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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Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
7751 | 2^346414+165775 | 104282 | Stefano Morozzi | 11/2024 |
7752 | 10^(2*52140+1)-10^52140-1 | 104281 | Robert Price | 07/2023 |
7753 | 2^346411+106893 | 104281 | Stefano Morozzi | 11/2024 |
7754 | 2^346412+157935 | 104281 | Stefano Morozzi | 11/2024 |
7755 | 2^346413+117485 | 104281 | Stefano Morozzi | 11/2024 |
7756 | 2^346408+8085 | 104280 | Stefano Morozzi | 11/2024 |
7757 | 2^346408+24423 | 104280 | Stefano Morozzi | 11/2024 |
7758 | 2^346409+145047 | 104280 | Stefano Morozzi | 11/2024 |
7759 | 2^346410+172533 | 104280 | Stefano Morozzi | 11/2024 |
7760 | 2^346406+58417 | 104279 | Stefano Morozzi | 11/2024 |
7761 | 2^346406+198315 | 104279 | Stefano Morozzi | 11/2024 |
7762 | 2^346407+172509 | 104279 | Stefano Morozzi | 11/2024 |
7763 | 2^346401+180129 | 104278 | Stefano Morozzi | 11/2024 |
7764 | 2^346402+16897 | 104278 | Stefano Morozzi | 11/2024 |
7765 | 2^346402+114829 | 104278 | Stefano Morozzi | 11/2024 |
7766 | 2^346398+91623 | 104277 | Stefano Morozzi | 11/2024 |
7767 | 2^346398+117369 | 104277 | Stefano Morozzi | 11/2024 |
7768 | 2^346400+100141 | 104277 | Stefano Morozzi | 11/2024 |
7769 | 2^346400+183625 | 104277 | Stefano Morozzi | 11/2024 |
7770 | 2^346395+87281 | 104276 | Stefano Morozzi | 11/2024 |
7771 | 2^346391+28833 | 104275 | Stefano Morozzi | 11/2024 |
7772 | 2^346392+33715 | 104275 | Stefano Morozzi | 11/2024 |
7773 | 2^346392+37507 | 104275 | Stefano Morozzi | 11/2024 |
7774 | 2^346392+197617 | 104275 | Stefano Morozzi | 11/2024 |
7775 | 2^346393+45929 | 104275 | Stefano Morozzi | 11/2024 |
7776 | 2^346388+27223 | 104274 | Stefano Morozzi | 11/2024 |
7777 | 2^346388+29187 | 104274 | Stefano Morozzi | 11/2024 |
7778 | 2^346388+114657 | 104274 | Stefano Morozzi | 11/2024 |
7779 | 2^346388+158667 | 104274 | Stefano Morozzi | 11/2024 |
7780 | (22*10^104272-61)/3 | 104273 | Robert Price | 03/2022 |
7781 | 2^346385+150947 | 104273 | Stefano Morozzi | 11/2024 |
7782 | 2^346385+179309 | 104273 | Stefano Morozzi | 11/2024 |
7783 | 2^346387+80549 | 104273 | Stefano Morozzi | 11/2024 |
7784 | 2^346387+90309 | 104273 | Stefano Morozzi | 11/2024 |
7785 | 2^346387+157473 | 104273 | Stefano Morozzi | 11/2024 |
7786 | 2^346381+67497 | 104272 | Stefano Morozzi | 11/2024 |
7787 | 2^346379+72419 | 104271 | Stefano Morozzi | 11/2024 |
7788 | 2^346379+118811 | 104271 | Stefano Morozzi | 11/2024 |
7789 | 2^346377+97379 | 104270 | Stefano Morozzi | 11/2024 |
