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
See the Top discoverers
See the Latest PRPs
Search by form
| Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
| 8501 | 2^346204+127677 | 104218 | Stefano Morozzi | 11/2024 |
| 8502 | 2^346204+19573 | 104218 | Stefano Morozzi | 11/2024 |
| 8503 | 2^346204+161997 | 104218 | Stefano Morozzi | 11/2024 |
| 8504 | 2^346204+152665 | 104218 | Stefano Morozzi | 11/2024 |
| 8505 | 2^346199+90995 | 104217 | Stefano Morozzi | 11/2024 |
| 8506 | 2^346199+189629 | 104217 | Stefano Morozzi | 11/2024 |
| 8507 | 2^346200+159591 | 104217 | Stefano Morozzi | 11/2024 |
| 8508 | 2^346195+19733 | 104216 | Stefano Morozzi | 11/2024 |
| 8509 | 2^346196+141117 | 104216 | Stefano Morozzi | 11/2024 |
| 8510 | 2^346196+195171 | 104216 | Stefano Morozzi | 11/2024 |
| 8511 | 2^346197+113751 | 104216 | Stefano Morozzi | 11/2024 |
| 8512 | 2^346198+95305 | 104216 | Stefano Morozzi | 11/2024 |
| 8513 | 2^346198+106735 | 104216 | Stefano Morozzi | 11/2024 |
| 8515 | 18^83021-91 | 104214 | Lelio R Paula | 01/2017 |
| 8514 | 2^346189+194831 | 104214 | Stefano Morozzi | 11/2024 |
| 8516 | 10^104212+128779 | 104213 | Patrick De Geest | 05/2016 |
| 8517 | 10^104212+237447 | 104213 | Patrick De Geest | 05/2016 |
| 8518 | 10^104212+242139 | 104213 | Patrick De Geest | 05/2016 |
| 8519 | 10^104212+269199 | 104213 | Patrick De Geest | 05/2016 |
| 8523 | 24254^19803+19803^24254 | 104213 | Hans Havermann | 09/2020 |
| 8520 | 2^346186+93813 | 104213 | Stefano Morozzi | 11/2024 |
| 8521 | 2^346186+153687 | 104213 | Stefano Morozzi | 11/2024 |
| 8522 | 2^346187+102195 | 104213 | Stefano Morozzi | 11/2024 |
| 8528 | (10^104212-71)/1 | 104212 | Serge Batalov | 12/2014 |
| 8524 | 2^346182+118065 | 104212 | Stefano Morozzi | 11/2024 |
| 8525 | 2^346184+155085 | 104212 | Stefano Morozzi | 11/2024 |
| 8526 | 2^346184+187513 | 104212 | Stefano Morozzi | 11/2024 |
| 8527 | 2^346184+188455 | 104212 | Stefano Morozzi | 11/2024 |
| 8529 | 2^346180+82735 | 104211 | Stefano Morozzi | 11/2024 |
| 8530 | 2^346180+160593 | 104211 | Stefano Morozzi | 11/2024 |
| 8531 | 2^346180+192333 | 104211 | Stefano Morozzi | 11/2024 |
| 8532 | 2^346181+199821 | 104211 | Stefano Morozzi | 11/2024 |
| 8533 | 2^346176+123667 | 104210 | Stefano Morozzi | 11/2024 |
| 8534 | 2^346178+37455 | 104210 | Stefano Morozzi | 11/2024 |
| 8535 | 2^346178+95865 | 104210 | Stefano Morozzi | 11/2024 |
| 8536 | 2^346178+159517 | 104210 | Stefano Morozzi | 11/2024 |
| 8537 | 2^346174+12543 | 104209 | Stefano Morozzi | 11/2024 |
| 8538 | 2^346169+56049 | 104208 | Stefano Morozzi | 11/2024 |
| 8539 | 2^346169+118965 | 104208 | Stefano Morozzi | 11/2024 |
