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 ? |
5751 | 28243^17308+17308^28243 | 119701 | Hans Havermann | 02/2021 |
5752 | 77*10^119688+3 | 119690 | Robert Price | 06/2020 |
5753 | 586*25^85601+3717 | 119668 | Eric Chen | 10/2023 |
5754 | (2^397504+1698)/2 | 119661 | Stefano Morozzi | 09/2020 |
5755 | (58^67853-1)/57 | 119653 | Paul Bourdelais | 09/2017 |
5756 | 2^397426+73849 | 119638 | Enzo Doria | 04/2016 |
5757 | 8*10^119509+29 | 119510 | Robert Price | 11/2021 |
5758 | 2^396933-112723 | 119489 | Enzo Doria | 06/2014 |
5759 | 11^114738-150 | 119488 | Enzo Doria | 10/2012 |
5760 | (4*10^119474+149)/9 | 119474 | Robert Price | 04/2018 |
5761 | 26964^26964-13^13 | 119472 | Henri Lifchitz | 08/2024 |
5762 | 2^396790-21 | 119446 | Lelio R Paula | 04/2013 |
5763 | 32061^5300+5300^32061 | 119405 | Hans Havermann | 01/2021 |
5764 | (2^396633-7)/5 | 119398 | Lelio R Paula | 04/2014 |
5765 | 27382^22913+22913^27382 | 119388 | Hans Havermann | 03/2021 |
5766 | (2^396577+2522)/2 | 119382 | Stefano Morozzi | 09/2020 |
5767 | (2^396492+2230)/2 | 119356 | Stefano Morozzi | 01/2021 |
5768 | (47*10^119354+259)/9 | 119355 | Robert Price | 03/2022 |
5770 | 105^59050+104 | 119352 | Norbert Schneider | 11/2016 |
5769 | 126^56824-125 | 119352 | Norbert Schneider | 12/2018 |
5771 | 2^396469+111546435 | 119350 | Paul Bourdelais | 10/2021 |
5772 | 139^55690-138 | 119345 | Norbert Schneider | 04/2019 |
5773 | 790^41179+41179^790 | 119322 | Norbert Schneider | 04/2019 |
5774 | 2^396374+73729 | 119321 | Enzo Doria | 04/2016 |
5775 | 88*10^119295+3 | 119297 | Robert Price | 05/2020 |
5776 | 2^396258-459491 | 119286 | Enzo Doria | 05/2015 |
5777 | (2^396248+3126)/2 | 119283 | Stefano Morozzi | 09/2020 |
5778 | 2^396128-396128-1 | 119247 | Karsten Bonath | 06/2018 |
5779 | (893*10^119228+7)/9 | 119230 | Robert Price | 06/2021 |
5780 | (31*10^119229+257)/9 | 119230 | Robert Price | 12/2021 |
5781 | (28*10^119206-67)/3 | 119207 | Robert Price | 10/2020 |
5782 | (2^395986+5)/76881 | 119199 | Lelio R Paula | 04/2014 |
5783 | 11^114458+6 | 119196 | Paul Bourdelais | 02/2021 |
5784 | (23*2^395942-1)/91 | 119190 | Lelio R Paula | 04/2014 |
5785 | (2^395902+202)/2 | 119179 | Stefano Morozzi | 09/2020 |
5786 | (2^395825+582)/2 | 119155 | Stefano Morozzi | 09/2020 |
5787 | (2^395733+1130)/2 | 119128 | Stefano Morozzi | 09/2020 |
5788 | 29548^10725+10725^29548 | 119091 | Hans Havermann | 02/2021 |
5789 | (11*2^395548+1)/3 | 119073 | Lelio R Paula | 04/2014 |
5790 | (30^80599+1)/31 | 119054 | Robert Price | 07/2013 |
5791 | (232*10^119047+17)/3 | 119049 | Robert Price | 04/2021 |
5792 | (43*10^119024-403)/9 | 119025 | Robert Price | 01/2019 |
5793 | (4*10^119021+47)/3 | 119022 | Robert Price | 01/2022 |
5794 | fibonacci(569433)+3 | 119005 | Jon Grantham | 08/2023 |
