## PRP Records

### Probable Primes Top 10000

#### (294613 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) !!!

See the Top discoverers
See the Latest PRPs
Search by form

 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 2^946274+218407 284857 Enzo Doria 03/2024 1002 7*10^284751+9 284752 Robert Price 04/2023 1003 2^944561-21 284342 Stefano Morozzi 07/2022 1004 (4*10^284330-31)/9 284330 Serge Batalov 11/2022 1005 (32*10^283826-23)/9 283827 Serge Batalov 01/2023 1006 2^942533+82067 283731 Enzo Doria 09/2016 1007 2^941469+39 283411 Jon Grantham 08/2023 1008 (10^283342-31)/3 283342 Robert Price 03/2023 1009 2^940950+1874989 283255 Enzo Doria 06/2016 1010 2^940426-2786141 283097 Enzo Doria 11/2015 1011 (2*10^282948-11)/9 282948 Serge Batalov 11/2022 1012 2^939881-114115 282933 Enzo Doria 12/2014 1013 (14*10^282673-143)/3 282674 Robert Price 05/2023 1014 10^282493+632551 282494 Patrick De Geest 02/2017 1016 10^282493-9^282493 282493 Jean-Louis Charton 03/2007 1015 10^282493-132327 282493 Patrick De Geest 02/2017 1017 3^591827-2^591827 282374 Mike Oakes 08/2009 1018 Tau(509^18946) 282048 Nik Lygeros / Olivier Rozier 05/2015 1019 2^936716-1835519 281980 Enzo Doria 04/2015 1020 2^936588+79411 281942 Enzo Doria 06/2016 1021 2^936047+1877423 281779 Enzo Doria 08/2016 1022 2^935713+1869377 281678 Enzo Doria 05/2016 1023 2^933082+1877059 280886 Enzo Doria 08/2016 1024 (5*10^280710+1)/3 280711 Serge Batalov 10/2014 1025 2^932064+26521 280580 Enzo Doria 12/2023 1026 2^931976+25 280553 Stefano Morozzi 05/2021 1027 (42^172663+1)/43 280274 Paul Bourdelais 07/2019 1028 (10^279978+11)/3 279978 Serge Batalov 07/2015 1029 2^929524-1864829 279815 Enzo Doria 01/2016 1030 2^929329+22697 279756 Enzo Doria 09/2023 1031 2^929152+60181 279703 Enzo Doria 02/2016 1032 2^928621-2787883 279543 Enzo Doria 11/2015 1033 (2^927763+lucasV(-1,2,927763)+1)/2 279285 Mike Oakes 04/2017 1034 2^927429+1882277 279184 Enzo Doria 12/2016 1035 2^926766-11 278985 Stefano Morozzi 07/2022 1036 (71^150697-1)/70 278978 Paul Bourdelais 07/2019 1037 (33^183661-1)/32 278891 Paul Bourdelais 12/2018 1038 (166*10^278633-7)/3 278635 Robert Price 02/2023 1039 (2^925391+lucasV(-1,2,925391)+1)/2 278571 Mike Oakes 03/2017 1040 2^925330-1301 278553 Yves Minet 06/2015 1041 (299*10^278546+1)/3 278548 Robert Price 01/2023 1042 2^925299+216053 278543 Enzo Doria 11/2023 1043 (21^210599+1)/22 278457 Paul Bourdelais 08/2013 1044 (266*10^278325+1)/3 278327 Robert Price 01/2023 1045 2^923261-69175 277930 Enzo Doria 11/2015 1046 757^96487-756^96487 277796 Jean-Louis Charton 12/2012 1047 2^922301+57 277641 Stefano Morozzi 05/2021 1048 7*10^277478-39 277479 Robert Price 07/2023 1049 ((((((((((((((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 1050 (5^396413-1)/4 277081 Paul Bourdelais 06/2010 1051 2^920318+2792299 277044 Enzo Doria 02/2016 1052 (16*10^276537-31)/3 276538 Robert Price 03/2023 1053 2^918596-2786939 276525 Enzo Doria 11/2015 1054 2^917910+28369 276319 Enzo Doria 01/2024 1055 (6737^72361-1)/(6737^269-1) 276002 Ryan Propper 11/2023 1056 2^916639+60563 275936 Enzo Doria 04/2016 1057 (2*10^275922+1)/3 275922 Serge Batalov 11/2022 1058 2^916385-2786383 275860 Enzo Doria 11/2015 1059 