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 ? |
| 8753 | 23678^23821-23821^23678 | 104202 | Norbert Schneider | 01/2020 |
| 8751 | 2^346150+111579 | 104202 | Stefano Morozzi | 11/2024 |
| 8752 | 2^346151+21539 | 104202 | Stefano Morozzi | 11/2024 |
| 8754 | 2^346143+119183 | 104200 | Stefano Morozzi | 11/2024 |
| 8755 | 2^346143+130361 | 104200 | Stefano Morozzi | 11/2024 |
| 8756 | 2^346143+171791 | 104200 | Stefano Morozzi | 11/2024 |
| 8757 | 2^346144+4731 | 104200 | Stefano Morozzi | 11/2024 |
| 8758 | 2^346144+158097 | 104200 | Stefano Morozzi | 11/2024 |
| 8759 | 2^346139+68459 | 104199 | Stefano Morozzi | 11/2024 |
| 8760 | 2^346140+121711 | 104199 | Stefano Morozzi | 11/2024 |
| 8761 | 2^346135+122913 | 104198 | Stefano Morozzi | 11/2024 |
| 8762 | 2^346135+125453 | 104198 | Stefano Morozzi | 11/2024 |
| 8763 | 2^346135+184869 | 104198 | Stefano Morozzi | 11/2024 |
| 8764 | 2^346136+135721 | 104198 | Stefano Morozzi | 11/2024 |
| 8765 | 2^346133+46695 | 104197 | Stefano Morozzi | 11/2024 |
| 8766 | 2^346129+87819 | 104196 | Stefano Morozzi | 11/2024 |
| 8767 | 2^346130+127369 | 104196 | Stefano Morozzi | 11/2024 |
| 8768 | 2^346130+177619 | 104196 | Stefano Morozzi | 11/2024 |
| 8769 | 2^346125+105609 | 104195 | Stefano Morozzi | 11/2024 |
| 8770 | 2^346127+71201 | 104195 | Stefano Morozzi | 11/2024 |
| 8771 | 2^346122+74469 | 104194 | Stefano Morozzi | 11/2024 |
| 8772 | 2^346122+124119 | 104194 | Stefano Morozzi | 11/2024 |
| 8773 | 2^346122+124227 | 104194 | Stefano Morozzi | 11/2024 |
| 8774 | 2^346124+83973 | 104194 | Stefano Morozzi | 11/2024 |
| 8775 | 2^346124+186877 | 104194 | Stefano Morozzi | 11/2024 |
| 8776 | 2^346121+174729 | 104193 | Stefano Morozzi | 11/2024 |
| 8777 | 2^346116+166317 | 104192 | Stefano Morozzi | 11/2024 |
| 8778 | 2^346117+98015 | 104192 | Stefano Morozzi | 11/2024 |
| 8779 | (13*31^69863+12407)/30 | 104191 | Eric Chen | 04/2024 |
| 8780 | 2^346112+20827 | 104191 | Stefano Morozzi | 11/2024 |
| 8781 | 2^346112+77533 | 104191 | Stefano Morozzi | 11/2024 |
| 8782 | 2^346114+76959 | 104191 | Stefano Morozzi | 11/2024 |
| 8783 | 2^346115+30513 | 104191 | Stefano Morozzi | 11/2024 |
| 8784 | 2^346115+90105 | 104191 | Stefano Morozzi | 11/2024 |
| 8785 | 2^346115+155859 | 104191 | Stefano Morozzi | 11/2024 |
| 8786 | 2^346115+157809 | 104191 | Stefano Morozzi | 11/2024 |
| 8787 | 2^346109+118587 | 104190 | Stefano Morozzi | 11/2024 |
| 8788 | 2^346110+105763 | 104190 | Stefano Morozzi | 11/2024 |
| 8789 | 2^346110+175197 | 104190 | Stefano Morozzi | 11/2024 |
| 8790 | 2^346110+197725 | 104190 | Stefano Morozzi | 11/2024 |
| 8791 | 2^346111+143313 | 104190 | Stefano Morozzi | 11/2024 |
