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
See the Top discoverers
See the Latest PRPs
Search by form
| Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
| 8001 | 2^346115+30513 | 104191 | Stefano Morozzi | 11/2024 |
| 8002 | 2^346115+90105 | 104191 | Stefano Morozzi | 11/2024 |
| 8003 | 2^346115+155859 | 104191 | Stefano Morozzi | 11/2024 |
| 8004 | 2^346115+157809 | 104191 | Stefano Morozzi | 11/2024 |
| 8005 | 2^346109+118587 | 104190 | Stefano Morozzi | 11/2024 |
| 8006 | 2^346110+105763 | 104190 | Stefano Morozzi | 11/2024 |
| 8007 | 2^346110+175197 | 104190 | Stefano Morozzi | 11/2024 |
| 8008 | 2^346110+197725 | 104190 | Stefano Morozzi | 11/2024 |
| 8009 | 2^346111+143313 | 104190 | Stefano Morozzi | 11/2024 |
| 8010 | 2^346107+153513 | 104189 | Stefano Morozzi | 11/2024 |
| 8011 | 2^346108+153897 | 104189 | Stefano Morozzi | 11/2024 |
| 8012 | 2^346102+79435 | 104188 | Stefano Morozzi | 11/2024 |
| 8013 | 2^346102+131949 | 104188 | Stefano Morozzi | 11/2024 |
| 8014 | 2^346103+123009 | 104188 | Stefano Morozzi | 11/2024 |
| 8015 | 2^346104+115845 | 104188 | Stefano Morozzi | 11/2024 |
| 8016 | 2^346105+29141 | 104188 | Stefano Morozzi | 11/2024 |
| 8017 | 2^346105+85035 | 104188 | Stefano Morozzi | 11/2024 |
| 8018 | 2^346098+80323 | 104186 | Stefano Morozzi | 11/2024 |
| 8019 | 2^346092+69855 | 104185 | Stefano Morozzi | 11/2024 |
| 8020 | 2^346093+3627 | 104185 | Stefano Morozzi | 11/2024 |
| 8021 | 2^346089+90947 | 104184 | Stefano Morozzi | 11/2024 |
| 8022 | 2^346089+186749 | 104184 | Stefano Morozzi | 11/2024 |
| 8023 | 2^346091+71279 | 104184 | Stefano Morozzi | 11/2024 |
| 8024 | 2^346084+69211 | 104182 | Stefano Morozzi | 11/2024 |
| 8025 | 2^346084+112237 | 104182 | Stefano Morozzi | 11/2024 |
| 8026 | 2^346079+10371 | 104181 | Stefano Morozzi | 11/2024 |
| 8027 | 2^346079+82811 | 104181 | Stefano Morozzi | 11/2024 |
| 8031 | 2^346078+7695 | 104180 | Lelio R Paula | 12/2016 |
| 8028 | 2^346076+85903 | 104180 | Stefano Morozzi | 11/2024 |
| 8029 | 2^346076+111577 | 104180 | Stefano Morozzi | 11/2024 |
| 8030 | 2^346076+143047 | 104180 | Stefano Morozzi | 11/2024 |
| 8032 | 2^346072+126673 | 104179 | Stefano Morozzi | 11/2024 |
| 8033 | 2^346073+37899 | 104179 | Stefano Morozzi | 11/2024 |
| 8034 | 2^346075+21519 | 104179 | Stefano Morozzi | 11/2024 |
| 8035 | 2^346075+27255 | 104179 | Stefano Morozzi | 11/2024 |
| 8036 | 2^346075+115331 | 104179 | Stefano Morozzi | 11/2024 |
| 8037 | 2^346069+53615 | 104178 | Stefano Morozzi | 11/2024 |
| 8038 | 2^346069+188087 | 104178 | Stefano Morozzi | 11/2024 |
| 8039 | 2^346066+29949 | 104177 | Stefano Morozzi | 11/2024 |
| 8040 | 2^346066+133909 | 104177 | Stefano Morozzi | 11/2024 |
