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 ? |
7501 | 2^346664+16377 | 104357 | Stefano Morozzi | 11/2024 |
7502 | 2^346666+29595 | 104357 | Stefano Morozzi | 11/2024 |
7503 | 2^346660+61095 | 104356 | Stefano Morozzi | 11/2024 |
7504 | 2^346661+114311 | 104356 | Stefano Morozzi | 11/2024 |
7505 | 2^346662+75745 | 104356 | Stefano Morozzi | 11/2024 |
7506 | 2^346663+123305 | 104356 | Stefano Morozzi | 11/2024 |
7507 | 2^346662+150475 | 104356 | Stefano Morozzi | 11/2024 |
7508 | 2^346658+28393 | 104355 | Stefano Morozzi | 11/2024 |
7509 | 2^346658+137619 | 104355 | Stefano Morozzi | 11/2024 |
7510 | 2^346659+86415 | 104355 | Stefano Morozzi | 11/2024 |
7511 | 2^346659+117849 | 104355 | Stefano Morozzi | 11/2024 |
7512 | 2^346655+199859 | 104354 | Stefano Morozzi | 11/2024 |
7513 | 2^346656+100627 | 104354 | Stefano Morozzi | 11/2024 |
7514 | 2^346651+88491 | 104353 | Stefano Morozzi | 11/2024 |
7515 | 2^346652+32971 | 104353 | Stefano Morozzi | 11/2024 |
7516 | 2^346652+85321 | 104353 | Stefano Morozzi | 11/2024 |
7517 | 2^346652+100627 | 104353 | Stefano Morozzi | 11/2024 |
7518 | 2^346652+190255 | 104353 | Stefano Morozzi | 11/2024 |
7519 | 2^346652+194667 | 104353 | Stefano Morozzi | 11/2024 |
7520 | 2^346652+197073 | 104353 | Stefano Morozzi | 11/2024 |
7524 | 2^346649+65 | 104352 | Lelio R Paula | 09/2011 |
7521 | 2^346647+128475 | 104352 | Stefano Morozzi | 11/2024 |
7522 | 2^346647+181169 | 104352 | Stefano Morozzi | 11/2024 |
7523 | 2^346648+97381 | 104352 | Stefano Morozzi | 11/2024 |
7525 | (19*33^68718-600883)/32 | 104350 | Eric Chen | 05/2023 |
7526 | 2^346640+73723 | 104350 | Stefano Morozzi | 11/2024 |
7527 | 2^346641+169667 | 104350 | Stefano Morozzi | 11/2024 |
7528 | 2^346642+100395 | 104350 | Stefano Morozzi | 11/2024 |
7529 | 2^346643+61025 | 104350 | Stefano Morozzi | 11/2024 |
7530 | 2^346643+160785 | 104350 | Stefano Morozzi | 11/2024 |
7532 | 2^346638-17265 | 104349 | Enzo Doria | 05/2013 |
7531 | 2^346637+34139 | 104349 | Stefano Morozzi | 11/2024 |
7533 | 2^346635+13071 | 104348 | Stefano Morozzi | 11/2024 |
7534 | 2^346630+66003 | 104347 | Stefano Morozzi | 11/2024 |
7535 | 2^346630+187137 | 104347 | Stefano Morozzi | 11/2024 |
7536 | 2^346631+27393 | 104347 | Stefano Morozzi | 11/2024 |
7537 | 2^346632+21883 | 104347 | Stefano Morozzi | 11/2024 |
7538 | 2^346632+136015 | 104347 | Stefano Morozzi | 11/2024 |
7539 | 2^346628+87907 | 104346 | Stefano Morozzi | 11/2024 |
7540 | 2^346624+174075 | 104345 | Stefano Morozzi | 11/2024 |
7541 | 2^346620+87451 | 104344 | Stefano Morozzi | 11/2024 |
