## PRP Records

### Probable Primes Top 10000

#### (293510 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 ? 8751 2^331746-11655 99866 Lelio R Paula 09/2016 8752 11^95891-28 99861 Lelio R Paula 08/2016 8753 (2^331694-5)/11 99849 Lelio R Paula 10/2013 8754 (3^209246+7)/64 99834 Lelio R Paula 09/2013 8755 25062^9617+9617^25062 99823 Hans Havermann 04/2018 8756 15^84866-52 99811 Lelio R Paula 08/2016 8757 13^89600+30 99810 Lelio R Paula 08/2016 8758 2^331527+100280245065 99800 Paul Bourdelais 10/2021 8759 22950^22309+22309^22950 99798 Hans Havermann 03/2018 8760 5^142772-38 99794 Lelio R Paula 08/2016 8761 (7482^25759-1)/7481 99787 Serge Batalov 06/2022 8762 (23*2^331459+1)/475 99778 Lelio R Paula 11/2013 8763 2^331416-331416+1 99767 Robert Price 10/2014 8764 2^331256-57 99718 Lelio R Paula 12/2012 8765 28192^3443+3443^28192 99714 Hans Havermann 03/2018 8766 2^331185+737 99697 Lelio R Paula 01/2013 8767 (4*10^99693+149)/9 99693 Robert Price 03/2017 8768 2^331154+1880527 99688 Enzo Doria 10/2016 8770 (19^77951+1)/20 99679 Paul Bourdelais 03/2010 8769 24354^12385+12385^24354 99679 Hans Havermann 03/2018 8771 2^331110+1870459 99675 Enzo Doria 05/2016 8772 5*2^331075+7 99665 Lelio R Paula 08/2014 8773 25776^7351+7351^25776 99659 Hans Havermann 02/2018 8774 (16*10^99656-31)/3 99657 Robert Price 03/2016 8775 (6059^26347-1)/6058 99652 Serge Batalov 06/2022 8776 (15544^23773-1)/15543 99642 Serge Batalov 06/2022 8778 2^330968+345 99632 Lelio R Paula 09/2016 8777 (2^330969+690)/2 99632 Stefano Morozzi 09/2020 8780 2*5^142528-7 99624 Lelio R Paula 11/2014 8779 2^330942+77329 99624 Enzo Doria 05/2016 8781 14^86914-99 99615 Lelio R Paula 08/2016 8782 (19*2^330902+1)/77 99611 Lelio R Paula 11/2013 8783 22971^21692+21692^22971 99610 Hans Havermann 03/2018 8784 2^330845+71687 99595 Enzo Doria 04/2016 8785 (26667^22501-1)/26666 99585 Serge Batalov 06/2022 8786 (23*2^330770+1)/3 99573 Lelio R Paula 11/2013 8787 24494^11613+11613^24494 99567 Hans Havermann 03/2018 8788 2^330735+8415 99562 Lelio R Paula 09/2016 8789 2^330720+74071 99557 Enzo Doria 04/2016 8790 (10405^24781-1)/10404 99548 Serge Batalov 06/2022 8792 31^66738-2 99531 Lelio R Paula 09/2013 8791 (9002^25171-1)/9001 99531 Serge Batalov 06/2022 8793 (5023^26893-1)/5022 99527 Serge Batalov 06/2022 8794 7*3^208567+4 99513 Lelio R Paula 08/2014 8795 (15881^23689-1)/15880 99511 Serge Batalov 06/2022 8796 (13*10^99508+47)/3 99509 Robert Price 01/2017 8797 2^330553+779 99507 Lelio R Paula 01/2013 8798 15^84606-94 99505 Lelio R Paula 08/2016 8799 (10^99497+173)/3 99497 Robert Price 05/2021 8800 9*10^99493-43 99494 Robert Price 09/2021 8801 6^127858+47 99493 Lelio R Paula 08/2016 8802 5^142337+48 99490 Lelio R Paula 08/2016 8803 7^117724-20 99489 Lelio R Paula 08/2016 8804 (559^36209-1)/558 99479 Serge Batalov 06/2022 8805 (13470^24091-1)/13469 99477 Serge Batalov 06/2022 8806 (29*10^99474-17)/3 99475 Erik Branger 09/2014 8807 (185*10^99466-11)/3 99468 Robert Price 10/2020 8808 (2^330410+2038)/2 99464 Stefano Morozzi 09/2020 8809 (9*2^330407-1)/7 99463 Lelio R Paula 03/2014 8810 (516*32^66077-175)/31 99458 Eric Chen 04/2023 8811 (2863^28771-1)/2862 99453 Serge Batalov 06/2022 8812 (2^330373+2114)/2 99452 Stefano