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 ? |
9501 | 2^303698-1847231 | 91423 | Enzo Doria | 07/2015 |
9502 | (38^28933-1)^2-2 | 91416 | Norbert Schneider | 06/2016 |
9503 | 25660^3643+3643^25660 | 91388 | Hans Havermann | 08/2020 |
9504 | 2^303554+77299 | 91379 | Enzo Doria | 05/2016 |
9505 | 2^303542+12705 | 91376 | Lelio R Paula | 02/2016 |
9506 | 31^61269-2 | 91375 | Lelio R Paula | 09/2013 |
9507 | (2^303525+2774)/2 | 91370 | Stefano Morozzi | 01/2021 |
9508 | 2^303516-64875 | 91368 | Lelio R Paula | 02/2016 |
9509 | (2^303497+1266)/2 | 91362 | Stefano Morozzi | 09/2020 |
9510 | (2^303497+3710)/2 | 91362 | Stefano Morozzi | 09/2020 |
9511 | (31*10^91352+257)/9 | 91353 | Robert Price | 12/2021 |
9512 | 21856^15121+15121^21856 | 91349 | Hans Havermann | 09/2020 |
9513 | (24737*2^303428+1)/3 | 91345 | Lelio R Paula | 06/2014 |
9514 | (21181*2^303357+1)/32361 | 91320 | Lelio R Paula | 06/2014 |
9515 | 23081^9046+9046^23081 | 91319 | Hans Havermann | 09/2020 |
9516 | 2^303344-2786969 | 91316 | Enzo Doria | 03/2016 |
9517 | 6^117346+65 | 91313 | Lelio R Paula | 05/2016 |
9518 | 2^303321+855 | 91309 | Lelio R Paula | 02/2016 |
9519 | (2^303315+3746)/2 | 91307 | Stefano Morozzi | 01/2021 |
9520 | 12^84606+47 | 91306 | Lelio R Paula | 06/2016 |
9521 | 2^303288+1874311 | 91299 | Enzo Doria | 06/2016 |
9522 | 197^39788-2 | 91293 | Lelio R Paula | 10/2017 |
9523 | 11^87663-1710 | 91292 | Enzo Doria | 12/2012 |
9524 | (4*10^91284-61)/3 | 91285 | Robert Price | 12/2021 |
9526 | 2^303224+2533 | 91280 | Henri Lifchitz | 05/2005 |
9525 | (2^303226+1830)/2 | 91280 | Stefano Morozzi | 02/2021 |
9527 | 6^117302+143 | 91279 | Lelio R Paula | 05/2016 |
9528 | 3^191306-112880 | 91277 | Enzo Doria | 07/2014 |
9529 | (10052^22807-1)/10051 | 91276 | Serge Batalov | 08/2020 |
9530 | 2^303207+12915 | 91275 | Lelio R Paula | 02/2016 |
9531 | 2^303191-111259 | 91270 | Enzo Doria | 05/2014 |
9532 | 81539!4+32 | 91267 | Robert Price | 09/2019 |
9533 | (2^303116+3570)/2 | 91247 | Stefano Morozzi | 09/2020 |
9534 | 10^91230+9^(91230+1) | 91231 | Robert Price | 08/2016 |
9535 | 10^91230+7921 | 91231 | Patrick De Geest | 11/2016 |
9536 | 10^91230-911141 | 91230 | Patrick De Geest | 11/2016 |
9537 | 10^91229+348793 | 91230 | Patrick De Geest | 07/2019 |
9538 | 10^91229-2471 | 91229 | Patrick De Geest | 01/2019 |
9540 | 2996^26241+26241^2996 | 91228 | Norbert Schneider | 01/2020 |
9539 | 2^303249-494953 | 91228 | Harrison Mesh | 06/2022 |
9542 | 10^91225+5271 | 91226 | Patrick De Geest | 01/2019 |
9541 | 2816^26445+26445^2816 | 91226 | Norbert Schneider | 02/2020 |
9544 | 6^117232-17423 | 91225 | Enzo Doria | 02/2013 |
9543 | 10^91225-147219 | 91225 | Patrick De Geest | 07/2019 |
9545 | 7*10^91215+3 | 91216 | Erik Branger | 11/2009 |
9546 | 10^91215+230611 | 91216 | Patrick De Geest | 07/2019 |
9547 | 10^91215-4539 | 91215 | Patrick De Geest | 01/2019 |
9548 | (2^303007+606)/2 | 91214 | Stefano Morozzi | 09/2020 |
9549 | 9*10^91212-47 | 91213 | Robert Price | 11/2021 |