7542 | 2^346622+12247 | 104344 | Stefano Morozzi | 11/2024 |
7543 | 2^346623+69161 | 104344 | Stefano Morozzi | 11/2024 |
7544 | 2^346614+85737 | 104342 | Stefano Morozzi | 11/2024 |
7545 | 2^346611+183923 | 104341 | Stefano Morozzi | 11/2024 |
7546 | 2^346607+36209 | 104340 | Stefano Morozzi | 11/2024 |
7547 | 2^346607+65291 | 104340 | Stefano Morozzi | 11/2024 |
7548 | 2^346609+47471 | 104340 | Stefano Morozzi | 11/2024 |
7553 | (2^346606+2082)/2 | 104339 | Stefano Morozzi | 09/2020 |
7554 | (2^346607+2070)/2 | 104339 | Stefano Morozzi | 09/2020 |
7549 | 2^346605+1041 | 104339 | Stefano Morozzi | 11/2024 |
7550 | 2^346605+181167 | 104339 | Stefano Morozzi | 11/2024 |
7551 | 2^346606+1035 | 104339 | Stefano Morozzi | 11/2024 |
7552 | 2^346606+103863 | 104339 | Stefano Morozzi | 11/2024 |
7555 | 2^346601+26529 | 104338 | Stefano Morozzi | 11/2024 |
7556 | 2^346603+133431 | 104338 | Stefano Morozzi | 11/2024 |
7557 | 2^346597+97661 | 104337 | Stefano Morozzi | 11/2024 |
7558 | 2^346597+186809 | 104337 | Stefano Morozzi | 11/2024 |
7559 | 2^346598+31719 | 104337 | Stefano Morozzi | 11/2024 |
7560 | 2^346598+162513 | 104337 | Stefano Morozzi | 11/2024 |
7561 | 2^346599+45731 | 104337 | Stefano Morozzi | 11/2024 |
7562 | 2^346599+187061 | 104337 | Stefano Morozzi | 11/2024 |
7563 | 2^346600+175993 | 104337 | Stefano Morozzi | 11/2024 |
7564 | 2^346595+89753 | 104336 | Stefano Morozzi | 11/2024 |
7565 | 2^346595+114491 | 104336 | Stefano Morozzi | 11/2024 |
7566 | 2^346596+120183 | 104336 | Stefano Morozzi | 11/2024 |
7567 | 2^346591+183651 | 104335 | Stefano Morozzi | 11/2024 |
7568 | 2^346591+192149 | 104335 | Stefano Morozzi | 11/2024 |
7569 | 2^346592+77347 | 104335 | Stefano Morozzi | 11/2024 |
7570 | 2^346592+178161 | 104335 | Stefano Morozzi | 11/2024 |
7571 | 2^346592+195985 | 104335 | Stefano Morozzi | 11/2024 |
7572 | 2^346589+40607 | 104334 | Stefano Morozzi | 11/2024 |
7573 | 2^346590+151533 | 104334 | Stefano Morozzi | 11/2024 |
7574 | 2^346584+105103 | 104333 | Stefano Morozzi | 11/2024 |
7575 | 2^346585+56861 | 104333 | Stefano Morozzi | 11/2024 |
7581 | (2^346582+3202)/2 | 104332 | Stefano Morozzi | 09/2020 |
7576 | 2^346581+1601 | 104332 | Stefano Morozzi | 11/2024 |
7577 | 2^346581+82115 | 104332 | Stefano Morozzi | 11/2024 |
7578 | 2^346581+193979 | 104332 | Stefano Morozzi | 11/2024 |
7579 | 2^346582+197767 | 104332 | Stefano Morozzi | 11/2024 |
7580 | 2^346583+116579 | 104332 | Stefano Morozzi | 11/2024 |
7582 | 26092^9967+9967^26092 | 104331 | Hans Havermann | 09/2020 |
7583 | 2^346577+47501 | 104331 | Stefano Morozzi | 11/2024 |
