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 ? |
4751 | (4^167933+17)/3 | 101106 | Robert Price | 02/2017 |
4753 | 2^335858+153 | 101104 | Lelio R Paula | 10/2009 |
4752 | (2^335872-2776871)/5/5/479 | 101104 | Tony Prest / Never Odd Or Even | 01/2019 |
4754 | (2^335872-2758787)/23/31/20809 | 101101 | Tony Prest / Never Odd Or Even | 01/2019 |
4755 | (2^335839+2114)/2 | 101098 | Stefano Morozzi | 09/2020 |
4756 | (2^335872-2795083)/3/3/113/283/148367 | 101097 | Tony Prest / Never Odd Or Even | 01/2019 |
4757 | 6^129918-35 | 101096 | Lelio R Paula | 10/2016 |
4758 | (2*10^101096-107)/3 | 101096 | Robert Price | 11/2020 |
4759 | 3^211885-70 | 101095 | Lelio R Paula | 09/2016 |
4761 | (29*2^335835-1)/550599 | 101093 | Lelio R Paula | 03/2014 |
4760 | (2^335872-2794771)/3/5/5/61/232312440293 | 101093 | Tony Prest / Never Odd Or Even | 01/2019 |
4762 | 2^335818-20033 | 101092 | Enzo Doria | 06/2013 |
4763 | 2^335813-110083 | 101090 | Enzo Doria | 04/2014 |
4764 | 2^335804+2155 | 101088 | Lelio R Paula | 09/2016 |
4765 | (2^335872-2756679)/7/7/7/13/31/4987/437653/8734021 | 101087 | Tony Prest / Never Odd Or Even | 01/2019 |
4766 | 2^335784-16145 | 101082 | Enzo Doria | 04/2013 |
4767 | 11^97051+62 | 101069 | Lelio R Paula | 10/2016 |
4768 | 3*10^101065+11 | 101066 | Robert Price | 07/2018 |
4769 | 27820^4293+4293^27820 | 101064 | Hans Havermann | 10/2018 |
4770 | (2^335714+3750)/2 | 101060 | Stefano Morozzi | 01/2021 |
4771 | (2^335690+1038)/2 | 101053 | Stefano Morozzi | 09/2020 |
4772 | (2^335691-3)/26515 | 101049 | Lelio R Paula | 12/2013 |
4773 | 2^335658-94395 | 101044 | Lelio R Paula | 09/2016 |
4774 | 24514^13215+13215^24514 | 101024 | Hans Havermann | 11/2018 |
4775 | 2^335586+169 | 101022 | Lelio R Paula | 10/2009 |
4776 | (56^57787-1)/55 | 101021 | Paul Bourdelais | 08/2017 |
4777 | (2^335562+1258)/2 | 101014 | Stefano Morozzi | 09/2020 |
4778 | (19*10^100997+737)/9 | 100998 | Robert Price | 07/2018 |
4779 | 47599!2+1024 | 100991 | Robert Price | 02/2015 |
4780 | 2^335468-18629 | 100986 | Enzo Doria | 05/2013 |
4781 | 2^335454-20961 | 100982 | Enzo Doria | 06/2013 |
4782 | 10^100978+61 | 100979 | Lelio R Paula | 09/2016 |
4783 | 10^100978-156437 | 100978 | Patrick De Geest | 11/2016 |
4784 | (2^335422+3114)/2 | 100972 | Stefano Morozzi | 09/2020 |
4785 | (15*2^335417+1)/481 | 100970 | Lelio R Paula | 12/2013 |
4786 | 2^335403-1859167 | 100967 | Enzo Doria | 03/2016 |
4787 | 23599^18976+18976^23599 | 100962 | Hans Havermann | 10/2018 |
4788 | 6*10^100958+43 | 100959 | Robert Price | 07/2020 |
4789 | 9*2^335364-5 | 100956 | Lelio R Paula | 08/2014 |
