PRP Records

Probable Primes Top 10000

(295765 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 ? 6001 (2^376967+258)/2 113479 Stefano Morozzi 09/2020 6002 (29*10^113468-17)/3 113469 Robert Price 09/2019 6003 35^73477-34^73477 113454 Robert Price 05/2012 6004 (14*10^113451-89)/3 113452 Robert Price 05/2020 6005 2^376790+27 113426 Lelio R Paula 03/2013 6006 2^376786-112701 113424 Enzo Doria 06/2014 6007 2^376731+21 113408 Lelio R Paula 03/2013 6008 9*10^113394-73 113395 Robert Price 01/2021 6009 29660^6651+6651^29660 113387 Hans Havermann 01/2021 6011 2^376634+1871245 113379 Enzo Doria 05/2016 6010 (4^188318+17)/3 113379 Robert Price 02/2017 6012 E(29532)/492842728006750534663978950979381235 113367 Thomas Ritschel 01/2021 6013 2^376576-344369 113361 Enzo Doria 07/2015 6014 2^376549-4543 113353 Yves Minet 03/2019 6015 (17*2^376526-1)/223 113345 Lelio R Paula 03/2014 6016 (27*2^376441-1)/811 113319 Lelio R Paula 03/2014 6017 (2^376350+3538)/2 113293 Stefano Morozzi 09/2020 6018 27265^14272+14272^27265 113273 Hans Havermann 02/2021 6019 32174^3315+3315^32174 113269 Hans Havermann 02/2021 6020 (2*10^113248+73)/3 113248 Robert Price 09/2020 6021 2^376128-21237 113226 Enzo Doria 06/2013 6022 5*10^113224-81 113225 Robert Price 01/2019 6023 10^113220+51409 113221 Patrick De Geest 02/2021 6025 10^113220-1000001 113220 Robert Price 08/2020 6024 10^113220-61779 113220 Patrick De Geest 02/2021 6026 (2^376102+1578)/2 113218 Stefano Morozzi 09/2020 6027 (2^375996+3102)/2 113186 Stefano Morozzi 09/2020 6028 37258^1091+1091^37258 113184 Hans Havermann 02/2021 6029 (94*10^113176+11)/3 113178 Robert Price 04/2020 6030 (46*10^113162+521)/9 113163 Robert Price 02/2019 6031 (2^375885+3614)/2 113153 Stefano Morozzi 09/2020 6032 (2^375873+2006)/2 113149 Stefano Morozzi 09/2020 6033 3*10^113137+23 113138 Robert Price 03/2022 6034 (8*10^113135-269)/9 113135 Robert Price 09/2021 6035 (2^375726+694)/2 113105 Stefano Morozzi 09/2020 6036 26050^21959+21959^26050 113100 Hans Havermann 02/2021 6037 2^375638-1787171 113079 Enzo Doria 03/2016 6038 (2^375563+2178)/2 113056 Stefano Morozzi 09/2020 6039 2^375537+4847 113048 Yves Minet 02/2011 6040 (17^91837+16^91837)/33 113000 Robert Price 08/2013 6041 5*F(270343)*(F(270343)+1)+1 112997 Serge Batalov 04/2015 6042 2^375350-3221 112992 Yves Minet 07/2011 6043 (13*2^375306+1)/7 112979 Lelio R Paula 03/2014 6044 2^375305+76757 112979 Enzo Doria 05/2016 6045 2^375258+1874989 112964 Enzo Doria 07/2016 6046 (29^77237-1)/28 112950 Robert Price 04/2012 6047 26620^17483+17483^26620 112939 Hans Havermann 01/2021 6048 2^375154+74959 112933 Enzo Doria 04/2016 6049 (266*10^112930-17)/3 112932 Robert Price 07/2020 6050 (2^375134+778)/2 112927 Stefano Morozzi 09/2020 6051 (85*10^112919+293)/9 112920 Robert Price 12/2019 6052 29412^6899+6899^29412 112907 Hans Havermann 02/2021 6053 (191*10^112903-17)/3 112905 Robert Price 11/2021 6054 (2^375022+1210)/2 112893 Stefano Morozzi 09/2020 6055 25992^22039+22039^25992 112889 Hans Havermann 02/2021 6056 2^374993-2787163 112885 Enzo Doria 11/2015 6057 (697*10^112869+23)/9 112871 Robert Price 04/2021 6058 (19*10^112851+377)/9 112852 Alfred Reich 11/2022 6059 30420^5111+5111^30420 112813 Hans Havermann 02/2021 6060 13699^27268+27268^13699 112800 Norbert Schneider 12/2020 6061 123^53970+2 112793 Lelio R Paula 06/2013 6062 