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) !!!
Submit your PRPs
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See the Latest PRPs
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Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
8144 | 25206!+p(4114) | 100001 | Henri Lifchitz | 09/2005 |
8145 | 25206!-p(5447) | 100001 | Henri Lifchitz | 10/2005 |
8146 | 25206!-p(12402) | 100001 | Henri Lifchitz | 04/2006 |
8147 | 25206!-p(16290) | 100001 | Henri Lifchitz | 09/2006 |
8148 | 25206!-p(19647) | 100001 | Henri Lifchitz | 02/2007 |
8149 | 2^332194+11473 | 100001 | Henri Lifchitz | 03/2007 |
8139 | 10^100000+342909 | 100001 | Milton L. Brown | 12/2007 |
8140 | 10^100000+346579 | 100001 | Robert Price | 04/2012 |
8141 | 10^100000+829767 | 100001 | Robert Price | 05/2012 |
8142 | 10^100000+871899 | 100001 | Robert Price | 05/2012 |
8143 | 10^100000+1475997 | 100001 | Robert Price | 07/2012 |
8132 | 10^100000+1751769 | 100001 | Robert Price | 08/2012 |
8133 | 10^100000+2155489 | 100001 | Robert Price | 10/2012 |
8134 | 10^100000+2483527 | 100001 | Robert Price | 12/2012 |
8135 | 10^100000+2503087 | 100001 | Robert Price | 12/2012 |
8136 | 10^100000+2686179 | 100001 | Robert Price | 12/2012 |
8137 | 10^100000+2688933 | 100001 | Robert Price | 12/2012 |
8138 | 10^100000+3667159 | 100001 | Robert Price | 08/2013 |
8001 | 10^100000+9225987 | 100001 | Robert Price | 04/2017 |
8002 | 10^100000+9265587 | 100001 | Robert Price | 04/2017 |
8003 | 10^100000+9287049 | 100001 | Robert Price | 04/2017 |
8004 | 10^100000+9425053 | 100001 | Robert Price | 05/2017 |
8005 | 10^100000+9450769 | 100001 | Robert Price | 05/2017 |
8006 | 10^100000+9528747 | 100001 | Robert Smith | 05/2017 |
8007 | 10^100000+9548071 | 100001 | Robert Price | 06/2017 |
8008 | 10^100000+10064287 | 100001 | Robert Price | 08/2017 |
8009 | 10^100000+10229569 | 100001 | Robert Price | 10/2017 |
8010 | 10^100000+11992051 | 100001 | Robert Price | 09/2018 |
8011 | 2^332196-1-2*29696 | 100001 | Matt Stath | 11/2018 |
8012 | 10^100000+12363957 | 100001 | Robert Price | 11/2018 |
8013 | 2^332196+1+2*17152 | 100001 | Matt Stath | 12/2018 |
8014 | 10^100000+12778033 | 100001 | Robert Price | 02/2019 |
8015 | 10^100000+13581679 | 100001 | Robert Price | 05/2019 |
8016 | 10^100000+13613199 | 100001 | Robert Price | 05/2019 |
8017 | 10^100000+13752327 | 100001 | Robert Price | 05/2019 |
8018 | 10^100000+14139243 | 100001 | Robert Price | 06/2019 |
8019 | 10^100000+14151057 | 100001 | Robert Price | 06/2019 |
8020 | 10^100000+14218923 | 100001 | Robert Price | 06/2019 |
8021 | 10^100000+15136771 | 100001 | Robert Price | 09/2019 |
8022 | 10^100000+15219873 | 100001 | Robert Price | 10/2019 |
8023 | 10^100000+15274039 | 100001 | Robert Price | 10/2019 |
8024 | 10^100000+15394069 | 100001 | Robert Price | 10/2019 |
8025 | 10^100000+15547119 | 100001 | Robert Price | 10/2019 |
8026 | 10^100000+15932923 | 100001 | Robert Price | 11/2019 |
8027 | 10^100000+16345467 | 100001 | Robert Price | 12/2019 |
8028 | 10^100000+16672143 | 100001 | Robert Price | 01/2020 |
8029 | 10^100000+16731939 | 100001 | Robert Price | 02/2020 |