| 8792 | 2^346107+153513 | 104189 | Stefano Morozzi | 11/2024 |
| 8793 | 2^346108+153897 | 104189 | Stefano Morozzi | 11/2024 |
| 8794 | 2^346102+79435 | 104188 | Stefano Morozzi | 11/2024 |
| 8795 | 2^346102+131949 | 104188 | Stefano Morozzi | 11/2024 |
| 8796 | 2^346103+123009 | 104188 | Stefano Morozzi | 11/2024 |
| 8797 | 2^346104+115845 | 104188 | Stefano Morozzi | 11/2024 |
| 8798 | 2^346105+29141 | 104188 | Stefano Morozzi | 11/2024 |
| 8799 | 2^346105+85035 | 104188 | Stefano Morozzi | 11/2024 |
| 8800 | 2^346098+80323 | 104186 | Stefano Morozzi | 11/2024 |
| 8801 | 2^346092+69855 | 104185 | Stefano Morozzi | 11/2024 |
| 8802 | 2^346093+3627 | 104185 | Stefano Morozzi | 11/2024 |
| 8803 | 2^346089+90947 | 104184 | Stefano Morozzi | 11/2024 |
| 8804 | 2^346089+186749 | 104184 | Stefano Morozzi | 11/2024 |
| 8805 | 2^346091+71279 | 104184 | Stefano Morozzi | 11/2024 |
| 8806 | 2^346084+69211 | 104182 | Stefano Morozzi | 11/2024 |
| 8807 | 2^346084+112237 | 104182 | Stefano Morozzi | 11/2024 |
| 8808 | 2^346079+10371 | 104181 | Stefano Morozzi | 11/2024 |
| 8809 | 2^346079+82811 | 104181 | Stefano Morozzi | 11/2024 |
| 8813 | 2^346078+7695 | 104180 | Lelio R Paula | 12/2016 |
| 8810 | 2^346076+85903 | 104180 | Stefano Morozzi | 11/2024 |
| 8811 | 2^346076+111577 | 104180 | Stefano Morozzi | 11/2024 |
| 8812 | 2^346076+143047 | 104180 | Stefano Morozzi | 11/2024 |
| 8814 | 2^346072+126673 | 104179 | Stefano Morozzi | 11/2024 |
| 8815 | 2^346073+37899 | 104179 | Stefano Morozzi | 11/2024 |
| 8816 | 2^346075+21519 | 104179 | Stefano Morozzi | 11/2024 |
| 8817 | 2^346075+27255 | 104179 | Stefano Morozzi | 11/2024 |
| 8818 | 2^346075+115331 | 104179 | Stefano Morozzi | 11/2024 |
| 8819 | 2^346069+53615 | 104178 | Stefano Morozzi | 11/2024 |
| 8820 | 2^346069+188087 | 104178 | Stefano Morozzi | 11/2024 |
| 8821 | 2^346066+29949 | 104177 | Stefano Morozzi | 11/2024 |
| 8822 | 2^346066+133909 | 104177 | Stefano Morozzi | 11/2024 |
| 8823 | 2^346066+188535 | 104177 | Stefano Morozzi | 11/2024 |
| 8824 | 2^346068+159553 | 104177 | Stefano Morozzi | 11/2024 |
| 8825 | 2^346064+122683 | 104176 | Stefano Morozzi | 11/2024 |
| 8826 | 2^346060+20325 | 104175 | Stefano Morozzi | 11/2024 |
| 8827 | 2^346060+110755 | 104175 | Stefano Morozzi | 11/2024 |
| 8828 | 2^346058+57933 | 104174 | Stefano Morozzi | 11/2024 |
| 8834 | 2^346055-19537 | 104173 | Enzo Doria | 05/2013 |
| 8835 | (3*2^346057+1)/77 | 104173 | Lelio R Paula | 12/2013 |
| 8829 | 2^346052+26655 | 104173 | Stefano Morozzi | 11/2024 |
| 8830 | 2^346052+31611 | 104173 | Stefano Morozzi | 11/2024 |
| 8831 | 2^346053+67667 | 104173 | Stefano Morozzi | 11/2024 |
