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 | 25316^16017+16017^25316 | 106444 | Hans Havermann | 11/2020 |
7502 | 2^353553+54615 | 106431 | Lelio R Paula | 01/2017 |
7503 | 2^353544-18897 | 106428 | Enzo Doria | 05/2013 |
7504 | 28894^4823+4823^28894 | 106426 | Hans Havermann | 11/2020 |
7505 | (19*10^106422+29)/3 | 106423 | Robert Price | 12/2021 |
7506 | (694*10^106418+53)/9 | 106420 | Robert Price | 02/2022 |
7507 | 6*10^106412-13 | 106413 | Robert Price | 07/2022 |
7508 | 25696^13829+13829^25696 | 106402 | Hans Havermann | 11/2020 |
7509 | 6^136729-133 | 106396 | Lelio R Paula | 02/2017 |
7510 | 2^353418+1605 | 106390 | Lelio R Paula | 01/2017 |
7511 | 2^353387+65 | 106381 | Lelio R Paula | 10/2011 |
7512 | 2^353372+74311 | 106376 | Enzo Doria | 04/2016 |
7513 | 2^353344-3693 | 106368 | Yves Minet | 03/2017 |
7514 | (772*10^106365-7)/9 | 106367 | Robert Price | 06/2022 |
7515 | (56*10^106351+619)/9 | 106352 | Robert Price | 05/2021 |
7516 | 2^353277-20089 | 106347 | Enzo Doria | 06/2013 |
7517 | 2^353275+72173 | 106347 | Enzo Doria | 04/2016 |
7518 | 2^353268-17705 | 106345 | Enzo Doria | 05/2013 |
7519 | 2^353267-19857 | 106344 | Enzo Doria | 06/2013 |
7520 | (46*10^106343+143)/9 | 106344 | Robert Price | 01/2019 |
7522 | (2^353189+3054)/2 | 106321 | Stefano Morozzi | 09/2020 |
7521 | 35087^1072+1072^35087 | 106321 | Hans Havermann | 10/2020 |
7523 | (2^353184+1290)/2 | 106319 | Stefano Morozzi | 01/2021 |
7524 | F(508799)/24738824977/1990778864897 | 106310 | Serge Batalov | 07/2024 |
7525 | 26985^8684+8684^26985 | 106287 | Hans Havermann | 10/2020 |
7526 | (2^353051+606)/2 | 106279 | Stefano Morozzi | 09/2020 |
7528 | 222748^3+3^222748 | 106278 | Anatoly F. Selevich | 12/2010 |
7527 | (46*10^106277+107)/9 | 106278 | Robert Price | 06/2022 |
7529 | (9179*2^353019-1)/9 | 106273 | Lelio R Paula | 05/2015 |
7530 | 2^353025+72257 | 106272 | Enzo Doria | 04/2016 |
7533 | 2^352932-20345 | 106244 | Enzo Doria | 06/2013 |
7531 | (2^353011-3)/745325861246794515484535 | 106244 | Lelio R Paula | 12/2013 |
7532 | 25628^13983+13983^25628 | 106244 | Hans Havermann | 10/2020 |
7534 | 2^352883-187 | 106229 | Lelio R Paula | 10/2011 |
7535 | 20^81649-19^81649 | 106228 | Jean-Louis Charton | 03/2011 |
7536 | (55*10^106222+377)/9 | 106223 | Robert Price | 02/2019 |
7537 | 2^352814-131 | 106208 | Lelio R Paula | 10/2011 |
7538 | 2^352752+73951 | 106189 | Enzo Doria | 04/2016 |
7539 | 11876*25^75945+357 | 106171 | Eric Chen | 10/2023 |
7540 | 6^136434+5 | 106167 | Lelio R Paula | 11/2014 |