8030 | 10^100000+16907049 | 100001 | Robert Price | 03/2020 |
8031 | 10^100000+17652523 | 100001 | Robert Price | 05/2020 |
8032 | 10^100000+18047167 | 100001 | Robert Price | 05/2020 |
8033 | 10^100000+18471819 | 100001 | Robert Price | 06/2020 |
8034 | 10^100000+18494793 | 100001 | Robert Price | 07/2020 |
8035 | 10^100000+18762609 | 100001 | Robert Price | 07/2020 |
8036 | 10^100000+19204141 | 100001 | Robert Price | 08/2020 |
8037 | 10^100000+19349793 | 100001 | Robert Price | 08/2020 |
8038 | 10^100000+19495699 | 100001 | Robert Price | 09/2020 |
8039 | 10^100000+19668927 | 100001 | Robert Price | 09/2020 |
8040 | 10^100000+19704313 | 100001 | Robert Price | 09/2020 |
8101 | 10^100000+19956229 | 100001 | Robert Price | 09/2020 |
8102 | 10^100000+3*(10^37093-1)/9*10^31454+1 | 100001 | Makoto Morimoto | 09/2020 |
8103 | 10^100000+4*(10^36149-1)/9*10^31926+1 | 100001 | Makoto Morimoto | 09/2020 |
8104 | 10^100000+6*(10^41029-1)/9*10^29486+1 | 100001 | Makoto Morimoto | 09/2020 |
8105 | 10^100000+7*(10^55505-1)/9*10^22248+1 | 100001 | Makoto Morimoto | 09/2020 |
8106 | 10^100000+20234607 | 100001 | Robert Price | 10/2020 |
8107 | 10^100000+20752303 | 100001 | Robert Price | 11/2020 |
8108 | 10^100000+20774041 | 100001 | Robert Price | 11/2020 |
8109 | 10^100000+20854741 | 100001 | Robert Price | 11/2020 |
8110 | 10^100000+20908917 | 100001 | Robert Price | 11/2020 |
8111 | 10^100000+20994793 | 100001 | Robert Price | 11/2020 |
8112 | 10^100000+21354249 | 100001 | Robert Price | 12/2020 |
8113 | 10^100000+21455559 | 100001 | Robert Price | 12/2020 |
8114 | 10^100000+21538873 | 100001 | Robert Price | 12/2020 |
8115 | 10^100000+21830901 | 100001 | Robert Price | 01/2021 |
8116 | 10^100000+21842629 | 100001 | Robert Price | 01/2021 |
8117 | 10^100000+21930861 | 100001 | Robert Price | 01/2021 |
8118 | 10^100000+22092943 | 100001 | Robert Price | 03/2021 |
8119 | 10^100000+22278417 | 100001 | Robert Price | 03/2021 |
8120 | 10^100000+22388581 | 100001 | Robert Price | 03/2021 |
8121 | 10^100000+22390933 | 100001 | Robert Price | 03/2021 |
8122 | 10^100000+22436169 | 100001 | Robert Price | 03/2021 |
8123 | 10^100000+22714557 | 100001 | Robert Price | 04/2021 |
8124 | 10^100000+22847671 | 100001 | Robert Price | 04/2021 |
8125 | 10^100000+23178567 | 100001 | Robert Price | 05/2021 |
8126 | 10^100000+23332003 | 100001 | Robert Price | 05/2021 |
8127 | 10^100000+23414571 | 100001 | Robert Price | 05/2021 |
8128 | 10^100000+23529979 | 100001 | Robert Price | 05/2021 |
8129 | 10^100000+23749243 | 100001 | Robert Price | 06/2021 |
8130 | 10^100000+23821771 | 100001 | Robert Price | 06/2021 |
8131 | 10^100000+24179307 | 100001 | Robert Price | 07/2021 |
8041 | 10^100000+24543147 | 100001 | Robert Price | 08/2021 |
8042 | 10^100000+24781659 | 100001 | Robert Price | 08/2021 |
8043 | 10^100000+24906153 | 100001 | Robert Price | 08/2021 |
8044 | 10^100000+25682679 | 100001 | Robert Price | 10/2021 |
8045 | 10^100000+25905301 | 100001 | Robert Price | 10/2021 |
8046 | 10^100000+25923967 | 100001 | Robert Price | 10/2021 |
8047 | 10^100000+26061691 | 100001 | Robert Price | 10/2021 |