Morozzi 09/2020 8813 (68*10^99441+7)/3 99443 Robert Price 03/2016 8814 10^99434+155571 99435 Patrick De Geest 04/2020 8815 10^99434-123456789 99434 Robert Price 02/2020 8816 10^99434-191237 99434 Patrick De Geest 04/2020 8817 46^59791-45^59791 99418 Jean-Louis Charton 01/2013 8818 23839^14802+14802^23839 99417 Hans Havermann 02/2018 8819 (2*10^99408+529)/9 99408 Robert Price 01/2017 8820 (2^330216+3510)/2 99405 Stefano Morozzi 09/2020 8821 53^57646-2 99398 Lelio R Paula 09/2013 8822 2^330165+1870025 99390 Enzo Doria 05/2016 8823 7*10^99383+97 99384 Robert Price 09/2021 8824 2^330142-155 99383 Lelio R Paula 12/2012 8825 2^330088-115259 99367 Enzo Doria 06/2015 8826 24216^12671+12671^24216 99354 Hans Havermann 01/2018 8827 Phi(200548,10)/3208769 99354 Makoto Kamada 04/2019 8828 (746*10^99303+1)/9 99305 Robert Price 02/2017 8829 3^208107+40 99293 Lelio R Paula 08/2016 8830 2^329843+211343 99293 Enzo Doria 08/2023 8831 (3939^27617-1)/3938 99291 Serge Batalov 06/2022 8832 (5*2^329833-1)/369 99288 Lelio R Paula 02/2014 8833 8*3^208093+5 99287 Lelio R Paula 08/2014 8834 5^142043+56 99284 Lelio R Paula 08/2016 8835 (13*10^99282-157)/9 99283 Robert Price 05/2021 8836 (10^99284+7)/53/67 99281 Alfred Reich 06/2021 8837 22*10^99275+7 99277 Robert Price 04/2016 8838 2^329778+1876189 99274 Enzo Doria 07/2016 8839 (6580^25997-1)/6579 99259 Serge Batalov 06/2022 8840 (2249^29611-1)/2248 99253 Serge Batalov 06/2022 8841 (10^99239-13)/3 99239 Robert Price 02/2017 8842 (1199^32233-1)/1198 99237 Serge Batalov 06/2022 8844 3^207987+62 99236 Lelio R Paula 08/2016 8843 (62*10^99235+91)/9 99236 Robert Price 07/2021 8845 2^329638+49 99231 Lelio R Paula 12/2012 8846 7^117413-18 99226 Lelio R Paula 08/2016 8847 2^329586-458903 99216 Enzo Doria 04/2015 8848 (6290^26119-1)/6289 99214 Serge Batalov 06/2022 8850 2^329553+101 99206 Lelio R Paula 12/2012 8849 (21297^22921-1)/21296 99206 Serge Batalov 06/2022 8851 2^329551-112897 99205 Enzo Doria 06/2014 8852 (3^207925+7)/50 99204 Lelio R Paula 09/2013 8853 6^127458-17993 99182 Enzo Doria 03/2013 8854 27197^4428+4428^27197 99166 Hans Havermann 10/2017 8855 (46*10^99143-1)/9 99144 Robert Price 12/2014 8856 (64*10^99135+161)/9 99136 Robert Price 08/2022 8857 7*10^99133+69 99134 Robert Price 10/2017 8858 (21701^22861-1)/21700 99132 Serge Batalov 06/2022 8859 18^78968-3065 99127 Enzo Doria 03/2013 8861 25927^6654+6654^25927 99122 Hans Havermann 10/2017 8860 87915!4+16 99122 Robert Price 09/2019 8862 2^329259+189 99117 Lelio R Paula 12/2012 8863 8*10^99113+39 99114 Robert Price 01/2017 8864 6^127364+77 99109 Lelio R Paula 08/2016 8865 (82*10^99103+143)/9 99104 Robert Price 06/2021 8866 (11414^24421-1)/11413 99083 Serge Batalov 06/2022 8867 (2^329135+1110)/2 99080 Stefano Morozzi 09/2020 8868 (22089^22807-1)/22088 99074 Serge Batalov 06/2022 8869 (59*10^99069+391)/9 99070 Robert Price 03/2021 8870 (797*10^99061-41)/9 99063 Robert Price 04/2022 8871 2^329058-287681 99057 Harrison Mesh 06/2022 8872 6^127285+13 99047 Lelio R Paula 08/2016 8873 (228581#+235862)/(2^3*11*71*151) 99044 Makoto Morimoto 10/2017 8874 2^329007+73283 99041 Enzo Doria 04/2016 8875 5*3^207543-8 99024 Lelio R Paula 08/2014 8876 (2^328930+570)/2 99018 Stefano Morozzi 