## PRP Records

### Probable Primes Top 10000

#### (295829 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 ? 9751 23*31^66974+2970 99884 Eric Chen 04/2024 9752 2^331746-11655 99866 Lelio R Paula 09/2016 9753 11^95891-28 99861 Lelio R Paula 08/2016 9754 (2^331694-5)/11 99849 Lelio R Paula 10/2013 9755 (3^209246+7)/64 99834 Lelio R Paula 09/2013 9756 25062^9617+9617^25062 99823 Hans Havermann 04/2018 9757 15^84866-52 99811 Lelio R Paula 08/2016 9758 13^89600+30 99810 Lelio R Paula 08/2016 9759 2^331527+100280245065 99800 Paul Bourdelais 10/2021 9760 22950^22309+22309^22950 99798 Hans Havermann 03/2018 9761 5^142772-38 99794 Lelio R Paula 08/2016 9762 (7482^25759-1)/7481 99787 Serge Batalov 06/2022 9763 (23*2^331459+1)/475 99778 Lelio R Paula 11/2013 9764 2^331416-331416+1 99767 Robert Price 10/2014 9765 2^331256-57 99718 Lelio R Paula 12/2012 9766 28192^3443+3443^28192 99714 Hans Havermann 03/2018 9767 2^331185+737 99697 Lelio R Paula 01/2013 9768 (4*10^99693+149)/9 99693 Robert Price 03/2017 9769 2^331154+1880527 99688 Enzo Doria 10/2016 9771 (19^77951+1)/20 99679 Paul Bourdelais 03/2010 9770 24354^12385+12385^24354 99679 Hans Havermann 03/2018 9772 2^331110+1870459 99675 Enzo Doria 05/2016 9773 5*2^331075+7 99665 Lelio R Paula 08/2014 9774 25776^7351+7351^25776 99659 Hans Havermann 02/2018 9775 (16*10^99656-31)/3 99657 Robert Price 03/2016 9776 (6059^26347-1)/6058 99652 Serge Batalov 06/2022 9777 (15544^23773-1)/15543 99642 Serge Batalov 06/2022 9779 2^330968+345 99632 Lelio R Paula 09/2016 9778 (2^330969+690)/2 99632 Stefano Morozzi 09/2020 9781 2*5^142528-7 99624 Lelio R Paula 11/2014 9780 2^330942+77329 99624 Enzo Doria 05/2016 9782 14^86914-99 99615 Lelio R Paula 08/2016 9783 (19*2^330902+1)/77 99611 Lelio R Paula 11/2013 9784 22971^21692+21692^22971 99610 Hans Havermann 03/2018 9785 2^330845+71687 99595 Enzo Doria 04/2016 9786 (26667^22501-1)/26666 99585 Serge Batalov 06/2022 9787 (23*2^330770+1)/3 99573 Lelio R Paula 11/2013 9788 24494^11613+11613^24494 99567 Hans Havermann 03/2018 9789 2^330735+8415 99562 Lelio R Paula 09/2016 9790 2^330720+74071 99557 Enzo Doria 04/2016 9791 (10405^24781-1)/10404 99548 Serge Batalov 06/2022 9793 31^66738-2 99531 Lelio R Paula 09/2013 9792 (9002^25171-1)/9001 99531 Serge Batalov 06/2022 9794 (5023^26893-1)/5022 99527 Serge Batalov 06/2022 9795 7*3^208567+4 99513 Lelio R Paula 08/2014 9796 (15881^23689-1)/15880 99511 Serge Batalov 06/2022 9797 (13*10^99508+47)/3 99509 Robert Price 01/2017 9798 2^330553+779 99507 Lelio R Paula 01/2013 9799 15^84606-94 99505 Lelio R Paula 08/2016 9800 (10^99497+173)/3 99497 Robert Price 05/2021 9801 9*10^99493-43 99494 Robert Price 09/2021 9802 6^127858+47 99493 Lelio R Paula 08/2016 9803 5^142337+48 99490 Lelio R Paula 08/2016 9804 7^117724-20 99489 Lelio R Paula 08/2016 9805 (559^36209-1)/558 99479 Serge Batalov 06/2022 9806 (13470^24091-1)/13469 99477 Serge Batalov 06/2022 9807 (29*10^99474-17)/3 99475 Erik Branger 09/2014 9808 (185*10^99466-11)/3 99468 Robert Price 10/2020 9809 (2^330410+2038)/2 99464 Stefano Morozzi 09/2020 9810 (9*2^330407-1)/7 99463 Lelio R Paula 03/2014 9811 (516*32^66077-175)/31 99458 Eric Chen 04/2023 9812 (2863^28771-1)/2862 99453 Serge Batalov 06/2022 