| 8832 | 2^346054+30507 | 104173 | Stefano Morozzi | 11/2024 |
| 8833 | 2^346054+194589 | 104173 | Stefano Morozzi | 11/2024 |
| 8836 | 2^346049+59067 | 104172 | Stefano Morozzi | 11/2024 |
| 8837 | 2^346050+3129 | 104172 | Stefano Morozzi | 11/2024 |
| 8838 | 2^346050+167125 | 104172 | Stefano Morozzi | 11/2024 |
| 8839 | 2^346051+52563 | 104172 | Stefano Morozzi | 11/2024 |
| 8840 | 2^346051+90941 | 104172 | Stefano Morozzi | 11/2024 |
| 8841 | 2^346046+172107 | 104171 | Stefano Morozzi | 11/2024 |
| 8842 | 2^346048+63415 | 104171 | Stefano Morozzi | 11/2024 |
| 8843 | 2^346041+197885 | 104169 | Stefano Morozzi | 11/2024 |
| 8847 | 2^346037-20125 | 104168 | Enzo Doria | 06/2013 |
| 8844 | 2^346036+80773 | 104168 | Stefano Morozzi | 11/2024 |
| 8845 | 2^346037+116429 | 104168 | Stefano Morozzi | 11/2024 |
| 8846 | 2^346038+147549 | 104168 | Stefano Morozzi | 11/2024 |
| 8848 | 2^346034+2205 | 104167 | Stefano Morozzi | 11/2024 |
| 8849 | 2^346031+56429 | 104166 | Stefano Morozzi | 11/2024 |
| 8850 | 2^346031+68439 | 104166 | Stefano Morozzi | 11/2024 |
| 8851 | 2^346031+114891 | 104166 | Stefano Morozzi | 11/2024 |
| 8852 | 2^346031+190563 | 104166 | Stefano Morozzi | 11/2024 |
| 8853 | 2^346026+179305 | 104165 | Stefano Morozzi | 11/2024 |
| 8854 | 2^346027+159425 | 104165 | Stefano Morozzi | 11/2024 |
| 8855 | 2^346028+12517 | 104165 | Stefano Morozzi | 11/2024 |
| 8856 | 2^346022+84705 | 104164 | Stefano Morozzi | 11/2024 |
| 8857 | 2^346019+73673 | 104163 | Stefano Morozzi | 11/2024 |
| 8858 | 2^346019+78999 | 104163 | Stefano Morozzi | 11/2024 |
| 8859 | 2^346019+79955 | 104163 | Stefano Morozzi | 11/2024 |
| 8860 | 2^346020+72993 | 104163 | Stefano Morozzi | 11/2024 |
| 8861 | 2^346020+188673 | 104163 | Stefano Morozzi | 11/2024 |
| 8862 | 2^346021+100311 | 104163 | Stefano Morozzi | 11/2024 |
| 8866 | (34*10^104168-7)/9/13/551179 | 104162 | Makoto Morimoto | 05/2016 |
| 8863 | 2^346016+84007 | 104162 | Stefano Morozzi | 11/2024 |
| 8864 | 2^346017+122397 | 104162 | Stefano Morozzi | 11/2024 |
| 8865 | 2^346017+165791 | 104162 | Stefano Morozzi | 11/2024 |
| 8867 | 2^346014+27949 | 104161 | Stefano Morozzi | 11/2024 |
| 8868 | 2^346014+46743 | 104161 | Stefano Morozzi | 11/2024 |
| 8869 | 2^346015+166089 | 104161 | Stefano Morozzi | 11/2024 |
| 8870 | 2^346009+107705 | 104160 | Stefano Morozzi | 11/2024 |
| 8871 | 2^346012+35043 | 104160 | Stefano Morozzi | 11/2024 |
| 8872 | 2^346012+83091 | 104160 | Stefano Morozzi | 11/2024 |
| 8880 | 6^133854-17993 | 104159 | Enzo Doria | 03/2013 |
| 8873 | 2^346006+77727 | 104159 | Stefano Morozzi | 11/2024 |
| 8874 | 2^346008+9007 | 104159 | Stefano Morozzi | 11/2024 |
