## PRP Records

### Probable Primes Top 10000

#### (295461 PRPs in the top)

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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See the Latest PRPs
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 1-250 251-500 501-750 751-1000 1001-1250 1251-1500 1501-1750 1751-2000 2001-2250 2251-2500 2501-2750 2751-3000 3001-3250 3251-3500 3501-3750 3751-4000 4001-4250 4251-4500 4501-4750 4751-5000 5001-5250 5251-5500 5501-5750 5751-6000 6001-6250 6251-6500 6501-6750 6751-7000 7001-7250 7251-7500 7501-7750 7751-8000 8001-8250 8251-8500 8501-8750 8751-9000 9001-9250 9251-9500 9501-9750 9751-10000

 Rank Probable prime Digits (> 50000) Who ? When ? 9563 10^100000+15136771 100001 Robert Price 09/2019 9564 10^100000+15219873 100001 Robert Price 10/2019 9565 10^100000+15274039 100001 Robert Price 10/2019 9566 10^100000+15394069 100001 Robert Price 10/2019 9567 10^100000+15547119 100001 Robert Price 10/2019 9568 10^100000+15932923 100001 Robert Price 11/2019 9569 10^100000+16345467 100001 Robert Price 12/2019 9570 10^100000+16672143 100001 Robert Price 01/2020 9571 10^100000+16731939 100001 Robert Price 02/2020 9572 10^100000+16907049 100001 Robert Price 03/2020 9573 10^100000+17652523 100001 Robert Price 05/2020 9574 10^100000+18047167 100001 Robert Price 05/2020 9575 10^100000+18471819 100001 Robert Price 06/2020 9576 10^100000+18494793 100001 Robert Price 07/2020 9577 10^100000+18762609 100001 Robert Price 07/2020 9578 10^100000+19204141 100001 Robert Price 08/2020 9579 10^100000+19349793 100001 Robert Price 08/2020 9580 10^100000+19495699 100001 Robert Price 09/2020 9581 10^100000+19668927 100001 Robert Price 09/2020 9582 10^100000+19704313 100001 Robert Price 09/2020 9532 10^100000+19956229 100001 Robert Price 09/2020 9533 10^100000+3*(10^37093-1)/9*10^31454+1 100001 Makoto Morimoto 09/2020 9534 10^100000+4*(10^36149-1)/9*10^31926+1 100001 Makoto Morimoto 09/2020 9535 10^100000+6*(10^41029-1)/9*10^29486+1 100001 Makoto Morimoto 09/2020 9536 10^100000+7*(10^55505-1)/9*10^22248+1 100001 Makoto Morimoto 09/2020 9537 10^100000+20234607 100001 Robert Price 10/2020 9538 10^100000+20752303 100001 Robert Price 11/2020 9539 10^100000+20774041 100001 Robert Price 11/2020 9540 10^100000+20854741 100001 Robert Price 11/2020 9541 10^100000+20908917 100001 Robert Price 11/2020 9542 10^100000+20994793 100001 Robert Price 11/2020 9543 10^100000+21354249 100001 Robert Price 12/2020 9544 10^100000+21455559 100001 Robert Price 12/2020 9545 10^100000+21538873 100001 Robert Price 12/2020 9546 10^100000+21830901 100001 Robert Price 01/2021 9547 10^100000+21842629 100001 Robert Price 01/2021 9548 10^100000+21930861 100001 Robert Price 01/2021 9549 10^100000+22092943 100001 Robert Price 03/2021 9550 10^100000+22278417 100001 Robert Price 03/2021 9551 10^100000+22388581 100001 Robert Price 03/2021 9552 10^100000+22390933 100001 Robert Price 03/2021 9553 10^100000+22436169 100001 Robert Price 03/2021 9554 10^100000+22714557 100001 Robert Price 04/2021 9555 10^100000+22847671 100001 Robert Price 04/2021 9556 10^100000+23178567 100001 Robert Price 05/2021 9557 10^100000+23332003 100001 Robert Price 05/2021 9558 10^100000+23414571 100001 Robert Price 05/2021 9559 10^100000+23529979 100001 Robert Price 05/2021 9560 10^100000+23749243 100001 Robert Price 06/2021 9561 10^100000+23821771 100001 Robert Price 06/2021 9562 10^100000+24179307 100001 Robert Price 07/2021 9501 10^100000+64067989 