## PRP Records

### Probable Primes Top 10000

#### (295503 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 ? 1001 69478^20987+20987^69478 300281 Hans Havermann 07/2021 1002 64088^48393+48393^64088 300239 Hans Havermann 07/2021 1003 64605^44146+44146^64605 300084 Hans Havermann 08/2021 1004 2^996845+29027 300081 Enzo Doria 02/2024 1005 7^355039-6^355039 300043 Jean-Louis Charton 05/2011 1006 67594^27465+27465^67594 300035 Hans Havermann 06/2021 1007 10^300000+287389 300001 Patrick De Geest 10/2019 1008 10^300000-83657 300000 Patrick De Geest 10/2019 1009 70599^17756+17756^70599 300000 Hans Havermann 06/2021 1010 numbpart(72526161452) 299999 Serge Batalov 04/2017 1011 2^996182-114431 299881 Enzo Doria 02/2015 1012 3*2^996126+5 299865 Jon Grantham 07/2023 1013 2^996034-17 299837 Stefano Morozzi 07/2022 1014 (19*10^299640+77)/3 299641 Robert Price 03/2023 1015 2^995214-2788361 299590 Enzo Doria 12/2015 1016 2^994791-114319 299462 Enzo Doria 01/2015 1017 2^994490-1863791 299372 Enzo Doria 01/2016 1018 2^993322+1885729 299020 Enzo Doria 03/2017 1019 (36395^65536+36393^65536)/2 298913 Kellen Shenton 04/2022 1020 2^992711-2788807 298836 Enzo Doria 12/2015 1021 2^992525-114199 298780 Enzo Doria 12/2014 1022 (7^353501-3^353501)/4 298743 Jon Grantham 08/2023 1023 2^992329+1884707 298721 Enzo Doria 02/2017 1024 2^992052+215491 298638 Enzo Doria 11/2023 1025 2^991968-23 298613 Stefano Morozzi 07/2022 1026 2^991715-19 298536 Stefano Morozzi 07/2022 1027 (10^298414+7)/191/823/56921/1334467 298398 Alfred Reich 10/2021 1028 2^989562+25 297888 Stefano Morozzi 05/2021 1029 2^988580+214051 297593 Enzo Doria 10/2023 1030 2^988537+218837 297580 Enzo Doria 03/2024 1031 (19*10^297497+77)/3 297498 Robert Price 03/2023 1032 (2*10^297488-23)/3 297488 Robert Price 10/2022 1033 (2^986191+1)/3 296873 Vincent Diepeveen 06/2008 1034 2^985217-114553 296580 Enzo Doria 03/2015 1035 (76^157649-1)/75 296507 Paul Bourdelais 07/2019 1036 2^984650+21529 296410 Enzo Doria 08/2023 1037 2^984131-1828009 296253 Enzo Doria 01/2015 1038 2^983620+60451 296100 Phil Moore 03/2008 1039 2^982721-2683 295829 Yves Minet 02/2016 1040 (23*10^295581+7)/3 295582 Robert Price 05/2023 1041 2^981298-2788421 295401 Enzo Doria 12/2015 1042 2^981163-2790967 295360 Enzo Doria 12/2015 1043 2^981016-15 295316 Stefano Morozzi 07/2022 1044 8*10^295160-13 295161 Robert Price 08/2023 1045 2^979594+1865839 294888 Enzo Doria 02/2016 1046 2^979502+221029 294860 Enzo Doria 03/2024 1047 2*10^294527-91 294528 Robert Price 02/2023 1048 (49363^63001-1)/(49363^251-1) 294511 Ryan Propper 11/2023 1049 10^294475+49 294476 Robert Price 02/2023 1050 (11*10^294308+91)/3 294309 Robert Price 03/2023 1051 2^976760+1885021 294035 Enzo Doria 02/2017 1052 3*2^976518+5 293962 Jon Grantham 07/2023 1053 2^975798+218599 293745 Enzo Doria 01/2024 1054 2^974441+1878407 293336 Enzo Doria 08/2016 1055 2^974180+1876831 293258 Enzo Doria 07/2016 1056 2^974170+453319 293255 Enzo Doria 01/2017 1057 (211^126023-1)/210 292911 Anonymous 05/2024 1058 2^972744-114419 292826 Enzo Doria 03/2015 1059 11^281143+6 292781 Paul Bourdelais 03/2021 1060 (4*10^292619-91)/3 292620 Robert Price 12/2022 1061 E(69468)/13247122135 292549 Sergey Batalov 10/2023 1062 