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 ? |
| 8756 | (166*10^104230+11)/3 | 104232 | Robert Price | 03/2021 |
| 8751 | 2^346248+3075 | 104232 | Stefano Morozzi | 11/2024 |
| 8752 | 2^346248+39081 | 104232 | Stefano Morozzi | 11/2024 |
| 8753 | 2^346249+38339 | 104232 | Stefano Morozzi | 11/2024 |
| 8754 | 2^346251+32831 | 104232 | Stefano Morozzi | 11/2024 |
| 8755 | 2^346251+116175 | 104232 | Stefano Morozzi | 11/2024 |
| 8757 | 2^346247+197309 | 104231 | Stefano Morozzi | 11/2024 |
| 8758 | 2^346245+95429 | 104231 | Stefano Morozzi | 11/2024 |
| 8759 | 2^346243+58163 | 104230 | Stefano Morozzi | 11/2024 |
| 8760 | 2^346243+130931 | 104230 | Stefano Morozzi | 11/2024 |
| 8761 | 2^346244+10381 | 104230 | Stefano Morozzi | 11/2024 |
| 8762 | 2^346241+41057 | 104229 | Stefano Morozzi | 11/2024 |
| 8763 | 2^346235+152303 | 104228 | Stefano Morozzi | 11/2024 |
| 8764 | 2^346236+106617 | 104228 | Stefano Morozzi | 11/2024 |
| 8765 | 2^346232+103317 | 104227 | Stefano Morozzi | 11/2024 |
| 8766 | 2^346232+193681 | 104227 | Stefano Morozzi | 11/2024 |
| 8767 | 2^346233+115671 | 104227 | Stefano Morozzi | 11/2024 |
| 8768 | 2^346229+73157 | 104226 | Stefano Morozzi | 11/2024 |
| 8769 | 2^346229+145377 | 104226 | Stefano Morozzi | 11/2024 |
| 8770 | 2^346230+171103 | 104226 | Stefano Morozzi | 11/2024 |
| 8771 | 2^346225+55527 | 104225 | Stefano Morozzi | 11/2024 |
| 8772 | 2^346225+132251 | 104225 | Stefano Morozzi | 11/2024 |
| 8773 | 2^346225+140637 | 104225 | Stefano Morozzi | 11/2024 |
| 8774 | 2^346223+27335 | 104224 | Stefano Morozzi | 11/2024 |
| 8775 | 2^346223+74591 | 104224 | Stefano Morozzi | 11/2024 |
| 8776 | 2^346224+70905 | 104224 | Stefano Morozzi | 11/2024 |
| 8777 | 2^346220+12355 | 104223 | Stefano Morozzi | 11/2024 |
| 8778 | 2^346220+110805 | 104223 | Stefano Morozzi | 11/2024 |
| 8779 | 2^346220+161361 | 104223 | Stefano Morozzi | 11/2024 |
| 8780 | 2^346220+176523 | 104223 | Stefano Morozzi | 11/2024 |
| 8781 | 2^346220+185625 | 104223 | Stefano Morozzi | 11/2024 |
| 8782 | 2^346216+62973 | 104222 | Stefano Morozzi | 11/2024 |
| 8783 | 2^346217+88391 | 104222 | Stefano Morozzi | 11/2024 |
| 8784 | 2^346217+170121 | 104222 | Stefano Morozzi | 11/2024 |
| 8785 | 2^346217+111567 | 104222 | Stefano Morozzi | 11/2024 |
| 8789 | 2^346213+484049 | 104221 | Enzo Doria | 04/2017 |
| 8786 | 2^346212+31773 | 104221 | Stefano Morozzi | 11/2024 |
| 8787 | 2^346213+37151 | 104221 | Stefano Morozzi | 11/2024 |
| 8788 | 2^346213+162399 | 104221 | Stefano Morozzi | 11/2024 |
| 8790 | 2^346209+173231 | 104220 | Stefano Morozzi | 11/2024 |
| 8791 | 2^346207+125243 | 104219 | Stefano Morozzi | 11/2024 |