7584 | 2^346578+163287 | 104331 | Stefano Morozzi | 11/2024 |
7585 | 2^346579+37019 | 104331 | Stefano Morozzi | 11/2024 |
7586 | 2^346579+119645 | 104331 | Stefano Morozzi | 11/2024 |
7587 | 2^346579+157611 | 104331 | Stefano Morozzi | 11/2024 |
7588 | 2^346576+100803 | 104330 | Stefano Morozzi | 11/2024 |
7589 | 2^346576+144495 | 104330 | Stefano Morozzi | 11/2024 |
7590 | 2^346573+13859 | 104329 | Stefano Morozzi | 11/2024 |
7591 | 2^346568+110181 | 104328 | Stefano Morozzi | 11/2024 |
7593 | 5*10^104326+77 | 104327 | Robert Price | 12/2018 |
7592 | 2^346564+151101 | 104327 | Stefano Morozzi | 11/2024 |
7599 | (2^346564+2026)/2 | 104326 | Stefano Morozzi | 09/2020 |
7594 | 2^346561+53385 | 104326 | Stefano Morozzi | 11/2024 |
7595 | 2^346561+139791 | 104326 | Stefano Morozzi | 11/2024 |
7596 | 2^346562+110383 | 104326 | Stefano Morozzi | 11/2024 |
7597 | 2^346563+1013 | 104326 | Stefano Morozzi | 11/2024 |
7598 | 2^346563+9305 | 104326 | Stefano Morozzi | 11/2024 |
7600 | 2^346558+97033 | 104325 | Stefano Morozzi | 11/2024 |
7601 | 2^346556+101283 | 104324 | Stefano Morozzi | 11/2024 |
7602 | 2^346551+55043 | 104323 | Stefano Morozzi | 11/2024 |
7603 | 2^346547+71855 | 104322 | Stefano Morozzi | 11/2024 |
7604 | 2^346548+119695 | 104322 | Stefano Morozzi | 11/2024 |
7605 | 2^346550+55249 | 104322 | Stefano Morozzi | 11/2024 |
7606 | 2^346550+158655 | 104322 | Stefano Morozzi | 11/2024 |
7607 | 2^346545+87885 | 104321 | Stefano Morozzi | 11/2024 |
7608 | 2^346545+95105 | 104321 | Stefano Morozzi | 11/2024 |
7609 | 2^346546+126763 | 104321 | Stefano Morozzi | 11/2024 |
7610 | 2^346546+149397 | 104321 | Stefano Morozzi | 11/2024 |
7611 | (8925^26569-1)/(8925^163-1) | 104320 | Ryan Propper | 11/2023 |
7612 | 2^346542+128005 | 104320 | Stefano Morozzi | 11/2024 |
7613 | 2^346538+123507 | 104319 | Stefano Morozzi | 11/2024 |
7614 | 2^346540+118251 | 104319 | Stefano Morozzi | 11/2024 |
7615 | 2^346540+128965 | 104319 | Stefano Morozzi | 11/2024 |
7616 | 2^346535+138485 | 104318 | Stefano Morozzi | 11/2024 |
7617 | 2^346536+149013 | 104318 | Stefano Morozzi | 11/2024 |
7618 | 2^346531+98801 | 104317 | Stefano Morozzi | 11/2024 |
7619 | 2^346533+12035 | 104317 | Stefano Morozzi | 11/2024 |
7623 | 2^346527-111817 | 104316 | Enzo Doria | 05/2014 |
7622 | 6^134055+101 | 104316 | Lelio R Paula | 11/2016 |
7620 | fibonacci(499147)-4 | 104316 | Jon Grantham | 08/2023 |
7621 | 2^346529+101351 | 104316 | Stefano Morozzi | 11/2024 |
7624 | 2^346524+81585 | 104315 | Stefano Morozzi | 11/2024 |