CopelandErdos(292447) 292447 Mark Rodenkirch 12/2015 1063 3*10^292344-97 292345 Robert Price 01/2023 1064 2^970911+1873373 292274 Enzo Doria 07/2016 1065 2^970670+383059 292201 Enzo Doria 12/2016 1066 2^970141-100363 292042 Enzo Doria 02/2014 1067 2^969945+1874717 291983 Enzo Doria 06/2016 1068 2^969384+1880701 291814 Enzo Doria 10/2016 1069 (13*10^291721-43)/3 291722 Robert Price 08/2023 1070 (3^611333-2^611333)/(99035947*87109884549431) 291659 Mike Oakes 02/2017 1071 3*2^963892+5 290161 Jon Grantham 07/2023 1072 (151*10^289877-1)/3 289879 Robert Price 07/2023 1073 2^962194+60139 289650 Enzo Doria 02/2016 1074 2^959307-1861507 288781 Enzo Doria 11/2015 1075 (17*10^288692+31)/3 288693 Robert Price 04/2023 1076 14^251797-3 288592 Paul Bourdelais 12/2020 1077 (8745^73441-1)/(8745^271-1) 288419 Ryan Propper 11/2023 1078 (2*10^288371-23)/3 288371 Robert Price 10/2022 1079 (31*10^288238-1)/3 288240 Robert Price 02/2023 1080 (7^341063-2^341063)/5 288231 Jon Grantham 08/2023 1081 2^957372+283531 288198 Enzo Doria 02/2017 1082 2^957192-1864049 288144 Enzo Doria 01/2016 1083 (95774^58081-1)/(95774^241-1) 288116 Ryan Propper 11/2023 1084 2^956446+1875199 287919 Enzo Doria 06/2016 1085 2^956283+219143 287870 Enzo Doria 02/2024 1086 7*10^287854+39 287855 Robert Price 01/2023 1087 2^956082+28309 287810 Enzo Doria 02/2024 1088 (17^233689+1)/18 287542 Paul Bourdelais 09/2013 1089 2^955178+1883587 287538 Enzo Doria 12/2016 1090 2^954127-954127^2 287221 Henri Lifchitz 01/2021 1091 2^954001+1875257 287183 Enzo Doria 07/2016 1092 2*10^287175-49 287176 Robert Price 05/2023 1093 (22*10^287085-19)/3 287086 Robert Price 07/2023 1094 2^953488+22411 287029 Enzo Doria 09/2023 1095 (23891^65536+1)/2 286932 Serge Batalov 03/2018 1096 5*3^601336-2^601336 286911 Jon Grantham 08/2023 1097 2^952268+1878601 286662 Enzo Doria 09/2016 1098 2^950801+81557 286220 Enzo Doria 08/2016 1099 2^949403+217523 285799 Enzo Doria 01/2024 1100 22845^65536+22844^65536 285658 Kellen Shenton 03/2021 1101 (11*2^948635-13)/15 285568 Renaud Lifchitz 11/2011 1102 (54^164839+1)/55 285565 Paul Bourdelais 07/2019 1103 2^948510+782569 285530 Enzo Doria 10/2016 1104 2^948374-114137 285490 Enzo Doria 01/2015 1105 2^947739+1872923 285298 Enzo Doria 06/2016 1106 2^946274+218407 284857 Enzo Doria 03/2024 1107 7*10^284751+9 284752 Robert Price 04/2023 1108 2^944561-21 284342 Stefano Morozzi 07/2022 1109 (4*10^284330-31)/9 284330 Serge Batalov 11/2022 1110 (32*10^283826-23)/9 283827 Serge Batalov 01/2023 1111 2^942533+82067 283731 Enzo Doria 09/2016 1112 2^941469+39 283411 Jon Grantham 08/2023 1113 (10^283342-31)/3 283342 Robert Price 03/2023 1114 2^940950+1874989 283255 Enzo Doria 06/2016 1115 2^940426-2786141 283097 Enzo Doria 11/2015 1116 (2*10^282948-11)/9 282948 Serge Batalov 11/2022 1117 2^939881-114115 282933 Enzo Doria 12/2014 1118 (14*10^282673-143)/3 282674 Robert Price 05/2023 1119 10^282493+632551 282494 Patrick De Geest 02/2017 1121 10^282493-9^282493 282493 Jean-Louis Charton 03/2007 1120 10^282493-132327 282493 Patrick De Geest 02/2017 1122 3^591827-2^591827 282374 Mike Oakes 08/2009 1123 Tau(509^18946) 282048 Nik Lygeros / Olivier Rozier 05/2015 1124 2^936716-1835519 281980 Enzo Doria 04/2015 1125 2^936588+79411 