| 8792 | 2^346208+79825 | 104219 | Stefano Morozzi | 11/2024 |
| 8793 | 2^346208+176463 | 104219 | Stefano Morozzi | 11/2024 |
| 8794 | 2^346206+195363 | 104219 | Stefano Morozzi | 11/2024 |
| 8795 | 2^346202+67065 | 104218 | Stefano Morozzi | 11/2024 |
| 8796 | 2^346202+107377 | 104218 | Stefano Morozzi | 11/2024 |
| 8797 | 2^346204+127677 | 104218 | Stefano Morozzi | 11/2024 |
| 8798 | 2^346204+19573 | 104218 | Stefano Morozzi | 11/2024 |
| 8799 | 2^346204+161997 | 104218 | Stefano Morozzi | 11/2024 |
| 8800 | 2^346204+152665 | 104218 | Stefano Morozzi | 11/2024 |
| 8801 | 2^346199+90995 | 104217 | Stefano Morozzi | 11/2024 |
| 8802 | 2^346199+189629 | 104217 | Stefano Morozzi | 11/2024 |
| 8803 | 2^346200+159591 | 104217 | Stefano Morozzi | 11/2024 |
| 8804 | 2^346195+19733 | 104216 | Stefano Morozzi | 11/2024 |
| 8805 | 2^346196+141117 | 104216 | Stefano Morozzi | 11/2024 |
| 8806 | 2^346196+195171 | 104216 | Stefano Morozzi | 11/2024 |
| 8807 | 2^346197+113751 | 104216 | Stefano Morozzi | 11/2024 |
| 8808 | 2^346198+95305 | 104216 | Stefano Morozzi | 11/2024 |
| 8809 | 2^346198+106735 | 104216 | Stefano Morozzi | 11/2024 |
| 8811 | 18^83021-91 | 104214 | Lelio R Paula | 01/2017 |
| 8810 | 2^346189+194831 | 104214 | Stefano Morozzi | 11/2024 |
| 8812 | 10^104212+128779 | 104213 | Patrick De Geest | 05/2016 |
| 8813 | 10^104212+237447 | 104213 | Patrick De Geest | 05/2016 |
| 8814 | 10^104212+242139 | 104213 | Patrick De Geest | 05/2016 |
| 8815 | 10^104212+269199 | 104213 | Patrick De Geest | 05/2016 |
| 8819 | 24254^19803+19803^24254 | 104213 | Hans Havermann | 09/2020 |
| 8816 | 2^346186+93813 | 104213 | Stefano Morozzi | 11/2024 |
| 8817 | 2^346186+153687 | 104213 | Stefano Morozzi | 11/2024 |
| 8818 | 2^346187+102195 | 104213 | Stefano Morozzi | 11/2024 |
| 8824 | (10^104212-71)/1 | 104212 | Serge Batalov | 12/2014 |
| 8820 | 2^346182+118065 | 104212 | Stefano Morozzi | 11/2024 |
| 8821 | 2^346184+155085 | 104212 | Stefano Morozzi | 11/2024 |
| 8822 | 2^346184+187513 | 104212 | Stefano Morozzi | 11/2024 |
| 8823 | 2^346184+188455 | 104212 | Stefano Morozzi | 11/2024 |
| 8825 | 2^346180+82735 | 104211 | Stefano Morozzi | 11/2024 |
| 8826 | 2^346180+160593 | 104211 | Stefano Morozzi | 11/2024 |
| 8827 | 2^346180+192333 | 104211 | Stefano Morozzi | 11/2024 |
| 8828 | 2^346181+199821 | 104211 | Stefano Morozzi | 11/2024 |
| 8829 | 2^346176+123667 | 104210 | Stefano Morozzi | 11/2024 |
| 8830 | 2^346178+37455 | 104210 | Stefano Morozzi | 11/2024 |
| 8831 | 2^346178+95865 | 104210 | Stefano Morozzi | 11/2024 |
| 8832 | 2^346178+159517 | 104210 | Stefano Morozzi | 11/2024 |
| 8833 | 2^346174+12543 | 104209 | Stefano Morozzi | 11/2024 |
