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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| Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
| 4751 | 2^304578-16713 | 91688 | Enzo Doria | 05/2013 |
| 4752 | 6^117824-18713 | 91685 | Enzo Doria | 03/2013 |
| 4753 | (17^74509-1)/16 | 91679 | Paul Bourdelais | 03/2010 |
| 4754 | (2^304551-7)/8912231 | 91673 | Lelio R Paula | 06/2013 |
| 4755 | (2^304532-3)/3013 | 91670 | Lelio R Paula | 06/2013 |
| 4756 | 2^304507-16645 | 91666 | Enzo Doria | 04/2013 |
| 4757 | (29*2^304489+1)/31 | 91661 | Lelio R Paula | 09/2013 |
| 4758 | 2^304471-1836127 | 91655 | Enzo Doria | 04/2015 |
| 4759 | 2^304433+32769 | 91644 | Lelio R Paula | 02/2016 |
| 4760 | 2^304410-16625 | 91637 | Enzo Doria | 04/2013 |
| 4761 | 183^40500-2 | 91630 | Lelio R Paula | 10/2017 |
| 4762 | (203*10^91613+1)/3 | 91615 | Robert Price | 09/2017 |
| 4763 | 4*5^131052+7 | 91603 | Lelio R Paula | 10/2014 |
| 4764 | 2^304278-4001 | 91597 | Yves Minet | 04/2017 |
| 4765 | 2^304272-1866377 | 91595 | Enzo Doria | 03/2016 |
| 4766 | 2^304268+19683 | 91594 | Lelio R Paula | 02/2016 |
| 4767 | 2^304162-161 | 91562 | Lelio R Paula | 11/2012 |
| 4768 | 5*7^108331+6 | 91552 | Lelio R Paula | 10/2014 |
| 4769 | 2^304082-2787821 | 91538 | Enzo Doria | 03/2016 |
| 4770 | 2^304015+64133 | 91518 | David Broadhurst | 06/2002 |
| 4771 | (7*2^303963+1)/3 | 91503 | Lelio R Paula | 09/2013 |
| 4772 | (2^303945-9)/3617 | 91494 | Lelio R Paula | 06/2013 |
| 4773 | 2^303930+1880527 | 91493 | Enzo Doria | 10/2016 |
| 4774 | 3^191684-68 | 91457 | Lelio R Paula | 04/2016 |
| 4775 | (21*2^303813-1)/169 | 91456 | Lelio R Paula | 02/2014 |
| 4776 | 11^87797-120 | 91432 | Enzo Doria | 07/2012 |
| 4777 | 2^303698-1847231 | 91423 | Enzo Doria | 07/2015 |
| 4778 | (38^28933-1)^2-2 | 91416 | Norbert Schneider | 06/2016 |
| 4779 | 2^303554+77299 | 91379 | Enzo Doria | 05/2016 |
| 4780 | 2^303542+12705 | 91376 | Lelio R Paula | 02/2016 |
| 4781 | 31^61269-2 | 91375 | Lelio R Paula | 09/2013 |
| 4782 | 2^303516-64875 | 91368 | Lelio R Paula | 02/2016 |
| 4783 | (24737*2^303428+1)/3 | 91345 | Lelio R Paula | 06/2014 |
| 4784 | (21181*2^303357+1)/32361 | 91320 | Lelio R Paula | 06/2014 |
| 4785 | 2^303344-2786969 | 91316 | Enzo Doria | 03/2016 |
| 4786 | 6^117346+65 | 91313 | Lelio R Paula | 05/2016 |
| 4787 | 2^303321+855 | 91309 | Lelio R Paula | 02/2016 |
| 4788 | 12^84606+47 | 91306 | Lelio R Paula | 06/2016 |
| 4789 | 2^303288+1874311 | 91299 | Enzo Doria | 06/2016 |
| 4790 | 197^39788-2 | 91293 | Lelio R Paula | 10/2017 |
| 4791 | 11^87663-1710 | 91292 | Enzo Doria | 12/2012 |