9813 (2^330373+2114)/2 99452 Stefano Morozzi 09/2020 9814 179^44142-44142^179 99446 Norman Luhn 08/2024 9815 (68*10^99441+7)/3 99443 Robert Price 03/2016 9816 10^99434+155571 99435 Patrick De Geest 04/2020 9817 10^99434-123456789 99434 Robert Price 02/2020 9818 10^99434-191237 99434 Patrick De Geest 04/2020 9819 46^59791-45^59791 99418 Jean-Louis Charton 01/2013 9820 23839^14802+14802^23839 99417 Hans Havermann 02/2018 9821 (2*10^99408+529)/9 99408 Robert Price 01/2017 9822 (2^330216+3510)/2 99405 Stefano Morozzi 09/2020 9823 53^57646-2 99398 Lelio R Paula 09/2013 9824 2^330165+1870025 99390 Enzo Doria 05/2016 9825 7*10^99383+97 99384 Robert Price 09/2021 9826 2^330142-155 99383 Lelio R Paula 12/2012 9827 2^330088-115259 99367 Enzo Doria 06/2015 9828 24216^12671+12671^24216 99354 Hans Havermann 01/2018 9829 Phi(200548,10)/3208769 99354 Makoto Kamada 04/2019 9830 (746*10^99303+1)/9 99305 Robert Price 02/2017 9831 3^208107+40 99293 Lelio R Paula 08/2016 9832 2^329843+211343 99293 Enzo Doria 08/2023 9833 (3939^27617-1)/3938 99291 Serge Batalov 06/2022 9834 (5*2^329833-1)/369 99288 Lelio R Paula 02/2014 9835 8*3^208093+5 99287 Lelio R Paula 08/2014 9836 5^142043+56 99284 Lelio R Paula 08/2016 9837 (13*10^99282-157)/9 99283 Robert Price 05/2021 9838 (10^99284+7)/53/67 99281 Alfred Reich 06/2021 9839 22*10^99275+7 99277 Robert Price 04/2016 9840 2^329778+1876189 99274 Enzo Doria 07/2016 9841 (149557^19321-1)/(149557^139-1) 99264 Ryan Propper 11/2023 9842 (6580^25997-1)/6579 99259 Serge Batalov 06/2022 9843 (2249^29611-1)/2248 99253 Serge Batalov 06/2022 9844 (10^99239-13)/3 99239 Robert Price 02/2017 9845 (1199^32233-1)/1198 99237 Serge Batalov 06/2022 9847 3^207987+62 99236 Lelio R Paula 08/2016 9846 (62*10^99235+91)/9 99236 Robert Price 07/2021 9848 2^329638+49 99231 Lelio R Paula 12/2012 9849 7^117413-18 99226 Lelio R Paula 08/2016 9850 2^329586-458903 99216 Enzo Doria 04/2015 9851 (6290^26119-1)/6289 99214 Serge Batalov 06/2022 9853 2^329553+101 99206 Lelio R Paula 12/2012 9852 (21297^22921-1)/21296 99206 Serge Batalov 06/2022 9854 2^329551-112897 99205 Enzo Doria 06/2014 9855 (3^207925+7)/50 99204 Lelio R Paula 09/2013 9856 U(477331)/57279721 99202 Serge Batalov 07/2024 9857 6^127458-17993 99182 Enzo Doria 03/2013 9858 27197^4428+4428^27197 99166 Hans Havermann 10/2017 9859 (46*10^99143-1)/9 99144 Robert Price 12/2014 9860 (64*10^99135+161)/9 99136 Robert Price 08/2022 9861 7*10^99133+69 99134 Robert Price 10/2017 9862 (21701^22861-1)/21700 99132 Serge Batalov 06/2022 9863 18^78968-3065 99127 Enzo Doria 03/2013 9864 25927^6654+6654^25927 99122 Hans Havermann 10/2017 9865 87915!4+16 99122 Robert Price 09/2019 9866 2^329259+189 99117 Lelio R Paula 12/2012 9867 8*10^99113+39 99114 Robert Price 01/2017 9868 6^127364+77 99109 Lelio R Paula 08/2016 9869 (82*10^99103+143)/9 99104 Robert Price 06/2021 9870 (11414^24421-1)/11413 99083 Serge Batalov 06/2022 9871 (2^329135+1110)/2 99080 Stefano Morozzi 09/2020 9872 (22089^22807-1)/22088 99074 Serge Batalov 06/2022 9873 (59*10^99069+391)/9 99070 Robert Price 03/2021 9874 (797*10^99061-41)/9 99063 Robert Price 04/2022 9875 2^329058-287681 99057 Harrison Mesh 06/2022 9876 6^127285+13 99047 Lelio R Paula 08/2016 9877 (228581#+235862)/(2^3*11*71*151) 99044 Makoto Morimoto 10/2017 9878 2^329007+73283 99041 Enzo Doria 04/2016 9879 (145413^19321-1)/(145413^139-1) 99030 Ryan Propper 11/2023 9880 5*3^207543-8 99024 Lelio R Paula 08/2014 9881 (2^328930+570)/2 99018 Stefano Morozzi 09/2020 9882 2^328885+149 99005 Lelio R Paula 12/2012 9883 23392^17075+17075^23392 99004 Hans Havermann 09/2017 9884 (7424^25579-1)/7423 99004 Serge Batalov 06/2022 9885 (2^328879-9)/119 99001 Lelio R Paula 10/2013 9886 140^46129-46129^140 98999 Norman Luhn 08/2024 9887 169^44432-44432^169 98990 Norman Luhn 08/2024 9888 5^141618+54 98987 Lelio R Paula 08/2016 9889 2^328824+24391 98986 Enzo Doria 10/2023 9890 8*10^98982+51 98983 Robert Price 05/2017 9891 (21*2^328809-1)/7709 98979 Lelio R Paula 03/2014 9892 2^328794-2797601 98977 Enzo Doria 04/2016 9893 (88331^20011-1)/88330 98972 Serge Batalov 06/2022 9894 6^127176+5 98963 Lelio R Paula 11/2014 9895 2*10^98961-21 98962 Robert Price 09/2020 9896 24262^11989+11989^24262 98960 Hans Havermann 09/2017 9897 (60138^20707-1)/60137 98958 Serge Batalov 06/2022 9898 2^328700-109709 98949 Enzo Doria 04/2014 9899 (2^328698+1810)/2 98948 Stefano Morozzi 01/2021 9900 (1014^32917-1)/1013 98947 Serge Batalov 06/2022 9901 87771!4-128 98944 Robert Price 11/2019 9902 (4576^27031-1)/4575 98943 Serge Batalov 06/2022 9903 (2^328658+3042)/2 98936 Stefano Morozzi 09/2020 9904 (1933^30103-1)/1932 98923 Serge Batalov 06/2022 9905 46711!2-2^46711 98916 Robert Price 09/2015 9906 9*7^117037+4 98909 Lelio R Paula 11/2014 9907 127^47012+126 98905 Norbert Schneider 01/2019 9908 (93826^19891-1)/93825 98900 Serge Batalov 06/2022 9910 (2^328525+1250)/2 98896 Stefano Morozzi 09/2020 9909 2^328524+625 98896 Henri Lifchitz 09/2024 9911 (10^98890+149)/3 98890 Serge Batalov 12/2014 9912 22775^21978+21978^22775 98889 Hans Havermann 08/2017 9913 2^328497-216933 98888 Enzo Doria 05/2014 9914 2^328487+32769 98885 Lelio R Paula 08/2016 9915 3^207250-112358 98884 Enzo Doria 06/2014 9916 13^88754-90 98867 Lelio R Paula 08/2016 9917 2^328406+709 98861 Lelio R Paula 02/2013 9918 2*10^98860-21 98861 Robert Price 09/2020 9919 (17*2^328413-1)/16173 98860 Lelio R Paula 03/2014 9920 7^116976+76 98857 Lelio R Paula 08/2016 9921 (2^328378+2710)/2 98852 Stefano Morozzi 09/2020 9922 (25411^22441-1)/25410 98849 Serge Batalov 06/2022 9923 (18668^23143-1)/18667 98842 Serge Batalov 06/2022 9925 2^328335+1155 98839 Lelio R Paula 08/2016 9924 2^328333-349003 98839 Harrison Mesh 06/2022 9927 (3*2^328311+1)/5 98832 Lelio R Paula 11/2013 9926 287^40210+40210^287 98832 Norbert Schneider 11/2014 9928 (2^328284+9)/1325 98821 Lelio R Paula 10/2013 9929 (21*2^328258+1)/2125 98814 Lelio R Paula 11/2013 9930 (28623^22171-1)/28622 98806 Serge Batalov 06/2022 9931 24746^9825+9825^24746 98795 Hans Havermann 07/2020 9932 26620^5143+5143^26620 98793 Hans Havermann 07/2020 9933 65^54491+48 98788 Lelio R Paula 04/2016 9934 3^207042+98 98785 Lelio R Paula 08/2016 9935 (2^328121+3110)/2 98774 Stefano Morozzi 09/2020 9936 10^98754+73383 98755 Patrick De Geest 02/2021 9939 3^206977-112756 98754 Enzo Doria 07/2014 9938 10^98754-40000000001 98754 Robert Price 09/2020 9937 10^98754-169343 98754 Patrick De Geest 02/2021 9940 7^116846-50 98747 Lelio R