| 8834 | 2^346169+56049 | 104208 | Stefano Morozzi | 11/2024 |
| 8835 | 2^346169+118965 | 104208 | Stefano Morozzi | 11/2024 |
| 8836 | 2^346170+31363 | 104208 | Stefano Morozzi | 11/2024 |
| 8837 | 2^346165+61767 | 104207 | Stefano Morozzi | 11/2024 |
| 8838 | 2^346166+189919 | 104207 | Stefano Morozzi | 11/2024 |
| 8839 | 2^346167+41681 | 104207 | Stefano Morozzi | 11/2024 |
| 8840 | 2^346162+85765 | 104206 | Stefano Morozzi | 11/2024 |
| 8841 | 2^346164+152925 | 104206 | Stefano Morozzi | 11/2024 |
| 8842 | 2^346160+131703 | 104205 | Stefano Morozzi | 11/2024 |
| 8843 | 2^346155+166433 | 104204 | Stefano Morozzi | 11/2024 |
| 8844 | 2^346157+7137 | 104204 | Stefano Morozzi | 11/2024 |
| 8845 | 2^346158+31483 | 104204 | Stefano Morozzi | 11/2024 |
| 8846 | 2^346158+183253 | 104204 | Stefano Morozzi | 11/2024 |
| 8847 | 2^346152+136287 | 104203 | Stefano Morozzi | 11/2024 |
| 8848 | 2^346154+107499 | 104203 | Stefano Morozzi | 11/2024 |
| 8849 | 2^346154+187987 | 104203 | Stefano Morozzi | 11/2024 |
| 8853 | 23678^23821-23821^23678 | 104202 | Norbert Schneider | 01/2020 |
| 8850 | 2^346149+45857 | 104202 | Stefano Morozzi | 11/2024 |
| 8851 | 2^346150+111579 | 104202 | Stefano Morozzi | 11/2024 |
| 8852 | 2^346151+21539 | 104202 | Stefano Morozzi | 11/2024 |
| 8854 | 2^346143+119183 | 104200 | Stefano Morozzi | 11/2024 |
| 8855 | 2^346143+130361 | 104200 | Stefano Morozzi | 11/2024 |
| 8856 | 2^346143+171791 | 104200 | Stefano Morozzi | 11/2024 |
| 8857 | 2^346144+4731 | 104200 | Stefano Morozzi | 11/2024 |
| 8858 | 2^346144+158097 | 104200 | Stefano Morozzi | 11/2024 |
| 8859 | 2^346139+68459 | 104199 | Stefano Morozzi | 11/2024 |
| 8860 | 2^346140+121711 | 104199 | Stefano Morozzi | 11/2024 |
| 8861 | 2^346135+122913 | 104198 | Stefano Morozzi | 11/2024 |
| 8862 | 2^346135+125453 | 104198 | Stefano Morozzi | 11/2024 |
| 8863 | 2^346135+184869 | 104198 | Stefano Morozzi | 11/2024 |
| 8864 | 2^346136+135721 | 104198 | Stefano Morozzi | 11/2024 |
| 8865 | 2^346133+46695 | 104197 | Stefano Morozzi | 11/2024 |
| 8866 | 2^346129+87819 | 104196 | Stefano Morozzi | 11/2024 |
| 8867 | 2^346130+127369 | 104196 | Stefano Morozzi | 11/2024 |
| 8868 | 2^346130+177619 | 104196 | Stefano Morozzi | 11/2024 |
| 8869 | 2^346125+105609 | 104195 | Stefano Morozzi | 11/2024 |
| 8870 | 2^346127+71201 | 104195 | Stefano Morozzi | 11/2024 |
| 8871 | 2^346122+74469 | 104194 | Stefano Morozzi | 11/2024 |
| 8872 | 2^346122+124119 | 104194 | Stefano Morozzi | 11/2024 |
| 8873 | 2^346122+124227 | 104194 | Stefano Morozzi | 11/2024 |
| 8874 | 2^346124+83973 | 104194 | Stefano Morozzi | 11/2024 |