| 8540 | 2^346170+31363 | 104208 | Stefano Morozzi | 11/2024 |
| 8541 | 2^346165+61767 | 104207 | Stefano Morozzi | 11/2024 |
| 8542 | 2^346166+189919 | 104207 | Stefano Morozzi | 11/2024 |
| 8543 | 2^346167+41681 | 104207 | Stefano Morozzi | 11/2024 |
| 8544 | 2^346162+85765 | 104206 | Stefano Morozzi | 11/2024 |
| 8545 | 2^346164+152925 | 104206 | Stefano Morozzi | 11/2024 |
| 8546 | 2^346160+131703 | 104205 | Stefano Morozzi | 11/2024 |
| 8547 | 2^346155+166433 | 104204 | Stefano Morozzi | 11/2024 |
| 8548 | 2^346157+7137 | 104204 | Stefano Morozzi | 11/2024 |
| 8549 | 2^346158+31483 | 104204 | Stefano Morozzi | 11/2024 |
| 8550 | 2^346158+183253 | 104204 | Stefano Morozzi | 11/2024 |
| 8551 | 2^346152+136287 | 104203 | Stefano Morozzi | 11/2024 |
| 8552 | 2^346154+107499 | 104203 | Stefano Morozzi | 11/2024 |
| 8553 | 2^346154+187987 | 104203 | Stefano Morozzi | 11/2024 |
| 8557 | 23678^23821-23821^23678 | 104202 | Norbert Schneider | 01/2020 |
| 8554 | 2^346149+45857 | 104202 | Stefano Morozzi | 11/2024 |
| 8555 | 2^346150+111579 | 104202 | Stefano Morozzi | 11/2024 |
| 8556 | 2^346151+21539 | 104202 | Stefano Morozzi | 11/2024 |
| 8558 | 2^346143+119183 | 104200 | Stefano Morozzi | 11/2024 |
| 8559 | 2^346143+130361 | 104200 | Stefano Morozzi | 11/2024 |
| 8560 | 2^346143+171791 | 104200 | Stefano Morozzi | 11/2024 |
| 8561 | 2^346144+4731 | 104200 | Stefano Morozzi | 11/2024 |
| 8562 | 2^346144+158097 | 104200 | Stefano Morozzi | 11/2024 |
| 8563 | 2^346139+68459 | 104199 | Stefano Morozzi | 11/2024 |
| 8564 | 2^346140+121711 | 104199 | Stefano Morozzi | 11/2024 |
| 8565 | 2^346135+122913 | 104198 | Stefano Morozzi | 11/2024 |
| 8566 | 2^346135+125453 | 104198 | Stefano Morozzi | 11/2024 |
| 8567 | 2^346135+184869 | 104198 | Stefano Morozzi | 11/2024 |
| 8568 | 2^346136+135721 | 104198 | Stefano Morozzi | 11/2024 |
| 8569 | 2^346133+46695 | 104197 | Stefano Morozzi | 11/2024 |
| 8570 | 2^346129+87819 | 104196 | Stefano Morozzi | 11/2024 |
| 8571 | 2^346130+127369 | 104196 | Stefano Morozzi | 11/2024 |
| 8572 | 2^346130+177619 | 104196 | Stefano Morozzi | 11/2024 |
| 8573 | 2^346125+105609 | 104195 | Stefano Morozzi | 11/2024 |
| 8574 | 2^346127+71201 | 104195 | Stefano Morozzi | 11/2024 |
| 8575 | 2^346122+74469 | 104194 | Stefano Morozzi | 11/2024 |
| 8576 | 2^346122+124119 | 104194 | Stefano Morozzi | 11/2024 |
| 8577 | 2^346122+124227 | 104194 | Stefano Morozzi | 11/2024 |
| 8578 | 2^346124+83973 | 104194 | Stefano Morozzi | 11/2024 |
| 8579 | 2^346124+186877 | 104194 | Stefano Morozzi | 11/2024 |
| 8580 | 2^346121+174729 | 104193 | Stefano Morozzi | 11/2024 |
| 8581 | 2^346116+166317 | 104192 | Stefano Morozzi | 11/2024 |
