## PRP Records

### Probable Primes Top 10000

#### (295503 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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 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 ? 6501 6^138956-59 108129 Lelio R Paula 02/2017 6502 2^359184+30285 108126 Lelio R Paula 04/2017 6503 13^97059+10 108119 Lelio R Paula 03/2017 6504 2^359137-81 108112 Lelio R Paula 12/2011 6506 (15185*2^359105-1)/567 108103 Lelio R Paula 05/2015 6505 2^359110-11655 108103 Lelio R Paula 04/2017 6507 2^359069-933075 108091 Paul Bourdelais 06/2021 6508 26227^13222+13222^26227 108090 Hans Havermann 10/2020 6509 8*6^138875+5 108067 Lelio R Paula 11/2014 6510 2^358987-216919 108066 Enzo Doria 05/2014 6511 (2^358977+2714)/2 108063 Stefano Morozzi 09/2020 6512 39^67918-67918^39 108062 Norbert Schneider 02/2017 6513 24^78283-1*78283^24 108048 Dylan Delgado 12/2019 6514 25282^18767+18767^25282 108040 Hans Havermann 11/2020 6515 2^358785-16933 108006 Enzo Doria 05/2013 6516 (2^358783+5)/33383 108000 Lelio R Paula 12/2013 6517 6^138770-77 107985 Lelio R Paula 02/2017 6518 (2^358727-1017)/94178479 107980 Lelio R Paula 12/2013 6519 10^107976+19 107977 Lelio R Paula 02/2017 6520 10^107976-202103 107976 Patrick De Geest 03/2017 6521 2^358684+75781 107975 Enzo Doria 04/2016 6522 24928^21411+21411^24928 107955 Hans Havermann 10/2020 6523 99^54094+2 107952 Lelio R Paula 06/2013 6524 (2^358583-9)/391 107942 Lelio R Paula 12/2013 6525 (2^358562+838)/2 107938 Stefano Morozzi 02/2021 6526 2^358538+55 107931 Lelio R Paula 12/2011 6527 2^358517-109009 107925 Enzo Doria 03/2014 6528 26395^12258+12258^26395 107914 Hans Havermann 10/2020 6529 3^226159+104 107906 Lelio R Paula 03/2017 6530 7*10^107870+39 107871 Robert Price 01/2023 6531 2^358310-11655 107863 Lelio R Paula 03/2017 6532 (68*10^107852-329)/9 107853 Robert Price 03/2021 6533 2^358275-112987 107852 Enzo Doria 07/2014 6534 3^226038+4 107848 Tyler NeSmith 01/2021 6535 2^358233-20005 107839 Enzo Doria 06/2013 6536 2^358194+175 107828 Lelio R Paula 12/2011 6537 107^53125-106 107812 Norbert Schneider 12/2016 6538 (25*10^107804+161)/3 107805 Robert Price 09/2019 6539 3^225922-2 107793 Lelio R Paula 10/2013 6540 12^99874-95 107783 Lelio R Paula 03/2017 6541 (2^358042+3042)/2 107782 Stefano Morozzi 09/2020 6542 2^358030-171 107778 Lelio R Paula 12/2011 6543 11^103488-4170 107772 Enzo Doria 12/2012 6544 2^357930-4547 107748 Yves Minet 03/2019 6545 2^357911-20089 107742 Enzo Doria 06/2013 6546 2^357885+12857 107735 Yves Minet 07/2010 6547 (248587#+9289)/(7*1327*111512899) 107733 Makoto Morimoto 06/2019 6548 7^127473+40 107728 Lelio R Paula 03/2017 6549 5*2^357850+9 107725 Lelio R Paula 09/2014 6550 2^357786-291191 107705 Enzo Doria 06/2015 6551 28907^5320+5320^28907 107705 Hans Havermann 10/2020 6552 18^85798-23 107700 Lelio R Paula 04/2017 6553 3*10^107697+61 107698 Robert Price 09/2020 6554 (14*10^107694-83)/3 107695 Robert Price 12/2018 6555 2^357688-1854269 107675 Enzo Doria 09/2015 6556 2^357671-112225 107670 Enzo Doria 06/2014 6557 34323^1370+1370^34323 107662 Hans Havermann 11/2020 6558 2^357618-21005 107654 Enzo Doria 06/2013 6559 2^357615-17505 107653 Enzo Doria 05/2013 6560 26350^12171+12171^26350 107649 Hans Havermann 11/2020 6561 (30^72871-1)/29 107638 Robert