| 4792 | 2^303224+2533 | 91280 | Henri Lifchitz | 05/2005 |
| 4793 | 6^117302+143 | 91279 | Lelio R Paula | 05/2016 |
| 4794 | 3^191306-112880 | 91277 | Enzo Doria | 07/2014 |
| 4795 | 2^303207+12915 | 91275 | Lelio R Paula | 02/2016 |
| 4796 | 2^303191-111259 | 91270 | Enzo Doria | 05/2014 |
| 4797 | 81539!4+32 | 91267 | Robert Price | 09/2019 |
| 4799 | 10^91230+9^(91230+1) | 91231 | Robert Price | 08/2016 |
| 4798 | 10^91230+7921 | 91231 | Patrick De Geest | 11/2016 |
| 4801 | 10^91230-911141 | 91230 | Patrick De Geest | 11/2016 |
| 4800 | 10^91229+348793 | 91230 | Patrick De Geest | 07/2019 |
| 4802 | 10^91229-2471 | 91229 | Patrick De Geest | 01/2019 |
| 4803 | 10^91225+5271 | 91226 | Patrick De Geest | 01/2019 |
| 4805 | 6^117232-17423 | 91225 | Enzo Doria | 02/2013 |
| 4804 | 10^91225-147219 | 91225 | Patrick De Geest | 07/2019 |
| 4806 | 7*10^91215+3 | 91216 | Erik Branger | 11/2009 |
| 4807 | 10^91215+230611 | 91216 | Patrick De Geest | 07/2019 |
| 4808 | 10^91215-4539 | 91215 | Patrick De Geest | 01/2019 |
| 4809 | 10^91210+2421 | 91211 | Patrick De Geest | 01/2019 |
| 4810 | 10^91210-1737 | 91210 | Patrick De Geest | 01/2019 |
| 4811 | 97*10^91205-3 | 91207 | Robert Price | 01/2017 |
| 4812 | 2^302979-161181 | 91206 | Enzo Doria | 04/2013 |
| 4813 | 2^302949+81 | 91197 | Henri Lifchitz | 02/2007 |
| 4814 | 10^91194+200361 | 91195 | Patrick De Geest | 07/2019 |
| 4816 | 4*6^117192-5 | 91194 | Lelio R Paula | 10/2014 |
| 4815 | 10^91194-8663 | 91194 | Patrick De Geest | 01/2019 |
| 4817 | 2^302918+99 | 91188 | Lelio R Paula | 11/2012 |
| 4818 | 10^91186+268111 | 91187 | Patrick De Geest | 07/2019 |
| 4819 | 10^91186-7763 | 91186 | Patrick De Geest | 01/2019 |
| 4820 | 10^91181+550471 | 91182 | Patrick De Geest | 07/2019 |
| 4821 | 10^91181-1367 | 91181 | Patrick De Geest | 01/2019 |
| 4822 | 10^91178+71883 | 91179 | Patrick De Geest | 07/2019 |
| 4823 | 10^91178-4719 | 91178 | Patrick De Geest | 01/2019 |
| 4824 | 10^91165+3043 | 91166 | Patrick De Geest | 01/2019 |
| 4825 | 10^91165-399413 | 91165 | Patrick De Geest | 07/2019 |
| 4826 | 10^91156+3861 | 91157 | Patrick De Geest | 01/2019 |
| 4827 | 10^91156-231497 | 91156 | Patrick De Geest | 07/2019 |
| 4828 | 2^302797+1869587 | 91151 | Enzo Doria | 05/2016 |
| 4829 | 265^37614+37614^265 | 91148 | Norbert Schneider | 01/2015 |
| 4830 | 7^107852+82 | 91146 | Lelio R Paula | 04/2016 |
| 4831 | (38*10^91144-11)/9 | 91145 | Robert Price | 05/2015 |
| 4832 | (55*10^91142+377)/9 | 91143 | Robert Price | 10/2017 |
| 4833 | 10^91128+9961 | 91129 | Patrick De Geest | 01/2019 |