281942 Enzo Doria 06/2016 1126 2^936047+1877423 281779 Enzo Doria 08/2016 1127 2^935713+1869377 281678 Enzo Doria 05/2016 1128 2^933082+1877059 280886 Enzo Doria 08/2016 1129 (5*10^280710+1)/3 280711 Serge Batalov 10/2014 1130 2^932064+26521 280580 Enzo Doria 12/2023 1131 2^931976+25 280553 Stefano Morozzi 05/2021 1132 (42^172663+1)/43 280274 Paul Bourdelais 07/2019 1133 (10^279978+11)/3 279978 Serge Batalov 07/2015 1134 2^929524-1864829 279815 Enzo Doria 01/2016 1135 2^929329+22697 279756 Enzo Doria 09/2023 1136 2^929152+60181 279703 Enzo Doria 02/2016 1137 2^928621-2787883 279543 Enzo Doria 11/2015 1138 (2^927763+lucasV(-1,2,927763)+1)/2 279285 Mike Oakes 04/2017 1139 3*10^279271+77 279272 Robert Price 06/2024 1140 2^927429+1882277 279184 Enzo Doria 12/2016 1141 2^926766-11 278985 Stefano Morozzi 07/2022 1142 (71^150697-1)/70 278978 Paul Bourdelais 07/2019 1143 (33^183661-1)/32 278891 Paul Bourdelais 12/2018 1144 (166*10^278633-7)/3 278635 Robert Price 02/2023 1145 (2^925391+lucasV(-1,2,925391)+1)/2 278571 Mike Oakes 03/2017 1146 2^925330-1301 278553 Yves Minet 06/2015 1147 (299*10^278546+1)/3 278548 Robert Price 01/2023 1148 2^925299+216053 278543 Enzo Doria 11/2023 1149 (21^210599+1)/22 278457 Paul Bourdelais 08/2013 1150 (266*10^278325+1)/3 278327 Robert Price 01/2023 1151 2^923261-69175 277930 Enzo Doria 11/2015 1152 757^96487-756^96487 277796 Jean-Louis Charton 12/2012 1153 2^922301+57 277641 Stefano Morozzi 05/2021 1154 7*10^277478-39 277479 Robert Price 07/2023 1155 ((((((((((((((291487327^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2 277369 Serge Batalov 07/2016 1156 (5^396413-1)/4 277081 Paul Bourdelais 06/2010 1157 2^920318+2792299 277044 Enzo Doria 02/2016 1158 (16*10^276537-31)/3 276538 Robert Price 03/2023 1159 2^918596-2786939 276525 Enzo Doria 11/2015 1160 2^917910+28369 276319 Enzo Doria 01/2024 1161 (6737^72361-1)/(6737^269-1) 276002 Ryan Propper 11/2023 1162 2^916639+60563 275936 Enzo Doria 04/2016 1163 (2*10^275922+1)/3 275922 Serge Batalov 11/2022 1164 2^916385-2786383 275860 Enzo Doria 11/2015 1165 2^915928+82081 275722 Enzo Doria 09/2016 1166 (4*10^275671+11)/3 275672 Tyler Busby 02/2023 1167 2^915576-114137 275616 Enzo Doria 01/2015 1168 2^914828+1876741 275391 Enzo Doria 07/2016 1169 2^914757-2203 275370 Yves Minet 12/2015 1170 7*10^275157-27 275158 Robert Price 11/2022 1171 2^912744+20011 274764 Enzo Doria 06/2023 1172 2^911900+1871245 274510 Enzo Doria 05/2016 1173 (16*10^274251-91)/3 274252 Robert Price 11/2022 1174 2^910999+9 274239 Stefano Morozzi 05/2021 1175 (2^910869-7)/5 274199 Stefano Morozzi 08/2022 1176 2^910490+283429 274085 Enzo Doria 01/2017 1177 7*10^273983+39 273984 Robert Price 01/2023 1178 2^909988-1862249 273934 Enzo Doria 12/2015 1179 2^909297+1879157 273726 Enzo Doria 08/2016 1180 2^909257-1864423 273714 Enzo Doria 01/2016 1181 2^909254+31309 273713 Enzo Doria 03/2024 1182 2^908739-7 273558 Stefano Morozzi 07/2022 1183 2^908579-1861747 273510 Enzo Doria 12/2015 1184 3*2^908005-5 273338 Jon Grantham 07/2023 1185 2^907635-2791597 273226 Enzo Doria 01/2016 1186 2^907059+211193 273052 Enzo Doria 08/2023 1187 (53^158341+1)/54 273022 Paul Bourdelais 07/2019 1188 2^906594-113201 272912 Enzo Doria 08/2014 