## PRP Records

### Probable Primes Top 10000

#### (294113 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 ? 9751 (24728^21751-1)/24727 95552 Serge Batalov 06/2022 9752 (49764^20341-1)/49763 95536 Serge Batalov 06/2022 9753 (36155^20959-1)/36154 95531 Serge Batalov 06/2022 9754 (7725^24571-1)/7724 95526 Serge Batalov 06/2022 9755 (20546^22147-1)/20545 95510 Serge Batalov 06/2022 9756 2^317251+465 95503 Lelio R Paula 03/2016 9757 19^74684+58 95503 Lelio R Paula 06/2016 9758 (2^317250-7)/339 95500 Lelio R Paula 07/2013 9759 5*10^95498-21 95499 Robert Price 12/2021 9760 (21615^22031-1)/21614 95495 Serge Batalov 06/2022 9761 6^122718-79 95494 Lelio R Paula 05/2016 9762 22168^20291+20291^22168 95485 Hans Havermann 10/2019 9763 (77427^19531-1)/77426 95481 Serge Batalov 06/2022 9764 (13026^23203-1)/13025 95472 Serge Batalov 06/2022 9765 2^317141-110491 95469 Enzo Doria 05/2014 9766 (2^317097+3014)/2 95456 Stefano Morozzi 09/2020 9767 2^317094+76309 95455 Enzo Doria 05/2016 9768 2^317085+95 95453 Lelio R Paula 11/2012 9769 (17*10^95451-377)/9 95452 Robert Price 11/2017 9770 2^317057-109551 95444 Enzo Doria 04/2014 9771 3^200026+28 95437 Lelio R Paula 05/2016 9772 2^317024+93 95434 Donovan Johnson 06/2008 9773 (86*10^95428-437)/9 95429 Robert Price 03/2021 9774 10^95427+192591 95428 Patrick De Geest 05/2021 9777 2^316999+1605 95427 Lelio R Paula 03/2016 9776 (2^317000+3210)/2 95427 Stefano Morozzi 09/2020 9775 10^95427-10001 95427 Robert Price 02/2021 9778 2^316995-110427 95426 Enzo Doria 05/2014 9779 (69841^19699-1)/69840 95420 Serge Batalov 06/2022 9780 (59242^19993-1)/59241 95415 Serge Batalov 06/2022 9782 22300^18987+18987^22300 95410 Hans Havermann 06/2020 9781 (9478^23993-1)/9477 95410 Serge Batalov 06/2022 9784 2^316937+177 95408 Lelio R Paula 11/2012 9783 4*10^95407+91 95408 Robert Price 11/2017 9785 (94085^19321-1)/(94085^139-1) 95403 Ryan Propper 11/2023 9786 2^316908+1915 95399 Lelio R Paula 03/2016 9787 2^316894+99 95395 Lelio R Paula 11/2012 9788 (2^316887+2546)/2 95393 Stefano Morozzi 09/2020 9789 2*10^95374-21 95375 Robert Price 09/2020 9790 6^122547+11 95361 Lelio R Paula 05/2016 9791 2^316771+82875 95358 Lelio R Paula 03/2016 9792 (15609^22741-1)/15608 95358 Serge Batalov 06/2022 9793 (2^316765+3102)/2 95356 Stefano Morozzi 09/2020 9794 (2267^28411-1)/2266 95329 Serge Batalov 06/2022 9795 (824^32693-1)/823 95328 Serge Batalov 06/2022 9796 (23*10^95326+1)/3 95327 Serge Batalov 05/2009 9797 1*10^95326+57 95327 Robert Price 03/2011 9798 10^95326-393687 95326 Patrick De Geest 09/2013 9799 (3^199803+4)/479539 95325 Lelio R Paula 04/2013 9800 2^316654-109481 95323 Enzo Doria 04/2014 9801 8*10^95316+51 95317 Robert Price 05/2017 9802 (50^56099+43^56099)/93 95309 Serge Batalov 12/2016 9803 (23*2^316559+1)/3925 95292 Lelio R Paula 09/2013 9804 (71*10^95277-539)/9 95278 Robert Price 11/2017 9805 23422^11691+11691^23422 95278 Hans Havermann 10/2019 9806 19^74503-56 95271 Lelio R Paula 06/2016 9807 (5038^25733-1)/5037 95267 Serge Batalov 06/2022 9808 11^91475-4380 95262 Enzo Doria 01/2013 9809 (62*10^95251-611)/9 95252 Robert Price 05/2017 9810 (160090^18301-1)/160089 95240 Serge Batalov 06/2022 9811 (173205^18181-1)/173204 95238 Serge Batalov 06/2022 9812 (158710^18313-1)/158709 95234 Serge Batalov 06/2022 9813 (9979^23813-1)/9978 95227 Serge Batalov 06/2022 9814 (57376^20011-1)/57375 95223 Serge Batalov 06/2022 9815 (2^316321-509203)/69377 95218 Lelio R Paula 06/2013 9816 26541^3868+3868^26541 95216 Hans Havermann 07/2020 9817 (79*10^95214-43)/9 95215 Erik Branger 11/2013 9818 (7176^24691-1)/7175 95202 Anonymous 11/2020 9819 (9*2^316233-1)/1751 95194 Lelio R Paula 02/2014 9820 5*2^316213+9 95191 Lelio R Paula 08/2014 9821 2*10^95188-91 95189 Robert Price 04/2020 9822 2^316205-1848163 95188 Enzo Doria 07/2015 9823 2^316185-2787913 95182 Enzo Doria 04/2016 9824 (2^316174+3538)/2 95178 Stefano Morozzi 09/2020 9825 (9787*2^316142-1)/3 95172 Lelio R Paula 04/2015 9826 2^316140-5 95168 Henri Lifchitz 02/2006 9827 (15185*2^316117-1)/3 95165 Lelio R Paula 04/2015 9828 (34*10^95153-7)/9/19/19157 95149 Makoto Morimoto 05/2016 9829 2^316069+76817 95147 Enzo Doria 05/2016 9830 (199*10^95134-7)/3 95136 Robert Price 02/2017 9831 2^316027-97305 95134 Lelio R Paula 03/2016 9832 2^316006-2798051 95128 Enzo Doria 04/2016 9833 24994^6397+6397^24994 95127 Hans Havermann 02/2020 9835 2^315921-2797603 95102 Enzo Doria 04/2016 9834 (2^315921+1314)/2 95102 Stefano Morozzi 02/2021 9836 2*10^95095+63 95096 Robert Price 10/2017 9837 2^315857+1299 95083 Lelio R Paula 03/2016 9838 (2^315858+2598)/2 95083 Stefano Morozzi 09/2020 9840 14^82955-43 95078 Lelio R Paula 06/2016 9839 (8*10^95078-269)/9 95078 Robert Price 09/2021 9841 (23*10^95074-101)/3 95075 Robert Price 04/2021 9842 2^315827-933075 95074 Paul Bourdelais 04/2021 9843 (2*10^95072-17)/3 95072 Robert Price 08/2014 9844 (286*10^95059-1)/3 95061 Robert Price 11/2020 9845 (2^315779+1610)/2 95059 Stefano Morozzi 09/2020 9846 2^315775-111546435 95058 Paul Bourdelais 10/2021 9847 21938^21513+21513^21938 95051 Hans Havermann 09/2020 9848 2^315727+65 95044 Lelio R Paula 11/2012 9849 2^315725+1885757 95043 Enzo Doria 03/2017 9850 10^(2*47509+1)-10^47509-1 95019 Robert Price 07/2023 9851 23277^12058+12058^23277 95000 Hans Havermann 09/2020 9852 1*10^94983+21 94984 Robert Price 03/2011 9853 10^94983-717 94983 Patrick De Geest 08/2013 9854 17^77187-82 94975 Lelio R Paula 07/2016 9855 3*10^94964+37 94965 Robert Price 10/2017 9856 (2^315481-1017)/20627285 94962 Lelio R Paula 06/2013 9857 2^315423-110329 94952 Enzo Doria 05/2014 9858 2^315420+3493 94951 Riley Fisher 08/2023 9859 11^91169-7230 94943 Enzo Doria 02/2013 9860 7*10^94938+61 94939 Robert Price 02/2017 9861 2^315351+1025 94931 Lelio R Paula 03/2016 9862 2^315350-112253 94930 Enzo Doria 06/2014 9863 (2^315343+1766)/2 94928 Stefano Morozzi 09/2020 9864 (2^315343+3066)/2 94928 Stefano Morozzi 09/2020 9866 ((1001327^(15817)+1)/1001328) 94906 Faysal YAtim 10/2010 9865 2^315268+7 94906 Lelio R Paula 10/2012 9867 11^91133+62 94906 Lelio R Paula 05/2016 9868 (2^315264+1558)/2 94904 Stefano Morozzi 09/2020 9869 30^64244+41 94897 Lelio R Paula 08/2012 9870 (151*10^94885-7)/9 94887 Robert Price 07/2017 9871 fibonacci(453998)+2 94880 Jon Grantham 08/2023 9872 4^157583+22147 94875 Mike Oakes 01/2011 9873 (14*32^63026-190819)/31 94864 Eric Chen 04/2023 9874 2^315123+20513 94862 Enzo Doria 07/2023 9875 2^315098+123 94854 Lelio R Paula 11/2012 9876 