8048 | 10^100000+26173351 | 100001 | Robert Price | 11/2021 |
8049 | 10^100000+26673487 | 100001 | Robert Price | 11/2021 |
8050 | 10^100000+26849359 | 100001 | Robert Price | 12/2021 |
8051 | 10^100000+26893887 | 100001 | Robert Price | 12/2021 |
8052 | 10^100000+26954551 | 100001 | Robert Price | 12/2021 |
8053 | 10^100000+27024543 | 100001 | Robert Price | 12/2021 |
8054 | 10^100000+27060877 | 100001 | Robert Price | 12/2021 |
8055 | 10^100000+27617577 | 100001 | Robert Price | 03/2022 |
8056 | 10^100000+27869671 | 100001 | Robert Price | 03/2022 |
8057 | 10^100000+27956481 | 100001 | Robert Price | 03/2022 |
8058 | 10^100000+28078261 | 100001 | Robert Price | 03/2022 |
8059 | 10^100000+28150203 | 100001 | Robert Price | 03/2022 |
8060 | 10^100000+28626021 | 100001 | Robert Price | 05/2022 |
8061 | 10^100000+28649299 | 100001 | Robert Price | 05/2022 |
8062 | 10^100000+29409799 | 100001 | Robert Price | 06/2022 |
8063 | 10^100000+29415577 | 100001 | Robert Price | 06/2022 |
8064 | 10^100000+29424201 | 100001 | Robert Price | 06/2022 |
8065 | 10^100000+29610153 | 100001 | Robert Price | 07/2022 |
8066 | 10^100000+30166789 | 100001 | Robert Price | 07/2022 |
8067 | 10^100000+30338259 | 100001 | Robert Price | 07/2022 |
8068 | 10^100000+30540031 | 100001 | Robert Price | 07/2022 |
8069 | 10^100000+30635157 | 100001 | Robert Price | 07/2022 |
8070 | 10^100000+30762711 | 100001 | Robert Price | 07/2022 |
8071 | 10^100000+30862057 | 100001 | Robert Price | 07/2022 |
8072 | 10^100000+30998953 | 100001 | Robert Price | 07/2022 |
8073 | 10^100000+31405203 | 100001 | Robert Price | 07/2022 |
8074 | 10^100000+40159119 | 100001 | Robert Price | 07/2022 |
8075 | 10^100000+40181863 | 100001 | Robert Price | 07/2022 |
8076 | 10^100000+40277131 | 100001 | Robert Price | 07/2022 |
8077 | 10^100000+40326061 | 100001 | Robert Price | 07/2022 |
8078 | 10^100000+40417411 | 100001 | Robert Price | 07/2022 |
8079 | 10^100000+50049909 | 100001 | Robert Price | 07/2022 |
8080 | 10^100000+50510163 | 100001 | Robert Price | 07/2022 |
8081 | 10^100000+50591583 | 100001 | Robert Price | 07/2022 |
8082 | 10^100000+50850357 | 100001 | Robert Price | 07/2022 |
8083 | 10^100000+50974641 | 100001 | Robert Price | 07/2022 |
8084 | 10^100000+51046671 | 100001 | Robert Price | 07/2022 |
8085 | 10^100000+51459657 | 100001 | Robert Price | 07/2022 |
8086 | 10^100000+70081471 | 100001 | Robert Price | 07/2022 |
8087 | 10^100000+70159557 | 100001 | Robert Price | 07/2022 |
8088 | 10^100000+70262479 | 100001 | Robert Price | 07/2022 |
8089 | 10^100000+70417521 | 100001 | Robert Price | 07/2022 |
8090 | 10^100000+70476531 | 100001 | Robert Price | 07/2022 |
8091 | 10^100000+70534627 | 100001 | Robert Price | 07/2022 |
8092 | 10^100000+70873077 | 100001 | Robert Price | 07/2022 |
8093 | 10^100000+71114643 | 100001 | Robert Price | 07/2022 |
8094 | 10^100000+71272539 | 100001 | Robert Price | 07/2022 |
8095 | 10^100000+80025337 | 100001 | Robert Price | 07/2022 |
8096 | 10^100000+71580817 | 100001 | Robert Price | 07/2022 |
8097 | 10^100000+80270349 | 100001 | Robert Price | 07/2022 |
8098 | 10^100000+29831551 | 100001 | Robert Price | 07/2022 |