| 8041 | 2^346066+188535 | 104177 | Stefano Morozzi | 11/2024 |
| 8042 | 2^346068+159553 | 104177 | Stefano Morozzi | 11/2024 |
| 8043 | 2^346064+122683 | 104176 | Stefano Morozzi | 11/2024 |
| 8044 | 2^346060+20325 | 104175 | Stefano Morozzi | 11/2024 |
| 8045 | 2^346060+110755 | 104175 | Stefano Morozzi | 11/2024 |
| 8046 | 2^346058+57933 | 104174 | Stefano Morozzi | 11/2024 |
| 8052 | 2^346055-19537 | 104173 | Enzo Doria | 05/2013 |
| 8053 | (3*2^346057+1)/77 | 104173 | Lelio R Paula | 12/2013 |
| 8047 | 2^346052+26655 | 104173 | Stefano Morozzi | 11/2024 |
| 8048 | 2^346052+31611 | 104173 | Stefano Morozzi | 11/2024 |
| 8049 | 2^346053+67667 | 104173 | Stefano Morozzi | 11/2024 |
| 8050 | 2^346054+30507 | 104173 | Stefano Morozzi | 11/2024 |
| 8051 | 2^346054+194589 | 104173 | Stefano Morozzi | 11/2024 |
| 8054 | 2^346049+59067 | 104172 | Stefano Morozzi | 11/2024 |
| 8055 | 2^346050+3129 | 104172 | Stefano Morozzi | 11/2024 |
| 8056 | 2^346050+167125 | 104172 | Stefano Morozzi | 11/2024 |
| 8057 | 2^346051+52563 | 104172 | Stefano Morozzi | 11/2024 |
| 8058 | 2^346051+90941 | 104172 | Stefano Morozzi | 11/2024 |
| 8059 | 2^346046+172107 | 104171 | Stefano Morozzi | 11/2024 |
| 8060 | 2^346048+63415 | 104171 | Stefano Morozzi | 11/2024 |
| 8061 | 2^346041+197885 | 104169 | Stefano Morozzi | 11/2024 |
| 8065 | 2^346037-20125 | 104168 | Enzo Doria | 06/2013 |
| 8062 | 2^346036+80773 | 104168 | Stefano Morozzi | 11/2024 |
| 8063 | 2^346037+116429 | 104168 | Stefano Morozzi | 11/2024 |
| 8064 | 2^346038+147549 | 104168 | Stefano Morozzi | 11/2024 |
| 8066 | 2^346034+2205 | 104167 | Stefano Morozzi | 11/2024 |
| 8067 | 2^346031+56429 | 104166 | Stefano Morozzi | 11/2024 |
| 8068 | 2^346031+68439 | 104166 | Stefano Morozzi | 11/2024 |
| 8069 | 2^346031+114891 | 104166 | Stefano Morozzi | 11/2024 |
| 8070 | 2^346031+190563 | 104166 | Stefano Morozzi | 11/2024 |
| 8071 | 2^346026+179305 | 104165 | Stefano Morozzi | 11/2024 |
| 8072 | 2^346027+159425 | 104165 | Stefano Morozzi | 11/2024 |
| 8073 | 2^346028+12517 | 104165 | Stefano Morozzi | 11/2024 |
| 8074 | 2^346022+84705 | 104164 | Stefano Morozzi | 11/2024 |
| 8075 | 2^346019+73673 | 104163 | Stefano Morozzi | 11/2024 |
| 8076 | 2^346019+78999 | 104163 | Stefano Morozzi | 11/2024 |
| 8077 | 2^346019+79955 | 104163 | Stefano Morozzi | 11/2024 |
| 8078 | 2^346020+72993 | 104163 | Stefano Morozzi | 11/2024 |
| 8079 | 2^346020+188673 | 104163 | Stefano Morozzi | 11/2024 |
| 8080 | 2^346021+100311 | 104163 | Stefano Morozzi | 11/2024 |
| 8084 | (34*10^104168-7)/9/13/551179 | 104162 | Makoto Morimoto | 05/2016 |
| 8081 | 2^346016+84007 | 104162 | Stefano Morozzi | 11/2024 |