| 4835 | 249^38030+38030^249 | 91128 | Norbert Schneider | 01/2015 |
| 4834 | 10^91128-189153 | 91128 | Patrick De Geest | 07/2019 |
| 4836 | 6^117094-211049 | 91117 | Mike Oakes | 05/2011 |
| 4837 | 2^302602-1867181 | 91093 | Enzo Doria | 03/2016 |
| 4838 | 10^91092+56127 | 91093 | Patrick De Geest | 07/2019 |
| 4839 | 10^91092-9107 | 91092 | Patrick De Geest | 01/2019 |
| 4840 | (1017*2^302592-1)/53 | 91091 | Lelio R Paula | 04/2015 |
| 4841 | 15^77445-16 | 91083 | Lelio R Paula | 07/2016 |
| 4842 | 2^302505+81 | 91064 | Henri Lifchitz | 02/2007 |
| 4843 | 2^302496-112349 | 91061 | Enzo Doria | 06/2014 |
| 4844 | 17^73999-72 | 91052 | Lelio R Paula | 07/2016 |
| 4845 | 10^91047+9331 | 91048 | Patrick De Geest | 01/2019 |
| 4846 | 10^91047-671169 | 91047 | Patrick De Geest | 07/2019 |
| 4847 | 10^91044+2077 | 91045 | Patrick De Geest | 01/2019 |
| 4848 | 10^91044-136359 | 91044 | Patrick De Geest | 07/2019 |
| 4849 | 10^91041+9349 | 91042 | Patrick De Geest | 01/2019 |
| 4850 | 10^91041-7823 | 91041 | Patrick De Geest | 01/2019 |
| 4851 | 10^91040+4077 | 91041 | Patrick De Geest | 01/2019 |
| 4852 | 10^91040-119421 | 91040 | Patrick De Geest | 07/2019 |
| 4853 | 10^91037+2769 | 91038 | Patrick De Geest | 01/2019 |
| 4854 | 10^91037-22649 | 91037 | Patrick De Geest | 07/2019 |
| 4855 | (16*10^91032+41)/3 | 91033 | Robert Price | 10/2017 |
| 4856 | 10^91023+58039 | 91024 | Patrick De Geest | 07/2019 |
| 4857 | 10^91023-6471 | 91023 | Patrick De Geest | 01/2019 |
| 4858 | 10^91018+7873 | 91019 | Patrick De Geest | 01/2019 |
| 4859 | 10^91018-333177 | 91018 | Patrick De Geest | 07/2019 |
| 4860 | 10^91017+68767 | 91018 | Patrick De Geest | 07/2019 |
| 4861 | 10^91017-428327 | 91017 | Patrick De Geest | 07/2019 |
| 4862 | 10^91016+73111 | 91017 | Patrick De Geest | 07/2019 |
| 4863 | 10^91016-7973 | 91016 | Patrick De Geest | 01/2019 |
| 4864 | 2^302332+577294575 | 91012 | Lelio R Paula | 08/2016 |
| 4865 | 10^91004+9073 | 91005 | Patrick De Geest | 01/2019 |
| 4866 | 10^91004-491519 | 91004 | Patrick De Geest | 07/2019 |
| 4867 | 10^91003+74269 | 91004 | Patrick De Geest | 07/2019 |
| 4868 | 10^91003-3903 | 91003 | Patrick De Geest | 01/2019 |
| 4869 | 2^302274+74209 | 90994 | Enzo Doria | 04/2016 |
| 4870 | 10^90991+81147 | 90992 | Patrick De Geest | 07/2019 |
| 4871 | 10^90991-6279 | 90991 | Patrick De Geest | 01/2019 |
| 4872 | 10^90983+1393 | 90984 | Patrick De Geest | 01/2019 |
| 4873 | 10^90983-562383 | 90983 | Patrick De Geest | 07/2019 |
| 4874 | (311^36497-1)/310 | 90976 | Eric Chen | 09/2017 |
| 4875 | (3^190668+2)/89 | 90970 | Lelio R Paula | 04/2013 |