| 8875 | 2^346124+186877 | 104194 | Stefano Morozzi | 11/2024 |
| 8876 | 2^346121+174729 | 104193 | Stefano Morozzi | 11/2024 |
| 8877 | 2^346116+166317 | 104192 | Stefano Morozzi | 11/2024 |
| 8878 | 2^346117+98015 | 104192 | Stefano Morozzi | 11/2024 |
| 8879 | (13*31^69863+12407)/30 | 104191 | Eric Chen | 04/2024 |
| 8880 | 2^346112+20827 | 104191 | Stefano Morozzi | 11/2024 |
| 8881 | 2^346112+77533 | 104191 | Stefano Morozzi | 11/2024 |
| 8882 | 2^346114+76959 | 104191 | Stefano Morozzi | 11/2024 |
| 8883 | 2^346115+30513 | 104191 | Stefano Morozzi | 11/2024 |
| 8884 | 2^346115+90105 | 104191 | Stefano Morozzi | 11/2024 |
| 8885 | 2^346115+155859 | 104191 | Stefano Morozzi | 11/2024 |
| 8886 | 2^346115+157809 | 104191 | Stefano Morozzi | 11/2024 |
| 8887 | 2^346109+118587 | 104190 | Stefano Morozzi | 11/2024 |
| 8888 | 2^346110+105763 | 104190 | Stefano Morozzi | 11/2024 |
| 8889 | 2^346110+175197 | 104190 | Stefano Morozzi | 11/2024 |
| 8890 | 2^346110+197725 | 104190 | Stefano Morozzi | 11/2024 |
| 8891 | 2^346111+143313 | 104190 | Stefano Morozzi | 11/2024 |
| 8892 | 2^346107+153513 | 104189 | Stefano Morozzi | 11/2024 |
| 8893 | 2^346108+153897 | 104189 | Stefano Morozzi | 11/2024 |
| 8894 | 2^346102+79435 | 104188 | Stefano Morozzi | 11/2024 |
| 8895 | 2^346102+131949 | 104188 | Stefano Morozzi | 11/2024 |
| 8896 | 2^346103+123009 | 104188 | Stefano Morozzi | 11/2024 |
| 8897 | 2^346104+115845 | 104188 | Stefano Morozzi | 11/2024 |
| 8898 | 2^346105+29141 | 104188 | Stefano Morozzi | 11/2024 |
| 8899 | 2^346105+85035 | 104188 | Stefano Morozzi | 11/2024 |
| 8900 | 2^346098+80323 | 104186 | Stefano Morozzi | 11/2024 |
| 8901 | 2^346092+69855 | 104185 | Stefano Morozzi | 11/2024 |
| 8902 | 2^346093+3627 | 104185 | Stefano Morozzi | 11/2024 |
| 8903 | 2^346089+90947 | 104184 | Stefano Morozzi | 11/2024 |
| 8904 | 2^346089+186749 | 104184 | Stefano Morozzi | 11/2024 |
| 8905 | 2^346091+71279 | 104184 | Stefano Morozzi | 11/2024 |
| 8906 | 2^346084+69211 | 104182 | Stefano Morozzi | 11/2024 |
| 8907 | 2^346084+112237 | 104182 | Stefano Morozzi | 11/2024 |
| 8908 | 2^346079+10371 | 104181 | Stefano Morozzi | 11/2024 |
| 8909 | 2^346079+82811 | 104181 | Stefano Morozzi | 11/2024 |
| 8913 | 2^346078+7695 | 104180 | Lelio R Paula | 12/2016 |
| 8910 | 2^346076+85903 | 104180 | Stefano Morozzi | 11/2024 |
| 8911 | 2^346076+111577 | 104180 | Stefano Morozzi | 11/2024 |
| 8912 | 2^346076+143047 | 104180 | Stefano Morozzi | 11/2024 |
| 8914 | 2^346072+126673 | 104179 | Stefano Morozzi | 11/2024 |
| 8915 | 2^346073+37899 | 104179 | Stefano Morozzi | 11/2024 |
| 8916 | 2^346075+21519 | 104179 | Stefano Morozzi | 11/2024 |