12308*27^78796+23 112790 Eric Chen 07/2023 6063 28942^7887+7887^28942 112785 Hans Havermann 01/2021 6064 2^374640-4685 112778 Yves Minet 05/2019 6065 12^104501-11 112776 Riley Fisher 12/2023 6066 57290^93+93^57290 112775 Hans Havermann 01/2021 6067 13608^27277-27277^13608 112758 Norbert Schneider 12/2022 6068 (2^374556+682)/2 112753 Stefano Morozzi 09/2020 6069 p(22852)#/2+512 112745 Robert Price 05/2017 6070 (11*10^112742-131)/3 112743 Robert Price 09/2018 6071 2^374441-21049 112718 Enzo Doria 06/2013 6072 4*10^112706-93 112707 Robert Price 07/2020 6073 (2^374321+1)/3 112682 H.&R. Lifchitz 12/2000 6074 (2^374213+1766)/2 112650 Stefano Morozzi 09/2020 6075 (2^374094+2674)/2 112614 Stefano Morozzi 09/2020 6076 (13^101089-1)/12 112607 Paul Bourdelais 03/2010 6077 3^236011-8828 112606 Enzo Doria 05/2014 6078 31854^3427+3427^31854 112602 Hans Havermann 02/2021 6079 (85*10^112530-373)/9 112531 Robert Price 05/2021 6080 (2^373748+1090)/2 112510 Stefano Morozzi 09/2020 6081 (2^373727+1806)/2 112503 Stefano Morozzi 01/2021 6082 27618^11821+11821^27618 112479 Hans Havermann 01/2021 6083 U(602921)/4823369 112479 Serge Batalov 07/2024 6084 26343^18580+18580^26343 112460 Hans Havermann 01/2021 6085 39^70666+2 112435 Lelio R Paula 11/2013 6086 (134*10^112400+7)/3 112402 Robert Price 02/2020 6087 (2^373365+326)/2 112394 Stefano Morozzi 09/2020 6088 (2^373350-7)/3 112390 Lelio R Paula 03/2014 6089 2^373306-1840931 112377 Enzo Doria 06/2015 6090 8*10^112371-37 112372 Robert Price 03/2022 6091 (2^373262+270)/2 112363 Stefano Morozzi 09/2020 6092 6*10^112359-79 112360 Robert Price 03/2022 6093 34409^1842+1842^34409 112356 Hans Havermann 02/2021 6094 (142*10^112352-7)/9 112354 Robert Price 12/2019 6095 25580^24633+24633^25580 112336 Hans Havermann 01/2021 6096 2^373117+1872107 112320 Enzo Doria 05/2016 6097 (2^373083+2226)/2 112309 Stefano Morozzi 01/2021 6098 (35*10^112308+37)/9 112309 Robert Price 05/2022 6099 27963^10376+10376^27963 112301 Hans Havermann 01/2021 6100 2^373040+2792761 112297 Enzo Doria 03/2016 6101 (156^51203-1)/155 112293 Anonymous 06/2024 6102 EPrime(112280) 112280 Eric W. Weisstein 10/2010 6103 2^372950+7 112270 Lelio R Paula 03/2013 6104 2^372945+1872167 112268 Enzo Doria 05/2016 6105 36274^1243+1243^36274 112249 Hans Havermann 02/2021 6106 (55*10^112246+629)/9 112247 Robert Price 01/2022 6107 (2^372872+3798)/2 112246 Stefano Morozzi 02/2021 6108 25513^25060+25060^25513 112232 Hans Havermann 02/2021 6109 (53*10^112229-611)/9 112230 Robert Price 02/2022 6110 (2^372754+3094)/2 112210 Stefano Morozzi 09/2020 6111 6*10^112208+43 112209 Robert Price 07/2020 6112 (2^372728+3058)/2 112203 Stefano Morozzi 09/2020 6113 32061^3158+3158^32061 112195 Hans Havermann 02/2021 6114 2^372695+72113 112193 Enzo Doria 04/2016 6115 2^372689-2563 112191 Yves Minet 07/2014 6116 2^372638-1859441 112176 Enzo Doria 03/2016 6117 3^235074-113056 112159 Enzo Doria 07/2014 6118 -E(29242)/489848365125303139750087 112140 Thomas Ritschel 01/2021 6119 (2^372514+1822)/2 112138 Stefano Morozzi 02/2021 6120 29468^6387+6387^29468 112135 Hans Havermann 02/2021 6121 (2^372428+3742)/2 112112 Stefano Morozzi 01/2021 6122 25375^25454-25454^25375 112110 Norbert Schneider 01/2021 6123 131^52949-130 112108 Norbert Schneider 02/2019 6124 (91*10^112098-1)/9 112100 Robert Price 04/2015 6125 (68*10^112087-149)/9 