| 8875 | 2^346008+51567 | 104159 | Stefano Morozzi | 11/2024 |
| 8876 | 2^346008+107787 | 104159 | Stefano Morozzi | 11/2024 |
| 8877 | 2^346008+146191 | 104159 | Stefano Morozzi | 11/2024 |
| 8878 | 2^346008+170823 | 104159 | Stefano Morozzi | 11/2024 |
| 8879 | (131^49201-1)/7538466025870 | 104159 | Paul Vanderveen | 06/2025 |
| 8881 | 2^346003+191519 | 104158 | Stefano Morozzi | 11/2024 |
| 8882 | 2^345990+1874239 | 104154 | Enzo Doria | 06/2016 |
| 8883 | 2^345988-20373 | 104153 | Enzo Doria | 06/2013 |
| 8884 | (2^345965+2214)/2 | 104146 | Stefano Morozzi | 09/2020 |
| 8885 | (26*10^104132-503)/9 | 104133 | Robert Price | 07/2018 |
| 8886 | 3*5^148968+8 | 104125 | Lelio R Paula | 11/2014 |
| 8887 | (7*10^104113+53)/3 | 104114 | Robert Price | 05/2018 |
| 8888 | p(21253)#/2+8 | 104113 | Robert Price | 01/2017 |
| 8889 | 33582^1259+1259^33582 | 104106 | Hans Havermann | 09/2020 |
| 8890 | 32958^1441+1441^32958 | 104104 | Hans Havermann | 09/2020 |
| 8891 | 29127^3748+3748^29127 | 104095 | Hans Havermann | 09/2020 |
| 8892 | 322^41507+41507^322 | 104094 | Norbert Schneider | 12/2014 |
| 8893 | 6^133768-17423 | 104092 | Enzo Doria | 03/2013 |
| 8894 | 2^345786-19557 | 104092 | Enzo Doria | 05/2013 |
| 8895 | 171^46606-2 | 104072 | Lelio R Paula | 10/2017 |
| 8896 | (29*10^104071+91)/3 | 104072 | Robert Price | 04/2020 |
| 8897 | norm(Mod(x,x^3-x-1)^852167-1) | 104070 | Paul Vanderveen | 09/2022 |
| 8898 | 2^345704-149 | 104068 | Lelio R Paula | 09/2011 |
| 8899 | 25821^10712+10712^25821 | 104056 | Hans Havermann | 09/2020 |
| 8900 | (2^345662+2038)/2 | 104055 | Stefano Morozzi | 09/2020 |
| 8901 | 6^133704-17273 | 104042 | Enzo Doria | 02/2013 |
| 8902 | (3*2^345590-1)/23 | 104033 | Lelio R Paula | 03/2014 |
| 8903 | (19*2^345590+1)/33859 | 104030 | Lelio R Paula | 12/2013 |
| 8904 | 2^345547+11 | 104021 | Lelio R Paula | 09/2011 |
| 8905 | (19*10^104014-49)/3 | 104015 | Robert Price | 05/2019 |
| 8906 | (2^345519+1794)/2 | 104012 | Stefano Morozzi | 01/2021 |
| 8907 | 2^345504+723 | 104008 | Lelio R Paula | 09/2011 |
| 8908 | 2^345498-20037 | 104006 | Enzo Doria | 06/2013 |
| 8910 | 18^82854-37 | 104005 | Lelio R Paula | 01/2017 |
| 8909 | (2^345497+2070)/2 | 104005 | Stefano Morozzi | 09/2020 |
| 8911 | 2^345486-109065 | 104002 | Enzo Doria | 04/2014 |
| 8912 | 2^345487-1851507 | 104002 | Enzo Doria | 08/2015 |
| 8913 | 2^345476+777 | 103999 | Lelio R Paula | 09/2011 |
| 8914 | (2^345477+1554)/2 | 103999 | Stefano Morozzi | 09/2020 |
| 8915 | 4*10^103981-83 | 103982 | Robert Price | 10/2018 |
| 8916 | (2^345327+3206)/2 | 103954 | Stefano Morozzi | 09/2020 |
| 8917 | (5*2^345321-1)/3 | 103953 | Lelio R Paula | 03/2014 |