1189 9*10^272800+91 272801 Robert Price 05/2023 1190 2*10^272710-49 272711 Robert Price 05/2023 1191 2*10^272403-91 272404 Robert Price 02/2023 1192 2^904773+1872167 272364 Enzo Doria 06/2016 1193 6^349903+5 272278 Paul Bourdelais 02/2021 1194 2^904149-1862473 272176 Enzo Doria 12/2015 1195 (7*10^271757-61)/9 271757 Erik Branger 03/2012 1196 2^902497+1880117 271679 Enzo Doria 09/2016 1197 2^901858+77689 271487 Enzo Doria 06/2016 1198 2^901372+1875301 271341 Enzo Doria 06/2016 1199 2^901146+219049 271272 Enzo Doria 02/2024 1200 (8*10^271039-77)/3 271040 Robert Price 04/2023 1201 2^899999+1144031 270927 Norman Luhn 09/2023 1202 2*10^270802-91 270803 Robert Price 02/2023 1203 23*10^270799-7 270801 Robert Price 10/2022 1204 2^899121-115033 270663 Enzo Doria 07/2015 1205 2^898900+883021 270596 Enzo Doria 12/2016 1206 2^898762-251511 270555 Enzo Doria 12/2013 1207 2^898589+47 270503 Lelio R Paula 03/2016 1208 187322*10^270343-187321 270349 Danilo Nitsche 09/2013 1209 48358*10^270343-48357 270348 Danilo Nitsche 09/2013 1210 (10^270343-1)/9 270343 Maksym Voznyy 07/2007 1211 2^897867-3217 270285 Yves Minet 12/2016 1212 2^897849-115273 270280 Enzo Doria 07/2015 1213 2^897367+26289 270135 Enzo Doria 03/2024 1214 2^896616-114179 269909 Enzo Doria 12/2014 1215 (12648^66049-1)/(12648^257-1) 269881 Ryan Propper 11/2023 1216 (22*10^269517-19)/3 269518 Robert Price 07/2023 1217 10^(2*134739+1)-7*10^134739-1 269479 Robert Price 07/2023 1218 2^894928+583561 269401 Enzo Doria 04/2017 1219 2^894673-39343 269324 Enzo Doria 08/2015 1220 2^893836+23221 269072 Enzo Doria 10/2023 1221 2^892718+29539 268735 Enzo Doria 03/2024 1222 2^892660+213901 268718 Enzo Doria 10/2023 1223 F(1285607) 268676 Henri Lifchitz 11/2008 1224 2^892234+22189 268590 Enzo Doria 09/2023 1225 2^892151+24863 268565 Enzo Doria 11/2023 1226 2^892112+187663 268553 Enzo Doria 08/2016 1227 (266*10^268407-17)/3 268409 Robert Price 02/2023 1228 (10^268207+1)/11 268206 Paul Bourdelais 02/2010 1229 2^890957-69583 268205 Enzo Doria 12/2015 1230 32841!^2+32840!^2+...+2!^2+1!^2 268128 Serge Batalov 07/2017 1231 2^890122-351401 267954 Enzo Doria 07/2015 1232 (19^209359-1)/18 267718 Paul Bourdelais 08/2010 1233 (85^138647+1)/86 267507 Paul Bourdelais 07/2019 1234 (1005^89087-1)/1004 267451 Jinyuan Wang 01/2024 1235 (485^99523-1)/484 267291 Michael Stocker 05/2020 1236 2^886324+77791 266811 Enzo Doria 06/2016 1237 7*10^266731+87 266732 Robert Price 11/2022 1238 2^886040+213901 266725 Enzo Doria 10/2023 1239 2^885242+217909 266485 Enzo Doria 01/2024 1240 2^884738+26809 266333 Enzo Doria 12/2023 1241 2^884714+1880527 266326 Enzo Doria 10/2016 1242 7*10^266024-47 266025 Robert Price 08/2023 1243 11^255426+255426^11 265999 Serge Batalov 05/2014 1244 2^883462-343421 265949 Enzo Doria 07/2015 1245 2^883442+1875019 265943 Enzo Doria 06/2016 1246 2^883333-291583 265910 Enzo Doria 07/2015 1247 2^883132+30421 265850 Enzo Doria 03/2024 1248 10^265566+3593037 265567 Paul Bourdelais 08/2023 1249 (2*10^265321-17)/3 265321 Serge Batalov 11/2022 1250 (16*10^265052-91)/3 265053 Robert Price 11/2022

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: July, 22 2024 13:34 (Time in France)

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