7541 | 25296^15737+15737^25296 | 106166 | Hans Havermann | 09/2020 |
7542 | 8*10^106157-13 | 106158 | Robert Price | 08/2019 |
7543 | 2^352641+225677 | 106156 | Enzo Doria | 08/2024 |
7544 | 7*5^151872-8 | 106155 | Lelio R Paula | 11/2014 |
7545 | 105^52520-2 | 106153 | Lelio R Paula | 10/2017 |
7546 | (23*10^106152-29)/3 | 106153 | Robert Price | 03/2022 |
7547 | 2^352601-1604809 | 106144 | Enzo Doria | 05/2015 |
7548 | 12^98353-43 | 106141 | Lelio R Paula | 02/2017 |
7549 | 2^352585-18901 | 106139 | Enzo Doria | 05/2013 |
7550 | 26363^10614+10614^26363 | 106135 | Hans Havermann | 09/2020 |
7551 | (2^352554-3)/193 | 106128 | Lelio R Paula | 12/2013 |
7552 | 2^352540+15015 | 106126 | Lelio R Paula | 01/2017 |
7553 | 25068^17119+17119^25068 | 106125 | Hans Havermann | 09/2020 |
7554 | 2^352524-3149 | 106121 | Yves Minet | 10/2014 |
7555 | (7*10^106119-67)/3 | 106120 | Robert Price | 10/2021 |
7556 | 2^352486-1858781 | 106109 | Enzo Doria | 04/2016 |
7557 | 2^352444+12705 | 106097 | Lelio R Paula | 01/2017 |
7558 | 28561^5182+5182^28561 | 106090 | Hans Havermann | 10/2020 |
7559 | (182*10^106083+43)/9 | 106085 | Robert Price | 02/2020 |
7560 | (266*10^106066+1)/3 | 106068 | Robert Price | 04/2020 |
7561 | (7*10^106066-187)/9 | 106066 | Tyler Busby | 01/2023 |
7562 | 2^352228-18953 | 106032 | Enzo Doria | 05/2013 |
7563 | (2^352223+1118)/2 | 106030 | Stefano Morozzi | 09/2020 |
7564 | (2^352212+2250)/2 | 106027 | Stefano Morozzi | 01/2021 |
7565 | (2^352136+2638)/2 | 106004 | Stefano Morozzi | 09/2020 |
7566 | 2^352107+1872533 | 105995 | Enzo Doria | 05/2016 |
7567 | (2^352096+2086)/2 | 105992 | Stefano Morozzi | 09/2020 |
7568 | 2^352066-2591 | 105983 | Yves Minet | 07/2014 |
7569 | 2^352030+715 | 105972 | Lelio R Paula | 10/2011 |
7570 | 9*6^136176-5 | 105967 | Lelio R Paula | 11/2014 |
7571 | 17099*2^351991+58329 | 105965 | Paul Vanderveen | 12/2017 |
7572 | 122^50789-50789^122 | 105965 | Norman Luhn | 09/2024 |
7573 | 28582^5097+5097^28582 | 105963 | Hans Havermann | 09/2020 |
7574 | 155^48377+2 | 105962 | Lelio R Paula | 08/2013 |
7575 | (23*10^105944-119)/3 | 105945 | Robert Price | 07/2021 |
7576 | 2^351865+1869707 | 105922 | Enzo Doria | 05/2016 |
7577 | 24974^17427+17427^24974 | 105921 | Hans Havermann | 09/2020 |
7578 | 25163^16194+16194^25163 | 105920 | Hans Havermann | 09/2020 |
7579 | 2^351831+23 | 105912 | Lelio R Paula | 10/2011 |
7580 | (2^351818+3798)/2 | 105908 | Stefano Morozzi | 02/2021 |
7581 | 9*2^351784-5 | 105899 | Lelio R Paula | 09/2014 |
7582 | (2^351776+2766)/2 | 105895 | Stefano Morozzi | 01/2021 |