8099 | 10^100000+29955417 | 100001 | Robert Price | 08/2022 |
8100 | 479072067*10^99992+1+2*1779 | 100001 | Matt Stath | 12/2022 |
8150 | 10^99999+309403 | 100000 | Daniel Heuer | 01/2004 |
8151 | 10^100000-260199 | 100000 | Patrick De Geest | 01/2010 |
8152 | 2^332192+10192681 | 100000 | Sujan Das | 06/2022 |
8153 | 1610172603059^8192+1610172602878^8192 | 100000 | Youcef Lemsafer | 01/2023 |
8155 | 10^99999-59511 | 99999 | Patrick De Geest | 07/2009 |
8154 | 10^99998+235437 | 99999 | Patrick De Geest | 02/2020 |
8156 | 10^99998-286587 | 99998 | Patrick De Geest | 02/2020 |
8157 | 10^99997+72297 | 99998 | Patrick De Geest | 02/2020 |
8158 | 10^99997-402627 | 99997 | Patrick De Geest | 02/2020 |
8159 | 10^99996+279853 | 99997 | Patrick De Geest | 02/2020 |
8160 | 10^99997-500000001 | 99997 | Robert Price | 12/2020 |
8161 | 10^99996-94961 | 99996 | Patrick De Geest | 02/2020 |
8162 | 10^99995+54633 | 99996 | Patrick De Geest | 02/2020 |
8163 | 10^99995-101429 | 99995 | Patrick De Geest | 02/2020 |
8164 | 10^99994+117271 | 99995 | Patrick De Geest | 02/2020 |
8165 | 10^99994-452289 | 99994 | Patrick De Geest | 02/2020 |
8166 | 10^99993+371311 | 99994 | Patrick De Geest | 02/2020 |
8167 | 10^99993-186491 | 99993 | Patrick De Geest | 02/2020 |
8168 | 10^99992+17431 | 99993 | Patrick De Geest | 02/2020 |
8169 | 10^99992-28607 | 99992 | Patrick De Geest | 02/2020 |
8170 | 10^99991+125391 | 99992 | Patrick De Geest | 02/2020 |
8171 | 10^99991-204573 | 99991 | Patrick De Geest | 02/2020 |
8172 | 10^99990+13899 | 99991 | Patrick De Geest | 02/2020 |
8173 | 10^99990-8111 | 99990 | Patrick De Geest | 02/2020 |
8174 | 2^332141-113073 | 99985 | Enzo Doria | 07/2014 |
8175 | (1610172603037^8192+1610172602919^8192)/17110948127473666 | 99983 | Youcef Lemsafer | 01/2023 |
8176 | 6*10^99979-79 | 99980 | Robert Price | 03/2022 |
8178 | (3^209561+2)/728101255 | 99978 | Lelio R Paula | 09/2013 |
8177 | 23827^15702+15702^23827 | 99978 | Hans Havermann | 04/2018 |
8179 | 2^332085+1865897 | 99968 | Enzo Doria | 03/2016 |
8180 | (9787*2^332070-1)/936402369 | 99959 | Lelio R Paula | 05/2015 |
8181 | 2^332023+191 | 99949 | Lelio R Paula | 02/2011 |
8182 | (6271^26321-1)/6270 | 99946 | Serge Batalov | 06/2022 |
8183 | 7*10^99944+27 | 99945 | Robert Price | 11/2020 |
8184 | 2^331938+71149 | 99924 | Enzo Doria | 04/2016 |
8185 | 2^331932-78795 | 99922 | Lelio R Paula | 09/2016 |
8186 | 2^331921+771 | 99919 | Lelio R Paula | 01/2013 |
8187 | (3^209419-2)/5132755 | 99912 | Lelio R Paula | 09/2013 |
8188 | 2^331860-114989 | 99900 | Enzo Doria | 05/2015 |
8189 | 2^331746-11655 | 99866 | Lelio R Paula | 09/2016 |
8190 | 11^95891-28 | 99861 | Lelio R Paula | 08/2016 |
8191 | (2^331694-5)/11 | 99849 | Lelio R Paula | 10/2013 |
8192 | (3^209246+7)/64 | 99834 | Lelio R Paula | 09/2013 |
8193 | 25062^9617+9617^25062 | 99823 | Hans Havermann | 04/2018 |
8194 | 15^84866-52 | 99811 | Lelio R Paula | 08/2016 |
8195 | 13^89600+30 | 99810 | Lelio R Paula | 08/2016 |
8196 | 2^331527+100280245065 | 99800 | Paul Bourdelais | 10/2021 |
8197 | 22950^22309+22309^22950 | 99798 | Hans Havermann | 03/2018 |
8198 | 5^142772-38 | 99794 | Lelio R Paula | 08/2016 |