7625 | 2^346524+184821 | 104315 | Stefano Morozzi | 11/2024 |
7626 | 2^346525+41051 | 104315 | Stefano Morozzi | 11/2024 |
7627 | 2^346525+61845 | 104315 | Stefano Morozzi | 11/2024 |
7628 | 2^346521+47439 | 104314 | Stefano Morozzi | 11/2024 |
7629 | 2^346522+34689 | 104314 | Stefano Morozzi | 11/2024 |
7630 | 2^346519+24543 | 104313 | Stefano Morozzi | 11/2024 |
7631 | 2^346519+75119 | 104313 | Stefano Morozzi | 11/2024 |
7635 | 92105!4+8 | 104312 | Robert Price | 09/2019 |
7632 | 2^346514+11023 | 104312 | Stefano Morozzi | 11/2024 |
7633 | 2^346514+22009 | 104312 | Stefano Morozzi | 11/2024 |
7634 | 2^346516+107031 | 104312 | Stefano Morozzi | 11/2024 |
7636 | 2^346511+65675 | 104311 | Stefano Morozzi | 11/2024 |
7637 | 2^346512+105345 | 104311 | Stefano Morozzi | 11/2024 |
7638 | 2^346513+80387 | 104311 | Stefano Morozzi | 11/2024 |
7639 | 2^346510+104955 | 104310 | Stefano Morozzi | 11/2024 |
7640 | 2^346510+145347 | 104310 | Stefano Morozzi | 11/2024 |
7641 | 2^346506+105537 | 104309 | Stefano Morozzi | 11/2024 |
7642 | 2^346506+145353 | 104309 | Stefano Morozzi | 11/2024 |
7643 | 2^346503+160109 | 104308 | Stefano Morozzi | 11/2024 |
7644 | 2^346494+155215 | 104306 | Stefano Morozzi | 11/2024 |
7645 | 2^346495+26243 | 104306 | Stefano Morozzi | 11/2024 |
7646 | 2^346497+108749 | 104306 | Stefano Morozzi | 11/2024 |
7647 | 2^346488+146631 | 104304 | Stefano Morozzi | 11/2024 |
7648 | 2^346489+6035 | 104304 | Stefano Morozzi | 11/2024 |
7649 | 2^346489+16389 | 104304 | Stefano Morozzi | 11/2024 |
7650 | 2^346489+175959 | 104304 | Stefano Morozzi | 11/2024 |
7651 | 2^346484+119491 | 104303 | Stefano Morozzi | 11/2024 |
7652 | 2^346487+12125 | 104303 | Stefano Morozzi | 11/2024 |
7653 | 2^346487+92103 | 104303 | Stefano Morozzi | 11/2024 |
7654 | 2^346481+199815 | 104302 | Stefano Morozzi | 11/2024 |
7655 | 2^346478+2335 | 104301 | Stefano Morozzi | 11/2024 |
7656 | 2^346478+121773 | 104301 | Stefano Morozzi | 11/2024 |
7657 | 2^346479+80703 | 104301 | Stefano Morozzi | 11/2024 |
7658 | 2^346479+164693 | 104301 | Stefano Morozzi | 11/2024 |
7659 | 2^346480+156951 | 104301 | Stefano Morozzi | 11/2024 |
7660 | 2^346480+176247 | 104301 | Stefano Morozzi | 11/2024 |
7661 | 2^346475+178953 | 104300 | Stefano Morozzi | 11/2024 |
7662 | 2^346476+83935 | 104300 | Stefano Morozzi | 11/2024 |
7663 | 2^346470+182623 | 104298 | Stefano Morozzi | 11/2024 |
7664 | 2^346464+54007 | 104297 | Stefano Morozzi | 11/2024 |
7665 | 2^346464+55287 | 104297 | Stefano Morozzi | 11/2024 |
7666 | 2^346464+84411 | 104297 | Stefano Morozzi | 11/2024 |