7790 | 2^346371+144159 | 104269 | Stefano Morozzi | 11/2024 |
7791 | 2^346371+167213 | 104269 | Stefano Morozzi | 11/2024 |
7792 | 2^346373+31301 | 104269 | Stefano Morozzi | 11/2024 |
7793 | 2^346373+103665 | 104269 | Stefano Morozzi | 11/2024 |
7794 | 2^346368+19155 | 104268 | Stefano Morozzi | 11/2024 |
7795 | 2^346370+10107 | 104268 | Stefano Morozzi | 11/2024 |
7796 | 2^346370+38649 | 104268 | Stefano Morozzi | 11/2024 |
7797 | 2^346365+8411 | 104267 | Stefano Morozzi | 11/2024 |
7798 | 2^346367+6735 | 104267 | Stefano Morozzi | 11/2024 |
7799 | 2^346367+140303 | 104267 | Stefano Morozzi | 11/2024 |
7800 | 2^346361+17507 | 104266 | Stefano Morozzi | 11/2024 |
7801 | 2^346361+46401 | 104266 | Stefano Morozzi | 11/2024 |
7802 | 2^346361+64875 | 104266 | Stefano Morozzi | 11/2024 |
7803 | 2^346364+182271 | 104266 | Stefano Morozzi | 11/2024 |
7804 | 2^346360+33403 | 104265 | Stefano Morozzi | 11/2024 |
7805 | 2^346355+7121 | 104264 | Stefano Morozzi | 11/2024 |
7806 | 2^346356+128607 | 104264 | Stefano Morozzi | 11/2024 |
7807 | 2^346356+152841 | 104264 | Stefano Morozzi | 11/2024 |
7808 | 2^346351+12735 | 104263 | Stefano Morozzi | 11/2024 |
7809 | 2^346354+12247 | 104263 | Stefano Morozzi | 11/2024 |
7810 | 2^346354+93177 | 104263 | Stefano Morozzi | 11/2024 |
7811 | 2^346354+152067 | 104263 | Stefano Morozzi | 11/2024 |
7812 | 2^346348+55023 | 104262 | Stefano Morozzi | 11/2024 |
7813 | 2^346349+92945 | 104262 | Stefano Morozzi | 11/2024 |
7814 | 2^346350+124873 | 104262 | Stefano Morozzi | 11/2024 |
7815 | 2^346350+141253 | 104262 | Stefano Morozzi | 11/2024 |
7816 | 2^346345+36681 | 104261 | Stefano Morozzi | 11/2024 |
7817 | 2^346346+142767 | 104261 | Stefano Morozzi | 11/2024 |
7818 | 2^346331+13743 | 104257 | Stefano Morozzi | 11/2024 |
7819 | 2^346333+100331 | 104257 | Stefano Morozzi | 11/2024 |
7820 | 2^346333+157209 | 104257 | Stefano Morozzi | 11/2024 |
7821 | 2^346330+186837 | 104256 | Stefano Morozzi | 11/2024 |
7822 | 2^346325+144891 | 104255 | Stefano Morozzi | 11/2024 |
7823 | 2^346326+148237 | 104255 | Stefano Morozzi | 11/2024 |
7824 | 2^346321+5877 | 104254 | Stefano Morozzi | 11/2024 |
7825 | 2^346323+35999 | 104254 | Stefano Morozzi | 11/2024 |
7826 | 2^346323+133109 | 104254 | Stefano Morozzi | 11/2024 |
7827 | 2^346318+50695 | 104253 | Stefano Morozzi | 11/2024 |
7828 | 2^346319+78975 | 104253 | Stefano Morozzi | 11/2024 |
7833 | (2^346318+862)/2 | 104252 | Stefano Morozzi | 02/2021 |
7829 | 2^346315+46235 | 104252 | Stefano Morozzi | 11/2024 |
7830 | 2^346316+84571 | 104252 | Stefano Morozzi | 11/2024 |
7831 | 2^346316+168015 | 104252 | Stefano Morozzi | 11/2024 |