112088 Robert Price 07/2022 6126 2^372314+212419 112078 Enzo Doria 08/2023 6127 2^372310-85061 112077 Paul Bourdelais 02/2012 6128 (10^112067+53)/9 112067 Serge Batalov 07/2015 6129 (2^372237+2082)/2 112055 Stefano Morozzi 09/2020 6130 75^59760+2 112054 Lelio R Paula 08/2013 6131 (2^372200+1710)/2 112044 Stefano Morozzi 09/2020 6132 (10^112048+7)/8747/373157 112039 Alfred Reich 06/2021 6133 (2^372181+2250)/2 112038 Stefano Morozzi 01/2021 6134 F(536233)/825798821/1102495049/5641839306317 112036 Serge Batalov 07/2024 6135 (2^372161+2574)/2 112032 Stefano Morozzi 09/2020 6136 8*10^112018-49 112019 Robert Price 08/2019 6138 2^372108+74221 112016 Enzo Doria 04/2016 6137 (2^372109+2046)/2 112016 Stefano Morozzi 09/2020 6139 8*10^112011-73 112012 Robert Price 01/2022 6140 (184*10^112007-1)/3 112009 Robert Price 02/2020 6141 5*10^112003+81 112004 Robert Price 03/2019 6142 215^48018+48018^215 112000 Norbert Schneider 10/2018 6143 25549^24148+24148^25549 111979 Hans Havermann 02/2021 6144 2^371970-459491 111975 Enzo Doria 05/2015 6145 41^69427-40^69427 111971 Robert Price 07/2012 6146 (2^371782+358)/2 111918 Stefano Morozzi 01/2021 6147 15*25^80056+446 111915 Eric Chen 10/2023 6148 (34*10^111902-547)/9 111903 Robert Price 03/2021 6149 (10^111902+71)/9 111902 Serge Batalov 07/2015 6150 (2^371625+1610)/2 111870 Stefano Morozzi 09/2020 6151 29080^7027+7027^29080 111865 Hans Havermann 01/2021 6152 31307^3730+3730^31307 111820 Hans Havermann 02/2021 6153 2^371440-112865 111815 Enzo Doria 06/2014 6154 2^371426-459161 111811 Enzo Doria 05/2015 6155 25768^21771+21771^25768 111779 Hans Havermann 02/2021 6156 28022^9747+9747^28022 111777 Hans Havermann 02/2021 6157 (94*10^111770+11)/3 111772 Robert Price 04/2020 6158 2^371276-461267 111766 Enzo Doria 07/2015 6159 6*10^111760+43 111761 Robert Price 07/2020 6160 98079!4-1024 111747 Robert Price 11/2019 6161 (2^371186+3162)/2 111738 Stefano Morozzi 09/2020 6162 10^(2*55862+1)-4*10^55862-1 111725 Robert Price 07/2023 6163 2^371098-113261 111712 Enzo Doria 07/2014 6164 (7*10^111706-61)/9 111706 Erik Branger 01/2011 6165 2^371044+1869391 111696 Enzo Doria 05/2016 6166 26310^17581+17581^26310 111688 Hans Havermann 01/2021 6167 88^57416+87 111645 Norbert Schneider 11/2015 6168 2^370829-109693 111631 Enzo Doria 04/2014 6169 15^94906-2 111619 Lelio R Paula 11/2013 6170 25835^20904+20904^25835 111614 Hans Havermann 02/2021 6171 (2^370726+1198)/2 111600 Stefano Morozzi 09/2020 6172 27758^10479+10479^27758 111597 Hans Havermann 02/2021 6173 2^370695-4627 111591 Yves Minet 05/2019 6174 7*10^111579-87 111580 Robert Price 06/2020 6175 2^370643-37 111575 Yves Minet 01/2012 6176 (2^370655-5)/2439 111575 Lelio R Paula 03/2014 6177 2^370610-3911 111565 Yves Minet 04/2017 6178 (154*10^111549+17)/9 111551 Robert Price 06/2022 6179 26200^18097+18097^26200 111550 Hans Havermann 01/2021 6180 286^45405+45405^286 111532 Norbert Schneider 04/2015 6181 4*5^159563-9 111531 Lelio R Paula 11/2014 6182 5*10^111528-21 111529 Robert Price 12/2021 6183 (4^185225+23)/3 111517 Robert Price 10/2018 6184 2^370393-2797093 111500 Enzo Doria 03/2016 6185 (21*2^370382-1)/629 111495 Lelio R Paula 03/2014 6186 (2^370371+554)/2 111493 Stefano Morozzi 09/2020 6187 6^143273-5 111489 Paul Bourdelais 01/2021 6188 2^370292-2791979 111469 Enzo Doria 03/2016 6189 (14*10^111443-11)/3 