7667 | 2^346465+15905 | 104297 | Stefano Morozzi | 11/2024 |
7668 | 2^346465+27797 | 104297 | Stefano Morozzi | 11/2024 |
7669 | 2^346465+85815 | 104297 | Stefano Morozzi | 11/2024 |
7670 | 2^346465+92787 | 104297 | Stefano Morozzi | 11/2024 |
7671 | 2^346466+133369 | 104297 | Stefano Morozzi | 11/2024 |
7672 | 2^346461+30591 | 104296 | Stefano Morozzi | 11/2024 |
7673 | 2^346462+74067 | 104296 | Stefano Morozzi | 11/2024 |
7674 | 2^346458+68947 | 104295 | Stefano Morozzi | 11/2024 |
7675 | 2^346459+39333 | 104295 | Stefano Morozzi | 11/2024 |
7676 | 2^346459+110355 | 104295 | Stefano Morozzi | 11/2024 |
7677 | 2^346454+166035 | 104294 | Stefano Morozzi | 11/2024 |
7678 | 2^346456+132385 | 104294 | Stefano Morozzi | 11/2024 |
7679 | 2^346456+138727 | 104294 | Stefano Morozzi | 11/2024 |
7680 | 2^346456+176767 | 104294 | Stefano Morozzi | 11/2024 |
7681 | 2^346451+72969 | 104293 | Stefano Morozzi | 11/2024 |
7682 | 2^346452+10441 | 104293 | Stefano Morozzi | 11/2024 |
7683 | 2^346449+170595 | 104292 | Stefano Morozzi | 11/2024 |
7684 | 2^346450+70143 | 104292 | Stefano Morozzi | 11/2024 |
7685 | (7^123407-5^123407)/2 | 104291 | Jon Grantham | 08/2023 |
7686 | 2^346445+194585 | 104291 | Stefano Morozzi | 11/2024 |
7687 | 2^346447+13715 | 104291 | Stefano Morozzi | 11/2024 |
7688 | 2^346447+188493 | 104291 | Stefano Morozzi | 11/2024 |
7689 | 2^346441+43529 | 104290 | Stefano Morozzi | 11/2024 |
7690 | 2^346441+105707 | 104290 | Stefano Morozzi | 11/2024 |
7691 | 2^346443+97995 | 104290 | Stefano Morozzi | 11/2024 |
7692 | 2^346438+125667 | 104289 | Stefano Morozzi | 11/2024 |
7693 | 2^346438+173595 | 104289 | Stefano Morozzi | 11/2024 |
7694 | 2^346434+155605 | 104288 | Stefano Morozzi | 11/2024 |
7695 | 2^346435+110823 | 104288 | Stefano Morozzi | 11/2024 |
7696 | 2^346435+139281 | 104288 | Stefano Morozzi | 11/2024 |
7697 | 2^346431+2543 | 104287 | Stefano Morozzi | 11/2024 |
7698 | 2^346432+177181 | 104287 | Stefano Morozzi | 11/2024 |
7699 | 2^346433+35699 | 104287 | Stefano Morozzi | 11/2024 |
7700 | 2^346433+108015 | 104287 | Stefano Morozzi | 11/2024 |
7701 | 2^346429+100365 | 104286 | Stefano Morozzi | 11/2024 |
7702 | 2^346424+104841 | 104285 | Stefano Morozzi | 11/2024 |
7703 | 2^346425+136095 | 104285 | Stefano Morozzi | 11/2024 |
7704 | 2^346425+184971 | 104285 | Stefano Morozzi | 11/2024 |
7705 | 2^346426+74325 | 104285 | Stefano Morozzi | 11/2024 |
7706 | 2^346427+30795 | 104285 | Stefano Morozzi | 11/2024 |
7707 | 2^346421+42971 | 104284 | Stefano Morozzi | 11/2024 |
7708 | 2^346421+82577 | 104284 | Stefano Morozzi | 11/2024 |
