## PRP Records

### Probable Primes Top 10000

#### (290751 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 ? 8001 3*10^95776-59 95777 Robert Price 10/2017 8002 (82970^19471-1)/82969 95772 Serge Batalov 06/2022 8003 193^41901-2 95768 Lelio R Paula 10/2017 8004 (2^318124+2502)/2 95765 Stefano Morozzi 09/2020 8005 (12900^23297-1)/12899 95761 Serge Batalov 06/2022 8006 4*10^95752-71 95753 Robert Price 11/2017 8007 (16955^22639-1)/16954 95743 Serge Batalov 06/2022 8008 (81795^19489-1)/81794 95740 Serge Batalov 06/2022 8009 (2742^27847-1)/2741 95737 Serge Batalov 06/2022 8010 (6072^25303-1)/6071 95726 Serge Batalov 06/2022 8011 23640^11197+11197^23640 95721 Hans Havermann 12/2019 8012 10^95712-4000001 95712 Robert Price 07/2021 8013 (60657^20011-1)/60656 95706 Serge Batalov 06/2022 8014 ((10^47850-1)*10000/9+6421)*10^47850+(10^47850-1)/9 95704 Hans Havermann 05/2019 8015 (509203*2^317881-1)/52805 95693 Lelio R Paula 04/2015 8016 (26161^21661-1)/26160 95687 Serge Batalov 06/2022 8017 (2^317853+1086)/2 95683 Stefano Morozzi 09/2020 8018 4*10^95672+91 95673 Robert Price 11/2017 8019 6*10^95665+43 95666 Robert Price 07/2020 8020 (20819^22153-1)/20818 95663 Serge Batalov 06/2022 8021 (64464^19891-1)/64463 95658 Serge Batalov 06/2022 8022 (934^32203-1)/933 95652 Serge Batalov 06/2022 8023 (11*10^95641-113)/3 95642 Robert Price 01/2017 8024 (72330^19681-1)/72329 95632 Serge Batalov 06/2022 8025 (13224^23203-1)/13223 95624 Serge Batalov 06/2022 8026 (18211^22441-1)/18210 95602 Serge Batalov 06/2022 8027 (71975^19681-1)/71974 95590 Serge Batalov 06/2022 8028 (13*10^95588+11)/3 95589 Robert Price 05/2015 8029 Phi(191188,10)/191189 95587 Maksym Voznyy 11/2015 8030 (13368^23167-1)/13367 95585 Serge Batalov 06/2022 8031 (25874^21661-1)/25873 95583 Serge Batalov 06/2022 8032 3^200325+70 95580 Lelio R Paula 05/2016 8033 (25*10^95574-7)/9 95575 Robert Price 12/2014 8034 (2^317485-3)/21313 95569 Lelio R Paula 06/2013 8035 2^317464+31 95567 Lelio R Paula 11/2012 8036 (2^317451+2114)/2 95562 Stefano Morozzi 09/2020 8037 7^113073+82 95558 Lelio R Paula 04/2016 8038 (24728^21751-1)/24727 95552 Serge Batalov 06/2022 8039 (49764^20341-1)/49763 95536 Serge Batalov 06/2022 8040 (36155^20959-1)/36154 95531 Serge Batalov 06/2022 8041 (7725^24571-1)/7724 95526 Serge Batalov 06/2022 8042 (20546^22147-1)/20545 95510 Serge Batalov 06/2022 8043 2^317251+465 95503 Lelio R Paula 03/2016 8044 19^74684+58 95503 Lelio R Paula 06/2016 8045 (2^317250-7)/339 95500 Lelio R Paula 07/2013 8046 5*10^95498-21 95499 Robert Price 12/2021 8047 (21615^22031-1)/21614 95495 Serge Batalov 06/2022 8048 6^122718-79 95494 Lelio R Paula 05/2016 8049 22168^20291+20291^22168 95485 Hans Havermann 10/2019 8050 (77427^19531-1)/77426 95481 Serge Batalov 06/2022 8051 (13026^23203-1)/13025 95472 Serge Batalov 06/2022 8052 2^317141-110491 95469 Enzo Doria 05/2014 8053 (2^317097+3014)/2 95456 Stefano Morozzi 09/2020 8054 2^317094+76309 95455 Enzo Doria 05/2016 8055 2^317085+95 95453 Lelio R Paula 11/2012 8056 (17*10^95451-377)/9 95452 Robert Price 11/2017 8057 2^317057-109551 95444 Enzo Doria 04/2014 8058 3^200026+28 95437 Lelio R Paula 05/2016 8059 2^317024+93 95434 Donovan Johnson 06/2008 8060 (86*10^95428-437)/9 95429 Robert Price 03/2021 