4790 | 2^335349+72287 | 100951 | Enzo Doria | 04/2016 |
4791 | 2^335329+16095 | 100945 | Lelio R Paula | 09/2016 |
4792 | 232823#+233663 | 100937 | Makoto Morimoto | 10/2017 |
4793 | (232823#+10141)/(10141*1674461) | 100927 | Makoto Morimoto | 06/2019 |
4794 | 2^335237-20893 | 100917 | Enzo Doria | 06/2013 |
4795 | 2^335222-19337 | 100912 | Enzo Doria | 05/2013 |
4796 | 2^335222-109985 | 100912 | Enzo Doria | 04/2014 |
4797 | 2^335182-17237 | 100900 | Enzo Doria | 05/2013 |
4798 | (2^335107+1634)/2 | 100877 | Stefano Morozzi | 09/2020 |
4800 | 2^335043-16737 | 100858 | Enzo Doria | 05/2013 |
4799 | (21181*2^335049+1)/1343811 | 100858 | Lelio R Paula | 07/2014 |
4801 | 2^335038-20633 | 100857 | Enzo Doria | 06/2013 |
4802 | 2^335031+1873373 | 100855 | Enzo Doria | 06/2016 |
4803 | 23489^19650+19650^23489 | 100847 | Hans Havermann | 10/2018 |
4804 | 3^211354-8816 | 100842 | Enzo Doria | 05/2014 |
4805 | 2^334984-112757 | 100841 | Enzo Doria | 06/2014 |
4806 | (746*10^100827+1)/9 | 100829 | Robert Price | 03/2020 |
4807 | 29451^2648+2648^29451 | 100809 | Hans Havermann | 09/2018 |
4808 | 25583^8716+8716^25583 | 100806 | Hans Havermann | 08/2018 |
4810 | 2^334857+48527 | 100803 | Lelio R Paula | 08/2011 |
4809 | 12^93406+29 | 100803 | Lelio R Paula | 10/2016 |
4811 | 28780^3179+3179^28780 | 100796 | Hans Havermann | 09/2018 |
4812 | (5*2^334825+1)/47 | 100792 | Lelio R Paula | 12/2013 |
4813 | 2^334809-13 | 100788 | Lelio R Paula | 04/2011 |
4814 | (82*10^100780-1)/9 | 100781 | Robert Price | 12/2014 |
4815 | 31395^1622+1622^31395 | 100780 | Hans Havermann | 09/2018 |
4816 | (2^334779+47)/5 | 100778 | Lelio R Paula | 12/2013 |
4817 | 2^334751+2049 | 100771 | Lelio R Paula | 09/2016 |
4818 | 13^90443-98 | 100749 | Lelio R Paula | 10/2016 |
4819 | (2^334674+3190)/2 | 100747 | Stefano Morozzi | 09/2020 |
4820 | (2^334651+1050)/2 | 100740 | Stefano Morozzi | 09/2020 |
4821 | (7*10^100737+71)/3 | 100738 | Robert Price | 05/2018 |
4822 | (24737*2^334628+1)/3 | 100737 | Lelio R Paula | 07/2014 |
4823 | 15^85639-28 | 100720 | Lelio R Paula | 10/2016 |
4824 | 27068^5259+5259^27068 | 100718 | Hans Havermann | 08/2018 |
4825 | 2^334562+577294575 | 100711 | Lelio R Paula | 09/2016 |
4826 | 4*3^211077-5 | 100710 | Lelio R Paula | 08/2014 |
4827 | 2^334524+145 | 100702 | Lelio R Paula | 07/2009 |
4828 | (2^334451+714)/2 | 100680 | Stefano Morozzi | 09/2020 |
4829 | 27648^4375+4375^27648 | 100666 | Hans Havermann | 09/2018 |
4830 | (1017*2^334391-1)/3535 | 100662 | Lelio R Paula | 05/2015 |
4831 | (2^334309+3122)/2 | 100637 | Stefano Morozzi | 09/2020 |
4832 | 2^334294-113111 | 100633 | Enzo Doria | 07/2014 |