7832 | 2^346317+431 | 104252 | Stefano Morozzi | 11/2024 |
7841 | 18^83049-89 | 104250 | Lelio R Paula | 01/2017 |
7840 | (2^346311+606)/2 | 104250 | Stefano Morozzi | 09/2020 |
7834 | 2^346308+92347 | 104250 | Stefano Morozzi | 11/2024 |
7835 | 2^346308+182521 | 104250 | Stefano Morozzi | 11/2024 |
7836 | 2^346309+128897 | 104250 | Stefano Morozzi | 11/2024 |
7837 | 2^346309+184955 | 104250 | Stefano Morozzi | 11/2024 |
7838 | 2^346310+303 | 104250 | Stefano Morozzi | 11/2024 |
7839 | 2^346311+32693 | 104250 | Stefano Morozzi | 11/2024 |
7842 | 2^346305+165741 | 104249 | Stefano Morozzi | 11/2024 |
7843 | 2^346302+75075 | 104248 | Stefano Morozzi | 11/2024 |
7844 | 2^346304+33411 | 104248 | Stefano Morozzi | 11/2024 |
7845 | 2^346298+147849 | 104247 | Stefano Morozzi | 11/2024 |
7846 | 2^346300+144855 | 104247 | Stefano Morozzi | 11/2024 |
7847 | 2^346296+44865 | 104246 | Stefano Morozzi | 11/2024 |
7848 | 2^346297+116291 | 104246 | Stefano Morozzi | 11/2024 |
7849 | 2^346297+142667 | 104246 | Stefano Morozzi | 11/2024 |
7850 | 2^346293+39285 | 104245 | Stefano Morozzi | 11/2024 |
7851 | 2^346293+58929 | 104245 | Stefano Morozzi | 11/2024 |
7852 | 2^346294+151075 | 104245 | Stefano Morozzi | 11/2024 |
7853 | 2^346290+162153 | 104244 | Stefano Morozzi | 11/2024 |
7854 | 2^346286+139935 | 104243 | Stefano Morozzi | 11/2024 |
7855 | 2^346282+184705 | 104242 | Stefano Morozzi | 11/2024 |
7856 | 2^346283+116913 | 104242 | Stefano Morozzi | 11/2024 |
7857 | 2^346284+118191 | 104242 | Stefano Morozzi | 11/2024 |
7858 | 2^346284+186595 | 104242 | Stefano Morozzi | 11/2024 |
7859 | 2^346279+29591 | 104241 | Stefano Morozzi | 11/2024 |
7860 | 2^346279+122385 | 104241 | Stefano Morozzi | 11/2024 |
7861 | 2^346280+18925 | 104241 | Stefano Morozzi | 11/2024 |
7862 | 2^346281+69725 | 104241 | Stefano Morozzi | 11/2024 |
7863 | 2^346281+156401 | 104241 | Stefano Morozzi | 11/2024 |
7864 | 2^346275+182519 | 104240 | Stefano Morozzi | 11/2024 |
7865 | 2^346276+14101 | 104240 | Stefano Morozzi | 11/2024 |
7866 | 2^346276+189937 | 104240 | Stefano Morozzi | 11/2024 |
7867 | 2^346273+121425 | 104239 | Stefano Morozzi | 11/2024 |
7868 | 2^346274+72363 | 104239 | Stefano Morozzi | 11/2024 |
7869 | 2^346274+92047 | 104239 | Stefano Morozzi | 11/2024 |
7870 | 2^346268+44233 | 104238 | Stefano Morozzi | 11/2024 |
7871 | 2^346270+19539 | 104238 | Stefano Morozzi | 11/2024 |
7872 | 2^346265+133877 | 104237 | Stefano Morozzi | 11/2024 |
7873 | 2^346267+64613 | 104237 | Stefano Morozzi | 11/2024 |
7874 | 2^346267+70461 | 104237 | Stefano Morozzi | 11/2024 |