9550 | (2^302998+3102)/2 | 91212 | Stefano Morozzi | 09/2020 |
9551 | 10^91210+2421 | 91211 | Patrick De Geest | 01/2019 |
9552 | 10^91210-1737 | 91210 | Patrick De Geest | 01/2019 |
9553 | 97*10^91205-3 | 91207 | Robert Price | 01/2017 |
9554 | 2^302979-161181 | 91206 | Enzo Doria | 04/2013 |
9555 | (166*10^91199-7)/3 | 91201 | Robert Price | 11/2020 |
9556 | 2^302949+81 | 91197 | Henri Lifchitz | 02/2007 |
9557 | 10^91194+200361 | 91195 | Patrick De Geest | 07/2019 |
9559 | 4*6^117192-5 | 91194 | Lelio R Paula | 10/2014 |
9558 | 10^91194-8663 | 91194 | Patrick De Geest | 01/2019 |
9560 | 2^302918+99 | 91188 | Lelio R Paula | 11/2012 |
9561 | 10^91186+268111 | 91187 | Patrick De Geest | 07/2019 |
9562 | 10^91186-7763 | 91186 | Patrick De Geest | 01/2019 |
9563 | 10^91181+550471 | 91182 | Patrick De Geest | 07/2019 |
9564 | (26*10^91181-83)/3 | 91182 | Robert Price | 12/2021 |
9565 | 10^91181-1367 | 91181 | Patrick De Geest | 01/2019 |
9566 | 10^91178+71883 | 91179 | Patrick De Geest | 07/2019 |
9567 | 10^91178-4719 | 91178 | Patrick De Geest | 01/2019 |
9568 | 24686^4935+4935^24686 | 91173 | Hans Havermann | 08/2020 |
9569 | 10^91165+3043 | 91166 | Patrick De Geest | 01/2019 |
9570 | 10^91165-399413 | 91165 | Patrick De Geest | 07/2019 |
9571 | (19*10^91167+107)/9/11/11/151 | 91164 | Alfred Reich | 11/2022 |
9572 | 10^91156+3861 | 91157 | Patrick De Geest | 01/2019 |
9573 | 10^91156-231497 | 91156 | Patrick De Geest | 07/2019 |
9574 | 2^302797+1869587 | 91151 | Enzo Doria | 05/2016 |
9575 | 265^37614+37614^265 | 91148 | Norbert Schneider | 01/2015 |
9576 | 7^107852+82 | 91146 | Lelio R Paula | 04/2016 |
9577 | (38*10^91144-11)/9 | 91145 | Robert Price | 05/2015 |
9578 | (55*10^91142+377)/9 | 91143 | Robert Price | 10/2017 |
9579 | 10^91128+9961 | 91129 | Patrick De Geest | 01/2019 |
9581 | 249^38030+38030^249 | 91128 | Norbert Schneider | 01/2015 |
9580 | 10^91128-189153 | 91128 | Patrick De Geest | 07/2019 |
9582 | (2^302718+2814)/2 | 91127 | Stefano Morozzi | 02/2021 |
9583 | 6^117094-211049 | 91117 | Mike Oakes | 05/2011 |
9584 | 21353^18472+18472^21353 | 91103 | Hans Havermann | 05/2020 |
9586 | 2^302602-1867181 | 91093 | Enzo Doria | 03/2016 |
9585 | 10^91092+56127 | 91093 | Patrick De Geest | 07/2019 |
9587 | 10^91092-9107 | 91092 | Patrick De Geest | 01/2019 |
9588 | (1017*2^302592-1)/53 | 91091 | Lelio R Paula | 04/2015 |
9589 | 15^77445-16 | 91083 | Lelio R Paula | 07/2016 |
9590 | 21656^16053+16053^21656 | 91076 | Hans Havermann | 05/2020 |
9591 | 2^302505+81 | 91064 | Henri Lifchitz | 02/2007 |
9592 | 2^302496-112349 | 91061 | Enzo Doria | 06/2014 |
9593 | (2^302475+1790)/2 | 91054 | Stefano Morozzi | 01/2021 |
9594 | 17^73999-72 | 91052 | Lelio R Paula | 07/2016 |
9595 | 10^91047+9331 | 91048 | Patrick De Geest | 01/2019 |
9596 | 10^91047-671169 | 91047 | Patrick De Geest | 07/2019 |
9597 | 10^91044+2077 | 91045 | Patrick De Geest | 01/2019 |
9598 | 10^91044-136359 | 91044 | Patrick De Geest | 07/2019 |
9599 | 10^91041+9349 | 91042 | Patrick De Geest | 01/2019 |