111444 Robert Price 08/2022 6190 2^370177-461551 111435 Enzo Doria 07/2015 6191 (2^370169+1706)/2 111432 Stefano Morozzi 09/2020 6192 109^54683-108 111413 Norbert Schneider 02/2017 6193 (83*10^111406-173)/9 111407 Robert Price 04/2021 6194 (2^370043+1010)/2 111394 Stefano Morozzi 09/2020 6195 32961^2396+2396^32961 111392 Hans Havermann 10/2020 6196 numbpart(10^10+76282) 111391 Serge Batalov 04/2015 6197 (19*10^111385+11)/3 111386 Robert Price 07/2023 6198 (23*10^111380-29)/3 111381 Robert Price 03/2022 6199 2^369974+733 111374 Lelio R Paula 05/2013 6200 121^53470+120 111367 Norbert Schneider 10/2018 6201 2^369915-286267 111356 Enzo Doria 07/2015 6202 (62*10^111347-629)/9 111348 Robert Price 07/2021 6203 2^369855-1615 111338 Lelio R Paula 05/2017 6204 7*10^111325+3 111326 Robert Price 08/2015 6205 51^65176+2 111293 Lelio R Paula 08/2013 6206 2^369643-1865767 111274 Enzo Doria 03/2016 6207 2^369603+885 111262 Lelio R Paula 05/2017 6208 25555^22564+22564^25555 111252 Hans Havermann 10/2020 6209 F(532391)/89441689/1425422598617 111243 Serge Batalov 07/2024 6210 L(532277) 111240 Renaud Lifchitz 03/2004 6211 105^55033-2 111233 Lelio R Paula 10/2017 6212 (35*10^111232-737)/9 111233 Robert Price 07/2018 6213 26970^13307+13307^26970 111227 Hans Havermann 10/2020 6214 25419^23716+23716^25419 111210 Hans Havermann 10/2020 6215 9*10^111201-29 111202 Robert Price 09/2019 6216 2^369392+29835 111199 Lelio R Paula 05/2017 6217 3^233059+16 111198 Robert Price 03/2020 6218 2^369354-3413 111187 Yves Minet 12/2016 6219 2^369296-27 111170 Lelio R Paula 02/2013 6220 (2468^40960+1)/(2468^8192+1) 111161 Martin Hopf 08/2024 6221 2^369239-109837 111153 Enzo Doria 05/2014 6222 2^369224-291839 111148 Enzo Doria 07/2015 6223 2^369216+2798881 111146 Enzo Doria 04/2016 6224 26842^13817+13817^26842 111137 Hans Havermann 11/2020 6225 (5*10^111119-191)/3 111120 Robert Price 05/2021 6226 (29*10^111112-23)/3 111113 Robert Price 03/2022 6227 10^111111+163849 111112 Patrick De Geest 03/2017 6228 10^111111-312911 111111 Patrick De Geest 03/2017 6229 2^369092-216923 111108 Enzo Doria 05/2014 6230 2^369081-55 111105 Lelio R Paula 02/2013 6231 (2^369047+3618)/2 111094 Stefano Morozzi 09/2020 6232 88^57124-87 111077 Norbert Schneider 11/2015 6233 2^368980+753 111075 Lelio R Paula 05/2013 6234 2^368946-3623 111064 Yves Minet 03/2017 6235 2^368929+29835 111059 Lelio R Paula 05/2017 6236 4^184463-3^184463 111058 Jean-Louis Charton 12/2004 6237 111^54298+110 111057 Norbert Schneider 04/2017 6238 (4*10^111032-7)/3 111033 Ray Chandler 04/2011 6239 (29*10^111020-41)/3 111021 Tyler Busby 03/2024 6240 35799^1262+1262^35799 111015 Hans Havermann 10/2020 6241 (298*10^111004+11)/3 111006 Robert Price 11/2020 6242 27648^10349+10349^27648 111004 Hans Havermann 11/2020 6243 28899^6932+6932^28899 110997 Hans Havermann 11/2020 6244 (749^38809+1)/(749^197+1) 110990 Martin Hopf 11/2023 6245 2^368641-460303 110972 Enzo Doria 06/2015 6246 2^368619-109087 110966 Enzo Doria 04/2014 6247 (74*10^110961+313)/9 110962 Robert Price 06/2019 6248 25258^24711+24711^25258 110956 Hans Havermann 11/2020 6249 (2^368539+1290)/2 110941 Stefano Morozzi 01/2021 6250 3*2^368489+7 110927 Lelio R Paula 09/2014

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 13 2024 17:43 (Time in France)

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