7875 | 2^346267+118715 | 104237 | Stefano Morozzi | 11/2024 |
7876 | 2^346263+110721 | 104236 | Stefano Morozzi | 11/2024 |
7877 | 2^346263+165009 | 104236 | Stefano Morozzi | 11/2024 |
7878 | 2^346264+50481 | 104236 | Stefano Morozzi | 11/2024 |
7879 | 2^346264+134047 | 104236 | Stefano Morozzi | 11/2024 |
7880 | 2^346264+179617 | 104236 | Stefano Morozzi | 11/2024 |
7881 | 2^346260+176391 | 104235 | Stefano Morozzi | 11/2024 |
7882 | 2^346256+36111 | 104234 | Stefano Morozzi | 11/2024 |
7883 | 2^346254+52299 | 104233 | Stefano Morozzi | 11/2024 |
7889 | (166*10^104230+11)/3 | 104232 | Robert Price | 03/2021 |
7884 | 2^346248+3075 | 104232 | Stefano Morozzi | 11/2024 |
7885 | 2^346248+39081 | 104232 | Stefano Morozzi | 11/2024 |
7886 | 2^346249+38339 | 104232 | Stefano Morozzi | 11/2024 |
7887 | 2^346251+32831 | 104232 | Stefano Morozzi | 11/2024 |
7888 | 2^346251+116175 | 104232 | Stefano Morozzi | 11/2024 |
7890 | 2^346247+197309 | 104231 | Stefano Morozzi | 11/2024 |
7891 | 2^346245+95429 | 104231 | Stefano Morozzi | 11/2024 |
7892 | 2^346243+58163 | 104230 | Stefano Morozzi | 11/2024 |
7893 | 2^346243+130931 | 104230 | Stefano Morozzi | 11/2024 |
7894 | 2^346244+10381 | 104230 | Stefano Morozzi | 11/2024 |
7895 | 2^346241+41057 | 104229 | Stefano Morozzi | 11/2024 |
7896 | 2^346235+152303 | 104228 | Stefano Morozzi | 11/2024 |
7897 | 2^346236+106617 | 104228 | Stefano Morozzi | 11/2024 |
7898 | 2^346232+103317 | 104227 | Stefano Morozzi | 11/2024 |
7899 | 2^346232+193681 | 104227 | Stefano Morozzi | 11/2024 |
7900 | 2^346233+115671 | 104227 | Stefano Morozzi | 11/2024 |
7901 | 2^346229+73157 | 104226 | Stefano Morozzi | 11/2024 |
7902 | 2^346229+145377 | 104226 | Stefano Morozzi | 11/2024 |
7903 | 2^346230+171103 | 104226 | Stefano Morozzi | 11/2024 |
7904 | 2^346225+55527 | 104225 | Stefano Morozzi | 11/2024 |
7905 | 2^346225+132251 | 104225 | Stefano Morozzi | 11/2024 |
7906 | 2^346225+140637 | 104225 | Stefano Morozzi | 11/2024 |
7907 | 2^346223+27335 | 104224 | Stefano Morozzi | 11/2024 |
7908 | 2^346223+74591 | 104224 | Stefano Morozzi | 11/2024 |
7909 | 2^346224+70905 | 104224 | Stefano Morozzi | 11/2024 |
7910 | 2^346220+12355 | 104223 | Stefano Morozzi | 11/2024 |
7911 | 2^346220+110805 | 104223 | Stefano Morozzi | 11/2024 |
7912 | 2^346220+161361 | 104223 | Stefano Morozzi | 11/2024 |
7913 | 2^346220+176523 | 104223 | Stefano Morozzi | 11/2024 |
7914 | 2^346220+185625 | 104223 | Stefano Morozzi | 11/2024 |
7915 | 2^346216+62973 | 104222 | Stefano Morozzi | 11/2024 |
7916 | 2^346217+88391 | 104222 | Stefano Morozzi | 11/2024 |