9600 | 10^91041-7823 | 91041 | Patrick De Geest | 01/2019 |
9601 | 10^91040+4077 | 91041 | Patrick De Geest | 01/2019 |
9602 | 10^91040-119421 | 91040 | Patrick De Geest | 07/2019 |
9603 | 10^91037+2769 | 91038 | Patrick De Geest | 01/2019 |
9604 | 10^91037-22649 | 91037 | Patrick De Geest | 07/2019 |
9605 | (16*10^91032+41)/3 | 91033 | Robert Price | 10/2017 |
9606 | 10^91023+58039 | 91024 | Patrick De Geest | 07/2019 |
9607 | 10^91023-6471 | 91023 | Patrick De Geest | 01/2019 |
9608 | 10^91018+7873 | 91019 | Patrick De Geest | 01/2019 |
9609 | 10^91018-333177 | 91018 | Patrick De Geest | 07/2019 |
9610 | 10^91017+68767 | 91018 | Patrick De Geest | 07/2019 |
9611 | 10^91017-428327 | 91017 | Patrick De Geest | 07/2019 |
9612 | 10^91016+73111 | 91017 | Patrick De Geest | 07/2019 |
9613 | 10^91016-7973 | 91016 | Patrick De Geest | 01/2019 |
9614 | 1949^27666+27666^1949 | 91016 | Norbert Schneider | 04/2020 |
9615 | 2^302332+577294575 | 91012 | Lelio R Paula | 08/2016 |
9616 | 10^91004+9073 | 91005 | Patrick De Geest | 01/2019 |
9617 | 10^91004-491519 | 91004 | Patrick De Geest | 07/2019 |
9618 | 10^91003+74269 | 91004 | Patrick De Geest | 07/2019 |
9619 | 10^91003-3903 | 91003 | Patrick De Geest | 01/2019 |
9620 | 2^302274+74209 | 90994 | Enzo Doria | 04/2016 |
9621 | 10^90991+81147 | 90992 | Patrick De Geest | 07/2019 |
9622 | 10^90991-6279 | 90991 | Patrick De Geest | 01/2019 |
9623 | 10^90983+1393 | 90984 | Patrick De Geest | 01/2019 |
9624 | 11*10^90982+9 | 90984 | Robert Price | 08/2020 |
9625 | 10^90983-562383 | 90983 | Patrick De Geest | 07/2019 |
9626 | (311^36497-1)/310 | 90976 | Eric Chen | 09/2017 |
9627 | (2^302210+1014)/2 | 90974 | Stefano Morozzi | 09/2020 |
9628 | (3^190668+2)/89 | 90970 | Lelio R Paula | 04/2013 |
9629 | 2^302188+90195 | 90968 | Lelio R Paula | 02/2016 |
9630 | (53*10^90965-71)/9 | 90966 | Robert Price | 09/2015 |
9631 | 10^90965+573987 | 90966 | Patrick De Geest | 07/2019 |
9632 | 10^90965-6833 | 90965 | Patrick De Geest | 01/2019 |
9633 | 10^90964+48789 | 90965 | Patrick De Geest | 07/2019 |
9634 | 10^90964-52103 | 90964 | Patrick De Geest | 07/2019 |
9635 | 10^90963+191889 | 90964 | Patrick De Geest | 07/2019 |
9636 | 10^90963-3659 | 90963 | Patrick De Geest | 01/2019 |
9637 | 10^90962+7657 | 90963 | Patrick De Geest | 01/2019 |
9638 | 10^90962-215633 | 90962 | Patrick De Geest | 07/2019 |
9639 | 10^90961+67471 | 90962 | Patrick De Geest | 07/2019 |
9640 | 10^90961-211043 | 90961 | Patrick De Geest | 07/2019 |
9641 | 10^90960+1072117 | 90961 | Patrick De Geest | 07/2019 |
9642 | 10^90959+8791 | 90960 | Patrick De Geest | 01/2019 |
9643 | 10^90960-610659 | 90960 | Patrick De Geest | 07/2019 |
9644 | 10^90959-275213 | 90959 | Patrick De Geest | 07/2019 |
9645 | (2^302129+3110)/2 | 90950 | Stefano Morozzi | 09/2020 |
9647 | 10^90948+9867 | 90949 | Patrick De Geest | 01/2019 |
9646 | 21665^15774+15774^21665 | 90949 | Hans Havermann | 04/2020 |
9648 | 10^90948-109239 | 90948 | Patrick De Geest | 07/2019 |
9649 | 2^302113+74105 | 90946 | Enzo Doria | 04/2016 |