| 8918 | (2^345267-9)/539049127 | 103927 | Lelio R Paula | 12/2013 |
| 8919 | (19*10^103907+77)/3 | 103908 | Robert Price | 05/2019 |
| 8920 | (78557*2^345163+1)/78589 | 103905 | Lelio R Paula | 07/2014 |
| 8921 | 2^345106-112181 | 103888 | Enzo Doria | 06/2014 |
| 8922 | (2^345105+1326)/2 | 103887 | Stefano Morozzi | 02/2021 |
| 8923 | 2^345079+99 | 103880 | Lelio R Paula | 09/2011 |
| 8924 | (2^345034+1198)/2 | 103866 | Stefano Morozzi | 09/2020 |
| 8925 | 11^99736-1500 | 103865 | Enzo Doria | 12/2012 |
| 8926 | (569^37699-1)/568 | 103863 | Serge Batalov | 06/2022 |
| 8927 | (2^345010+2082)/2 | 103859 | Stefano Morozzi | 09/2020 |
| 8928 | 23263^23784-23784^23263 | 103857 | Norbert Schneider | 01/2020 |
| 8929 | 3*10^103844+31 | 103845 | Robert Price | 06/2021 |
| 8930 | 444*33^68368+19 | 103821 | Eric Chen | 05/2023 |
| 8931 | 23927^21814+21814^23927 | 103813 | Hans Havermann | 09/2020 |
| 8932 | 2^344842-20157 | 103808 | Enzo Doria | 06/2013 |
| 8933 | (47*2^344822+1)/1071 | 103801 | Lelio R Paula | 05/2015 |
| 8934 | 2^344802-20765 | 103796 | Enzo Doria | 06/2013 |
| 8935 | 2^344794-3821 | 103794 | Yves Minet | 05/2011 |
| 8936 | 2^344782-109103 | 103790 | Enzo Doria | 04/2014 |
| 8937 | 3^217521-112292 | 103784 | Enzo Doria | 06/2014 |
| 8938 | 2^344759-3505 | 103783 | Lelio R Paula | 11/2016 |
| 8939 | 2^344735-147 | 103776 | Lelio R Paula | 09/2011 |
| 8940 | L(496533)-p(496533) | 103770 | Robert Price | 02/2018 |
| 8941 | 2*10^103749-69 | 103750 | Robert Price | 03/2018 |
| 8942 | (55459*2^344617+1)/3 | 103745 | Lelio R Paula | 07/2014 |
| 8943 | 2^344607-108891 | 103738 | Enzo Doria | 03/2014 |
| 8945 | (2^344608+3798)/2 | 103738 | Stefano Morozzi | 02/2021 |
| 8944 | (1097^34123-1)/1096 | 103738 | Serge Batalov | 06/2022 |
| 8946 | 2^344560+22411 | 103723 | Enzo Doria | 09/2023 |
| 8947 | (148*10^103718-1)/3 | 103720 | Robert Price | 03/2020 |
| 8948 | 2^344541-19561 | 103718 | Enzo Doria | 05/2013 |
| 8949 | (1017*2^344529-1)/569 | 103714 | Lelio R Paula | 05/2015 |
| 8950 | (8896^26263-1)/8895 | 103714 | Serge Batalov | 06/2022 |
| 8951 | (2^344503+1758)/2 | 103706 | Stefano Morozzi | 09/2020 |
| 8952 | (4*10^103703-1)/3 | 103704 | Serge Batalov | 08/2009 |
| 8953 | 2^344444-455 | 103688 | Yves Minet | 03/2012 |
| 8954 | (4*10^103678-43)/3 | 103679 | Robert Price | 01/2022 |
| 8955 | (13*53^238539*617^9)/10^307661 | 103673 | Hans Havermann | 06/2017 |
| 8956 | (2^344367+2738)/2 | 103665 | Stefano Morozzi | 01/2021 |
| 8958 | 2^344317-109933 | 103650 | Enzo Doria | 04/2014 |
| 8957 | 26055^9508+9508^26055 | 103650 | Hans Havermann | 09/2020 |
| 8959 | 2^344309-1852033 | 103648 | Enzo Doria | 08/2015 |