4833 | 25581^8582+8582^25581 | 100626 | Hans Havermann | 08/2018 |
4834 | 6^129308-17723 | 100622 | Enzo Doria | 03/2013 |
4835 | 6^129305+95 | 100619 | Lelio R Paula | 10/2016 |
4836 | 2^334244-1167 | 100618 | Lelio R Paula | 09/2016 |
4837 | (2^334233+3066)/2 | 100614 | Stefano Morozzi | 09/2020 |
4838 | (76*10^100611+77)/9 | 100612 | Robert Price | 10/2019 |
4839 | 7*10^100606-93 | 100607 | Robert Price | 08/2020 |
4840 | (26*10^100566+49)/3 | 100567 | Robert Price | 08/2019 |
4841 | (21*2^334050+1)/935 | 100558 | Lelio R Paula | 12/2013 |
4842 | 24885^10984+10984^24885 | 100555 | Hans Havermann | 07/2018 |
4843 | (78557*2^334018+1)/4326021 | 100548 | Lelio R Paula | 07/2014 |
4844 | (35*10^100542+1)/9 | 100543 | Serge Batalov | 11/2010 |
4845 | 23578^18367+18367^23578 | 100538 | Hans Havermann | 07/2018 |
4846 | 13^90251+24 | 100535 | Lelio R Paula | 10/2016 |
4847 | 2^333963+789 | 100533 | Lelio R Paula | 08/2011 |
4848 | 2^333919-1840087 | 100520 | Enzo Doria | 06/2015 |
4849 | (2^333916+1698)/2 | 100519 | Stefano Morozzi | 09/2020 |
4850 | 2^333911+72623 | 100518 | Enzo Doria | 04/2016 |
4851 | 24605^12168+12168^24605 | 100517 | Hans Havermann | 08/2018 |
4852 | 66*10^100502+7 | 100504 | Robert Price | 07/2020 |
4853 | 18^80064-67 | 100503 | Lelio R Paula | 10/2016 |
4854 | 5^143742-48 | 100472 | Lelio R Paula | 10/2016 |
4855 | 24095^14784+14784^24095 | 100472 | Hans Havermann | 08/2018 |
4856 | 2^333757-112123 | 100471 | Enzo Doria | 06/2014 |
4857 | 7*10^100457-57 | 100458 | Robert Price | 06/2020 |
4858 | 27358^4693+4693^27358 | 100444 | Hans Havermann | 07/2018 |
4859 | 8*10^100439-51 | 100440 | Robert Price | 08/2019 |
4860 | 2^333603-108861 | 100425 | Enzo Doria | 03/2014 |
4861 | 9*7^118818-2 | 100414 | Lelio R Paula | 11/2014 |
4862 | 2^333546-17097 | 100408 | Enzo Doria | 05/2013 |
4863 | 17^81597+72 | 100401 | Lelio R Paula | 10/2016 |
4864 | p(20559)#/2+8 | 100384 | Robert Price | 01/2017 |
4865 | 11^96390-24 | 100380 | Lelio R Paula | 10/2016 |
4866 | (2^333385+2730)/2 | 100359 | Stefano Morozzi | 09/2020 |
4868 | 4832563059*2^333333+30029 | 100353 | Donovan Johnson | 01/2008 |
4867 | 23565^18136+18136^23565 | 100353 | Hans Havermann | 07/2018 |
4869 | 2^333354+763 | 100350 | Lelio R Paula | 08/2011 |
4870 | (25*10^100343-67)/3 | 100344 | Robert Price | 06/2019 |
4871 | 2^333289-109483 | 100330 | Enzo Doria | 04/2014 |
4872 | 2^333240-2790209 | 100316 | Enzo Doria | 03/2016 |
4873 | 23601^17798+17798^23601 | 100314 | Hans Havermann | 05/2018 |
4875 | (2^333227-2^166614+1)/5 | 100311 | | 11/2006 |