7583 | (85*10^105881+203)/9 | 105882 | Robert Price | 09/2020 |
7584 | 2^351671-112387 | 105864 | Enzo Doria | 06/2014 |
7585 | 2^351669-109501 | 105863 | Enzo Doria | 04/2014 |
7586 | 2^351644+74731 | 105856 | Enzo Doria | 04/2016 |
7587 | 13^95025-42 | 105853 | Lelio R Paula | 12/2016 |
7588 | 2^351599+15015 | 105842 | Lelio R Paula | 01/2017 |
7589 | 19^82763+90 | 105834 | Lelio R Paula | 01/2017 |
7590 | (205*10^105831-1)/3 | 105833 | Robert Price | 11/2021 |
7591 | 26050^11551+11551^26050 | 105832 | Hans Havermann | 09/2020 |
7592 | (9179*2^351540-1)/221 | 105826 | Lelio R Paula | 05/2015 |
7593 | 20^81329-51 | 105812 | Lelio R Paula | 01/2017 |
7594 | (5*10^105811+211)/9 | 105811 | Robert Price | 02/2018 |
7595 | 2^351483+28425 | 105807 | Lelio R Paula | 01/2017 |
7596 | 25231^15610+15610^25231 | 105804 | Hans Havermann | 09/2020 |
7597 | 15^89960+86 | 105802 | Lelio R Paula | 02/2017 |
7598 | 2^351460-17289 | 105801 | Enzo Doria | 05/2013 |
7599 | 19^82735+22 | 105798 | Lelio R Paula | 01/2017 |
7600 | 2^351435-109077 | 105793 | Enzo Doria | 04/2014 |
7601 | 2^351393+1089 | 105780 | Lelio R Paula | 01/2017 |
7602 | 2^351364+72631 | 105772 | Enzo Doria | 04/2016 |
7603 | (2^351333+3626)/2 | 105762 | Stefano Morozzi | 09/2020 |
7604 | 26818^8783+8783^26818 | 105761 | Hans Havermann | 09/2020 |
7607 | 2^351305+1872467 | 105754 | Enzo Doria | 05/2016 |
7606 | 3^221649+16 | 105754 | Lelio R Paula | 11/2016 |
7605 | 32511^1790+1790^32511 | 105754 | Hans Havermann | 09/2020 |
7608 | 8*3^221637-5 | 105749 | Lelio R Paula | 09/2014 |
7609 | 2^351279-2780449 | 105746 | Enzo Doria | 03/2016 |
7610 | (2^351263+3198)/2 | 105741 | Stefano Morozzi | 09/2020 |
7611 | 15^89903-26 | 105735 | Lelio R Paula | 02/2017 |
7613 | 2^351213-73 | 105726 | Lelio R Paula | 10/2011 |
7612 | (2^351214+1210)/2 | 105726 | Stefano Morozzi | 09/2020 |
7614 | 2^351192-4589 | 105720 | Yves Minet | 07/2011 |
7615 | 20^81250-33 | 105709 | Lelio R Paula | 12/2016 |
7616 | (2^351133+3530)/2 | 105702 | Stefano Morozzi | 09/2020 |
7617 | (2^351103+534)/2 | 105693 | Stefano Morozzi | 09/2020 |
7618 | 2^351076-113159 | 105685 | Enzo Doria | 07/2014 |
7619 | 93^53688-2 | 105684 | Lelio R Paula | 09/2013 |
7620 | 2^351060-4559 | 105680 | Yves Minet | 07/2011 |
7621 | ((10^52836-1)*10000/9+5927)*10^52836+(10^52836-1)/9 | 105676 | Hans Havermann | 08/2019 |
7622 | 11^101473-750 | 105674 | Enzo Doria | 11/2012 |
7623 | 3*5^151181-8 | 105672 | Lelio R Paula | 11/2014 |
7624 | 15^89831-34 | 105650 | Lelio R Paula | 02/2017 |