Paula 08/2016 9941 (19152^23059-1)/19151 98740 Serge Batalov 06/2022 9942 23267^17512+17512^23267 98730 Hans Havermann 04/2020 9943 2^327967-28635 98728 Lelio R Paula 08/2016 9944 707^34642+34642^707 98710 Norbert Schneider 12/2017 9945 (10771^24481-1)/10770 98710 Serge Batalov 06/2022 9946 6^126850-47 98709 Lelio R Paula 08/2016 9947 (2^327886+2170)/2 98704 Stefano Morozzi 09/2020 9948 (22*10^98697+47)/3 98698 Robert Price 06/2021 9949 (139706^19321-1)/(139706^139-1) 98696 Ryan Propper 11/2023 9950 8*6^126830-7 98694 Lelio R Paula 11/2014 9951 11^94770-270 98693 Enzo Doria 08/2012 9952 (2^327846+3250)/2 98692 Stefano Morozzi 01/2021 9953 2^327832+43 98688 Lelio R Paula 12/2012 9954 2^327795+761 98677 Lelio R Paula 02/2013 9955 (2^327796+1522)/2 98677 Stefano Morozzi 09/2020 9956 10^98669+147411 98670 Patrick De Geest 11/2016 9958 10^98669-9^(98669-1) 98669 Robert Price 05/2016 9957 10^98669-105249 98669 Patrick De Geest 11/2016 9959 (7911^25309-1)/7910 98657 Serge Batalov 06/2022 9960 2^327671-109801 98639 Enzo Doria 04/2014 9961 24398^11037+11037^24398 98638 Hans Havermann 10/2019 9962 5^141090-14 98618 Lelio R Paula 08/2016 9963 20^75799+47 98617 Lelio R Paula 08/2016 9964 (5452^26393-1)/5451 98616 Serge Batalov 06/2022 9965 28101^3226+3226^28101 98597 Hans Havermann 07/2020 9966 2^327515-1017 98592 Lelio R Paula 08/2016 9967 6^126692+97681 98586 Mike Oakes 04/2011 9968 2^327467-741 98578 Lelio R Paula 08/2016 9969 (2947^28411-1)/2946 98566 Serge Batalov 06/2022 9970 22713^21800+21800^22713 98540 Hans Havermann 05/2020 9971 (2^327329+9)/19 98535 Lelio R Paula 10/2013 9972 7^116577-66 98519 Lelio R Paula 08/2016 9973 (3*2^327250+1)/7 98512 Lelio R Paula 11/2013 9974 23220^17479+17479^23220 98512 Hans Havermann 03/2020 9975 (2^327240+3798)/2 98509 Stefano Morozzi 02/2021 9976 (28514^22111-1)/28513 98502 Serge Batalov 06/2022 9977 (19*2^327192+1)/275 98494 Lelio R Paula 11/2013 9978 2^327162-66945 98486 Lelio R Paula 08/2016 9979 30139^1852+1852^30139 98484 Hans Havermann 02/2020 9980 23182^17703+17703^23182 98479 Hans Havermann 01/2020 9981 4*10^98472-3 98473 Erik Branger 11/2013 9982 26167^5794+5794^26167 98466 Hans Havermann 01/2020 9983 (6883*2^327047-1)/77 98453 Lelio R Paula 05/2015 9984 (71*10^98446+1)/9 98447 Serge Batalov 11/2010 9985 (2009^29803-1)/2008 98436 Serge Batalov 06/2022 9986 13^88363+94 98432 Lelio R Paula 08/2016 9987 48^58543-47^58543 98425 Jean-Louis Charton 11/2005 9988 6^126481+41 98422 Lelio R Paula 08/2016 9989 78*10^98413-7 98415 Robert Price 05/2017 9990 22634^22263+22263^22634 98404 Hans Havermann 07/2020 9991 (47*10^98386+241)/9 98387 Robert Price 06/2022 9992 7^116416+46 98383 Lelio R Paula 08/2016 9993 7^116407-24 98376 Lelio R Paula 07/2016 9994 439^37228+37228^439 98374 Norbert Schneider 08/2018 9995 2^326782-1860671 98372 Enzo Doria 03/2016 9996 17^79948+58 98372 Lelio R Paula 08/2016 9997 22499^22602-22602^22499 98368 Norbert Schneider 08/2020 9998 3^206143-98 98356 Lelio R Paula 08/2016 9999 8*5^140705+7 98350 Lelio R Paula 11/2014 10000 (2^326632+1662)/2 98326 Stefano Morozzi 09/2020

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 18 2024 11:41 (Time in France)

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