4874 | 2^333225+719 | 100311 | Lelio R Paula | 08/2011 |
4876 | 2^333221-2785333 | 100310 | Enzo Doria | 10/2015 |
4877 | 76^53332-75 | 100308 | Norbert Schneider | 02/2015 |
4878 | 6^128892-17573 | 100298 | Enzo Doria | 03/2013 |
4879 | (47*10^100283-119)/9 | 100284 | Robert Price | 05/2019 |
4880 | 2^333105-113215 | 100275 | Enzo Doria | 07/2014 |
4881 | (31*2^333102+1)/2375 | 100272 | Lelio R Paula | 11/2013 |
4882 | 4*10^100257-83 | 100258 | Robert Price | 10/2018 |
4883 | 17^81476-74 | 100253 | Lelio R Paula | 10/2016 |
4884 | 23392^19207+19207^23392 | 100199 | Hans Havermann | 06/2018 |
4885 | (2^332830+750)/2 | 100192 | Stefano Morozzi | 09/2020 |
4886 | (206*10^100189-17)/9 | 100191 | Robert Price | 01/2020 |
4887 | 17^81417-16 | 100180 | Theodore Burton | 11/2005 |
4888 | (2^332773+590)/2 | 100175 | Stefano Morozzi | 09/2020 |
4889 | 2^332739-113215 | 100165 | Enzo Doria | 07/2014 |
4890 | 2^332730-1865621 | 100162 | Enzo Doria | 03/2016 |
4891 | 91^51127-2 | 100160 | Lelio R Paula | 09/2013 |
4892 | 15^85159-32 | 100155 | Lelio R Paula | 10/2016 |
4893 | 6^128661+97 | 100118 | Lelio R Paula | 10/2016 |
4894 | 19^78285+40 | 100108 | Lelio R Paula | 07/2016 |
4895 | 6^128640+5 | 100102 | Lelio R Paula | 11/2014 |
4896 | 22779^22970-22970^22779 | 100093 | Norbert Schneider | 08/2020 |
4897 | (2^332468+3130)/2 | 100083 | Stefano Morozzi | 09/2020 |
4898 | (14*10^100075+61)/3 | 100076 | Robert Price | 12/2018 |
4899 | (2^332435+3098)/2 | 100073 | Stefano Morozzi | 09/2020 |
4900 | 28562^3189+3189^28562 | 100072 | Hans Havermann | 05/2018 |
4901 | 6^128565-127 | 100044 | Lelio R Paula | 08/2016 |
4902 | (2^332317+2106)/2 | 100038 | Stefano Morozzi | 09/2020 |
4903 | 2^332309-133 | 100035 | Lelio R Paula | 02/2011 |
4904 | 2^332307+731 | 100035 | Lelio R Paula | 07/2011 |
4905 | 2^332301+12927 | 100033 | Lelio R Paula | 04/2013 |
4906 | 23406^18781+18781^23406 | 100031 | Hans Havermann | 04/2018 |
4907 | 2^332277-4573 | 100026 | Yves Minet | 03/2019 |
4908 | 12^92684-13 | 100023 | Lelio R Paula | 07/2016 |
4909 | 78557*2^332193+55669 | 100005 | Jorge Menendez | 04/2019 |
4910 | 78557*2^332192+72689 | 100005 | Jorge Menendez | 04/2019 |
4911 | 10^100003+45799 | 100004 | Stefano Morozzi | 04/2019 |
4912 | 10^100003+155461 | 100004 | Stefano Morozzi | 04/2019 |
4913 | 10^100003+211389 | 100004 | Stefano Morozzi | 04/2019 |
4914 | 10^100003+381027 | 100004 | Stefano Morozzi | 04/2019 |
4915 | 10^100003+540703 | 100004 | Stefano Morozzi | 04/2019 |
4916 | 10^100003+823977 | 100004 | Stefano Morozzi | 04/2019 |
4928 | 10^100002+236023 | 100003 | Stefano Morozzi | 05/2018 |