7917 | 2^346217+170121 | 104222 | Stefano Morozzi | 11/2024 |
7918 | 2^346217+111567 | 104222 | Stefano Morozzi | 11/2024 |
7922 | 2^346213+484049 | 104221 | Enzo Doria | 04/2017 |
7919 | 2^346212+31773 | 104221 | Stefano Morozzi | 11/2024 |
7920 | 2^346213+37151 | 104221 | Stefano Morozzi | 11/2024 |
7921 | 2^346213+162399 | 104221 | Stefano Morozzi | 11/2024 |
7923 | 2^346209+173231 | 104220 | Stefano Morozzi | 11/2024 |
7924 | 2^346207+125243 | 104219 | Stefano Morozzi | 11/2024 |
7925 | 2^346208+79825 | 104219 | Stefano Morozzi | 11/2024 |
7926 | 2^346208+176463 | 104219 | Stefano Morozzi | 11/2024 |
7927 | 2^346206+195363 | 104219 | Stefano Morozzi | 11/2024 |
7928 | 2^346202+67065 | 104218 | Stefano Morozzi | 11/2024 |
7929 | 2^346202+107377 | 104218 | Stefano Morozzi | 11/2024 |
7930 | 2^346204+127677 | 104218 | Stefano Morozzi | 11/2024 |
7931 | 2^346204+19573 | 104218 | Stefano Morozzi | 11/2024 |
7932 | 2^346204+161997 | 104218 | Stefano Morozzi | 11/2024 |
7933 | 2^346204+152665 | 104218 | Stefano Morozzi | 11/2024 |
7934 | 2^346199+90995 | 104217 | Stefano Morozzi | 11/2024 |
7935 | 2^346199+189629 | 104217 | Stefano Morozzi | 11/2024 |
7936 | 2^346200+159591 | 104217 | Stefano Morozzi | 11/2024 |
7937 | 2^346195+19733 | 104216 | Stefano Morozzi | 11/2024 |
7938 | 2^346196+141117 | 104216 | Stefano Morozzi | 11/2024 |
7939 | 2^346196+195171 | 104216 | Stefano Morozzi | 11/2024 |
7940 | 2^346197+113751 | 104216 | Stefano Morozzi | 11/2024 |
7941 | 2^346198+95305 | 104216 | Stefano Morozzi | 11/2024 |
7942 | 2^346198+106735 | 104216 | Stefano Morozzi | 11/2024 |
7944 | 18^83021-91 | 104214 | Lelio R Paula | 01/2017 |
7943 | 2^346189+194831 | 104214 | Stefano Morozzi | 11/2024 |
7945 | 10^104212+128779 | 104213 | Patrick De Geest | 05/2016 |
7946 | 10^104212+237447 | 104213 | Patrick De Geest | 05/2016 |
7947 | 10^104212+242139 | 104213 | Patrick De Geest | 05/2016 |
7948 | 10^104212+269199 | 104213 | Patrick De Geest | 05/2016 |
7952 | 24254^19803+19803^24254 | 104213 | Hans Havermann | 09/2020 |
7949 | 2^346186+93813 | 104213 | Stefano Morozzi | 11/2024 |
7950 | 2^346186+153687 | 104213 | Stefano Morozzi | 11/2024 |
7951 | 2^346187+102195 | 104213 | Stefano Morozzi | 11/2024 |
7957 | (10^104212-71)/1 | 104212 | Serge Batalov | 12/2014 |
7953 | 2^346182+118065 | 104212 | Stefano Morozzi | 11/2024 |
7954 | 2^346184+155085 | 104212 | Stefano Morozzi | 11/2024 |
7955 | 2^346184+187513 | 104212 | Stefano Morozzi | 11/2024 |
7956 | 2^346184+188455 | 104212 | Stefano Morozzi | 11/2024 |
7958 | 2^346180+82735 | 104211 | Stefano Morozzi | 11/2024 |