| 8582 | 2^346117+98015 | 104192 | Stefano Morozzi | 11/2024 |
| 8583 | (13*31^69863+12407)/30 | 104191 | Eric Chen | 04/2024 |
| 8584 | 2^346112+20827 | 104191 | Stefano Morozzi | 11/2024 |
| 8585 | 2^346112+77533 | 104191 | Stefano Morozzi | 11/2024 |
| 8586 | 2^346114+76959 | 104191 | Stefano Morozzi | 11/2024 |
| 8587 | 2^346115+30513 | 104191 | Stefano Morozzi | 11/2024 |
| 8588 | 2^346115+90105 | 104191 | Stefano Morozzi | 11/2024 |
| 8589 | 2^346115+155859 | 104191 | Stefano Morozzi | 11/2024 |
| 8590 | 2^346115+157809 | 104191 | Stefano Morozzi | 11/2024 |
| 8591 | 2^346109+118587 | 104190 | Stefano Morozzi | 11/2024 |
| 8592 | 2^346110+105763 | 104190 | Stefano Morozzi | 11/2024 |
| 8593 | 2^346110+175197 | 104190 | Stefano Morozzi | 11/2024 |
| 8594 | 2^346110+197725 | 104190 | Stefano Morozzi | 11/2024 |
| 8595 | 2^346111+143313 | 104190 | Stefano Morozzi | 11/2024 |
| 8596 | 2^346107+153513 | 104189 | Stefano Morozzi | 11/2024 |
| 8597 | 2^346108+153897 | 104189 | Stefano Morozzi | 11/2024 |
| 8598 | 2^346102+79435 | 104188 | Stefano Morozzi | 11/2024 |
| 8599 | 2^346102+131949 | 104188 | Stefano Morozzi | 11/2024 |
| 8600 | 2^346103+123009 | 104188 | Stefano Morozzi | 11/2024 |
| 8601 | 2^346104+115845 | 104188 | Stefano Morozzi | 11/2024 |
| 8602 | 2^346105+29141 | 104188 | Stefano Morozzi | 11/2024 |
| 8603 | 2^346105+85035 | 104188 | Stefano Morozzi | 11/2024 |
| 8604 | 2^346098+80323 | 104186 | Stefano Morozzi | 11/2024 |
| 8605 | 2^346092+69855 | 104185 | Stefano Morozzi | 11/2024 |
| 8606 | 2^346093+3627 | 104185 | Stefano Morozzi | 11/2024 |
| 8607 | 2^346089+90947 | 104184 | Stefano Morozzi | 11/2024 |
| 8608 | 2^346089+186749 | 104184 | Stefano Morozzi | 11/2024 |
| 8609 | 2^346091+71279 | 104184 | Stefano Morozzi | 11/2024 |
| 8610 | 2^346084+69211 | 104182 | Stefano Morozzi | 11/2024 |
| 8611 | 2^346084+112237 | 104182 | Stefano Morozzi | 11/2024 |
| 8612 | 2^346079+10371 | 104181 | Stefano Morozzi | 11/2024 |
| 8613 | 2^346079+82811 | 104181 | Stefano Morozzi | 11/2024 |
| 8617 | 2^346078+7695 | 104180 | Lelio R Paula | 12/2016 |
| 8614 | 2^346076+85903 | 104180 | Stefano Morozzi | 11/2024 |
| 8615 | 2^346076+111577 | 104180 | Stefano Morozzi | 11/2024 |
| 8616 | 2^346076+143047 | 104180 | Stefano Morozzi | 11/2024 |
| 8618 | 2^346072+126673 | 104179 | Stefano Morozzi | 11/2024 |
| 8619 | 2^346073+37899 | 104179 | Stefano Morozzi | 11/2024 |
| 8620 | 2^346075+21519 | 104179 | Stefano Morozzi | 11/2024 |
| 8621 | 2^346075+27255 | 104179 | Stefano Morozzi | 11/2024 |
| 8622 | 2^346075+115331 | 104179 | Stefano Morozzi | 11/2024 |
| 8623 | 2^346069+53615 | 104178 | Stefano Morozzi | 11/2024 |