Price 12/2011 6562 25021^20026+20026^25021 107631 Hans Havermann 11/2020 6563 2^357521+1870217 107625 Enzo Doria 05/2016 6564 2^357477-1203 107612 Lelio R Paula 03/2017 6565 26008^13693+13693^26008 107583 Hans Havermann 10/2020 6566 25432^16991+16991^25432 107583 Hans Havermann 10/2020 6567 (2^357371+3726)/2 107580 Stefano Morozzi 09/2020 6568 5^153894-18 107568 Lelio R Paula 02/2017 6569 2^357324-69059 107566 Enzo Doria 11/2015 6570 467^40296+40296^467 107563 Norbert Schneider 03/2019 6571 29446^4495+4495^29446 107559 Hans Havermann 10/2020 6572 (8*10^107556-149)/3 107557 Robert Price 12/2021 6573 2^357283-869688105 107553 Lelio R Paula 01/2017 6574 2^357280-16805 107552 Enzo Doria 05/2013 6575 10^107547+481719 107548 Patrick De Geest 03/2017 6576 10^107547-47 107547 Lelio R Paula 02/2017 6577 (23*10^107540+37)/3 107541 Robert Price 02/2022 6578 17^87396-32 107537 Lelio R Paula 04/2017 6579 (746*10^107505+1)/9 107507 Robert Price 03/2020 6580 (2^357125+1730)/2 107506 Stefano Morozzi 09/2020 6581 2^357081+107 107493 Lelio R Paula 12/2011 6582 2^357058-3911 107486 Yves Minet 04/2017 6583 3^225274+64 107484 Lelio R Paula 03/2017 6584 5*10^107482-57 107483 Robert Price 03/2021 6585 18^85619-95 107476 Lelio R Paula 04/2017 6586 (2^357013+2526)/2 107472 Stefano Morozzi 09/2020 6587 3^225248-130 107471 Lelio R Paula 03/2017 6588 (5*2^356961+1)/143 107455 Lelio R Paula 03/2014 6589 27029^9448+9448^27029 107450 Hans Havermann 11/2020 6590 2^356935-18085 107449 Enzo Doria 05/2013 6591 55396^87+87^55396 107442 Hans Havermann 10/2020 6592 (14*10^107439-137)/3 107440 Robert Price 04/2021 6593 10^107409+37 107410 Lelio R Paula 02/2017 6594 10^107409-329633 107409 Patrick De Geest 03/2017 6595 (2^356799+3134)/2 107407 Stefano Morozzi 09/2020 6596 2^356787-109027 107404 Enzo Doria 04/2014 6597 (2^356767+78557)/5 107397 Lelio R Paula 12/2013 6598 3*10^107389+77 107390 Robert Price 09/2018 6599 (11*10^107385+61)/9 107386 Tyler Busby 01/2023 6600 5^153622-42 107378 Lelio R Paula 02/2017 6601 2^356699-97305 107378 Lelio R Paula 03/2017 6602 13129^26072-26072^13129 107371 Norbert Schneider 09/2022 6603 2^356654+85 107364 Lelio R Paula 11/2011 6604 2^356641-19921 107360 Enzo Doria 06/2013 6605 5*10^107355+11 107356 Robert Price 08/2019 6606 2^356623-465 107355 Lelio R Paula 03/2017 6607 19^83945-92 107345 Lelio R Paula 02/2017 6608 25491^16246+16246^25491 107337 Hans Havermann 11/2020 6609 10^107334+28149 107335 Patrick De Geest 03/2017 6610 10^107334-83 107334 Lelio R Paula 02/2017 6611 2^356518+885 107323 Lelio R Paula 03/2017 6612 (59*10^107322+391)/9 107323 Robert Price 03/2021 6613 (3*2^356506-1)/467 107317 Lelio R Paula 03/2014 6614 (2^356468+1162)/2 107308 Stefano Morozzi 09/2020 6615 2^356442-114713 107300 Enzo Doria 04/2015 6616 2^356425+72257 107295 Enzo Doria 04/2016 6617 2^356351-112237 107273 Enzo Doria 06/2014 6619 (6^137845-11)/5 107264 Paul Bourdelais 11/2011 6618 2^356322+74539 107264 Enzo Doria 04/2016 6620 2^356274+1874479 107250 Enzo Doria 06/2016 6621 24606^22819+22819^24606 107241 Hans Havermann 10/2020 6622 (2^356243+3686)/2 107240 Stefano Morozzi 09/2020 6623 20^82422-93 107234 Lelio R Paula 02/2017 6624 2^356157-20365 107214 Enzo Doria 06/2013 6625 8*10^107209+99 107210 Robert Price 03/2021 6626 2^356129-18949 