| 8082 | 2^346017+122397 | 104162 | Stefano Morozzi | 11/2024 |
| 8083 | 2^346017+165791 | 104162 | Stefano Morozzi | 11/2024 |
| 8085 | 2^346014+27949 | 104161 | Stefano Morozzi | 11/2024 |
| 8086 | 2^346014+46743 | 104161 | Stefano Morozzi | 11/2024 |
| 8087 | 2^346015+166089 | 104161 | Stefano Morozzi | 11/2024 |
| 8088 | 2^346009+107705 | 104160 | Stefano Morozzi | 11/2024 |
| 8089 | 2^346012+35043 | 104160 | Stefano Morozzi | 11/2024 |
| 8090 | 2^346012+83091 | 104160 | Stefano Morozzi | 11/2024 |
| 8097 | 6^133854-17993 | 104159 | Enzo Doria | 03/2013 |
| 8091 | 2^346006+77727 | 104159 | Stefano Morozzi | 11/2024 |
| 8092 | 2^346008+9007 | 104159 | Stefano Morozzi | 11/2024 |
| 8093 | 2^346008+51567 | 104159 | Stefano Morozzi | 11/2024 |
| 8094 | 2^346008+107787 | 104159 | Stefano Morozzi | 11/2024 |
| 8095 | 2^346008+146191 | 104159 | Stefano Morozzi | 11/2024 |
| 8096 | 2^346008+170823 | 104159 | Stefano Morozzi | 11/2024 |
| 8098 | 2^346003+191519 | 104158 | Stefano Morozzi | 11/2024 |
| 8099 | 2^345990+1874239 | 104154 | Enzo Doria | 06/2016 |
| 8100 | 2^345988-20373 | 104153 | Enzo Doria | 06/2013 |
| 8101 | (2^345965+2214)/2 | 104146 | Stefano Morozzi | 09/2020 |
| 8102 | (26*10^104132-503)/9 | 104133 | Robert Price | 07/2018 |
| 8103 | 3*5^148968+8 | 104125 | Lelio R Paula | 11/2014 |
| 8104 | (7*10^104113+53)/3 | 104114 | Robert Price | 05/2018 |
| 8105 | p(21253)#/2+8 | 104113 | Robert Price | 01/2017 |
| 8106 | 33582^1259+1259^33582 | 104106 | Hans Havermann | 09/2020 |
| 8107 | 32958^1441+1441^32958 | 104104 | Hans Havermann | 09/2020 |
| 8108 | 29127^3748+3748^29127 | 104095 | Hans Havermann | 09/2020 |
| 8109 | 322^41507+41507^322 | 104094 | Norbert Schneider | 12/2014 |
| 8110 | 6^133768-17423 | 104092 | Enzo Doria | 03/2013 |
| 8111 | 2^345786-19557 | 104092 | Enzo Doria | 05/2013 |
| 8112 | 171^46606-2 | 104072 | Lelio R Paula | 10/2017 |
| 8113 | (29*10^104071+91)/3 | 104072 | Robert Price | 04/2020 |
| 8114 | norm(Mod(x,x^3-x-1)^852167-1) | 104070 | Paul Vanderveen | 09/2022 |
| 8115 | 2^345704-149 | 104068 | Lelio R Paula | 09/2011 |
| 8116 | 25821^10712+10712^25821 | 104056 | Hans Havermann | 09/2020 |
| 8117 | (2^345662+2038)/2 | 104055 | Stefano Morozzi | 09/2020 |
| 8118 | 6^133704-17273 | 104042 | Enzo Doria | 02/2013 |
| 8119 | (3*2^345590-1)/23 | 104033 | Lelio R Paula | 03/2014 |
| 8120 | (19*2^345590+1)/33859 | 104030 | Lelio R Paula | 12/2013 |
| 8121 | 2^345547+11 | 104021 | Lelio R Paula | 09/2011 |
| 8122 | (19*10^104014-49)/3 | 104015 | Robert Price | 05/2019 |
| 8123 | (2^345519+1794)/2 | 104012 | Stefano Morozzi | 01/2021 |
| 8124 | 2^345504+723 | 104008 | Lelio R Paula | 09/2011 |
| 8125 | 2^345498-20037 | 104006 | Enzo Doria | 06/2013 |