8061 10^95427+192591 95428 Patrick De Geest 05/2021 8064 2^316999+1605 95427 Lelio R Paula 03/2016 8063 (2^317000+3210)/2 95427 Stefano Morozzi 09/2020 8062 10^95427-10001 95427 Robert Price 02/2021 8065 2^316995-110427 95426 Enzo Doria 05/2014 8066 (69841^19699-1)/69840 95420 Serge Batalov 06/2022 8067 (59242^19993-1)/59241 95415 Serge Batalov 06/2022 8069 22300^18987+18987^22300 95410 Hans Havermann 06/2020 8068 (9478^23993-1)/9477 95410 Serge Batalov 06/2022 8070 2^316937+177 95408 Lelio R Paula 11/2012 8071 4*10^95407+91 95408 Robert Price 11/2017 8072 2^316908+1915 95399 Lelio R Paula 03/2016 8073 2^316894+99 95395 Lelio R Paula 11/2012 8074 (2^316887+2546)/2 95393 Stefano Morozzi 09/2020 8075 2*10^95374-21 95375 Robert Price 09/2020 8076 6^122547+11 95361 Lelio R Paula 05/2016 8077 2^316771+82875 95358 Lelio R Paula 03/2016 8078 (15609^22741-1)/15608 95358 Serge Batalov 06/2022 8079 (2^316765+3102)/2 95356 Stefano Morozzi 09/2020 8080 (2267^28411-1)/2266 95329 Serge Batalov 06/2022 8081 (824^32693-1)/823 95328 Serge Batalov 06/2022 8082 (23*10^95326+1)/3 95327 Serge Batalov 05/2009 8083 1*10^95326+57 95327 Robert Price 03/2011 8084 10^95326-393687 95326 Patrick De Geest 09/2013 8085 (3^199803+4)/479539 95325 Lelio R Paula 04/2013 8086 2^316654-109481 95323 Enzo Doria 04/2014 8087 8*10^95316+51 95317 Robert Price 05/2017 8088 (50^56099+43^56099)/93 95309 Serge Batalov 12/2016 8089 (23*2^316559+1)/3925 95292 Lelio R Paula 09/2013 8091 (71*10^95277-539)/9 95278 Robert Price 11/2017 8090 23422^11691+11691^23422 95278 Hans Havermann 10/2019 8092 19^74503-56 95271 Lelio R Paula 06/2016 8093 (5038^25733-1)/5037 95267 Serge Batalov 06/2022 8094 11^91475-4380 95262 Enzo Doria 01/2013 8095 (62*10^95251-611)/9 95252 Robert Price 05/2017 8096 (160090^18301-1)/160089 95240 Serge Batalov 06/2022 8097 (173205^18181-1)/173204 95238 Serge Batalov 06/2022 8098 (158710^18313-1)/158709 95234 Serge Batalov 06/2022 8099 (9979^23813-1)/9978 95227 Serge Batalov 06/2022 8100 (57376^20011-1)/57375 95223 Serge Batalov 06/2022 8101 (2^316321-509203)/69377 95218 Lelio R Paula 06/2013 8102 26541^3868+3868^26541 95216 Hans Havermann 07/2020 8103 (79*10^95214-43)/9 95215 Erik Branger 11/2013 8104 (7176^24691-1)/7175 95202 Anonymous 11/2020 8105 (9*2^316233-1)/1751 95194 Lelio R Paula 02/2014 8106 5*2^316213+9 95191 Lelio R Paula 08/2014 8107 2*10^95188-91 95189 Robert Price 04/2020 8108 2^316205-1848163 95188 Enzo Doria 07/2015 8109 2^316185-2787913 95182 Enzo Doria 04/2016 8110 (2^316174+3538)/2 95178 Stefano Morozzi 09/2020 8111 (9787*2^316142-1)/3 95172 Lelio R Paula 04/2015 8112 2^316140-5 95168 Henri Lifchitz 02/2006 8113 (15185*2^316117-1)/3 95165 Lelio R Paula 04/2015 8114 (34*10^95153-7)/9/19/19157 95149 Makoto Morimoto 05/2016 8115 2^316069+76817 95147 Enzo Doria 05/2016 8116 (199*10^95134-7)/3 95136 Robert Price 02/2017 8117 2^316027-97305 95134 Lelio R Paula 03/2016 8118 2^316006-2798051 95128 Enzo Doria 04/2016 8119 24994^6397+6397^24994 95127 Hans Havermann 02/2020 8121 2^315921-2797603 95102 Enzo Doria 04/2016 8120 (2^315921+1314)/2 95102 Stefano Morozzi 02/2021 8122 2*10^95095+63 95096 Robert Price 10/2017 8123 2^315857+1299 95083 Lelio R Paula 03/2016 8124 (2^315858+2598)/2 95083 Stefano