| 8917 | 2^346075+27255 | 104179 | Stefano Morozzi | 11/2024 |
| 8918 | 2^346075+115331 | 104179 | Stefano Morozzi | 11/2024 |
| 8919 | 2^346069+53615 | 104178 | Stefano Morozzi | 11/2024 |
| 8920 | 2^346069+188087 | 104178 | Stefano Morozzi | 11/2024 |
| 8921 | 2^346066+29949 | 104177 | Stefano Morozzi | 11/2024 |
| 8922 | 2^346066+133909 | 104177 | Stefano Morozzi | 11/2024 |
| 8923 | 2^346066+188535 | 104177 | Stefano Morozzi | 11/2024 |
| 8924 | 2^346068+159553 | 104177 | Stefano Morozzi | 11/2024 |
| 8925 | 2^346064+122683 | 104176 | Stefano Morozzi | 11/2024 |
| 8926 | 2^346060+20325 | 104175 | Stefano Morozzi | 11/2024 |
| 8927 | 2^346060+110755 | 104175 | Stefano Morozzi | 11/2024 |
| 8928 | 2^346058+57933 | 104174 | Stefano Morozzi | 11/2024 |
| 8934 | 2^346055-19537 | 104173 | Enzo Doria | 05/2013 |
| 8935 | (3*2^346057+1)/77 | 104173 | Lelio R Paula | 12/2013 |
| 8929 | 2^346052+26655 | 104173 | Stefano Morozzi | 11/2024 |
| 8930 | 2^346052+31611 | 104173 | Stefano Morozzi | 11/2024 |
| 8931 | 2^346053+67667 | 104173 | Stefano Morozzi | 11/2024 |
| 8932 | 2^346054+30507 | 104173 | Stefano Morozzi | 11/2024 |
| 8933 | 2^346054+194589 | 104173 | Stefano Morozzi | 11/2024 |
| 8936 | 2^346049+59067 | 104172 | Stefano Morozzi | 11/2024 |
| 8937 | 2^346050+3129 | 104172 | Stefano Morozzi | 11/2024 |
| 8938 | 2^346050+167125 | 104172 | Stefano Morozzi | 11/2024 |
| 8939 | 2^346051+52563 | 104172 | Stefano Morozzi | 11/2024 |
| 8940 | 2^346051+90941 | 104172 | Stefano Morozzi | 11/2024 |
| 8941 | 2^346046+172107 | 104171 | Stefano Morozzi | 11/2024 |
| 8942 | 2^346048+63415 | 104171 | Stefano Morozzi | 11/2024 |
| 8943 | 2^346041+197885 | 104169 | Stefano Morozzi | 11/2024 |
| 8947 | 2^346037-20125 | 104168 | Enzo Doria | 06/2013 |
| 8944 | 2^346036+80773 | 104168 | Stefano Morozzi | 11/2024 |
| 8945 | 2^346037+116429 | 104168 | Stefano Morozzi | 11/2024 |
| 8946 | 2^346038+147549 | 104168 | Stefano Morozzi | 11/2024 |
| 8948 | 2^346034+2205 | 104167 | Stefano Morozzi | 11/2024 |
| 8949 | 2^346031+56429 | 104166 | Stefano Morozzi | 11/2024 |
| 8950 | 2^346031+68439 | 104166 | Stefano Morozzi | 11/2024 |
| 8951 | 2^346031+114891 | 104166 | Stefano Morozzi | 11/2024 |
| 8952 | 2^346031+190563 | 104166 | Stefano Morozzi | 11/2024 |
| 8953 | 2^346026+179305 | 104165 | Stefano Morozzi | 11/2024 |
| 8954 | 2^346027+159425 | 104165 | Stefano Morozzi | 11/2024 |
| 8955 | 2^346028+12517 | 104165 | Stefano Morozzi | 11/2024 |
| 8956 | 2^346022+84705 | 104164 | Stefano Morozzi | 11/2024 |
| 8957 | 2^346019+73673 | 104163 | Stefano Morozzi | 11/2024 |
| 8958 | 2^346019+78999 | 104163 | Stefano Morozzi | 11/2024 |
| 8959 | 2^346019+79955 | 104163 | Stefano Morozzi | 11/2024 |