100001 Robert Price 07/2024 9502 10^100000+64537969 100001 Robert Price 07/2024 9503 10^100000+64684401 100001 Robert Price 07/2024 9504 10^100000+65078241 100001 Robert Price 07/2024 9505 10^100000+65108589 100001 Robert Price 07/2024 9506 10^100000+65321659 100001 Robert Price 07/2024 9507 10^100000+65530773 100001 Robert Price 07/2024 9508 10^100000+60000000+2860971 100001 Robert Price 07/2024 9509 10^100000+60000000+2993517 100001 Robert Price 07/2024 9510 10^100000+60000000+3372931 100001 Robert Price 07/2024 9511 10^100000+60000000+3571039 100001 Robert Price 07/2024 9512 10^100000+60000000+3701257 100001 Robert Price 07/2024 9513 10^100000+60000000+3765727 100001 Robert Price 07/2024 9514 10^100000+40000000+8024501 100001 Robert Price 07/2024 9515 10^100000+40000000+8234057 100001 Robert Price 07/2024 9516 10^100000+40000000+8313399 100001 Robert Price 07/2024 9517 10^100000+40000000+8831817 100001 Robert Price 07/2024 9518 10^100000+40000000+9154433 100001 Robert Price 07/2024 9519 10^100000+40000000+9457031 100001 Robert Price 07/2024 9520 10^100000+40000000+9741063 100001 Robert Price 07/2024 9521 10^100000+46334983 100001 Robert Price 07/2024 9522 10^100000+46408929 100001 Robert Price 07/2024 9523 10^100000+46477587 100001 Robert Price 07/2024 9524 10^100000+46484211 100001 Robert Price 07/2024 9525 10^100000+46496169 100001 Robert Price 07/2024 9526 10^100000+46629949 100001 Robert Price 07/2024 9527 10^100000+46655869 100001 Robert Price 07/2024 9528 10^100000+47167941 100001 Robert Price 07/2024 9529 10^100000+47225599 100001 Robert Price 07/2024 9530 10^100000+47784519 100001 Robert Price 07/2024 9531 10^100000+47831149 100001 Robert Price 07/2024 9585 10^99999+309403 100000 Daniel Heuer 01/2004 9586 10^100000-260199 100000 Patrick De Geest 01/2010 9583 2^332192+10192681 100000 Sujan Das 06/2022 9584 1610172603059^8192+1610172602878^8192 100000 Youcef Lemsafer 01/2023 9587 10^99999-59511 99999 Patrick De Geest 07/2009 9588 10^99998+235437 99999 Patrick De Geest 02/2020 9589 10^99998-286587 99998 Patrick De Geest 02/2020 9590 10^99997+72297 99998 Patrick De Geest 02/2020 9591 10^99997-402627 99997 Patrick De Geest 02/2020 9592 10^99996+279853 99997 Patrick De Geest 02/2020 9593 10^99997-500000001 99997 Robert Price 12/2020 9594 10^99996-94961 99996 Patrick De Geest 02/2020 9595 10^99995+54633 99996 Patrick De Geest 02/2020 9596 10^99995-101429 99995 Patrick De Geest 02/2020 9597 10^99994+117271 99995 Patrick De Geest 02/2020 9598 10^99994-452289 99994 Patrick De Geest 02/2020 9599 10^99993+371311 99994 Patrick De Geest 02/2020 9600 10^99993-186491 99993 Patrick De Geest 02/2020 9601 10^99992+17431 99993 Patrick De Geest 02/2020 9602 10^99992-28607 99992 Patrick De Geest 02/2020 9603 10^99991+125391 99992 Patrick De Geest 02/2020 9604 10^99991-204573 99991 Patrick De Geest 02/2020 9605 10^99990+13899 99991 Patrick De Geest 02/2020 9606 10^99990-8111 99990 Patrick De Geest 02/2020 9607 2^332141-113073 99985 Enzo Doria 07/2014 9608 (1610172603037^8192+1610172602919^8192)/17110948127473666 99983 Youcef Lemsafer 01/2023 9609 6*10^99979-79 99980 Robert Price 03/2022 9611 (3^209561+2)/728101255 99978 Lelio R Paula 09/2013 9610 23827^15702+15702^23827 99978 Hans Havermann 04/2018 9612 2^332085+1865897 99968 Enzo Doria 03/2016 9613 (9787*2^332070-1)/936402369 99959 Lelio R Paula 05/2015 9614 2^332023+191 99949 Lelio R Paula 02/2011 9615 (6271^26321-1)/6270 99946 Serge Batalov 06/2022 9616 