| 4876 | 2^302188+90195 | 90968 | Lelio R Paula | 02/2016 |
| 4878 | (53*10^90965-71)/9 | 90966 | Robert Price | 09/2015 |
| 4877 | 10^90965+573987 | 90966 | Patrick De Geest | 07/2019 |
| 4879 | 10^90965-6833 | 90965 | Patrick De Geest | 01/2019 |
| 4880 | 10^90964+48789 | 90965 | Patrick De Geest | 07/2019 |
| 4881 | 10^90964-52103 | 90964 | Patrick De Geest | 07/2019 |
| 4882 | 10^90963+191889 | 90964 | Patrick De Geest | 07/2019 |
| 4883 | 10^90963-3659 | 90963 | Patrick De Geest | 01/2019 |
| 4884 | 10^90962+7657 | 90963 | Patrick De Geest | 01/2019 |
| 4885 | 10^90962-215633 | 90962 | Patrick De Geest | 07/2019 |
| 4886 | 10^90961+67471 | 90962 | Patrick De Geest | 07/2019 |
| 4887 | 10^90961-211043 | 90961 | Patrick De Geest | 07/2019 |
| 4888 | 10^90960+1072117 | 90961 | Patrick De Geest | 07/2019 |
| 4889 | 10^90959+8791 | 90960 | Patrick De Geest | 01/2019 |
| 4890 | 10^90960-610659 | 90960 | Patrick De Geest | 07/2019 |
| 4891 | 10^90959-275213 | 90959 | Patrick De Geest | 07/2019 |
| 4892 | 10^90948+9867 | 90949 | Patrick De Geest | 01/2019 |
| 4893 | 10^90948-109239 | 90948 | Patrick De Geest | 07/2019 |
| 4894 | 2^302113+74105 | 90946 | Enzo Doria | 04/2016 |
| 4895 | 2^302102-6555 | 90942 | Lelio R Paula | 02/2016 |
| 4896 | 10^90930+95223 | 90931 | Patrick De Geest | 07/2019 |
| 4897 | 10^90930-3623 | 90930 | Patrick De Geest | 01/2019 |
| 4898 | 156*(10^(4*22731)-1)/101-1 | 90925 | Robert Price | 05/2014 |
| 4899 | 3^190568+38 | 90925 | Lelio R Paula | 04/2016 |
| 4900 | 10^90917+179863 | 90918 | Patrick De Geest | 07/2019 |
| 4901 | 10^90917-6693 | 90917 | Patrick De Geest | 01/2019 |
| 4902 | 2^302009-16449 | 90914 | Enzo Doria | 04/2013 |
| 4903 | 10^90908+3181 | 90909 | Patrick De Geest | 01/2019 |
| 4904 | 10^90908-139511 | 90908 | Patrick De Geest | 07/2019 |
| 4905 | 10^90904+106947 | 90905 | Patrick De Geest | 07/2019 |
| 4906 | 10^90904-5169 | 90904 | Patrick De Geest | 01/2019 |
| 4907 | 10^90903+120963 | 90904 | Patrick De Geest | 07/2019 |
| 4908 | 10^90902+2613 | 90903 | Patrick De Geest | 01/2019 |
| 4909 | 10^90903-190737 | 90903 | Patrick De Geest | 07/2019 |
| 4910 | 10^90902-952329 | 90902 | Patrick De Geest | 07/2019 |
| 4911 | (17*2^301951-1)/165 | 90896 | Lelio R Paula | 02/2014 |
| 4912 | 3^190497+74 | 90891 | Lelio R Paula | 04/2016 |
| 4913 | (24737*2^301896+1)/399 | 90882 | Lelio R Paula | 06/2014 |
| 4914 | 10^90880+5707 | 90881 | Patrick De Geest | 01/2019 |
| 4915 | 10^90880-152993 | 90880 | Patrick De Geest | 07/2019 |
| 4916 | 18^72397+89 | 90878 | Lelio R Paula | 06/2016 |