| 8127 | 18^82854-37 | 104005 | Lelio R Paula | 01/2017 |
| 8126 | (2^345497+2070)/2 | 104005 | Stefano Morozzi | 09/2020 |
| 8128 | 2^345486-109065 | 104002 | Enzo Doria | 04/2014 |
| 8129 | 2^345487-1851507 | 104002 | Enzo Doria | 08/2015 |
| 8130 | 2^345476+777 | 103999 | Lelio R Paula | 09/2011 |
| 8131 | (2^345477+1554)/2 | 103999 | Stefano Morozzi | 09/2020 |
| 8132 | 4*10^103981-83 | 103982 | Robert Price | 10/2018 |
| 8133 | (2^345327+3206)/2 | 103954 | Stefano Morozzi | 09/2020 |
| 8134 | (5*2^345321-1)/3 | 103953 | Lelio R Paula | 03/2014 |
| 8135 | (2^345267-9)/539049127 | 103927 | Lelio R Paula | 12/2013 |
| 8136 | (19*10^103907+77)/3 | 103908 | Robert Price | 05/2019 |
| 8137 | (78557*2^345163+1)/78589 | 103905 | Lelio R Paula | 07/2014 |
| 8138 | 2^345106-112181 | 103888 | Enzo Doria | 06/2014 |
| 8139 | (2^345105+1326)/2 | 103887 | Stefano Morozzi | 02/2021 |
| 8140 | 2^345079+99 | 103880 | Lelio R Paula | 09/2011 |
| 8141 | (2^345034+1198)/2 | 103866 | Stefano Morozzi | 09/2020 |
| 8142 | 11^99736-1500 | 103865 | Enzo Doria | 12/2012 |
| 8143 | (569^37699-1)/568 | 103863 | Serge Batalov | 06/2022 |
| 8144 | (2^345010+2082)/2 | 103859 | Stefano Morozzi | 09/2020 |
| 8145 | 23263^23784-23784^23263 | 103857 | Norbert Schneider | 01/2020 |
| 8146 | 3*10^103844+31 | 103845 | Robert Price | 06/2021 |
| 8147 | 444*33^68368+19 | 103821 | Eric Chen | 05/2023 |
| 8148 | 23927^21814+21814^23927 | 103813 | Hans Havermann | 09/2020 |
| 8149 | 2^344842-20157 | 103808 | Enzo Doria | 06/2013 |
| 8150 | (47*2^344822+1)/1071 | 103801 | Lelio R Paula | 05/2015 |
| 8151 | 2^344802-20765 | 103796 | Enzo Doria | 06/2013 |
| 8152 | 2^344794-3821 | 103794 | Yves Minet | 05/2011 |
| 8153 | 2^344782-109103 | 103790 | Enzo Doria | 04/2014 |
| 8154 | 3^217521-112292 | 103784 | Enzo Doria | 06/2014 |
| 8155 | 2^344759-3505 | 103783 | Lelio R Paula | 11/2016 |
| 8156 | 2^344735-147 | 103776 | Lelio R Paula | 09/2011 |
| 8157 | L(496533)-p(496533) | 103770 | Robert Price | 02/2018 |
| 8158 | 2*10^103749-69 | 103750 | Robert Price | 03/2018 |
| 8159 | (55459*2^344617+1)/3 | 103745 | Lelio R Paula | 07/2014 |
| 8160 | 2^344607-108891 | 103738 | Enzo Doria | 03/2014 |
| 8162 | (2^344608+3798)/2 | 103738 | Stefano Morozzi | 02/2021 |
| 8161 | (1097^34123-1)/1096 | 103738 | Serge Batalov | 06/2022 |
| 8163 | 2^344560+22411 | 103723 | Enzo Doria | 09/2023 |
| 8164 | (148*10^103718-1)/3 | 103720 | Robert Price | 03/2020 |
| 8165 | 2^344541-19561 | 103718 | Enzo Doria | 05/2013 |
| 8166 | (1017*2^344529-1)/569 | 103714 | Lelio R Paula | 05/2015 |
| 8167 | (8896^26263-1)/8895 | 103714 | Serge Batalov | 06/2022 |
| 8168 | (2^344503+1758)/2 | 103706 | Stefano Morozzi | 09/2020 |