7626 | 11^101448-360 | 105648 | Enzo Doria | 08/2012 |
7625 | 3*7^125011+4 | 105648 | Lelio R Paula | 11/2014 |
7627 | 2^350943-113269 | 105645 | Enzo Doria | 07/2014 |
7628 | 2*10^105636-91 | 105637 | Robert Price | 04/2020 |
7629 | 24231^22880+22880^24231 | 105634 | Hans Havermann | 09/2020 |
7630 | 35296^983+983^35296 | 105626 | Hans Havermann | 09/2020 |
7631 | 2^350868-19725 | 105622 | Enzo Doria | 06/2013 |
7632 | 2^350858-59291 | 105619 | Enzo Doria | 10/2015 |
7633 | V(758484)/1516967/19720583 | 105618 | Serge Batalov | 07/2024 |
7634 | 2^350851+135 | 105617 | Lelio R Paula | 10/2011 |
7635 | 2^350841-741 | 105614 | Lelio R Paula | 01/2017 |
7636 | 3*10^105582+77 | 105583 | Robert Price | 09/2018 |
7637 | 24915^17284+17284^24915 | 105581 | Hans Havermann | 09/2020 |
7638 | (5*10^105576-53)/3 | 105577 | Robert Price | 09/2020 |
7639 | 8*10^105571+3 | 105572 | Robert Price | 08/2015 |
7640 | 2^350674-78557 | 105564 | Jorge Menendez | 03/2018 |
7641 | 2*5^151026-3 | 105563 | Lelio R Paula | 11/2014 |
7642 | (2^350702+5)/34264674063 | 105562 | Lelio R Paula | 12/2013 |
7643 | 6^135647-5^135647 | 105554 | Jean-Louis Charton | 02/2009 |
7644 | 3^221211+236 | 105545 | Lelio R Paula | 11/2016 |
7645 | (32*10^105530-77)/9 | 105531 | Robert Price | 06/2018 |
7646 | 10^105515+33 | 105516 | Lelio R Paula | 11/2016 |
7647 | 24644^19125+19125^24644 | 105516 | Hans Havermann | 10/2020 |
7648 | 10^105515-41033 | 105515 | Patrick De Geest | 12/2016 |
7649 | (29*2^350473-1)/267927 | 105499 | Lelio R Paula | 03/2014 |
7650 | 2^350455-430567 | 105498 | Harrison Mesh | 06/2022 |
7651 | 17^85732-72 | 105489 | Lelio R Paula | 01/2017 |
7652 | (2^350399+3618)/2 | 105481 | Stefano Morozzi | 09/2020 |
7653 | (2^350379+1010)/2 | 105475 | Stefano Morozzi | 09/2020 |
7654 | 2^350356+24241 | 105468 | Enzo Doria | 10/2023 |
7655 | 25233^15118+15118^25233 | 105462 | Hans Havermann | 09/2020 |
7656 | 26261^10366+10366^26261 | 105454 | Hans Havermann | 09/2020 |
7657 | 2^350307-110329 | 105453 | Enzo Doria | 05/2014 |
7658 | 2^350253-20365 | 105437 | Enzo Doria | 06/2013 |
7659 | (3*29^72089-1075)/4 | 105423 | Curtis Bright | 05/2015 |
7660 | (2^350187+2658)/2 | 105417 | Stefano Morozzi | 09/2020 |
7661 | 4*10^105415-69 | 105416 | Robert Price | 01/2022 |
7662 | 21^79725-22 | 105414 | Anonymous | 09/2024 |
7663 | (22*10^105407+179)/3 | 105408 | Robert Price | 02/2022 |
7664 | 2^350139-109009 | 105403 | Enzo Doria | 04/2014 |
7665 | (2^350129+3026)/2 | 105400 | Stefano Morozzi | 09/2020 |
7666 | (2^350097+2070)/2 | 105390 | Stefano Morozzi | 09/2020 |