| 4917 | 134^42719-133 | 90868 | Norbert Schneider | 03/2019 |
| 4918 | 6^116769-47 | 90864 | Lelio R Paula | 05/2016 |
| 4919 | 10^90858+233433 | 90859 | Patrick De Geest | 07/2019 |
| 4920 | 10^90858-8301 | 90858 | Patrick De Geest | 01/2019 |
| 4921 | 10^90849+40141 | 90850 | Patrick De Geest | 07/2019 |
| 4922 | 10^90849-4721 | 90849 | Patrick De Geest | 01/2019 |
| 4923 | 2^301712-465 | 90825 | Lelio R Paula | 02/2016 |
| 4924 | 2^301693-69 | 90819 | Lelio R Paula | 11/2012 |
| 4925 | 2^301683-301683^2 | 90816 | Henri Lifchitz | 05/2005 |
| 4926 | 10^90807+7279 | 90808 | Patrick De Geest | 01/2019 |
| 4927 | 10^90807-162263 | 90807 | Patrick De Geest | 07/2019 |
| 4928 | 10^90800-6453 | 90800 | Patrick De Geest | 11/2018 |
| 4929 | 11^87187-1710 | 90796 | Enzo Doria | 12/2012 |
| 4930 | 5*10^90793+21 | 90794 | Robert Price | 01/2017 |
| 4931 | (22*10^90792-13)/9 | 90793 | Robert Price | 03/2015 |
| 4932 | 2^301591-1615 | 90788 | Lelio R Paula | 02/2016 |
| 4933 | (52^52901+1)/53 | 90777 | Paul Bourdelais | 08/2017 |
| 4934 | 2^301546-109037 | 90775 | Enzo Doria | 04/2014 |
| 4935 | 10^90772+4029 | 90773 | Patrick De Geest | 11/2018 |
| 4936 | 10^90772-36627 | 90772 | Patrick De Geest | 07/2019 |
| 4937 | 10^90771+67737 | 90772 | Patrick De Geest | 07/2019 |
| 4938 | 10^90771-441003 | 90771 | Patrick De Geest | 07/2019 |
| 4939 | 10^90770+28941 | 90771 | Patrick De Geest | 07/2019 |
| 4940 | 10^90770-431 | 90770 | Patrick De Geest | 11/2018 |
| 4941 | 14^79195-3 | 90768 | Lelio R Paula | 06/2016 |
| 4942 | 10^90766+877 | 90767 | Patrick De Geest | 11/2018 |
| 4945 | 2^301517-1861693 | 90766 | Enzo Doria | 11/2015 |
| 4943 | 10^90766-109241 | 90766 | Patrick De Geest | 07/2019 |
| 4944 | 10^90765+485361 | 90766 | Patrick De Geest | 07/2019 |
| 4946 | 10^90765-4797 | 90765 | Patrick De Geest | 11/2018 |
| 4947 | 10^90757+7573 | 90758 | Patrick De Geest | 11/2018 |
| 4948 | 10^90757-554979 | 90757 | Patrick De Geest | 07/2019 |
| 4949 | 10^90756+438109 | 90757 | Patrick De Geest | 07/2019 |
| 4950 | 10^90756-8727 | 90756 | Patrick De Geest | 11/2018 |
| 4951 | 10^90749+823 | 90750 | Patrick De Geest | 11/2018 |
| 4954 | 2^301460-173 | 90749 | Lelio R Paula | 11/2012 |
| 4952 | 10^90748+4213 | 90749 | Patrick De Geest | 11/2018 |
| 4953 | 10^90749-130413 | 90749 | Patrick De Geest | 07/2019 |
| 4955 | 10^90748-75411 | 90748 | Patrick De Geest | 07/2019 |
| 4956 | 10^90747+438471 | 90748 | Patrick De Geest | 07/2019 |
| 4957 | 10^90747-9279 | 90747 | Patrick De Geest | 11/2018 |
| 4958 | (85*10^90745-103)/9 | 90746 | Robert Price | 10/2017 |