| 8169 | (4*10^103703-1)/3 | 103704 | Serge Batalov | 08/2009 |
| 8170 | 2^344444-455 | 103688 | Yves Minet | 03/2012 |
| 8171 | (4*10^103678-43)/3 | 103679 | Robert Price | 01/2022 |
| 8172 | (13*53^238539*617^9)/10^307661 | 103673 | Hans Havermann | 06/2017 |
| 8173 | (2^344367+2738)/2 | 103665 | Stefano Morozzi | 01/2021 |
| 8175 | 2^344317-109933 | 103650 | Enzo Doria | 04/2014 |
| 8174 | 26055^9508+9508^26055 | 103650 | Hans Havermann | 09/2020 |
| 8176 | 2^344309-1852033 | 103648 | Enzo Doria | 08/2015 |
| 8177 | 25729^10672+10672^25729 | 103643 | Hans Havermann | 09/2020 |
| 8178 | (2^344289+1166)/2 | 103642 | Stefano Morozzi | 09/2020 |
| 8179 | 3*10^103637+61 | 103638 | Robert Price | 09/2020 |
| 8180 | (2^344246+1614)/2 | 103629 | Stefano Morozzi | 09/2020 |
| 8181 | 2^344213-21253 | 103619 | Enzo Doria | 06/2013 |
| 8182 | 2^344196-465 | 103614 | Lelio R Paula | 11/2016 |
| 8183 | 2^344187-20001 | 103611 | Enzo Doria | 06/2013 |
| 8184 | (117191#+(355573#)/(117191#))/(200233679) | 103602 | Makoto Morimoto | 10/2017 |
| 8185 | (237^43627-1)/236 | 103601 | Serge Batalov | 06/2022 |
| 8186 | 20^79621-19^79621 | 103590 | Jean-Louis Charton | 03/2011 |
| 8187 | Phi(155391,10)/1243129 | 103586 | Maksym Voznyy | 09/2015 |
| 8188 | (9^108553-2^108553)/7 | 103586 | Jon Grantham | 07/2023 |
| 8189 | 2^344085-20365 | 103580 | Enzo Doria | 06/2013 |
| 8190 | 5^148169+54 | 103566 | Lelio R Paula | 11/2016 |
| 8191 | 2^344017-108795 | 103560 | Enzo Doria | 03/2014 |
| 8192 | (2^343974+2670)/2 | 103547 | Stefano Morozzi | 09/2020 |
| 8193 | 2^343971-5077 | 103546 | Lelio R Paula | 09/2011 |
| 8194 | (7*10^103531+71)/3 | 103532 | Robert Price | 05/2018 |
| 8195 | 2^343899+141 | 103524 | Lelio R Paula | 08/2011 |
| 8196 | (2^343933+1)/(3*98294339989393) | 103520 | Gord Palameta | 08/2018 |
| 8197 | 6^133029-67 | 103517 | Lelio R Paula | 11/2016 |
| 8198 | (17*2^343877+1)/13625 | 103515 | Lelio R Paula | 12/2013 |
| 8199 | 66*10^103507+7 | 103509 | Robert Price | 07/2020 |
| 8200 | 26297^8614+8614^26297 | 103485 | Hans Havermann | 09/2020 |
| 8201 | (2^343764+2658)/2 | 103483 | Stefano Morozzi | 09/2020 |
| 8202 | 26499^8036+8036^26499 | 103480 | Hans Havermann | 09/2020 |
| 8203 | (136*10^103474-1)/9 | 103476 | Serge Batalov | 12/2014 |
| 8204 | 5^148014-24 | 103458 | Lelio R Paula | 11/2016 |
| 8205 | 25^74007-24 | 103458 | Anonymous | 09/2024 |
| 8206 | 28316^4503+4503^28316 | 103453 | Hans Havermann | 09/2020 |
| 8207 | (22*10^103450+53)/3 | 103451 | Robert Price | 07/2019 |
| 8208 | 2^343604+9931 | 103436 | Yves Minet | 01/2011 |
| 8209 | 2^343601-21189 | 103435 | Enzo Doria | 06/2013 |
| 8210 | (10^103423+173)/3 | 103423 | Robert Price | 05/2021 |