| 8960 | 2^346020+72993 | 104163 | Stefano Morozzi | 11/2024 |
| 8961 | 2^346020+188673 | 104163 | Stefano Morozzi | 11/2024 |
| 8962 | 2^346021+100311 | 104163 | Stefano Morozzi | 11/2024 |
| 8966 | (34*10^104168-7)/9/13/551179 | 104162 | Makoto Morimoto | 05/2016 |
| 8963 | 2^346016+84007 | 104162 | Stefano Morozzi | 11/2024 |
| 8964 | 2^346017+122397 | 104162 | Stefano Morozzi | 11/2024 |
| 8965 | 2^346017+165791 | 104162 | Stefano Morozzi | 11/2024 |
| 8967 | 2^346014+27949 | 104161 | Stefano Morozzi | 11/2024 |
| 8968 | 2^346014+46743 | 104161 | Stefano Morozzi | 11/2024 |
| 8969 | 2^346015+166089 | 104161 | Stefano Morozzi | 11/2024 |
| 8970 | 2^346009+107705 | 104160 | Stefano Morozzi | 11/2024 |
| 8971 | 2^346012+35043 | 104160 | Stefano Morozzi | 11/2024 |
| 8972 | 2^346012+83091 | 104160 | Stefano Morozzi | 11/2024 |
| 8980 | 6^133854-17993 | 104159 | Enzo Doria | 03/2013 |
| 8973 | 2^346006+77727 | 104159 | Stefano Morozzi | 11/2024 |
| 8974 | 2^346008+9007 | 104159 | Stefano Morozzi | 11/2024 |
| 8975 | 2^346008+51567 | 104159 | Stefano Morozzi | 11/2024 |
| 8976 | 2^346008+107787 | 104159 | Stefano Morozzi | 11/2024 |
| 8977 | 2^346008+146191 | 104159 | Stefano Morozzi | 11/2024 |
| 8978 | 2^346008+170823 | 104159 | Stefano Morozzi | 11/2024 |
| 8979 | (131^49201-1)/7538466025870 | 104159 | Paul Vanderveen | 06/2025 |
| 8981 | 2^346003+191519 | 104158 | Stefano Morozzi | 11/2024 |
| 8982 | 2^345990+1874239 | 104154 | Enzo Doria | 06/2016 |
| 8983 | 2^345988-20373 | 104153 | Enzo Doria | 06/2013 |
| 8984 | (2^345965+2214)/2 | 104146 | Stefano Morozzi | 09/2020 |
| 8985 | (26*10^104132-503)/9 | 104133 | Robert Price | 07/2018 |
| 8986 | 3*5^148968+8 | 104125 | Lelio R Paula | 11/2014 |
| 8987 | (7*10^104113+53)/3 | 104114 | Robert Price | 05/2018 |
| 8988 | p(21253)#/2+8 | 104113 | Robert Price | 01/2017 |
| 8989 | 33582^1259+1259^33582 | 104106 | Hans Havermann | 09/2020 |
| 8990 | 32958^1441+1441^32958 | 104104 | Hans Havermann | 09/2020 |
| 8991 | 29127^3748+3748^29127 | 104095 | Hans Havermann | 09/2020 |
| 8992 | 322^41507+41507^322 | 104094 | Norbert Schneider | 12/2014 |
| 8993 | 6^133768-17423 | 104092 | Enzo Doria | 03/2013 |
| 8994 | 2^345786-19557 | 104092 | Enzo Doria | 05/2013 |
| 8995 | 171^46606-2 | 104072 | Lelio R Paula | 10/2017 |
| 8996 | (29*10^104071+91)/3 | 104072 | Robert Price | 04/2020 |
| 8997 | norm(Mod(x,x^3-x-1)^852167-1) | 104070 | Paul Vanderveen | 09/2022 |
| 8998 | 2^345704-149 | 104068 | Lelio R Paula | 09/2011 |
| 8999 | 25821^10712+10712^25821 | 104056 | Hans Havermann | 09/2020 |
| 9000 | (2^345662+2038)/2 | 104055 | Stefano Morozzi | 09/2020 |