2^915928+82081 275722 Enzo Doria 09/2016 1060 (4*10^275671+11)/3 275672 Tyler Busby 02/2023 1061 2^915576-114137 275616 Enzo Doria 01/2015 1062 2^914828+1876741 275391 Enzo Doria 07/2016 1063 2^914757-2203 275370 Yves Minet 12/2015 1064 7*10^275157-27 275158 Robert Price 11/2022 1065 2^912744+20011 274764 Enzo Doria 06/2023 1066 2^911900+1871245 274510 Enzo Doria 05/2016 1067 (16*10^274251-91)/3 274252 Robert Price 11/2022 1068 2^910999+9 274239 Stefano Morozzi 05/2021 1069 (2^910869-7)/5 274199 Stefano Morozzi 08/2022 1070 2^910490+283429 274085 Enzo Doria 01/2017 1071 7*10^273983+39 273984 Robert Price 01/2023 1072 2^909988-1862249 273934 Enzo Doria 12/2015 1073 2^909297+1879157 273726 Enzo Doria 08/2016 1074 2^909257-1864423 273714 Enzo Doria 01/2016 1075 2^908739-7 273558 Stefano Morozzi 07/2022 1076 2^908579-1861747 273510 Enzo Doria 12/2015 1077 3*2^908005-5 273338 Jon Grantham 07/2023 1078 2^907635-2791597 273226 Enzo Doria 01/2016 1079 2^907059+211193 273052 Enzo Doria 08/2023 1080 (53^158341+1)/54 273022 Paul Bourdelais 07/2019 1081 2^906594-113201 272912 Enzo Doria 08/2014 1082 9*10^272800+91 272801 Robert Price 05/2023 1083 2*10^272710-49 272711 Robert Price 05/2023 1084 2*10^272403-91 272404 Robert Price 02/2023 1085 2^904773+1872167 272364 Enzo Doria 06/2016 1086 6^349903+5 272278 Paul Bourdelais 02/2021 1087 2^904149-1862473 272176 Enzo Doria 12/2015 1088 (7*10^271757-61)/9 271757 Erik Branger 03/2012 1089 2^902497+1880117 271679 Enzo Doria 09/2016 1090 2^901858+77689 271487 Enzo Doria 06/2016 1091 2^901372+1875301 271341 Enzo Doria 06/2016 1092 2^901146+219049 271272 Enzo Doria 02/2024 1093 (8*10^271039-77)/3 271040 Robert Price 04/2023 1094 2^899999+1144031 270927 Norman Luhn 09/2023 1095 2*10^270802-91 270803 Robert Price 02/2023 1096 23*10^270799-7 270801 Robert Price 10/2022 1097 2^899121-115033 270663 Enzo Doria 07/2015 1098 2^898900+883021 270596 Enzo Doria 12/2016 1099 2^898762-251511 270555 Enzo Doria 12/2013 1100 2^898589+47 270503 Lelio R Paula 03/2016 1101 187322*10^270343-187321 270349 Danilo Nitsche 09/2013 1102 48358*10^270343-48357 270348 Danilo Nitsche 09/2013 1103 (10^270343-1)/9 270343 Maksym Voznyy 07/2007 1104 2^897867-3217 270285 Yves Minet 12/2016 1105 2^897849-115273 270280 Enzo Doria 07/2015 1106 2^897367+26289 270135 Enzo Doria 03/2024 1107 2^896616-114179 269909 Enzo Doria 12/2014 1108 (12648^66049-1)/(12648^257-1) 269881 Ryan Propper 11/2023 1109 (22*10^269517-19)/3 269518 Robert Price 07/2023 1110 10^(2*134739+1)-7*10^134739-1 269479 Robert Price 07/2023 1111 2^894928+583561 269401 Enzo Doria 04/2017 1112 2^894673-39343 269324 Enzo Doria 08/2015 1113 2^893836+23221 269072 Enzo Doria 10/2023 1114 2^892718+29539 268735 Enzo Doria 03/2024 1115 2^892660+213901 268718 Enzo Doria 10/2023 1116 F(1285607) 268676 Henri Lifchitz 11/2008 1117 2^892234+22189 268590 Enzo Doria 09/2023 1118 2^892151+24863 268565 Enzo Doria 11/2023 1119 2^892112+187663 268553 Enzo Doria 08/2016 1120 (266*10^268407-17)/3 268409 Robert Price 02/2023 1121 (10^268207+1)/11 268206 Paul Bourdelais 02/2010 1122 2^890957-69583 268205 Enzo Doria 12/2015 1123 32841!^2+32840!^2+...+2!^2+1!