7959 | 2^346180+160593 | 104211 | Stefano Morozzi | 11/2024 |
7960 | 2^346180+192333 | 104211 | Stefano Morozzi | 11/2024 |
7961 | 2^346181+199821 | 104211 | Stefano Morozzi | 11/2024 |
7962 | 2^346176+123667 | 104210 | Stefano Morozzi | 11/2024 |
7963 | 2^346178+37455 | 104210 | Stefano Morozzi | 11/2024 |
7964 | 2^346178+95865 | 104210 | Stefano Morozzi | 11/2024 |
7965 | 2^346178+159517 | 104210 | Stefano Morozzi | 11/2024 |
7966 | 2^346174+12543 | 104209 | Stefano Morozzi | 11/2024 |
7967 | 2^346169+56049 | 104208 | Stefano Morozzi | 11/2024 |
7968 | 2^346169+118965 | 104208 | Stefano Morozzi | 11/2024 |
7969 | 2^346170+31363 | 104208 | Stefano Morozzi | 11/2024 |
7970 | 2^346165+61767 | 104207 | Stefano Morozzi | 11/2024 |
7971 | 2^346166+189919 | 104207 | Stefano Morozzi | 11/2024 |
7972 | 2^346167+41681 | 104207 | Stefano Morozzi | 11/2024 |
7973 | 2^346162+85765 | 104206 | Stefano Morozzi | 11/2024 |
7974 | 2^346164+152925 | 104206 | Stefano Morozzi | 11/2024 |
7975 | 2^346160+131703 | 104205 | Stefano Morozzi | 11/2024 |
7976 | 2^346155+166433 | 104204 | Stefano Morozzi | 11/2024 |
7977 | 2^346157+7137 | 104204 | Stefano Morozzi | 11/2024 |
7978 | 2^346158+31483 | 104204 | Stefano Morozzi | 11/2024 |
7979 | 2^346158+183253 | 104204 | Stefano Morozzi | 11/2024 |
7980 | 2^346152+136287 | 104203 | Stefano Morozzi | 11/2024 |
7981 | 2^346154+107499 | 104203 | Stefano Morozzi | 11/2024 |
7982 | 2^346154+187987 | 104203 | Stefano Morozzi | 11/2024 |
7986 | 23678^23821-23821^23678 | 104202 | Norbert Schneider | 01/2020 |
7983 | 2^346149+45857 | 104202 | Stefano Morozzi | 11/2024 |
7984 | 2^346150+111579 | 104202 | Stefano Morozzi | 11/2024 |
7985 | 2^346151+21539 | 104202 | Stefano Morozzi | 11/2024 |
7987 | 2^346143+119183 | 104200 | Stefano Morozzi | 11/2024 |
7988 | 2^346143+130361 | 104200 | Stefano Morozzi | 11/2024 |
7989 | 2^346143+171791 | 104200 | Stefano Morozzi | 11/2024 |
7990 | 2^346144+4731 | 104200 | Stefano Morozzi | 11/2024 |
7991 | 2^346144+158097 | 104200 | Stefano Morozzi | 11/2024 |
7992 | 2^346139+68459 | 104199 | Stefano Morozzi | 11/2024 |
7993 | 2^346140+121711 | 104199 | Stefano Morozzi | 11/2024 |
7994 | 2^346135+122913 | 104198 | Stefano Morozzi | 11/2024 |
7995 | 2^346135+125453 | 104198 | Stefano Morozzi | 11/2024 |
7996 | 2^346135+184869 | 104198 | Stefano Morozzi | 11/2024 |
7997 | 2^346136+135721 | 104198 | Stefano Morozzi | 11/2024 |
7998 | 2^346133+46695 | 104197 | Stefano Morozzi | 11/2024 |
7999 | 2^346129+87819 | 104196 | Stefano Morozzi | 11/2024 |
8000 | 2^346130+127369 | 104196 | Stefano Morozzi | 11/2024 |