| 8624 | 2^346069+188087 | 104178 | Stefano Morozzi | 11/2024 |
| 8625 | 2^346066+29949 | 104177 | Stefano Morozzi | 11/2024 |
| 8626 | 2^346066+133909 | 104177 | Stefano Morozzi | 11/2024 |
| 8627 | 2^346066+188535 | 104177 | Stefano Morozzi | 11/2024 |
| 8628 | 2^346068+159553 | 104177 | Stefano Morozzi | 11/2024 |
| 8629 | 2^346064+122683 | 104176 | Stefano Morozzi | 11/2024 |
| 8630 | 2^346060+20325 | 104175 | Stefano Morozzi | 11/2024 |
| 8631 | 2^346060+110755 | 104175 | Stefano Morozzi | 11/2024 |
| 8632 | 2^346058+57933 | 104174 | Stefano Morozzi | 11/2024 |
| 8638 | 2^346055-19537 | 104173 | Enzo Doria | 05/2013 |
| 8639 | (3*2^346057+1)/77 | 104173 | Lelio R Paula | 12/2013 |
| 8633 | 2^346052+26655 | 104173 | Stefano Morozzi | 11/2024 |
| 8634 | 2^346052+31611 | 104173 | Stefano Morozzi | 11/2024 |
| 8635 | 2^346053+67667 | 104173 | Stefano Morozzi | 11/2024 |
| 8636 | 2^346054+30507 | 104173 | Stefano Morozzi | 11/2024 |
| 8637 | 2^346054+194589 | 104173 | Stefano Morozzi | 11/2024 |
| 8640 | 2^346049+59067 | 104172 | Stefano Morozzi | 11/2024 |
| 8641 | 2^346050+3129 | 104172 | Stefano Morozzi | 11/2024 |
| 8642 | 2^346050+167125 | 104172 | Stefano Morozzi | 11/2024 |
| 8643 | 2^346051+52563 | 104172 | Stefano Morozzi | 11/2024 |
| 8644 | 2^346051+90941 | 104172 | Stefano Morozzi | 11/2024 |
| 8645 | 2^346046+172107 | 104171 | Stefano Morozzi | 11/2024 |
| 8646 | 2^346048+63415 | 104171 | Stefano Morozzi | 11/2024 |
| 8647 | 2^346041+197885 | 104169 | Stefano Morozzi | 11/2024 |
| 8651 | 2^346037-20125 | 104168 | Enzo Doria | 06/2013 |
| 8648 | 2^346036+80773 | 104168 | Stefano Morozzi | 11/2024 |
| 8649 | 2^346037+116429 | 104168 | Stefano Morozzi | 11/2024 |
| 8650 | 2^346038+147549 | 104168 | Stefano Morozzi | 11/2024 |
| 8652 | 2^346034+2205 | 104167 | Stefano Morozzi | 11/2024 |
| 8653 | 2^346031+56429 | 104166 | Stefano Morozzi | 11/2024 |
| 8654 | 2^346031+68439 | 104166 | Stefano Morozzi | 11/2024 |
| 8655 | 2^346031+114891 | 104166 | Stefano Morozzi | 11/2024 |
| 8656 | 2^346031+190563 | 104166 | Stefano Morozzi | 11/2024 |
| 8657 | 2^346026+179305 | 104165 | Stefano Morozzi | 11/2024 |
| 8658 | 2^346027+159425 | 104165 | Stefano Morozzi | 11/2024 |
| 8659 | 2^346028+12517 | 104165 | Stefano Morozzi | 11/2024 |
| 8660 | 2^346022+84705 | 104164 | Stefano Morozzi | 11/2024 |
| 8661 | 2^346019+73673 | 104163 | Stefano Morozzi | 11/2024 |
| 8662 | 2^346019+78999 | 104163 | Stefano Morozzi | 11/2024 |
| 8663 | 2^346019+79955 | 104163 | Stefano Morozzi | 11/2024 |
| 8664 | 2^346020+72993 | 104163 | Stefano Morozzi | 11/2024 |
| 8665 | 2^346020+188673 | 104163 | Stefano Morozzi | 11/2024 |
| 8666 | 2^346021+100311 | 104163 | Stefano Morozzi | 11/2024 |