^2 268128 Serge Batalov 07/2017 1124 2^890122-351401 267954 Enzo Doria 07/2015 1125 (19^209359-1)/18 267718 Paul Bourdelais 08/2010 1126 (85^138647+1)/86 267507 Paul Bourdelais 07/2019 1127 (1005^89087-1)/1004 267451 Jinyuan Wang 01/2024 1128 (485^99523-1)/484 267291 Michael Stocker 05/2020 1129 2^886324+77791 266811 Enzo Doria 06/2016 1130 7*10^266731+87 266732 Robert Price 11/2022 1131 2^886040+213901 266725 Enzo Doria 10/2023 1132 2^885242+217909 266485 Enzo Doria 01/2024 1133 2^884738+26809 266333 Enzo Doria 12/2023 1134 2^884714+1880527 266326 Enzo Doria 10/2016 1135 7*10^266024-47 266025 Robert Price 08/2023 1136 11^255426+255426^11 265999 Serge Batalov 05/2014 1137 2^883462-343421 265949 Enzo Doria 07/2015 1138 2^883442+1875019 265943 Enzo Doria 06/2016 1139 2^883333-291583 265910 Enzo Doria 07/2015 1140 10^265566+3593037 265567 Paul Bourdelais 08/2023 1141 (2*10^265321-17)/3 265321 Serge Batalov 11/2022 1142 (16*10^265052-91)/3 265053 Robert Price 11/2022 1143 2^880411+1882673 265031 Enzo Doria 12/2016 1144 (14*10^264791-11)/3 264792 Robert Price 08/2022 1145 2^879530-2788031 264765 Enzo Doria 12/2015 1146 2^879292+25171 264694 Enzo Doria 11/2023 1147 (2*10^264539+61)/9 264539 Serge Batalov 11/2022 1148 2^878118+2793079 264340 Enzo Doria 02/2016 1149 (2^878073-7)/5 264326 Stefano Morozzi 08/2022 1150 (37^168527-1)/36 264283 Paul Bourdelais 08/2019 1151 5^377865+3^377865-1 264117 Jon Grantham 08/2023 1152 (19*10^263971+131)/3 263972 Robert Price 08/2023 1153 2^876202-17 263764 Stefano Morozzi 07/2022 1154 (14*10^263720-11)/3 263721 Robert Price 08/2022 1155 2^875748-461129 263627 Enzo Doria 07/2015 1156 2^875518-15 263558 Stefano Morozzi 07/2022 1157 (29*10^263523-17)/3 263524 Robert Price 01/2023 1158 2^875181-2789923 263456 Enzo Doria 12/2015 1159 2^875101-350083 263432 Enzo Doria 08/2015 1160 2^874684+1883587 263307 Enzo Doria 01/2017 1161 2^874616+1872211 263286 Enzo Doria 05/2016 1162 3^551491+16 263129 Robert Price 04/2020 1163 2^874073+2792957 263123 Enzo Doria 02/2016 1164 (7*10^263006-19)/3 263007 Robert Price 10/2023 1165 2^873628+1878751 262989 Enzo Doria 08/2016 1166 2^873497+20837 262949 Enzo Doria 08/2023 1167 2^873288-269 262886 Yves Minet 01/2015 1168 (2*10^262874+7)/9 262874 Rytis Slatkevicius 01/2023 1169 (28*10^262655-43)/3 262656 Robert Price 04/2023 1170 (2*10^262603-11)/9 262603 Serge Batalov 11/2022 1171 2^871991-4207 262496 Yves Minet 03/2021 1172 (23*10^262324+7)/3 262325 Robert Price 05/2023 1173 2^871146-3173 262242 Yves Minet 07/2016 1174 2^869601-163 261776 Yves Minet 01/2015 1175 (2*10^261704+61)/9 261704 Serge Batalov 11/2022 1176 2^869326+282859 261694 Enzo Doria 11/2016 1177 2^869035-114181 261606 Enzo Doria 12/2014 1178 2^868817+26777 261540 Enzo Doria 12/2023 1179 3^547850+9000004 261391 Enzo Doria 10/2023 1180 4*10^261248+91 261249 Robert Price 11/2022 1181 2^865715+80303 260607 Enzo Doria 07/2016 1182 2^865474+23209 260534 Enzo Doria 10/2023 1183 2^865238+214759 260463 Enzo Doria 11/2023 1184 2^865048+1882411 260406 Enzo Doria 12/2016 1185 2^864899-113871 260361 Enzo Doria 10/2014 1186 (16*10^260256-91)/3 260257 Robert Price 11/2022 1187 (7*10^260198-61)/9 260198 Erik Branger 11/2011 1188 2^864298-2788421 260180 Enzo Doria 12/2015 1189 2^864039-2791357 