9650 | 2^302102-6555 | 90942 | Lelio R Paula | 02/2016 |
9651 | 10^90930+95223 | 90931 | Patrick De Geest | 07/2019 |
9652 | 10^90930-3623 | 90930 | Patrick De Geest | 01/2019 |
9653 | 156*(10^(4*22731)-1)/101-1 | 90925 | Robert Price | 05/2014 |
9654 | 3^190568+38 | 90925 | Lelio R Paula | 04/2016 |
9655 | 10^90917+179863 | 90918 | Patrick De Geest | 07/2019 |
9656 | 10^90917-6693 | 90917 | Patrick De Geest | 01/2019 |
9657 | 2^302009-16449 | 90914 | Enzo Doria | 04/2013 |
9658 | 10^90908+3181 | 90909 | Patrick De Geest | 01/2019 |
9659 | 10^90908-139511 | 90908 | Patrick De Geest | 07/2019 |
9660 | 10^90904+106947 | 90905 | Patrick De Geest | 07/2019 |
9661 | 10^90904-5169 | 90904 | Patrick De Geest | 01/2019 |
9662 | 10^90903+120963 | 90904 | Patrick De Geest | 07/2019 |
9663 | 10^90902+2613 | 90903 | Patrick De Geest | 01/2019 |
9664 | 10^90903-190737 | 90903 | Patrick De Geest | 07/2019 |
9665 | 25174^4083+4083^25174 | 90903 | Hans Havermann | 08/2020 |
9666 | 10^90902-952329 | 90902 | Patrick De Geest | 07/2019 |
9667 | (17*2^301951-1)/165 | 90896 | Lelio R Paula | 02/2014 |
9668 | 3^190497+74 | 90891 | Lelio R Paula | 04/2016 |
9669 | (24737*2^301896+1)/399 | 90882 | Lelio R Paula | 06/2014 |
9670 | 10^90880+5707 | 90881 | Patrick De Geest | 01/2019 |
9671 | 10^90880-152993 | 90880 | Patrick De Geest | 07/2019 |
9672 | 18^72397+89 | 90878 | Lelio R Paula | 06/2016 |
9673 | (2^301876+762)/2 | 90874 | Stefano Morozzi | 09/2020 |
9674 | 134^42719-133 | 90868 | Norbert Schneider | 03/2019 |
9675 | 6^116769-47 | 90864 | Lelio R Paula | 05/2016 |
9676 | 10^90858+233433 | 90859 | Patrick De Geest | 07/2019 |
9677 | 10^90858-8301 | 90858 | Patrick De Geest | 01/2019 |
9678 | 24298^5483+5483^24298 | 90851 | Hans Havermann | 08/2020 |
9679 | 10^90849+40141 | 90850 | Patrick De Geest | 07/2019 |
9680 | 10^90849-4721 | 90849 | Patrick De Geest | 01/2019 |
9681 | 2^301712-465 | 90825 | Lelio R Paula | 02/2016 |
9682 | 2^301693-69 | 90819 | Lelio R Paula | 11/2012 |
9683 | 2^301683-301683^2 | 90816 | Henri Lifchitz | 05/2005 |
9684 | 10^90807+7279 | 90808 | Patrick De Geest | 01/2019 |
9685 | 10^90807-162263 | 90807 | Patrick De Geest | 07/2019 |
9686 | 6*10^90803+79 | 90804 | Robert Price | 09/2020 |
9687 | 10^90800-6453 | 90800 | Patrick De Geest | 11/2018 |
9688 | 11^87187-1710 | 90796 | Enzo Doria | 12/2012 |
9689 | 5*10^90793+21 | 90794 | Robert Price | 01/2017 |
9690 | (22*10^90792-13)/9 | 90793 | Robert Price | 03/2015 |
9691 | 2^301591-1615 | 90788 | Lelio R Paula | 02/2016 |
9692 | (52^52901+1)/53 | 90777 | Paul Bourdelais | 08/2017 |
9693 | 2^301546-109037 | 90775 | Enzo Doria | 04/2014 |
9694 | 10^90772+4029 | 90773 | Patrick De Geest | 11/2018 |
9695 | 10^90772-36627 | 90772 | Patrick De Geest | 07/2019 |
9696 | 10^90771+67737 | 90772 | Patrick De Geest | 07/2019 |
9697 | 10^90771-441003 | 90771 | Patrick De Geest | 07/2019 |
9698 | 10^90770+28941 | 90771 | Patrick De Geest | 07/2019 |
9699 | 10^90770-431 | 90770 | Patrick De Geest | 11/2018 |
9700 | 14^79195-3 | 90768 | Lelio R Paula | 06/2016 |