5795 | 26603^26888-26888^26603 | 118978 | Norbert Schneider | 07/2021 |
5796 | 912^40193-40193^912 | 118972 | Norman Luhn | 09/2024 |
5797 | 681^41992-41992^681 | 118970 | Norman Luhn | 09/2024 |
5798 | 6*10^118964+43 | 118965 | Robert Price | 07/2020 |
5799 | (8*10^118960+49)/3 | 118961 | Robert Price | 05/2020 |
5800 | 31253^6402+6402^31253 | 118959 | Hans Havermann | 02/2021 |
5801 | (194*10^118925-17)/3 | 118927 | Robert Price | 09/2020 |
5802 | 2^395062-109121 | 118926 | Enzo Doria | 04/2014 |
5803 | 2^395055-4627 | 118924 | Yves Minet | 05/2019 |
5804 | (2^395054+702)/2 | 118923 | Stefano Morozzi | 09/2020 |
5805 | 2^395018-224141 | 118913 | Harrison Mesh | 06/2022 |
5806 | (2^395011+2526)/2 | 118910 | Stefano Morozzi | 09/2020 |
5807 | (2^394918+78557)/3 | 118882 | Lelio R Paula | 01/2015 |
5808 | 25771^26948-26948^25771 | 118872 | Frank Doornink | 02/2024 |
5809 | 374^46201-46201^374 | 118870 | Norman Luhn | 09/2024 |
5810 | (2^394858+1018)/2 | 118864 | Stefano Morozzi | 09/2020 |
5811 | (77*10^118862-149)/9 | 118863 | Robert Price | 03/2022 |
5812 | (16*10^118852+77)/3 | 118853 | Robert Price | 03/2019 |
5813 | fibonacci(568658)-2 | 118843 | Jon Grantham | 08/2023 |
5814 | (2^394739+3)/1883 | 118826 | Lelio R Paula | 04/2014 |
5815 | 10^118772+163599 | 118773 | Patrick De Geest | 02/2021 |
5817 | 10^118772-40000000001 | 118772 | Robert Price | 09/2020 |
5816 | 10^118772-207603 | 118772 | Patrick De Geest | 02/2021 |
5818 | 26842^26577+26577^26842 | 118763 | Hans Havermann | 02/2021 |
5819 | (2^394513+2034)/2 | 118760 | Stefano Morozzi | 09/2020 |
5820 | (2^394473+2774)/2 | 118748 | Stefano Morozzi | 02/2021 |
5821 | 27949^17710+17710^27949 | 118734 | Hans Havermann | 02/2021 |
5822 | 2^394266+71389 | 118686 | Enzo Doria | 04/2016 |
5823 | (10^118681-3^118681)/7 | 118681 | Jon Grantham | 08/2023 |
5824 | 2^394215-51261 | 118671 | Tony Prest / Never Odd Or Even | 04/2018 |
5825 | (2^394215-48793)/5/5 | 118670 | Tony Prest / Never Odd Or Even | 04/2018 |
5826 | (2^394215-17063)/3/3/5 | 118669 | Tony Prest / Never Odd Or Even | 04/2018 |
5827 | (2^394215-24393)/5/5/5/5/5 | 118668 | Tony Prest / Never Odd Or Even | 04/2018 |
5828 | (2^394215-35885)/3/71/173 | 118666 | Tony Prest / Never Odd Or Even | 04/2018 |
5829 | (2^394215-47925)/353/2269 | 118665 | Tony Prest / Never Odd Or Even | 04/2018 |
5830 | 29201^11568+11568^29201 | 118652 | Hans Havermann | 02/2021 |
5831 | (2^394215-62819)/3/3/3/3/3/3/3/7/21737/1082153/1953673 | 118650 | Tony Prest / Never Odd Or Even | 04/2018 |
5832 | (2^394131+2214)/2 | 118645 | Stefano Morozzi | 09/2020 |
5833 | (17*10^118635+13)/3 | 118636 | Robert Price | 01/2019 |
5834 | 5^169727+2 | 118635 | Lelio R Paula | 08/2013 |