Morozzi 09/2020 8126 14^82955-43 95078 Lelio R Paula 06/2016 8125 (8*10^95078-269)/9 95078 Robert Price 09/2021 8127 (23*10^95074-101)/3 95075 Robert Price 04/2021 8128 2^315827-933075 95074 Paul Bourdelais 04/2021 8129 (2*10^95072-17)/3 95072 Robert Price 08/2014 8130 (286*10^95059-1)/3 95061 Robert Price 11/2020 8131 (2^315779+1610)/2 95059 Stefano Morozzi 09/2020 8132 2^315775-111546435 95058 Paul Bourdelais 10/2021 8133 21938^21513+21513^21938 95051 Hans Havermann 09/2020 8134 2^315727+65 95044 Lelio R Paula 11/2012 8135 2^315725+1885757 95043 Enzo Doria 03/2017 8136 23277^12058+12058^23277 95000 Hans Havermann 09/2020 8137 1*10^94983+21 94984 Robert Price 03/2011 8138 10^94983-717 94983 Patrick De Geest 08/2013 8139 17^77187-82 94975 Lelio R Paula 07/2016 8140 3*10^94964+37 94965 Robert Price 10/2017 8141 (2^315481-1017)/20627285 94962 Lelio R Paula 06/2013 8142 2^315423-110329 94952 Enzo Doria 05/2014 8143 11^91169-7230 94943 Enzo Doria 02/2013 8144 7*10^94938+61 94939 Robert Price 02/2017 8145 2^315351+1025 94931 Lelio R Paula 03/2016 8146 2^315350-112253 94930 Enzo Doria 06/2014 8147 (2^315343+1766)/2 94928 Stefano Morozzi 09/2020 8148 (2^315343+3066)/2 94928 Stefano Morozzi 09/2020 8151 ((1001327^(15817)+1)/1001328) 94906 Faysal YAtim 10/2010 8150 2^315268+7 94906 Lelio R Paula 10/2012 8149 11^91133+62 94906 Lelio R Paula 05/2016 8152 (2^315264+1558)/2 94904 Stefano Morozzi 09/2020 8153 30^64244+41 94897 Lelio R Paula 08/2012 8154 (151*10^94885-7)/9 94887 Robert Price 07/2017 8155 4^157583+22147 94875 Mike Oakes 01/2011 8156 2^315098+123 94854 Lelio R Paula 11/2012 8157 3^198791-34 94848 Robert Price 11/2013 8158 3*2^315067+7 94846 Lelio R Paula 08/2014 8159 (9*2^315057+1)/73 94841 Lelio R Paula 09/2013 8160 22576^15875+15875^22576 94836 Hans Havermann 09/2020 8161 (16*10^94822+53)/3 94823 Robert Price 12/2016 8162 8*6^121849-7 94818 Lelio R Paula 10/2014 8163 (85*10^94802+473)/9 94803 Robert Price 03/2017 8164 21767^21852-21852^21767 94790 Norbert Schneider 06/2020 8165 2^314870-108761 94786 Enzo Doria 03/2014 8166 5*2^314841-3 94778 Lelio R Paula 08/2014 8167 (2^314842+550)/2 94777 Stefano Morozzi 09/2020 8168 11738^23289-23289^11738 94777 Norbert Schneider 05/2022 8169 (2^314787+2630)/2 94761 Stefano Morozzi 09/2020 8170 6^121772+113 94758 Lelio R Paula 05/2016 8171 (2^314740+3642)/2 94746 Stefano Morozzi 09/2020 8172 6^121756-16253 94745 Enzo Doria 02/2013 8173 2^314718-112793 94740 Enzo Doria 06/2014 8174 2^314697-1847293 94734 Enzo Doria 07/2015 8175 22836^14065+14065^22836 94727 Hans Havermann 09/2020 8177 2^314548-249 94689 Yves Minet 02/2012 8176 5^135469+42 94689 Lelio R Paula 04/2016 8178 gcd(V(1137755),5*F(227551)*(F(227551)-1)+1) 94676 Serge Batalov 04/2015 8179 25773^4712+4712^25773 94670 Hans Havermann 08/2020 8180 (2^314485+3614)/2 94670 Stefano Morozzi 09/2020 8181 (2*10^94604+547)/9 94604 Robert Price 10/2017 8182 (2^314164+2562)/2 94573 Stefano Morozzi 09/2020 8183 3*2^314152+5 94570 Lelio R Paula 08/2014 8184 2*6^121530-5 94570 Lelio R Paula 10/2014 8185 7*10^94563+87 94564 Robert Price 11/2016 8186 2^314114-109677 94558 Enzo Doria 04/2014 8187 (218389#+240867)/(3*11*811) 94557 Makoto Morimoto 10/2017 8188 2^314059+76583 94542 Enzo Doria 05/2016 8189 