7667 | 3*5^150763+4 | 105380 | Lelio R Paula | 11/2014 |
7668 | 12^97643+91 | 105375 | Lelio R Paula | 02/2017 |
7669 | 6*5^150744-7 | 105367 | Lelio R Paula | 11/2014 |
7670 | (2^350018+2074)/2 | 105366 | Stefano Morozzi | 09/2020 |
7671 | 4*10^105364-39 | 105365 | Robert Price | 09/2020 |
7673 | 2^349996-112169 | 105360 | Enzo Doria | 06/2014 |
7672 | (2^349997+3702)/2 | 105360 | Stefano Morozzi | 09/2020 |
7674 | (418*10^105343+23)/9 | 105345 | Robert Price | 02/2020 |
7675 | 25490^13563+13563^25490 | 105334 | Hans Havermann | 10/2020 |
7676 | (5^504004)%F(504004) | 105330 | Henri Lifchitz | 06/2025 |
7677 | 11^101142-1080 | 105329 | Enzo Doria | 12/2012 |
7678 | (68*10^105320-41)/9 | 105321 | Robert Price | 10/2013 |
7679 | 24800^17649+17649^24800 | 105319 | Hans Havermann | 09/2020 |
7680 | 3^220712-9934 | 105307 | Enzo Doria | 05/2014 |
7681 | 7*10^105296+9 | 105297 | Robert Price | 09/2015 |
7682 | 89*10^105284-7 | 105286 | Robert Price | 04/2020 |
7683 | 2^349739+1873373 | 105282 | Enzo Doria | 06/2016 |
7684 | 7^124574+24 | 105278 | Lelio R Paula | 11/2016 |
7685 | 2^349708-20957 | 105273 | Enzo Doria | 06/2013 |
7686 | 34115^1218+1218^34115 | 105267 | Hans Havermann | 09/2020 |
7687 | 24029^24029-24020^24020 | 105265 | Henri Lifchitz | 09/2024 |
7688 | 2^349649-20469 | 105255 | Enzo Doria | 06/2013 |
7689 | 2^349607-20109 | 105243 | Enzo Doria | 06/2013 |
7690 | (85*10^105242+473)/9 | 105243 | Robert Price | 01/2020 |
7691 | 2^349594-19085 | 105239 | Enzo Doria | 05/2013 |
7692 | 2^349530+1874479 | 105220 | Enzo Doria | 06/2016 |
7693 | (3^220528+8)/8081 | 105215 | Lelio R Paula | 12/2013 |
7694 | (106*10^105199+17)/3 | 105201 | Robert Price | 04/2021 |
7695 | (2^349452+3570)/2 | 105196 | Stefano Morozzi | 09/2020 |
7696 | 3^220464-112852 | 105189 | Enzo Doria | 07/2014 |
7697 | 2^349419-17349 | 105186 | Enzo Doria | 05/2013 |
7698 | 2^349400-2579 | 105180 | Yves Minet | 07/2014 |
7699 | 8*5^150471+3 | 105176 | Lelio R Paula | 11/2014 |
7700 | (2^349359+2298)/2 | 105168 | Stefano Morozzi | 02/2021 |
7701 | 655^37342+37342^655 | 105165 | Norbert Schneider | 08/2018 |
7702 | 13^94403+94 | 105160 | Lelio R Paula | 12/2016 |
7703 | 2^349301-112309 | 105151 | Enzo Doria | 06/2014 |
7704 | 30291^2960+2960^30291 | 105149 | Hans Havermann | 09/2020 |
7705 | 27350^6981+6981^27350 | 105132 | Hans Havermann | 09/2020 |
7707 | 9*2^349220+5 | 105127 | Lelio R Paula | 09/2014 |
7706 | (2^349225+3122)/2 | 105127 | Stefano Morozzi | 09/2020 |
7708 | 7*3^220317+8 | 105119 | Lelio R Paula | 09/2014 |