260102 Enzo Doria 01/2016 1190 2^863621-113833 259976 Enzo Doria 10/2014 1191 10^259945-11 259945 Mischa Rodermond 04/2023 1192 (28*10^259897+113)/3 259898 Robert Price 06/2023 1193 2^862837+75767 259740 Enzo Doria 05/2016 1194 2^862637-31 259680 Jorge Menendez 05/2019 1195 2^862088+1874941 259515 Enzo Doria 06/2016 1196 2^861987-134557 259484 Hans Havermann 10/2018 1197 (14*10^259431-143)/3 259432 Robert Price 05/2023 1198 2^861516-1854029 259343 Enzo Doria 09/2015 1199 2^860975-1853977 259180 Enzo Doria 09/2015 1200 3^543128+16 259138 Robert Price 04/2020 1201 2^860625-1858843 259074 Enzo Doria 10/2015 1202 2^860110+77689 258919 Enzo Doria 05/2016 1203 2^859600+1880371 258766 Enzo Doria 10/2016 1204 2^859433+494711 258716 Makoto Morimoto 10/2013 1205 (2^859433-44)/(2^2*3) 258715 Makoto Morimoto 08/2019 1206 (2^859431-11)/3 258715 Stefano Morozzi 08/2022 1207 (13*10^258710-43)/3 258711 Robert Price 08/2023 1208 (2^859433+39899)/(73*3907*46301) 258705 Makoto Morimoto 10/2016 1209 2^859240+1875271 258658 Enzo Doria 06/2016 1210 Tau(971^15738) 258571 Nik Lygeros / Olivier Rozier 05/2015 1211 (23*10^258494-47)/3 258495 Robert Price 09/2023 1212 (144^119671+1)/145 258292 Paul Bourdelais 08/2019 1213 2^857608+105 258166 Stefano Morozzi 05/2021 1214 (11*2^857159-13)/15 258031 Renaud Lifchitz 08/2011 1215 2^857016-633113 257988 Enzo Doria 12/2013 1216 2^855732-113969 257602 Enzo Doria 10/2014 1217 (5*10^257431+91)/3 257432 Robert Price 08/2023 1218 2^853682-3911 256984 Enzo Doria 05/2014 1219 11^246668-90 256879 Enzo Doria 12/2012 1220 5*2^852698+3 256689 Jon Grantham 07/2023 1221 (23*10^256654+7)/3 256655 Robert Price 05/2023 1222 2^851904-113939 256449 Enzo Doria 10/2014 1223 2^851725-851725^2 256395 Henri Lifchitz 03/2019 1224 11^246167-90 256357 Enzo Doria 12/2012 1225 (85*10^256301-1)/3 256303 Robert Price 12/2022 1226 (10^256187+7)/63443/148782853 256175 Alfred Reich 10/2021 1227 2^850700-569049 256087 Enzo Doria 11/2013 1228 2^850675+153 256079 Stefano Morozzi 05/2021 1229 21^193601-20^193601 255983 Jean-Louis Charton 02/2015 1230 (37^163193+1)/38 255918 Paul Bourdelais 07/2019 1231 (14*10^255805-83)/3 255806 Robert Price 11/2022 1232 2^849316+25861 255670 Enzo Doria 12/2023 1233 2^849177-114025 255628 Enzo Doria 12/2014 1234 2*10^255442-21 255443 Robert Price 08/2023 1235 2^848502-3173 255425 Yves Minet 07/2016 1236 2^848178-140291 255328 Enzo Doria 01/2014 1237 7*10^255167+87 255168 Robert Price 11/2022 1238 2^847622-2441 255160 Yves Minet 02/2016 1239 2^847291+182843 255061 Enzo Doria 11/2016 1240 2^847174+1879429 255025 Enzo Doria 09/2016 1241 2^846881+215837 254937 Enzo Doria 12/2023 1242 24*29^174239+13361 254809 Curtis Bright 04/2015 1243 22*10^254639+7 254641 Robert Price 10/2022 1244 2^845633-933075 254561 Paul Bourdelais 11/2021 1245 2^845610-1868591 254554 Enzo Doria 04/2016 1246 2^845484+81931 254517 Enzo Doria 08/2016 1247 2^845402-114761 254492 Enzo Doria 05/2015 1248 98*10^254173-9 254175 Robert Price 05/2023 1249 2^844334-2792441 254170 Enzo Doria 02/2016 1250 2*10^254162+69 254163 Robert Price 08/2023

Find by discoverer :

Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 04 2024 15:31 (Time in France)

Go back