 | 100001 | Robert Price | 09/2023 |
8625 | 10^100000+42048453 | 100001 | Robert Price | 09/2023 |
8626 | 10^100000+42336543 | 100001 | Robert Price | 09/2023 |
8627 | 10^100000+42394797 | 100001 | Robert Price | 09/2023 |
8628 | 10^100000+42880261 | 100001 | Robert Price | 09/2023 |
8629 | 10^100000+42906303 | 100001 | Robert Price | 09/2023 |
8630 | 10^100000+43061901 | 100001 | Robert Price | 09/2023 |
8631 | 10^100000+43089789 | 100001 | Robert Price | 09/2023 |
8632 | 10^100000+43418013 | 100001 | Robert Price | 09/2023 |
8633 | 10^100000+43813831 | 100001 | Robert Price | 09/2023 |
8634 | 10^100000+43950739 | 100001 | Robert Price | 09/2023 |
8635 | 10^100000+44108359 | 100001 | Robert Price | 09/2023 |
8636 | 10^100000+44183733 | 100001 | Robert Price | 09/2023 |
8637 | 10^100000+45126303 | 100001 | Robert Price | 09/2023 |
8638 | 10^100000+45218437 | 100001 | Robert Price | 09/2023 |
8639 | 10^100000+45241837 | 100001 | Robert Price | 09/2023 |
8640 | 10^100000+45665701 | 100001 | Robert Price | 09/2023 |
8710 | 10^99999+309403 | 100000 | Daniel Heuer | 01/2004 |
8711 | 10^100000-260199 | 100000 | Patrick De Geest | 01/2010 |
8712 | 2^332192+10192681 | 100000 | Sujan Das | 06/2022 |
8713 | 1610172603059^8192+1610172602878^8192 | 100000 | Youcef Lemsafer | 01/2023 |
8715 | 10^99999-59511 | 99999 | Patrick De Geest | 07/2009 |
8714 | 10^99998+235437 | 99999 | Patrick De Geest | 02/2020 |
8716 | 10^99998-286587 | 99998 | Patrick De Geest | 02/2020 |
8717 | 10^99997+72297 | 99998 | Patrick De Geest | 02/2020 |
8718 | 10^99997-402627 | 99997 | Patrick De Geest | 02/2020 |
8719 | 10^99996+279853 | 99997 | Patrick De Geest | 02/2020 |
8720 | 10^99997-500000001 | 99997 | Robert Price | 12/2020 |
8721 | 10^99996-94961 | 99996 | Patrick De Geest | 02/2020 |
8722 | 10^99995+54633 | 99996 | Patrick De Geest | 02/2020 |
8723 | 10^99995-101429 | 99995 | Patrick De Geest | 02/2020 |
8724 | 10^99994+117271 | 99995 | Patrick De Geest | 02/2020 |
8725 | 10^99994-452289 | 99994 | Patrick De Geest | 02/2020 |
8726 | 10^99993+371311 | 99994 | Patrick De Geest | 02/2020 |
8727 | 10^99993-186491 | 99993 | Patrick De Geest | 02/2020 |
8728 | 10^99992+17431 | 99993 | Patrick De Geest | 02/2020 |
8729 | 10^99992-28607 | 99992 | Patrick De Geest | 02/2020 |
8730 | 10^99991+125391 | 99992 | Patrick De Geest | 02/2020 |
8731 | 10^99991-204573 | 99991 | Patrick De Geest | 02/2020 |
8732 | 10^99990+13899 | 99991 | Patrick De Geest | 02/2020 |
8733 | 10^99990-8111 | 99990 | Patrick De Geest | 02/2020 |
8734 | 2^332141-113073 | 99985 | Enzo Doria | 07/2014 |
8735 | (1610172603037^8192+1610172602919^8192)/17110948127473666 | 99983 | Youcef Lemsafer | 01/2023 |
8736 | 6*10^99979-79 | 99980 | Robert Price | 03/2022 |
8738 | (3^209561+2)/728101255 | 99978 | Lelio R Paula | 09/2013 |
8737 | 23827^15702+15702^23827 | 99978 | Hans Havermann | 04/2018 |
8739 | 2^332085+1865897 | 99968 | Enzo Doria | 03/2016 |
8740 | (9787*2^332070-1)/936402369 | 99959 | Lelio R Paula | 05/2015 |
8741 | 2^332023+191 | 99949 | Lelio R Paula | 02/2011 |
8742 | (6271^26321-1)/6270 | 99946 | Serge Batalov | 06/2022 |
8743 | 7*10^99944+27 | 99945 | Robert Price | 11/2020 |
8744 | 3188^28523-28523^3188 | 99931 | Norbert Schneider | 06/2023 |
8745 | 2^331938+71149 | 99924 | Enzo Doria | 04/2016 |
8746 | 2^331932-78795 | 99922 | Lelio R Paula | 09/2016 |
8747 | 2^331921+771 | 99919 | Lelio R Paula | 01/2013 |
8748 | 7947^25618-25618^7947 | 99916 | Norbert Schneider | 08/2023 |
8749 | (3^209419-2)/5132755 | 99912 | Lelio R Paula | 09/2013 |
8750 | 2^331860-114989 | 99900 | Enzo Doria | 05/2015 |