4929 | 10^100002+433741 | 100003 | Stefano Morozzi | 05/2018 |
4917 | 2^332202+104659 | 100003 | Stefano Morozzi | 04/2019 |
4918 | 2^332202+857539 | 100003 | Stefano Morozzi | 04/2019 |
4919 | 2^332202+181773 | 100003 | Stefano Morozzi | 04/2019 |
4920 | 2^332202+687543 | 100003 | Stefano Morozzi | 04/2019 |
4921 | 2^332202+941595 | 100003 | Stefano Morozzi | 04/2019 |
4922 | 2^332202+445813 | 100003 | Stefano Morozzi | 04/2019 |
4923 | 2^332202+1599727 | 100003 | Stefano Morozzi | 04/2019 |
4924 | 2^332202+1389567 | 100003 | Stefano Morozzi | 04/2019 |
4925 | 2^332202+1206315 | 100003 | Stefano Morozzi | 04/2019 |
4926 | 2^332202+1958647 | 100003 | Stefano Morozzi | 04/2019 |
4927 | 10^100003-562857 | 100003 | Patrick De Geest | 07/2019 |
4930 | (10^100002-1)/9-10^33441 | 100002 | Akihiko Yoshida | 03/2018 |
4931 | (10^100002-1)/9-10^44692 | 100002 | Akihiko Yoshida | 03/2018 |
4932 | 10^100002-249519 | 100002 | Patrick De Geest | 07/2018 |
4933 | 10^100001+314199 | 100002 | Patrick De Geest | 07/2018 |
4973 | 10^100000+3938473 | 100001 | Robert Price | 05/2015 |
4974 | 10^100000+3979761 | 100001 | Robert Price | 05/2015 |
4975 | 10^100000+4293973 | 100001 | Robert Price | 09/2015 |
4950 | 10^100000+4858267 | 100001 | Robert Price | 12/2015 |
4951 | 10^100000+5113299 | 100001 | Robert Price | 02/2016 |
4952 | 10^100000+5169411 | 100001 | Robert Price | 02/2016 |
4976 | 10^100000+5354043 | 100001 | Robert Price | 05/2016 |
4977 | 10^100000+5717979 | 100001 | Robert Price | 05/2016 |
4978 | 10^100000+6080631 | 100001 | Robert Price | 07/2016 |
4979 | 10^100000+6308469 | 100001 | Robert Price | 07/2016 |
4980 | 10^100000+6512023 | 100001 | Robert Price | 08/2016 |
4981 | 10^100000+6596557 | 100001 | Robert Price | 08/2016 |
4982 | 10^100000+7115409 | 100001 | Robert Price | 10/2016 |
4983 | 10^100000+7235803 | 100001 | Robert Price | 10/2016 |
4934 | 10^100000+11187931 | 100001 | Robert Price | 03/2018 |
4935 | 10^100000+11264721 | 100001 | Robert Price | 04/2018 |
4936 | 10^100000+11477661 | 100001 | Robert Price | 05/2018 |
4937 | 10^100000+11644653 | 100001 | Robert Price | 07/2018 |
4938 | 10^100001-431439 | 100001 | Patrick De Geest | 07/2018 |
4939 | 10^100000+11769399 | 100001 | Robert Price | 08/2018 |
4940 | 10^100000+11848159 | 100001 | Robert Price | 08/2018 |
4941 | 10^100000+11863467 | 100001 | Robert Price | 08/2018 |
4970 | 10^100000+11992051 | 100001 | Robert Price | 09/2018 |
4971 | 2^332196-1-2*29696 | 100001 | Matt Stath | 11/2018 |
4972 | 10^100000+12363957 | 100001 | Robert Price | 11/2018 |
4942 | 2^332196+1+2*17152 | 100001 | Matt Stath | 12/2018 |