09/2020 8877 2^328885+149 99005 Lelio R Paula 12/2012 8879 23392^17075+17075^23392 99004 Hans Havermann 09/2017 8878 (7424^25579-1)/7423 99004 Serge Batalov 06/2022 8880 (2^328879-9)/119 99001 Lelio R Paula 10/2013 8881 5^141618+54 98987 Lelio R Paula 08/2016 8882 8*10^98982+51 98983 Robert Price 05/2017 8883 (21*2^328809-1)/7709 98979 Lelio R Paula 03/2014 8884 2^328794-2797601 98977 Enzo Doria 04/2016 8885 (88331^20011-1)/88330 98972 Serge Batalov 06/2022 8886 6^127176+5 98963 Lelio R Paula 11/2014 8887 2*10^98961-21 98962 Robert Price 09/2020 8888 24262^11989+11989^24262 98960 Hans Havermann 09/2017 8889 (60138^20707-1)/60137 98958 Serge Batalov 06/2022 8890 2^328700-109709 98949 Enzo Doria 04/2014 8891 (2^328698+1810)/2 98948 Stefano Morozzi 01/2021 8892 (1014^32917-1)/1013 98947 Serge Batalov 06/2022 8893 87771!4-128 98944 Robert Price 11/2019 8894 (4576^27031-1)/4575 98943 Serge Batalov 06/2022 8895 (2^328658+3042)/2 98936 Stefano Morozzi 09/2020 8896 (1933^30103-1)/1932 98923 Serge Batalov 06/2022 8897 46711!2-2^46711 98916 Robert Price 09/2015 8898 9*7^117037+4 98909 Lelio R Paula 11/2014 8899 127^47012+126 98905 Norbert Schneider 01/2019 8900 (93826^19891-1)/93825 98900 Serge Batalov 06/2022 8901 (2^328525+1250)/2 98896 Stefano Morozzi 09/2020 8902 (10^98890+149)/3 98890 Serge Batalov 12/2014 8903 22775^21978+21978^22775 98889 Hans Havermann 08/2017 8904 2^328497-216933 98888 Enzo Doria 05/2014 8905 2^328487+32769 98885 Lelio R Paula 08/2016 8906 3^207250-112358 98884 Enzo Doria 06/2014 8907 13^88754-90 98867 Lelio R Paula 08/2016 8908 2^328406+709 98861 Lelio R Paula 02/2013 8909 2*10^98860-21 98861 Robert Price 09/2020 8910 (17*2^328413-1)/16173 98860 Lelio R Paula 03/2014 8911 7^116976+76 98857 Lelio R Paula 08/2016 8912 (2^328378+2710)/2 98852 Stefano Morozzi 09/2020 8913 (25411^22441-1)/25410 98849 Serge Batalov 06/2022 8914 (18668^23143-1)/18667 98842 Serge Batalov 06/2022 8916 2^328335+1155 98839 Lelio R Paula 08/2016 8915 2^328333-349003 98839 Harrison Mesh 06/2022 8918 (3*2^328311+1)/5 98832 Lelio R Paula 11/2013 8917 287^40210+40210^287 98832 Norbert Schneider 11/2014 8919 (2^328284+9)/1325 98821 Lelio R Paula 10/2013 8920 (21*2^328258+1)/2125 98814 Lelio R Paula 11/2013 8921 (28623^22171-1)/28622 98806 Serge Batalov 06/2022 8922 24746^9825+9825^24746 98795 Hans Havermann 07/2020 8923 26620^5143+5143^26620 98793 Hans Havermann 07/2020 8924 65^54491+48 98788 Lelio R Paula 04/2016 8925 3^207042+98 98785 Lelio R Paula 08/2016 8926 (2^328121+3110)/2 98774 Stefano Morozzi 09/2020 8927 10^98754+73383 98755 Patrick De Geest 02/2021 8930 3^206977-112756 98754 Enzo Doria 07/2014 8929 10^98754-40000000001 98754 Robert Price 09/2020 8928 10^98754-169343 98754 Patrick De Geest 02/2021 8931 7^116846-50 98747 Lelio R Paula 08/2016 8932 (19152^23059-1)/19151 98740 Serge Batalov 06/2022 8933 23267^17512+17512^23267 98730 Hans Havermann 04/2020 8934 2^327967-28635 98728 Lelio R Paula 08/2016 8935 707^34642+34642^707 98710 Norbert Schneider 12/2017 8936 (10771^24481-1)/10770 98710 Serge Batalov 06/2022 8937 6^126850-47 98709 Lelio R Paula 08/2016 8938 (2^327886+2170)/2 98704 Stefano Morozzi 09/2020 8939 (22*10^98697+47)/3 98698 Robert Price 06/2021 