7709 | 7^124386+88 | 105119 | Lelio R Paula | 11/2016 |
7710 | (2^349197+570)/2 | 105119 | Stefano Morozzi | 09/2020 |
7711 | 2^349171-19657 | 105111 | Enzo Doria | 06/2013 |
7712 | (2^349115+590)/2 | 105094 | Stefano Morozzi | 09/2020 |
7713 | (2^(6*58185+1)-5)/3 | 105093 | Kevin Acres | 11/2013 |
7714 | (2^349111-5)/3 | 105093 | Lelio R Paula | 12/2013 |
7715 | 675^37142+37142^675 | 105087 | Norbert Schneider | 08/2018 |
7716 | 2^348981-2797573 | 105054 | Enzo Doria | 04/2016 |
7717 | (445^39667+1)/446 | 105050 | Jinyuan Wang | 05/2024 |
7718 | 2^348869-6555 | 105021 | Lelio R Paula | 01/2017 |
7719 | 10^105003-17319 | 105003 | Alfred Reich | 08/2024 |
7720 | 5^150217+78 | 104998 | Lelio R Paula | 11/2016 |
7721 | (88*10^104989-1)/3 | 104991 | Robert Price | 04/2020 |
7722 | (28*10^104972+149)/3 | 104973 | Robert Price | 12/2019 |
7723 | 24927^16262+16262^24927 | 104972 | Hans Havermann | 10/2020 |
7724 | 2^348703-113005 | 104971 | Enzo Doria | 06/2014 |
7725 | (191*10^104956-17)/3 | 104958 | Robert Price | 11/2021 |
7726 | 2^348612-809 | 104943 | Yves Minet | 05/2013 |
7727 | (73*10^104942-1)/9 | 104943 | Robert Price | 01/2015 |
7728 | 2^348583-350407 | 104934 | Enzo Doria | 06/2015 |
7729 | 2^348531-949 | 104919 | Yves Minet | 05/2012 |
7730 | 20^80636-59 | 104910 | Lelio R Paula | 12/2016 |
7731 | 8*10^104893-13 | 104894 | Robert Price | 08/2019 |
7733 | 2^348437+35 | 104890 | Lelio R Paula | 09/2011 |
7732 | 25208^14487+14487^25208 | 104890 | Hans Havermann | 09/2020 |
7734 | 2^348348+135 | 104864 | Lelio R Paula | 09/2011 |
7735 | (29*10^104858+349)/9 | 104859 | Robert Price | 06/2021 |
7736 | 6*10^104852-31 | 104853 | Robert Price | 07/2020 |
7738 | (2^348284+9)/25 | 104843 | Lelio R Paula | 12/2013 |
7737 | 75^55914-74 | 104843 | Norbert Schneider | 01/2015 |
7739 | 2^348268+255255 | 104840 | Lelio R Paula | 01/2017 |
7740 | 35540^891+891^35540 | 104839 | Hans Havermann | 09/2020 |
7741 | 5^149985-52 | 104836 | Lelio R Paula | 11/2016 |
7742 | 2^348224-20249 | 104826 | Enzo Doria | 06/2013 |
7743 | (2^348217+2522)/2 | 104824 | Stefano Morozzi | 09/2020 |
7744 | 2^348212-20105 | 104823 | Enzo Doria | 06/2013 |
7745 | 24647^17898+17898^24647 | 104819 | Hans Havermann | 10/2020 |
7746 | 20^80562+19 | 104814 | Lelio R Paula | 12/2016 |
7747 | 2*10^104811-87 | 104812 | Robert Price | 04/2018 |
7748 | 2^348149-20053 | 104804 | Enzo Doria | 06/2013 |
7749 | 2^348095-171 | 104788 | Lelio R Paula | 09/2011 |
7750 | 25383^13412+13412^25383 | 104769 | Hans Havermann | 09/2020 |