107206 Enzo Doria 05/2013 6627 2^356100-109587 107197 Enzo Doria 04/2014 6628 2*10^107173-37 107174 Robert Price 11/2021 6629 (2^355978+3262)/2 107160 Stefano Morozzi 02/2021 6630 (31*2^355970+1)/5 107159 Lelio R Paula 03/2014 6631 2^355968-64875 107158 Lelio R Paula 01/2017 6632 2^355952+1870321 107153 Enzo Doria 05/2016 6633 27069^9088+9088^27069 107152 Hans Havermann 11/2020 6634 2^355915-117 107142 Lelio R Paula 11/2011 6635 (16*10^107140+77)/3 107141 Robert Price 03/2019 6636 24628^22369+22369^24628 107124 Hans Havermann 11/2020 6637 (19*2^355838-1)/15 107119 Lelio R Paula 03/2014 6638 3^224495-8 107112 Lelio R Paula 12/2013 6639 3*10^107096+23 107097 Robert Price 03/2022 6640 25077^18632+18632^25077 107086 Hans Havermann 10/2020 6641 7^126691-44 107067 Lelio R Paula 03/2017 6642 4^177830-8243 107065 Mike Oakes 02/2011 6643 (509*10^107057+13)/9 107059 Robert Price 05/2022 6644 2^355604+214051 107048 Enzo Doria 10/2023 6645 (2^355562+1702)/2 107035 Stefano Morozzi 09/2020 6646 10^107028+3593037 107029 Paul Bourdelais 10/2021 6647 2^355524-21237 107024 Enzo Doria 06/2013 6648 (10223*2^355515+1)/4855 107022 Lelio R Paula 07/2014 6649 24843^20320+20320^24843 107022 Hans Havermann 10/2020 6650 2^355494-19901 107015 Enzo Doria 06/2013 6651 2^355454-869688105 107003 Lelio R Paula 01/2017 6652 4*10^106997+13 106998 Robert Price 02/2021 6653 (8*10^106985-629)/9 106985 Robert Price 01/2022 6654 2^355366+54615 106976 Lelio R Paula 01/2017 6655 (31*2^355346-1)/1563 106969 Lelio R Paula 03/2014 6657 2^355275-19861 106949 Enzo Doria 06/2013 6656 27503^7738+7738^27503 106949 Hans Havermann 11/2020 6658 (85*10^106943+77)/9 106944 Robert Price 07/2022 6659 (9179*2^355234-1)/1915 106937 Lelio R Paula 05/2015 6660 4*10^106914-93 106915 Robert Price 07/2020 6661 4*10^106892-3 106893 Robert Price 10/2015 6662 (66^58741+1)/67 106881 Paul Bourdelais 08/2017 6663 2^354946-3 106850 M. Frind & P. Underwood 08/2002 6664 (2^354945+3134)/2 106849 Stefano Morozzi 09/2020 6665 (46^64384+1)/(46^128+1) 106843 Martin Hopf 12/2023 6666 2^354873-18693 106828 Enzo Doria 05/2013 6667 (2^354831+3186)/2 106815 Stefano Morozzi 09/2020 6669 2^354828+4257 106814 Lelio R Paula 01/2017 6668 25216^17217+17217^25216 106814 Hans Havermann 10/2020 6670 (2^354799+1218)/2 106805 Stefano Morozzi 09/2020 6671 436^40459+40459^436 106791 Norbert Schneider 03/2019 6672 (21^80761+1)/22 106783 Paul Bourdelais 03/2010 6673 (115*10^106772-7)/9 106774 Robert Price 02/2020 6674 2^354640-354640+1 106758 Robert Price 10/2014 6675 (2^354603+2606)/2 106746 Stefano Morozzi 09/2020 6676 2^354585+95 106741 Lelio R Paula 10/2011 6677 (206*10^106737+1)/9 106739 Robert Price 04/2022 6678 2^354553+189 106732 Lelio R Paula 10/2011 6680 (2^354546+1338)/2 106729 Stefano Morozzi 02/2021 6679 (8*10^106729-71)/9 106729 Serge Batalov 11/2022 6681 2^354514-109031 106720 Enzo Doria 04/2014 6682 2^354509-109465 106718 Enzo Doria 04/2014 6683 fibonacci(510628)+2 106715 Jon Grantham 08/2023 6684 (15*2^354478-1)/26983 106706 Lelio R Paula 03/2014 6685 Phi(217618,10)/899798636917 106693 Makoto Kamada 06/2019 6686 15^90710+28 106684 Lelio R Paula 04/2017 6687 7^126237+34 106683 Lelio R Paula 03/2017 6688 2^354385-115315 106681 Enzo Doria 06/2015 6689 2^354327-19305 106664 Enzo Doria 06/2013 