| 8670 | (34*10^104168-7)/9/13/551179 | 104162 | Makoto Morimoto | 05/2016 |
| 8667 | 2^346016+84007 | 104162 | Stefano Morozzi | 11/2024 |
| 8668 | 2^346017+122397 | 104162 | Stefano Morozzi | 11/2024 |
| 8669 | 2^346017+165791 | 104162 | Stefano Morozzi | 11/2024 |
| 8671 | 2^346014+27949 | 104161 | Stefano Morozzi | 11/2024 |
| 8672 | 2^346014+46743 | 104161 | Stefano Morozzi | 11/2024 |
| 8673 | 2^346015+166089 | 104161 | Stefano Morozzi | 11/2024 |
| 8674 | 2^346009+107705 | 104160 | Stefano Morozzi | 11/2024 |
| 8675 | 2^346012+35043 | 104160 | Stefano Morozzi | 11/2024 |
| 8676 | 2^346012+83091 | 104160 | Stefano Morozzi | 11/2024 |
| 8684 | 6^133854-17993 | 104159 | Enzo Doria | 03/2013 |
| 8677 | 2^346006+77727 | 104159 | Stefano Morozzi | 11/2024 |
| 8678 | 2^346008+9007 | 104159 | Stefano Morozzi | 11/2024 |
| 8679 | 2^346008+51567 | 104159 | Stefano Morozzi | 11/2024 |
| 8680 | 2^346008+107787 | 104159 | Stefano Morozzi | 11/2024 |
| 8681 | 2^346008+146191 | 104159 | Stefano Morozzi | 11/2024 |
| 8682 | 2^346008+170823 | 104159 | Stefano Morozzi | 11/2024 |
| 8683 | (131^49201-1)/7538466025870 | 104159 | Paul Vanderveen | 06/2025 |
| 8685 | 2^346003+191519 | 104158 | Stefano Morozzi | 11/2024 |
| 8686 | 2^345990+1874239 | 104154 | Enzo Doria | 06/2016 |
| 8687 | 2^345988-20373 | 104153 | Enzo Doria | 06/2013 |
| 8688 | (2^345965+2214)/2 | 104146 | Stefano Morozzi | 09/2020 |
| 8689 | (26*10^104132-503)/9 | 104133 | Robert Price | 07/2018 |
| 8690 | 3*5^148968+8 | 104125 | Lelio R Paula | 11/2014 |
| 8691 | (7*10^104113+53)/3 | 104114 | Robert Price | 05/2018 |
| 8692 | p(21253)#/2+8 | 104113 | Robert Price | 01/2017 |
| 8693 | 33582^1259+1259^33582 | 104106 | Hans Havermann | 09/2020 |
| 8694 | 32958^1441+1441^32958 | 104104 | Hans Havermann | 09/2020 |
| 8695 | 29127^3748+3748^29127 | 104095 | Hans Havermann | 09/2020 |
| 8696 | 322^41507+41507^322 | 104094 | Norbert Schneider | 12/2014 |
| 8697 | 6^133768-17423 | 104092 | Enzo Doria | 03/2013 |
| 8698 | 2^345786-19557 | 104092 | Enzo Doria | 05/2013 |
| 8699 | 171^46606-2 | 104072 | Lelio R Paula | 10/2017 |
| 8700 | (29*10^104071+91)/3 | 104072 | Robert Price | 04/2020 |
| 8701 | norm(Mod(x,x^3-x-1)^852167-1) | 104070 | Paul Vanderveen | 09/2022 |
| 8702 | 2^345704-149 | 104068 | Lelio R Paula | 09/2011 |
| 8703 | 25821^10712+10712^25821 | 104056 | Hans Havermann | 09/2020 |
| 8704 | (2^345662+2038)/2 | 104055 | Stefano Morozzi | 09/2020 |
| 8705 | 6^133704-17273 | 104042 | Enzo Doria | 02/2013 |
| 8706 | (3*2^345590-1)/23 | 104033 | Lelio R Paula | 03/2014 |
| 8707 | (19*2^345590+1)/33859 | 104030 | Lelio R Paula | 12/2013 |