3^198791-34 94848 Robert Price 11/2013 9877 3*2^315067+7 94846 Lelio R Paula 08/2014 9878 (9*2^315057+1)/73 94841 Lelio R Paula 09/2013 9879 22576^15875+15875^22576 94836 Hans Havermann 09/2020 9880 (16*10^94822+53)/3 94823 Robert Price 12/2016 9881 8*6^121849-7 94818 Lelio R Paula 10/2014 9882 (85*10^94802+473)/9 94803 Robert Price 03/2017 9883 21767^21852-21852^21767 94790 Norbert Schneider 06/2020 9884 (2*34^61893-647)/3 94788 Eric Chen 03/2023 9885 2^314870-108761 94786 Enzo Doria 03/2014 9886 5*2^314841-3 94778 Lelio R Paula 08/2014 9888 (2^314842+550)/2 94777 Stefano Morozzi 09/2020 9887 11738^23289-23289^11738 94777 Norbert Schneider 05/2022 9889 (2^314787+2630)/2 94761 Stefano Morozzi 09/2020 9890 6^121772+113 94758 Lelio R Paula 05/2016 9891 (19812^22201-1)/(19812^149-1) 94756 Ryan Propper 11/2023 9892 2^314751+221873 94750 Enzo Doria 09/2023 9893 (2^314740+3642)/2 94746 Stefano Morozzi 09/2020 9894 6^121756-16253 94745 Enzo Doria 02/2013 9895 (5*25^67773-2267)/6 94743 Eric Chen 04/2023 9896 2^314718-112793 94740 Enzo Doria 06/2014 9897 2^314697-1847293 94734 Enzo Doria 07/2015 9898 22836^14065+14065^22836 94727 Hans Havermann 09/2020 9899 2^314548-249 94689 Yves Minet 02/2012 9900 5^135469+42 94689 Lelio R Paula 04/2016 9901 2^314545+22697 94688 Enzo Doria 09/2023 9902 gcd(V(1137755),5*F(227551)*(F(227551)-1)+1) 94676 Serge Batalov 04/2015 9903 25773^4712+4712^25773 94670 Hans Havermann 08/2020 9904 (2^314485+3614)/2 94670 Stefano Morozzi 09/2020 9905 (2*10^94604+547)/9 94604 Robert Price 10/2017 9906 (2^314164+2562)/2 94573 Stefano Morozzi 09/2020 9907 3*2^314152+5 94570 Lelio R Paula 08/2014 9908 2*6^121530-5 94570 Lelio R Paula 10/2014 9909 7*10^94563+87 94564 Robert Price 11/2016 9910 2^314114-109677 94558 Enzo Doria 04/2014 9911 (218389#+240867)/(3*11*811) 94557 Makoto Morimoto 10/2017 9912 2^314059+76583 94542 Enzo Doria 05/2016 9913 2^314041-4035 94536 Lelio R Paula 03/2016 9914 (2^314028+3102)/2 94532 Stefano Morozzi 09/2020 9915 (807*33^62250-7)/32 94529 Eric Chen 05/2023 9916 (2^314012+618)/2 94527 Stefano Morozzi 09/2020 9917 (7*2^314003-11)/15 94524 Renaud Lifchitz 03/2011 9918 11^90760-4710 94517 Enzo Doria 01/2013 9919 21675^21796+21796^21675 94507 Norbert Schneider 04/2020 9920 2^313942+100280245065 94506 Paul Bourdelais 10/2021 9921 (457829*27^66017-385)/26 94499 Eric Chen 02/2023 9922 (7*2^313926-1)/148821 94497 Lelio R Paula 02/2014 9923 94*10^94493-3 94495 Robert Price 11/2016 9924 (1000547^15749+1)/1000548 94492 Faysal YAtim 12/2008 9925 (2^313859+2706)/2 94481 Stefano Morozzi 09/2020 9926 (F(3*75345)^2+L(3*75345)^2)/4 94477 Henri Lifchitz 10/2017 9927 7^111792-32 94476 Lelio R Paula 04/2016 9928 (2^313800+822)/2 94463 Stefano Morozzi 01/2021 9929 9*10^94462-47 94463 Robert Price 11/2021 9930 11*10^94460+3 94462 Robert Price 07/2021 9931 (202*10^94441-1)/3 94443 Robert Price 05/2020 9932 11^90680-5850 94434 Enzo Doria 01/2013 9933 (752^32833-1)/751 94432 Michael Stocker 05/2020 9934 2^313675-110125 94426 Enzo Doria 04/2014 9935 (2999*29^64556-2427)/4 94410 Curtis Bright 05/2015 9936 2^313609-112225 94406 Enzo Doria 06/2014 9937 2^313584+72901 94399 Enzo Doria 04/2016 9938 (2^313567+1310)/2 94393 Stefano Morozzi 02/2021 9939 (2^313562+730)/2 