7709 | 2^346423+142533 | 104284 | Stefano Morozzi | 11/2024 |
7710 | 6^134013+163 | 104283 | Lelio R Paula | 11/2016 |
7711 | 2^346414+165775 | 104282 | Stefano Morozzi | 11/2024 |
7712 | 10^(2*52140+1)-10^52140-1 | 104281 | Robert Price | 07/2023 |
7713 | 2^346411+106893 | 104281 | Stefano Morozzi | 11/2024 |
7714 | 2^346412+157935 | 104281 | Stefano Morozzi | 11/2024 |
7715 | 2^346413+117485 | 104281 | Stefano Morozzi | 11/2024 |
7716 | 2^346408+8085 | 104280 | Stefano Morozzi | 11/2024 |
7717 | 2^346408+24423 | 104280 | Stefano Morozzi | 11/2024 |
7718 | 2^346409+145047 | 104280 | Stefano Morozzi | 11/2024 |
7719 | 2^346410+172533 | 104280 | Stefano Morozzi | 11/2024 |
7720 | 2^346406+58417 | 104279 | Stefano Morozzi | 11/2024 |
7721 | 2^346406+198315 | 104279 | Stefano Morozzi | 11/2024 |
7722 | 2^346407+172509 | 104279 | Stefano Morozzi | 11/2024 |
7723 | 2^346401+180129 | 104278 | Stefano Morozzi | 11/2024 |
7724 | 2^346402+16897 | 104278 | Stefano Morozzi | 11/2024 |
7725 | 2^346402+114829 | 104278 | Stefano Morozzi | 11/2024 |
7726 | 2^346398+91623 | 104277 | Stefano Morozzi | 11/2024 |
7727 | 2^346398+117369 | 104277 | Stefano Morozzi | 11/2024 |
7728 | 2^346400+100141 | 104277 | Stefano Morozzi | 11/2024 |
7729 | 2^346400+183625 | 104277 | Stefano Morozzi | 11/2024 |
7730 | 2^346395+87281 | 104276 | Stefano Morozzi | 11/2024 |
7731 | 2^346391+28833 | 104275 | Stefano Morozzi | 11/2024 |
7732 | 2^346392+33715 | 104275 | Stefano Morozzi | 11/2024 |
7733 | 2^346392+37507 | 104275 | Stefano Morozzi | 11/2024 |
7734 | 2^346392+197617 | 104275 | Stefano Morozzi | 11/2024 |
7735 | 2^346393+45929 | 104275 | Stefano Morozzi | 11/2024 |
7736 | 2^346388+27223 | 104274 | Stefano Morozzi | 11/2024 |
7737 | 2^346388+29187 | 104274 | Stefano Morozzi | 11/2024 |
7738 | 2^346388+114657 | 104274 | Stefano Morozzi | 11/2024 |
7739 | 2^346388+158667 | 104274 | Stefano Morozzi | 11/2024 |
7740 | (22*10^104272-61)/3 | 104273 | Robert Price | 03/2022 |
7741 | 2^346385+150947 | 104273 | Stefano Morozzi | 11/2024 |
7742 | 2^346385+179309 | 104273 | Stefano Morozzi | 11/2024 |
7743 | 2^346387+80549 | 104273 | Stefano Morozzi | 11/2024 |
7744 | 2^346387+90309 | 104273 | Stefano Morozzi | 11/2024 |
7745 | 2^346387+157473 | 104273 | Stefano Morozzi | 11/2024 |
7746 | 2^346381+67497 | 104272 | Stefano Morozzi | 11/2024 |
7747 | 2^346379+72419 | 104271 | Stefano Morozzi | 11/2024 |
7748 | 2^346379+118811 | 104271 | Stefano Morozzi | 11/2024 |
7749 | 2^346377+97379 | 104270 | Stefano Morozzi | 11/2024 |
7750 | 2^346371+144159 | 104269 | Stefano Morozzi | 11/2024 |