| 8708 | 2^345547+11 | 104021 | Lelio R Paula | 09/2011 |
| 8709 | (19*10^104014-49)/3 | 104015 | Robert Price | 05/2019 |
| 8710 | (2^345519+1794)/2 | 104012 | Stefano Morozzi | 01/2021 |
| 8711 | 2^345504+723 | 104008 | Lelio R Paula | 09/2011 |
| 8712 | 2^345498-20037 | 104006 | Enzo Doria | 06/2013 |
| 8714 | 18^82854-37 | 104005 | Lelio R Paula | 01/2017 |
| 8713 | (2^345497+2070)/2 | 104005 | Stefano Morozzi | 09/2020 |
| 8715 | 2^345486-109065 | 104002 | Enzo Doria | 04/2014 |
| 8716 | 2^345487-1851507 | 104002 | Enzo Doria | 08/2015 |
| 8717 | 2^345476+777 | 103999 | Lelio R Paula | 09/2011 |
| 8718 | (2^345477+1554)/2 | 103999 | Stefano Morozzi | 09/2020 |
| 8719 | 4*10^103981-83 | 103982 | Robert Price | 10/2018 |
| 8720 | (2^345327+3206)/2 | 103954 | Stefano Morozzi | 09/2020 |
| 8721 | (5*2^345321-1)/3 | 103953 | Lelio R Paula | 03/2014 |
| 8722 | (2^345267-9)/539049127 | 103927 | Lelio R Paula | 12/2013 |
| 8723 | (19*10^103907+77)/3 | 103908 | Robert Price | 05/2019 |
| 8724 | (78557*2^345163+1)/78589 | 103905 | Lelio R Paula | 07/2014 |
| 8725 | 2^345106-112181 | 103888 | Enzo Doria | 06/2014 |
| 8726 | (2^345105+1326)/2 | 103887 | Stefano Morozzi | 02/2021 |
| 8727 | 2^345079+99 | 103880 | Lelio R Paula | 09/2011 |
| 8728 | (2^345034+1198)/2 | 103866 | Stefano Morozzi | 09/2020 |
| 8729 | 11^99736-1500 | 103865 | Enzo Doria | 12/2012 |
| 8730 | (569^37699-1)/568 | 103863 | Serge Batalov | 06/2022 |
| 8731 | (2^345010+2082)/2 | 103859 | Stefano Morozzi | 09/2020 |
| 8732 | 23263^23784-23784^23263 | 103857 | Norbert Schneider | 01/2020 |
| 8733 | 3*10^103844+31 | 103845 | Robert Price | 06/2021 |
| 8734 | 444*33^68368+19 | 103821 | Eric Chen | 05/2023 |
| 8735 | 23927^21814+21814^23927 | 103813 | Hans Havermann | 09/2020 |
| 8736 | 2^344842-20157 | 103808 | Enzo Doria | 06/2013 |
| 8737 | (47*2^344822+1)/1071 | 103801 | Lelio R Paula | 05/2015 |
| 8738 | 2^344802-20765 | 103796 | Enzo Doria | 06/2013 |
| 8739 | 2^344794-3821 | 103794 | Yves Minet | 05/2011 |
| 8740 | 2^344782-109103 | 103790 | Enzo Doria | 04/2014 |
| 8741 | 3^217521-112292 | 103784 | Enzo Doria | 06/2014 |
| 8742 | 2^344759-3505 | 103783 | Lelio R Paula | 11/2016 |
| 8743 | 2^344735-147 | 103776 | Lelio R Paula | 09/2011 |
| 8744 | L(496533)-p(496533) | 103770 | Robert Price | 02/2018 |
| 8745 | 2*10^103749-69 | 103750 | Robert Price | 03/2018 |
| 8746 | (55459*2^344617+1)/3 | 103745 | Lelio R Paula | 07/2014 |
| 8747 | 2^344607-108891 | 103738 | Enzo Doria | 03/2014 |
| 8749 | (2^344608+3798)/2 | 103738 | Stefano Morozzi | 02/2021 |
| 8748 | (1097^34123-1)/1096 | 103738 | Serge Batalov | 06/2022 |
| 8750 | 2^344560+22411 | 103723 | Enzo Doria | 09/2023 |