8199 | (7482^25759-1)/7481 | 99787 | Serge Batalov | 06/2022 |
8200 | (23*2^331459+1)/475 | 99778 | Lelio R Paula | 11/2013 |
8201 | 2^331416-331416+1 | 99767 | Robert Price | 10/2014 |
8202 | 2^331256-57 | 99718 | Lelio R Paula | 12/2012 |
8203 | 28192^3443+3443^28192 | 99714 | Hans Havermann | 03/2018 |
8204 | 2^331185+737 | 99697 | Lelio R Paula | 01/2013 |
8205 | (4*10^99693+149)/9 | 99693 | Robert Price | 03/2017 |
8206 | 2^331154+1880527 | 99688 | Enzo Doria | 10/2016 |
8208 | (19^77951+1)/20 | 99679 | Paul Bourdelais | 03/2010 |
8207 | 24354^12385+12385^24354 | 99679 | Hans Havermann | 03/2018 |
8209 | 2^331110+1870459 | 99675 | Enzo Doria | 05/2016 |
8210 | 5*2^331075+7 | 99665 | Lelio R Paula | 08/2014 |
8211 | 25776^7351+7351^25776 | 99659 | Hans Havermann | 02/2018 |
8212 | (16*10^99656-31)/3 | 99657 | Robert Price | 03/2016 |
8213 | (6059^26347-1)/6058 | 99652 | Serge Batalov | 06/2022 |
8214 | (15544^23773-1)/15543 | 99642 | Serge Batalov | 06/2022 |
8216 | 2^330968+345 | 99632 | Lelio R Paula | 09/2016 |
8215 | (2^330969+690)/2 | 99632 | Stefano Morozzi | 09/2020 |
8218 | 2*5^142528-7 | 99624 | Lelio R Paula | 11/2014 |
8217 | 2^330942+77329 | 99624 | Enzo Doria | 05/2016 |
8219 | 14^86914-99 | 99615 | Lelio R Paula | 08/2016 |
8220 | (19*2^330902+1)/77 | 99611 | Lelio R Paula | 11/2013 |
8221 | 22971^21692+21692^22971 | 99610 | Hans Havermann | 03/2018 |
8222 | 2^330845+71687 | 99595 | Enzo Doria | 04/2016 |
8223 | (26667^22501-1)/26666 | 99585 | Serge Batalov | 06/2022 |
8224 | (23*2^330770+1)/3 | 99573 | Lelio R Paula | 11/2013 |
8225 | 24494^11613+11613^24494 | 99567 | Hans Havermann | 03/2018 |
8226 | 2^330735+8415 | 99562 | Lelio R Paula | 09/2016 |
8227 | 2^330720+74071 | 99557 | Enzo Doria | 04/2016 |
8228 | (10405^24781-1)/10404 | 99548 | Serge Batalov | 06/2022 |
8230 | 31^66738-2 | 99531 | Lelio R Paula | 09/2013 |
8229 | (9002^25171-1)/9001 | 99531 | Serge Batalov | 06/2022 |
8231 | (5023^26893-1)/5022 | 99527 | Serge Batalov | 06/2022 |
8232 | 7*3^208567+4 | 99513 | Lelio R Paula | 08/2014 |
8233 | (15881^23689-1)/15880 | 99511 | Serge Batalov | 06/2022 |
8234 | (13*10^99508+47)/3 | 99509 | Robert Price | 01/2017 |
8235 | 2^330553+779 | 99507 | Lelio R Paula | 01/2013 |
8236 | 15^84606-94 | 99505 | Lelio R Paula | 08/2016 |
8237 | (10^99497+173)/3 | 99497 | Robert Price | 05/2021 |
8238 | 9*10^99493-43 | 99494 | Robert Price | 09/2021 |
8239 | 6^127858+47 | 99493 | Lelio R Paula | 08/2016 |
8240 | 5^142337+48 | 99490 | Lelio R Paula | 08/2016 |
8241 | 7^117724-20 | 99489 | Lelio R Paula | 08/2016 |
8242 | (559^36209-1)/558 | 99479 | Serge Batalov | 06/2022 |
8243 | (13470^24091-1)/13469 | 99477 | Serge Batalov | 06/2022 |
8244 | (29*10^99474-17)/3 | 99475 | Erik Branger | 09/2014 |
8245 | (185*10^99466-11)/3 | 99468 | Robert Price | 10/2020 |
8246 | (2^330410+2038)/2 | 99464 | Stefano Morozzi | 09/2020 |
8247 | (9*2^330407-1)/7 | 99463 | Lelio R Paula | 03/2014 |
8248 | (2863^28771-1)/2862 | 99453 | Serge Batalov | 06/2022 |
8249 | (2^330373+2114)/2 | 99452 | Stefano Morozzi | 09/2020 |
8250 | (68*10^99441+7)/3 | 99443 | Robert Price | 03/2016 |