7*10^99944+27 99945 Robert Price 11/2020 9617 3188^28523-28523^3188 99931 Norbert Schneider 06/2023 9618 2^331938+71149 99924 Enzo Doria 04/2016 9619 2^331932-78795 99922 Lelio R Paula 09/2016 9620 2^331921+771 99919 Lelio R Paula 01/2013 9621 7947^25618-25618^7947 99916 Norbert Schneider 08/2023 9622 (3^209419-2)/5132755 99912 Lelio R Paula 09/2013 9623 21657^23042-23042^21657 99901 Norbert Schneider 04/2024 9624 2^331860-114989 99900 Enzo Doria 05/2015 9625 23*31^66974+2970 99884 Eric Chen 04/2024 9626 2^331746-11655 99866 Lelio R Paula 09/2016 9627 11^95891-28 99861 Lelio R Paula 08/2016 9628 (2^331694-5)/11 99849 Lelio R Paula 10/2013 9629 (3^209246+7)/64 99834 Lelio R Paula 09/2013 9630 25062^9617+9617^25062 99823 Hans Havermann 04/2018 9631 15^84866-52 99811 Lelio R Paula 08/2016 9632 13^89600+30 99810 Lelio R Paula 08/2016 9633 2^331527+100280245065 99800 Paul Bourdelais 10/2021 9634 22950^22309+22309^22950 99798 Hans Havermann 03/2018 9635 5^142772-38 99794 Lelio R Paula 08/2016 9636 (7482^25759-1)/7481 99787 Serge Batalov 06/2022 9637 (23*2^331459+1)/475 99778 Lelio R Paula 11/2013 9638 2^331416-331416+1 99767 Robert Price 10/2014 9639 2^331256-57 99718 Lelio R Paula 12/2012 9640 28192^3443+3443^28192 99714 Hans Havermann 03/2018 9641 2^331185+737 99697 Lelio R Paula 01/2013 9642 (4*10^99693+149)/9 99693 Robert Price 03/2017 9643 2^331154+1880527 99688 Enzo Doria 10/2016 9645 (19^77951+1)/20 99679 Paul Bourdelais 03/2010 9644 24354^12385+12385^24354 99679 Hans Havermann 03/2018 9646 2^331110+1870459 99675 Enzo Doria 05/2016 9647 5*2^331075+7 99665 Lelio R Paula 08/2014 9648 25776^7351+7351^25776 99659 Hans Havermann 02/2018 9649 (16*10^99656-31)/3 99657 Robert Price 03/2016 9650 (6059^26347-1)/6058 99652 Serge Batalov 06/2022 9651 (15544^23773-1)/15543 99642 Serge Batalov 06/2022 9653 2^330968+345 99632 Lelio R Paula 09/2016 9652 (2^330969+690)/2 99632 Stefano Morozzi 09/2020 9655 2*5^142528-7 99624 Lelio R Paula 11/2014 9654 2^330942+77329 99624 Enzo Doria 05/2016 9656 14^86914-99 99615 Lelio R Paula 08/2016 9657 (19*2^330902+1)/77 99611 Lelio R Paula 11/2013 9658 22971^21692+21692^22971 99610 Hans Havermann 03/2018 9659 2^330845+71687 99595 Enzo Doria 04/2016 9660 (26667^22501-1)/26666 99585 Serge Batalov 06/2022 9661 (23*2^330770+1)/3 99573 Lelio R Paula 11/2013 9662 24494^11613+11613^24494 99567 Hans Havermann 03/2018 9663 2^330735+8415 99562 Lelio R Paula 09/2016 9664 2^330720+74071 99557 Enzo Doria 04/2016 9665 (10405^24781-1)/10404 99548 Serge Batalov 06/2022 9667 31^66738-2 99531 Lelio R Paula 09/2013 9666 (9002^25171-1)/9001 99531 Serge Batalov 06/2022 9668 (5023^26893-1)/5022 99527 Serge Batalov 06/2022 9669 7*3^208567+4 99513 Lelio R Paula 08/2014 9670 (15881^23689-1)/15880 99511 Serge Batalov 06/2022 9671 (13*10^99508+47)/3 99509 Robert Price 01/2017 9672 2^330553+779 99507 Lelio R Paula 01/2013 9673 15^84606-94 99505 Lelio R Paula 08/2016 9674 (10^99497+173)/3 99497 Robert Price 05/2021 9675 9*10^99493-43 99494 Robert Price 09/2021 9676 6^127858+47 99493 Lelio R Paula 08/2016 9677 5^142337+48 99490 Lelio R Paula 08/2016 9678 7^117724-20 99489 Lelio R Paula 08/2016 9679 (559^36209-1)/558 99479 Serge Batalov 06/2022 9680 (13470^24091-1)/13469 99477 Serge Batalov 06/2022 9681 (29*10^99474-17)/3 99475 Erik Branger 09/2014 9682 (185*10^99466-11)/3 99468 Robert Price 10/2020 9683 (2^330410+2038)/2 99464 Stefano Morozzi 09/2020 9684 (9*2^330407-1)/7 99463 Lelio R Paula 03/2014 9685 (516*32^66077-175)/31 99458 Eric Chen 04/2023 9686 (2863^28771-1)/2862 99453 Serge Batalov 06/2022 9687 (2^330373+2114)/2 99452 Stefano Morozzi 09/2020 9688 (68*10^99441+7)/3 99443 Robert Price 03/2016 9689 10^99434+155571 99435 Patrick De Geest 04/2020 9690 10^99434-123456789 99434 Robert Price 02/2020 9691 10^99434-191237 99434 Patrick De Geest 04/2020 9692 46^59791-45^59791 99418 Jean-Louis Charton 01/2013 9693 23839^14802+14802^23839 99417 Hans Havermann 02/2018 9694 (2*10^99408+529)/9 99408 Robert Price 01/2017 9695 (2^330216+3510)/2 99405 Stefano Morozzi 09/2020 9696 53^57646-2 99398 Lelio R Paula 09/2013 9697 2^330165+1870025 99390 Enzo Doria 05/2016 9698 7*10^99383+97 99384 Robert Price 09/2021 9699 2^330142-155 99383 Lelio R Paula 12/2012 9700 2^330088-115259 99367 Enzo Doria 06/2015 9701 24216^12671+12671^24216 99354 Hans Havermann 01/2018 9702 Phi(200548,10)/3208769 99354 Makoto Kamada 04/2019 9703 (746*10^99303+1)/9 99305 Robert Price 02/2017 9704 3^208107+40 99293 Lelio R Paula 08/2016 9705 2^329843+211343 99293 Enzo Doria 08/2023 9706 (3939^27617-1)/3938 99291 Serge Batalov 06/2022 9707 (5*2^329833-1)/369 99288 Lelio R Paula 02/2014 9708 8*3^208093+5 99287 Lelio R Paula 08/2014 9709 5^142043+56 99284 Lelio R Paula 08/2016 9710 (13*10^99282-157)/9 99283 Robert Price 05/2021 9711 (10^99284+7)/53/67 99281 Alfred Reich 06/2021 9712 22*10^99275+7 99277 Robert Price 04/2016 9713 2^329778+1876189 99274 Enzo Doria 07/2016 9714 (149557^19321-1)/(149557^139-1) 99264 Ryan Propper 11/2023 9715 (6580^25997-1)/6579 99259 Serge Batalov 06/2022 9716 (2249^29611-1)/2248 99253 Serge Batalov 06/2022 9717 (10^99239-13)/3 99239 Robert Price 02/2017 9718 (1199^32233-1)/1198 99237 Serge Batalov 06/2022 9720 3^207987+62 99236 Lelio R Paula 08/2016 9719 (62*10^99235+91)/9 99236 Robert Price 07/2021 9721 2^329638+49 99231 Lelio R Paula 12/2012 9722 7^117413-18 99226 Lelio R Paula 08/2016 9723 2^329586-458903 99216 Enzo Doria 04/2015 9724 (6290^26119-1)/6289 99214 Serge Batalov 06/2022 9726 2^329553+101 99206 Lelio R Paula 12/2012 9725 (21297^22921-1)/21296 99206 Serge Batalov 06/2022 9727 2^329551-112897 99205 Enzo Doria 06/2014 9728 (3^207925+7)/50 99204 Lelio R Paula 09/2013 9729 6^127458-17993 99182 Enzo Doria 03/2013 9730 27197^4428+4428^27197 99166 Hans Havermann 10/2017 9731 (46*10^99143-1)/9 99144 Robert Price 12/2014 9732 (64*10^99135+161)/9 99136 Robert Price 08/2022 9733 7*10^99133+69 99134 Robert Price 10/2017 9734 (21701^22861-1)/21700 99132 Serge Batalov 06/2022 9735 18^78968-3065 99127 Enzo Doria 03/2013 9736 25927^6654+6654^25927 99122 Hans Havermann 10/2017 9737 87915!4+16 99122 Robert Price 09/2019 9738 2^329259+189 99117 Lelio R Paula 12/2012 9739 8*10^99113+39 99114 Robert Price 01/2017 9740 6^127364+77 99109 Lelio R Paula 08/2016 9741 (82*10^99103+143)/9 99104 Robert Price 06/2021 9742 (11414^24421-1)/11413 99083 Serge Batalov 06/2022 9743 (2^329135+1110)/2 99080 Stefano Morozzi 09/2020 9744 (22089^22807-1)/22088 99074 Serge Batalov 06/2022 9745 (59*10^99069+391)/9 99070 Robert Price 03/2021 9746 (797*10^99061-41)/9 99063 Robert Price 04/2022 9747 2^329058-287681 99057 Harrison Mesh 06/2022 9748 6^127285+13 99047 Lelio R Paula 08/2016 9749 (228581#+235862)/(2^3*11*71*151) 99044 Makoto Morimoto 10/2017 9750 2^329007+73283 99041 Enzo Doria 04/2016

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: July, 19 2024 15:29 (Time in France)

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