4943 | 10^100000+12778033 | 100001 | Robert Price | 02/2019 |
4944 | 10^100000+13581679 | 100001 | Robert Price | 05/2019 |
4945 | 10^100000+13613199 | 100001 | Robert Price | 05/2019 |
4946 | 10^100000+13752327 | 100001 | Robert Price | 05/2019 |
4947 | 10^100000+14139243 | 100001 | Robert Price | 06/2019 |
4948 | 10^100000+14151057 | 100001 | Robert Price | 06/2019 |
4949 | 10^100000+14218923 | 100001 | Robert Price | 06/2019 |
4984 | 10^100000+15136771 | 100001 | Robert Price | 09/2019 |
4985 | 10^100000+15219873 | 100001 | Robert Price | 10/2019 |
4986 | 10^100000+15274039 | 100001 | Robert Price | 10/2019 |
4987 | 10^100000+15394069 | 100001 | Robert Price | 10/2019 |
4988 | 10^100000+15547119 | 100001 | Robert Price | 10/2019 |
4989 | 10^100000+15932923 | 100001 | Robert Price | 11/2019 |
4990 | 10^100000+16345467 | 100001 | Robert Price | 12/2019 |
4991 | 10^100000+16672143 | 100001 | Robert Price | 01/2020 |
4992 | 10^100000+16731939 | 100001 | Robert Price | 02/2020 |
4993 | 10^100000+16907049 | 100001 | Robert Price | 03/2020 |
4994 | 10^100000+17652523 | 100001 | Robert Price | 05/2020 |
4995 | 10^100000+18047167 | 100001 | Robert Price | 05/2020 |
4996 | 10^100000+18471819 | 100001 | Robert Price | 06/2020 |
4997 | 10^100000+18494793 | 100001 | Robert Price | 07/2020 |
4998 | 10^100000+18762609 | 100001 | Robert Price | 07/2020 |
4999 | 10^100000+19204141 | 100001 | Robert Price | 08/2020 |
5000 | 10^100000+19349793 | 100001 | Robert Price | 08/2020 |
4953 | 10^100000+19956229 | 100001 | Robert Price | 09/2020 |
4954 | 10^100000+3*(10^37093-1)/9*10^31454+1 | 100001 | Makoto Morimoto | 09/2020 |
4955 | 10^100000+4*(10^36149-1)/9*10^31926+1 | 100001 | Makoto Morimoto | 09/2020 |
4956 | 10^100000+6*(10^41029-1)/9*10^29486+1 | 100001 | Makoto Morimoto | 09/2020 |
4957 | 10^100000+7*(10^55505-1)/9*10^22248+1 | 100001 | Makoto Morimoto | 09/2020 |
4958 | 10^100000+20234607 | 100001 | Robert Price | 10/2020 |
4959 | 10^100000+20752303 | 100001 | Robert Price | 11/2020 |
4960 | 10^100000+20774041 | 100001 | Robert Price | 11/2020 |
4961 | 10^100000+20854741 | 100001 | Robert Price | 11/2020 |
4962 | 10^100000+20908917 | 100001 | Robert Price | 11/2020 |
4963 | 10^100000+20994793 | 100001 | Robert Price | 11/2020 |
4964 | 10^100000+21354249 | 100001 | Robert Price | 12/2020 |
4965 | 10^100000+21455559 | 100001 | Robert Price | 12/2020 |
4966 | 10^100000+21538873 | 100001 | Robert Price | 12/2020 |
4967 | 10^100000+21830901 | 100001 | Robert Price | 01/2021 |
4968 | 10^100000+21842629 | 100001 | Robert Price | 01/2021 |
4969 | 10^100000+21930861 | 100001 | Robert Price | 01/2021 |