| 4959 | 10^90726+4077 | 90727 | Patrick De Geest | 11/2018 |
| 4960 | 10^90726-504951 | 90726 | Patrick De Geest | 07/2019 |
| 4961 | 10^90721+181 | 90722 | Patrick De Geest | 11/2018 |
| 4962 | 10^90721-177149 | 90721 | Patrick De Geest | 07/2019 |
| 4963 | 2^301312-89 | 90704 | Lelio R Paula | 11/2012 |
| 4964 | 10^90696+6349 | 90697 | Patrick De Geest | 11/2018 |
| 4966 | 2^301285-129 | 90696 | Lelio R Paula | 11/2012 |
| 4965 | 10^90696-635049 | 90696 | Patrick De Geest | 07/2019 |
| 4967 | 2^301282-109991 | 90695 | Enzo Doria | 04/2014 |
| 4968 | 10^90690+8877 | 90691 | Patrick De Geest | 11/2018 |
| 4969 | 10^90690-227433 | 90690 | Patrick De Geest | 07/2019 |
| 4970 | 10^90683+61411 | 90684 | Patrick De Geest | 07/2019 |
| 4971 | 10^90683-2577 | 90683 | Patrick De Geest | 11/2018 |
| 4972 | 2^301228-1854269 | 90679 | Enzo Doria | 09/2015 |
| 4973 | (151*10^90669-1)/3 | 90671 | Robert Price | 04/2017 |
| 4974 | (32*10^90669+13)/9 | 90670 | Robert Price | 04/2015 |
| 4975 | 10^90669+9793 | 90670 | Patrick De Geest | 11/2018 |
| 4976 | 10^90669-223931 | 90669 | Patrick De Geest | 07/2019 |
| 4977 | 10^90665+10989 | 90666 | Patrick De Geest | 07/2019 |
| 4978 | 10^90665-3087 | 90665 | Patrick De Geest | 11/2018 |
| 4979 | 10^90662+89637 | 90663 | Patrick De Geest | 07/2019 |
| 4980 | 10^90662-9519 | 90662 | Patrick De Geest | 11/2018 |
| 4981 | 10^90661+2373 | 90662 | Patrick De Geest | 11/2018 |
| 4982 | 10^90661-194781 | 90661 | Patrick De Geest | 07/2019 |
| 4983 | 3*5^129698+8 | 90656 | Lelio R Paula | 10/2014 |
| 4984 | F(433781) | 90655 | Henri Lifchitz | 09/2003 |
| 4985 | 19^70891+82 | 90653 | Lelio R Paula | 06/2016 |
| 4986 | (29*2^301124-1)/13 | 90648 | Lelio R Paula | 02/2014 |
| 4987 | 10^90636+64159 | 90637 | Patrick De Geest | 07/2019 |
| 4988 | 10^90636-3101 | 90636 | Patrick De Geest | 11/2018 |
| 4989 | 7*3^189953-8 | 90632 | Lelio R Paula | 08/2014 |
| 4990 | 10^90626+339289 | 90627 | Patrick De Geest | 07/2019 |
| 4991 | 10^90626-1131 | 90626 | Patrick De Geest | 11/2018 |
| 4992 | 11^87022-1800 | 90625 | Enzo Doria | 12/2012 |
| 4993 | 10^90623+861 | 90624 | Patrick De Geest | 11/2018 |
| 4994 | 10^90623-305841 | 90623 | Patrick De Geest | 07/2019 |
| 4995 | (2^301042+47)/12036969 | 90616 | Lelio R Paula | 06/2013 |
| 4997 | 2^301004-2786939 | 90612 | Enzo Doria | 03/2016 |
| 4996 | 10^90611+169977 | 90612 | Patrick De Geest | 07/2019 |
| 4999 | 10^90611-9737 | 90611 | Patrick De Geest | 11/2018 |
| 4998 | 10^90610+36747 | 90611 | Patrick De Geest | 07/2019 |
| 5000 | 10^90609+6823 | 90610 | Patrick De Geest | 11/2018 |