| 8960 | 25729^10672+10672^25729 | 103643 | Hans Havermann | 09/2020 |
| 8961 | (2^344289+1166)/2 | 103642 | Stefano Morozzi | 09/2020 |
| 8962 | 3*10^103637+61 | 103638 | Robert Price | 09/2020 |
| 8963 | (2^344246+1614)/2 | 103629 | Stefano Morozzi | 09/2020 |
| 8964 | 2^344213-21253 | 103619 | Enzo Doria | 06/2013 |
| 8965 | 2^344196-465 | 103614 | Lelio R Paula | 11/2016 |
| 8966 | 2^344187-20001 | 103611 | Enzo Doria | 06/2013 |
| 8967 | (117191#+(355573#)/(117191#))/(200233679) | 103602 | Makoto Morimoto | 10/2017 |
| 8968 | (237^43627-1)/236 | 103601 | Serge Batalov | 06/2022 |
| 8969 | 20^79621-19^79621 | 103590 | Jean-Louis Charton | 03/2011 |
| 8970 | Phi(155391,10)/1243129 | 103586 | Maksym Voznyy | 09/2015 |
| 8971 | (9^108553-2^108553)/7 | 103586 | Jon Grantham | 07/2023 |
| 8972 | 2^344085-20365 | 103580 | Enzo Doria | 06/2013 |
| 8973 | 5^148169+54 | 103566 | Lelio R Paula | 11/2016 |
| 8974 | 2^344017-108795 | 103560 | Enzo Doria | 03/2014 |
| 8975 | (2^343974+2670)/2 | 103547 | Stefano Morozzi | 09/2020 |
| 8976 | 2^343971-5077 | 103546 | Lelio R Paula | 09/2011 |
| 8977 | (7*10^103531+71)/3 | 103532 | Robert Price | 05/2018 |
| 8978 | 2^343899+141 | 103524 | Lelio R Paula | 08/2011 |
| 8979 | (2^343933+1)/(3*98294339989393) | 103520 | Gord Palameta | 08/2018 |
| 8980 | 6^133029-67 | 103517 | Lelio R Paula | 11/2016 |
| 8981 | (17*2^343877+1)/13625 | 103515 | Lelio R Paula | 12/2013 |
| 8982 | 66*10^103507+7 | 103509 | Robert Price | 07/2020 |
| 8983 | 26297^8614+8614^26297 | 103485 | Hans Havermann | 09/2020 |
| 8984 | (2^343764+2658)/2 | 103483 | Stefano Morozzi | 09/2020 |
| 8985 | 26499^8036+8036^26499 | 103480 | Hans Havermann | 09/2020 |
| 8986 | (103^51413-1)/4478483706 | 103477 | Paul Vanderveen | 06/2025 |
| 8987 | (136*10^103474-1)/9 | 103476 | Serge Batalov | 12/2014 |
| 8988 | 5^148014-24 | 103458 | Lelio R Paula | 11/2016 |
| 8989 | 25^74007-24 | 103458 | Anonymous | 09/2024 |
| 8990 | 28316^4503+4503^28316 | 103453 | Hans Havermann | 09/2020 |
| 8991 | (22*10^103450+53)/3 | 103451 | Robert Price | 07/2019 |
| 8992 | 2^343604+9931 | 103436 | Yves Minet | 01/2011 |
| 8993 | 2^343601-21189 | 103435 | Enzo Doria | 06/2013 |
| 8994 | (10^103423+173)/3 | 103423 | Robert Price | 05/2021 |
| 8995 | 2^343508-115229 | 103407 | Enzo Doria | 06/2015 |
| 8996 | (8766^26227-1)/8765 | 103404 | Serge Batalov | 06/2022 |
| 8997 | (509203*2^343491-1)/16147 | 103403 | Lelio R Paula | 05/2015 |
| 8998 | 3^216685-113056 | 103386 | Enzo Doria | 07/2014 |
| 8999 | 24829^14580+14580^24829 | 103382 | Hans Havermann | 08/2020 |
| 9000 | 91355!4+1024 | 103381 | Robert Price | 09/2019 |