2^314041-4035 94536 Lelio R Paula 03/2016 8190 (2^314028+3102)/2 94532 Stefano Morozzi 09/2020 8191 (2^314012+618)/2 94527 Stefano Morozzi 09/2020 8192 (7*2^314003-11)/15 94524 Renaud Lifchitz 03/2011 8193 11^90760-4710 94517 Enzo Doria 01/2013 8194 21675^21796+21796^21675 94507 Norbert Schneider 04/2020 8195 2^313942+100280245065 94506 Paul Bourdelais 10/2021 8196 (7*2^313926-1)/148821 94497 Lelio R Paula 02/2014 8197 94*10^94493-3 94495 Robert Price 11/2016 8198 (1000547^15749+1)/1000548 94492 Faysal YAtim 12/2008 8199 (2^313859+2706)/2 94481 Stefano Morozzi 09/2020 8200 (F(3*75345)^2+L(3*75345)^2)/4 94477 Henri Lifchitz 10/2017 8201 7^111792-32 94476 Lelio R Paula 04/2016 8202 (2^313800+822)/2 94463 Stefano Morozzi 01/2021 8203 9*10^94462-47 94463 Robert Price 11/2021 8204 11*10^94460+3 94462 Robert Price 07/2021 8205 (202*10^94441-1)/3 94443 Robert Price 05/2020 8206 11^90680-5850 94434 Enzo Doria 01/2013 8207 (752^32833-1)/751 94432 Michael Stocker 05/2020 8208 2^313675-110125 94426 Enzo Doria 04/2014 8209 (2999*29^64556-2427)/4 94410 Curtis Bright 05/2015 8210 2^313609-112225 94406 Enzo Doria 06/2014 8211 2^313584+72901 94399 Enzo Doria 04/2016 8212 (2^313567+1310)/2 94393 Stefano Morozzi 02/2021 8213 (2^313562+730)/2 94392 Stefano Morozzi 09/2020 8214 2^313510-112865 94376 Enzo Doria 06/2014 8215 7*10^94373+87 94374 Robert Price 11/2016 8216 (9^98897+8^98897)/17 94371 Robert Price 12/2012 8217 2^313453-114703 94359 Enzo Doria 04/2015 8218 8*10^94357-51 94358 Robert Price 10/2017 8219 25903^4392+4392^25903 94356 Hans Havermann 09/2020 8220 31706^945+945^31706 94340 Hans Havermann 09/2020 8221 (379*10^94337-1)/9 94339 Robert Price 08/2017 8222 2^313344-313344+1 94326 Robert Price 10/2014 8223 (2^313313+3662)/2 94317 Stefano Morozzi 09/2020 8224 20^72481-49 94300 Lelio R Paula 05/2016 8225 (34*10^94293-259)/9 94294 Robert Price 12/2021 8226 44725!2+128 94289 Robert Price 03/2015 8227 4*10^94286+9 94287 Robert Price 05/2015 8228 17^76621+24 94279 Lelio R Paula 07/2016 8229 26274^3875+3875^26274 94279 Hans Havermann 09/2020 8230 4*10^94270-33 94271 Robert Price 04/2021 8231 2^313156-112859 94270 Enzo Doria 06/2014 8232 (49*10^94262-211)/9 94263 Robert Price 06/2022 8233 6^121130-59 94258 Lelio R Paula 05/2016 8234 3^197542+28 94252 Robert Price 11/2013 8235 (2^313076+3550)/2 94245 Stefano Morozzi 09/2020 8236 (3^197521+2)/51655 94237 Lelio R Paula 04/2013 8237 2^313045-5955 94236 Lelio R Paula 03/2016 8238 22099^18358+18358^22099 94227 Hans Havermann 08/2020 8239 (67*10^94212+23)/9 94213 Ray Chandler 02/2011 8240 2^312909-1865203 94195 Enzo Doria 03/2016 8241 25013^5830+5830^25013 94191 Hans Havermann 09/2020 8242 2^312848-149 94177 Lelio R Paula 11/2012 8243 (2^312819+3278)/2 94168 Stefano Morozzi 02/2021 8244 4^156403-77597 94164 Mike Oakes 04/2011 8245 18^75004-85 94151 Lelio R Paula 06/2016 8246 19^73622-48 94145 Lelio R Paula 06/2016 8247 (11^90397-3^90397)/8 94138 Robert Price 04/2011 8248 (3^197287+5)/16 94129 Lelio R Paula 04/2013 8249 (23*10^94123-29)/3 94124 Robert Price 03/2022 8250 24220^7691+7691^24220 94119 Hans Havermann 09/2020

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 23 2022 21:24 (Time in France)

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