6690 (35*10^106649+1)/9 106650 Serge Batalov 11/2010 6691 10^106636+97 106637 Lelio R Paula 02/2017 6692 10^106636-22923 106636 Patrick De Geest 03/2017 6693 2^354220-57 106631 Lelio R Paula 10/2011 6694 (68*10^106628-329)/9 106629 Robert Price 03/2021 6695 (29*10^106620-77)/3 106621 Robert Price 02/2020 6696 (746*10^106618+1)/9 106620 Robert Price 03/2020 6697 2*10^106613+29 106614 Robert Price 02/2021 6698 2^354157-17041 106612 Enzo Doria 05/2013 6699 12^98778+73 106600 Lelio R Paula 02/2017 6700 33333^1576+1576^33333 106585 Hans Havermann 11/2020 6701 2^354064+1870651 106584 Enzo Doria 05/2016 6702 24568^21779+21779^24568 106577 Hans Havermann 11/2020 6703 2^353992-57 106563 Lelio R Paula 10/2011 6704 9*10^106559+59 106560 Robert Price 01/2020 6705 7*10^106553+27 106554 Robert Price 11/2020 6706 28847^4938+4938^28847 106548 Hans Havermann 10/2020 6707 NSW(139160) 106535 Robert Price 12/2018 6708 f(278321) 106535 Robert Price 07/2023 6709 (7*10^106516+113)/3 106517 Robert Price 02/2018 6710 2^353832-1853849 106515 Enzo Doria 09/2015 6711 (7^126037-1)/6 106513 Paul Bourdelais 09/2008 6712 2^353794-18453 106503 Enzo Doria 05/2013 6713 (2^353761+2094)/2 106493 Stefano Morozzi 09/2020 6714 2^353728+7695 106483 Lelio R Paula 01/2017 6715 26476^10509+10509^26476 106475 Hans Havermann 10/2020 6716 2^353672-303 106466 Yves Minet 02/2012 6717 6^136811+101 106460 Lelio R Paula 02/2017 6718 2^353641+1871981 106457 Enzo Doria 05/2016 6719 (8*10^106454-29)/3 106455 Robert Price 07/2018 6720 27845^6654+6654^27845 106454 Hans Havermann 11/2020 6721 10^106449-700001 106449 Robert Price 08/2021 6722 25316^16017+16017^25316 106444 Hans Havermann 11/2020 6723 2^353553+54615 106431 Lelio R Paula 01/2017 6724 2^353544-18897 106428 Enzo Doria 05/2013 6725 28894^4823+4823^28894 106426 Hans Havermann 11/2020 6726 (19*10^106422+29)/3 106423 Robert Price 12/2021 6727 (694*10^106418+53)/9 106420 Robert Price 02/2022 6728 6*10^106412-13 106413 Robert Price 07/2022 6729 25696^13829+13829^25696 106402 Hans Havermann 11/2020 6730 6^136729-133 106396 Lelio R Paula 02/2017 6731 2^353418+1605 106390 Lelio R Paula 01/2017 6732 2^353387+65 106381 Lelio R Paula 10/2011 6733 2^353372+74311 106376 Enzo Doria 04/2016 6734 2^353344-3693 106368 Yves Minet 03/2017 6735 (772*10^106365-7)/9 106367 Robert Price 06/2022 6736 (56*10^106351+619)/9 106352 Robert Price 05/2021 6738 2^353277-20089 106347 Enzo Doria 06/2013 6737 2^353275+72173 106347 Enzo Doria 04/2016 6739 2^353268-17705 106345 Enzo Doria 05/2013 6740 2^353267-19857 106344 Enzo Doria 06/2013 6741 (46*10^106343+143)/9 106344 Robert Price 01/2019 6742 (2^353189+3054)/2 106321 Stefano Morozzi 09/2020 6743 35087^1072+1072^35087 106321 Hans Havermann 10/2020 6744 (2^353184+1290)/2 106319 Stefano Morozzi 01/2021 6745 F(508799)/24738824977/1990778864897 106310 Serge Batalov 07/2024 6746 26985^8684+8684^26985 106287 Hans Havermann 10/2020 6747 (2^353051+606)/2 106279 Stefano Morozzi 09/2020 6749 222748^3+3^222748 106278 Anatoly F. Selevich 12/2010 6748 (46*10^106277+107)/9 106278 Robert Price 06/2022 6750 (9179*2^353019-1)/9 106273 Lelio R Paula 05/2015

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: July, 22 2024 13:34 (Time in France)

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