8940 8*6^126830-7 98694 Lelio R Paula 11/2014 8941 11^94770-270 98693 Enzo Doria 08/2012 8942 (2^327846+3250)/2 98692 Stefano Morozzi 01/2021 8943 2^327832+43 98688 Lelio R Paula 12/2012 8944 2^327795+761 98677 Lelio R Paula 02/2013 8945 (2^327796+1522)/2 98677 Stefano Morozzi 09/2020 8946 10^98669+147411 98670 Patrick De Geest 11/2016 8948 10^98669-9^(98669-1) 98669 Robert Price 05/2016 8947 10^98669-105249 98669 Patrick De Geest 11/2016 8949 (7911^25309-1)/7910 98657 Serge Batalov 06/2022 8950 2^327671-109801 98639 Enzo Doria 04/2014 8951 24398^11037+11037^24398 98638 Hans Havermann 10/2019 8952 5^141090-14 98618 Lelio R Paula 08/2016 8953 20^75799+47 98617 Lelio R Paula 08/2016 8954 (5452^26393-1)/5451 98616 Serge Batalov 06/2022 8955 28101^3226+3226^28101 98597 Hans Havermann 07/2020 8956 2^327515-1017 98592 Lelio R Paula 08/2016 8957 6^126692+97681 98586 Mike Oakes 04/2011 8958 2^327467-741 98578 Lelio R Paula 08/2016 8959 (2947^28411-1)/2946 98566 Serge Batalov 06/2022 8960 22713^21800+21800^22713 98540 Hans Havermann 05/2020 8961 (2^327329+9)/19 98535 Lelio R Paula 10/2013 8962 7^116577-66 98519 Lelio R Paula 08/2016 8963 (3*2^327250+1)/7 98512 Lelio R Paula 11/2013 8964 23220^17479+17479^23220 98512 Hans Havermann 03/2020 8965 (2^327240+3798)/2 98509 Stefano Morozzi 02/2021 8966 (28514^22111-1)/28513 98502 Serge Batalov 06/2022 8967 (19*2^327192+1)/275 98494 Lelio R Paula 11/2013 8968 2^327162-66945 98486 Lelio R Paula 08/2016 8969 30139^1852+1852^30139 98484 Hans Havermann 02/2020 8970 23182^17703+17703^23182 98479 Hans Havermann 01/2020 8971 4*10^98472-3 98473 Erik Branger 11/2013 8972 26167^5794+5794^26167 98466 Hans Havermann 01/2020 8973 (6883*2^327047-1)/77 98453 Lelio R Paula 05/2015 8974 (71*10^98446+1)/9 98447 Serge Batalov 11/2010 8975 (2009^29803-1)/2008 98436 Serge Batalov 06/2022 8976 13^88363+94 98432 Lelio R Paula 08/2016 8977 48^58543-47^58543 98425 Jean-Louis Charton 11/2005 8978 6^126481+41 98422 Lelio R Paula 08/2016 8979 78*10^98413-7 98415 Robert Price 05/2017 8980 22634^22263+22263^22634 98404 Hans Havermann 07/2020 8981 (47*10^98386+241)/9 98387 Robert Price 06/2022 8982 7^116416+46 98383 Lelio R Paula 08/2016 8983 7^116407-24 98376 Lelio R Paula 07/2016 8984 439^37228+37228^439 98374 Norbert Schneider 08/2018 8985 2^326782-1860671 98372 Enzo Doria 03/2016 8986 17^79948+58 98372 Lelio R Paula 08/2016 8987 22499^22602-22602^22499 98368 Norbert Schneider 08/2020 8988 3^206143-98 98356 Lelio R Paula 08/2016 8989 8*5^140705+7 98350 Lelio R Paula 11/2014 8990 (2^326632+1662)/2 98326 Stefano Morozzi 09/2020 8991 (638^35053-1)/637 98315 Serge Batalov 06/2022 8992 2^326585+11 98312 Lelio R Paula 12/2012 8993 2^326582-459161 98311 Enzo Doria 05/2015 8994 (1266^31687-1)/1265 98304 Serge Batalov 06/2022 8996 (2^326548+9)/5 98301 Lelio R Paula 10/2013 8995 (2^326549+18)/10 98301 Stefano Morozzi 03/2020 8997 2^326538+71659 98298 Enzo Doria 04/2016 8998 (2^326520+2082)/2 98293 Stefano Morozzi 09/2020 8999 (2^326521+1002)/2 98293 Stefano Morozzi 09/2020 9000 15^83575-58 98292 Lelio R Paula 08/2016

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 29 2023 15:19 (Time in France)

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