| 8211 | 2^343508-115229 | 103407 | Enzo Doria | 06/2015 |
| 8212 | (8766^26227-1)/8765 | 103404 | Serge Batalov | 06/2022 |
| 8213 | (509203*2^343491-1)/16147 | 103403 | Lelio R Paula | 05/2015 |
| 8214 | 3^216685-113056 | 103386 | Enzo Doria | 07/2014 |
| 8215 | 24829^14580+14580^24829 | 103382 | Hans Havermann | 08/2020 |
| 8216 | 91355!4+1024 | 103381 | Robert Price | 09/2019 |
| 8217 | 44^62903-43^62903 | 103379 | Jean-Louis Charton | 08/2012 |
| 8218 | 11^99262-20 | 103371 | Lelio R Paula | 12/2016 |
| 8219 | (509203*2^343357-1)/5 | 103366 | Lelio R Paula | 05/2015 |
| 8220 | (2^343363+3570)/2 | 103363 | Stefano Morozzi | 09/2020 |
| 8221 | 2^343356-2791889 | 103361 | Enzo Doria | 03/2016 |
| 8222 | (25*10^103360-241)/9 | 103361 | Robert Price | 05/2018 |
| 8223 | Phi(104989,10)/2939693 | 103350 | Maksym Voznyy | 09/2015 |
| 8224 | (371*33^68040-19)/32 | 103321 | Eric Chen | 05/2023 |
| 8225 | 24826^14511+14511^24826 | 103319 | Hans Havermann | 09/2020 |
| 8226 | 2^343182-171 | 103309 | Lelio R Paula | 08/2011 |
| 8227 | (23619^23619+23620^23620)/7187 | 103294 | David Broadhurst | 09/2009 |
| 8228 | (16487^24649-1)/(16487^157-1) | 103287 | Ryan Propper | 11/2023 |
| 8229 | (10680^25639-1)/10679 | 103285 | Serge Batalov | 06/2022 |
| 8230 | (7427^26683-1)/7426 | 103282 | Serge Batalov | 06/2022 |
| 8231 | 2^343079-1835611 | 103278 | Enzo Doria | 05/2015 |
| 8232 | 2^343063-1147 | 103273 | Yves Minet | 06/2013 |
| 8233 | 24741^14930+14930^24741 | 103271 | Hans Havermann | 09/2020 |
| 8234 | (16*10^103255-73)/3 | 103256 | Robert Price | 07/2020 |
| 8235 | (219^44119-1)/218 | 103256 | Serge Batalov | 06/2022 |
| 8236 | 9*6^132689+7 | 103254 | Lelio R Paula | 11/2014 |
| 8237 | 2^342979-18085 | 103247 | Enzo Doria | 05/2013 |
| 8238 | (16*10^103244-31)/3 | 103245 | Robert Price | 03/2019 |
| 8239 | 2^342966-16995 | 103244 | Lelio R Paula | 11/2016 |
| 8240 | 23797^21774+21774^23797 | 103230 | Hans Havermann | 09/2020 |
| 8241 | 25388^11637+11637^25388 | 103224 | Hans Havermann | 09/2020 |
| 8242 | (2^342876+2086)/2 | 103216 | Stefano Morozzi | 09/2020 |
| 8243 | (16*10^103214-31)/3 | 103215 | Robert Price | 03/2019 |
| 8245 | (37*10^103211+611)/9 | 103212 | Robert Price | 11/2018 |
| 8244 | (238*10^103210-1)/3 | 103212 | Robert Price | 04/2020 |
| 8246 | 5^147650+16 | 103203 | Lelio R Paula | 11/2016 |
| 8247 | gcd(Phi(852060,10),(10^42603+1)^3*(10^42603+1-10^21302)+(10^85206+10^42603)*(10^21302+1)+10^127809) | 103201 | Serge Batalov | 04/2015 |
| 8248 | 2^342817+2707067 | 103199 | Enzo Doria | 03/2016 |
| 8249 | 43^63177-42 | 103198 | Theodore Burton | 02/2007 |
| 8250 | 2^342805-21025 | 103195 | Enzo Doria | 06/2013 |