94392 Stefano Morozzi 09/2020 9940 2^313510-112865 94376 Enzo Doria 06/2014 9941 7*10^94373+87 94374 Robert Price 11/2016 9942 (9^98897+8^98897)/17 94371 Robert Price 12/2012 9943 2^313453-114703 94359 Enzo Doria 04/2015 9944 8*10^94357-51 94358 Robert Price 10/2017 9945 25903^4392+4392^25903 94356 Hans Havermann 09/2020 9946 31706^945+945^31706 94340 Hans Havermann 09/2020 9947 (379*10^94337-1)/9 94339 Robert Price 08/2017 9948 2^313344-313344+1 94326 Robert Price 10/2014 9949 (2^313313+3662)/2 94317 Stefano Morozzi 09/2020 9950 20^72481-49 94300 Lelio R Paula 05/2016 9951 (34*10^94293-259)/9 94294 Robert Price 12/2021 9952 44725!2+128 94289 Robert Price 03/2015 9953 4*10^94286+9 94287 Robert Price 05/2015 9954 17^76621+24 94279 Lelio R Paula 07/2016 9955 26274^3875+3875^26274 94279 Hans Havermann 09/2020 9956 4*10^94270-33 94271 Robert Price 04/2021 9957 2^313156-112859 94270 Enzo Doria 06/2014 9958 (49*10^94262-211)/9 94263 Robert Price 06/2022 9959 6^121130-59 94258 Lelio R Paula 05/2016 9960 3^197542+28 94252 Robert Price 11/2013 9961 (2^313076+3550)/2 94245 Stefano Morozzi 09/2020 9962 (81822^19321-1)/(81822^139-1) 94239 Ryan Propper 11/2023 9963 (3^197521+2)/51655 94237 Lelio R Paula 04/2013 9964 2^313045-5955 94236 Lelio R Paula 03/2016 9965 22099^18358+18358^22099 94227 Hans Havermann 08/2020 9966 (9*33^62046+53831)/16 94218 Eric Chen 05/2023 9967 (67*10^94212+23)/9 94213 Ray Chandler 02/2011 9968 2^312909-1865203 94195 Enzo Doria 03/2016 9969 25013^5830+5830^25013 94191 Hans Havermann 09/2020 9970 2^312848-149 94177 Lelio R Paula 11/2012 9971 (2^312819+3278)/2 94168 Stefano Morozzi 02/2021 9972 4^156403-77597 94164 Mike Oakes 04/2011 9973 18^75004-85 94151 Lelio R Paula 06/2016 9974 (19573*10^94146-7)/9 94150 Patrick De Geest 05/2023 9975 19^73622-48 94145 Lelio R Paula 06/2016 9976 (11^90397-3^90397)/8 94138 Robert Price 04/2011 9977 (3^197287+5)/16 94129 Lelio R Paula 04/2013 9978 (23*10^94123-29)/3 94124 Robert Price 03/2022 9979 24220^7691+7691^24220 94119 Hans Havermann 09/2020 9980 12^87212-37 94118 Lelio R Paula 06/2016 9981 11^90376+76 94117 Lelio R Paula 05/2016 9982 (6^120946-11)/5 94114 Paul Bourdelais 11/2011 9983 (2^312622+534)/2 94109 Stefano Morozzi 09/2020 9984 (10^94096+191)/3 94096 Robert Price 11/2017 9985 23794^9005+9005^23794 94093 Hans Havermann 09/2020 9986 2^312562-112685 94091 Enzo Doria 06/2014 9987 137^44026-2 94072 Lelio R Paula 10/2017 9988 s(164441) 94052 Robert Price 05/2020 9989 2^312404-869688105 94043 Lelio R Paula 09/2016 9990 2^312387+2793533 94038 Enzo Doria 03/2016 9992 10^94016+91 94017 Robert Price 04/2011 9991 (15*2^312325-1)/7201 94017 Lelio R Paula 02/2014 9993 10^94016-188963 94016 Patrick De Geest 08/2013 9994 (17*2^312315-1)/45 94016 Lelio R Paula 02/2014 9995 (401*10^94010+13)/9 94012 Robert Price 09/2021 9996 23866^8691+8691^23866 94010 Hans Havermann 08/2020 9997 6^120802+7661 94003 Mike Oakes 04/2011 9998 (67607*2^312254+1)/177 94001 Lelio R Paula 06/2014 9999 (2^312245+702)/2 93995 Stefano Morozzi 09/2020 10000 (56*10^93993+493)/9 93994 Robert Price 10/2021

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 05 2023 08:12 (Time in France)

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