9701 | 10^90766+877 | 90767 | Patrick De Geest | 11/2018 |
9702 | 2^301517-1861693 | 90766 | Enzo Doria | 11/2015 |
9703 | 10^90766-109241 | 90766 | Patrick De Geest | 07/2019 |
9704 | 10^90765+485361 | 90766 | Patrick De Geest | 07/2019 |
9705 | 10^90765-4797 | 90765 | Patrick De Geest | 11/2018 |
9706 | 10^90757+7573 | 90758 | Patrick De Geest | 11/2018 |
9707 | 10^90757-554979 | 90757 | Patrick De Geest | 07/2019 |
9708 | 10^90756+438109 | 90757 | Patrick De Geest | 07/2019 |
9709 | 10^90756-8727 | 90756 | Patrick De Geest | 11/2018 |
9710 | 10^90749+823 | 90750 | Patrick De Geest | 11/2018 |
9713 | 2^301460-173 | 90749 | Lelio R Paula | 11/2012 |
9711 | 10^90748+4213 | 90749 | Patrick De Geest | 11/2018 |
9712 | 10^90749-130413 | 90749 | Patrick De Geest | 07/2019 |
9714 | 10^90748-75411 | 90748 | Patrick De Geest | 07/2019 |
9715 | 10^90747+438471 | 90748 | Patrick De Geest | 07/2019 |
9716 | 10^90747-9279 | 90747 | Patrick De Geest | 11/2018 |
9717 | (85*10^90745-103)/9 | 90746 | Robert Price | 10/2017 |
9718 | (2^301439+1206)/2 | 90742 | Stefano Morozzi | 09/2020 |
9719 | 10^90726+4077 | 90727 | Patrick De Geest | 11/2018 |
9720 | 10^90726-504951 | 90726 | Patrick De Geest | 07/2019 |
9722 | 10^90721+181 | 90722 | Patrick De Geest | 11/2018 |
9721 | (2^301372+2722)/2 | 90722 | Stefano Morozzi | 09/2020 |
9723 | 10^90721-177149 | 90721 | Patrick De Geest | 07/2019 |
9724 | (2^301317+1146)/2 | 90706 | Stefano Morozzi | 09/2020 |
9725 | 2^301312-89 | 90704 | Lelio R Paula | 11/2012 |
9726 | 10^90696+6349 | 90697 | Patrick De Geest | 11/2018 |
9727 | 2^301285-129 | 90696 | Lelio R Paula | 11/2012 |
9728 | 10^90696-635049 | 90696 | Patrick De Geest | 07/2019 |
9729 | 2^301282-109991 | 90695 | Enzo Doria | 04/2014 |
9730 | 10^90690+8877 | 90691 | Patrick De Geest | 11/2018 |
9731 | 10^90690-227433 | 90690 | Patrick De Geest | 07/2019 |
9732 | 10^90683+61411 | 90684 | Patrick De Geest | 07/2019 |
9733 | (2^301244+1738)/2 | 90684 | Stefano Morozzi | 09/2020 |
9734 | 10^90683-2577 | 90683 | Patrick De Geest | 11/2018 |
9735 | 2^301228-1854269 | 90679 | Enzo Doria | 09/2015 |
9736 | 10^90674+138453 | 90675 | Patrick De Geest | 10/2022 |
9737 | 10^90674-5000001 | 90674 | Robert Price | 12/2021 |
9738 | 10^90674-59451 | 90674 | Patrick De Geest | 10/2022 |
9740 | (151*10^90669-1)/3 | 90671 | Robert Price | 04/2017 |
9739 | (2^301201+2046)/2 | 90671 | Stefano Morozzi | 09/2020 |
9742 | (32*10^90669+13)/9 | 90670 | Robert Price | 04/2015 |
9741 | 10^90669+9793 | 90670 | Patrick De Geest | 11/2018 |
9743 | 10^90669-223931 | 90669 | Patrick De Geest | 07/2019 |
9744 | (2^301191+2510)/2 | 90668 | Stefano Morozzi | 09/2020 |
9745 | 5*10^90666-63 | 90667 | Robert Price | 04/2021 |
9746 | 10^90665+10989 | 90666 | Patrick De Geest | 07/2019 |
9747 | 10^90665-3087 | 90665 | Patrick De Geest | 11/2018 |
9748 | 2^301177-227713 | 90664 | Harrison Mesh | 06/2022 |
9749 | 10^90662+89637 | 90663 | Patrick De Geest | 07/2019 |
9750 | 10^90662-9519 | 90662 | Patrick De Geest | 11/2018 |