5835 | 2^394034-3 | 118617 | M. Frind & P. Underwood | 09/2002 |
5836 | (7*10^118607+179)/3 | 118608 | Robert Price | 09/2018 |
5837 | 3^248572-6242 | 118599 | Enzo Doria | 05/2014 |
5838 | (3*2^393964-1)/181 | 118594 | Lelio R Paula | 04/2014 |
5839 | (49*10^118576-319)/9 | 118577 | Robert Price | 10/2021 |
5840 | 7^140303-6 | 118570 | Robert Price | 11/2014 |
5841 | (2^393864+2686)/2 | 118565 | Stefano Morozzi | 09/2020 |
5842 | (2^393862+3150)/2 | 118564 | Stefano Morozzi | 09/2020 |
5843 | (2^393849+3762)/2 | 118561 | Stefano Morozzi | 01/2021 |
5844 | (529*10^118554-7)/9 | 118556 | Robert Price | 08/2021 |
5845 | 26712^26777-26777^26712 | 118534 | Norbert Schneider | 07/2021 |
5846 | (2^393661+2666)/2 | 118504 | Stefano Morozzi | 09/2020 |
5847 | (2^393650+1614)/2 | 118501 | Stefano Morozzi | 09/2020 |
5848 | 27655^19264+19264^27655 | 118495 | Hans Havermann | 02/2021 |
5849 | 10^118485+469413 | 118486 | Patrick De Geest | 05/2021 |
5850 | 10^118485-50001 | 118485 | Robert Price | 08/2020 |
5851 | (2^393528+1030)/2 | 118464 | Stefano Morozzi | 09/2020 |
5852 | 2^393427+75683 | 118434 | Enzo Doria | 04/2016 |
5853 | 2^393376-114749 | 118418 | Enzo Doria | 04/2015 |
5854 | (65*10^118417+493)/9 | 118418 | Robert Price | 08/2021 |
5855 | 30960^6671+6671^30960 | 118397 | Hans Havermann | 02/2021 |
5856 | (2^393234+2010)/2 | 118375 | Stefano Morozzi | 09/2020 |
5857 | (2^393205+3030)/2 | 118367 | Stefano Morozzi | 09/2020 |
5858 | (2^393191+2174)/2 | 118362 | Stefano Morozzi | 09/2020 |
5859 | 2^393180+73 | 118359 | Lelio R Paula | 04/2013 |
5860 | 3*2^393125+5 | 118343 | Jon Grantham | 07/2023 |
5861 | 27546^19771+19771^27546 | 118339 | Hans Havermann | 02/2021 |
5862 | 822^40595-40595^822 | 118330 | Norman Luhn | 09/2024 |
5863 | p(23881)#/2+256 | 118328 | Robert Price | 05/2017 |
5864 | (10^118324+359)/9 | 118324 | Serge Batalov | 12/2014 |
5865 | (2^393048+570)/2 | 118319 | Stefano Morozzi | 09/2020 |
5866 | p(23879)#/2+64 | 118317 | Robert Price | 03/2017 |
5867 | 2^393033+20147 | 118315 | Enzo Doria | 08/2023 |
5868 | 8*10^118308+59 | 118309 | Robert Price | 11/2021 |
5869 | 9*10^118282+29 | 118283 | Robert Price | 03/2022 |
5870 | (238*10^118265-1)/3 | 118267 | Robert Price | 04/2020 |
5872 | (53*10^118216+1)/9 | 118217 | Serge Batalov | 11/2010 |
5871 | (2^392707+1710)/2 | 118217 | Stefano Morozzi | 09/2020 |
5873 | (7*2^392697+1)/15 | 118214 | Renaud Lifchitz | 03/2011 |
5874 | (157^53819-1)/156 | 118179 | Alexander Zhirkov | 06/2016 |
5875 | (2^392567+2750)/2 | 118175 | Stefano Morozzi | 01/2021 |
5876 | 55*10^118172+3 | 118174 | Robert Price | 07/2022 |
5877 | (19*2^392551+1)/3 | 118171 | Lelio R Paula | 04/2014 |
5878 | 27185^22222+22222^27185 | 118168 | Hans Havermann | 01/2021 |
5879 | 2^392516-29219 | 118160 | Enzo Doria | 07/2015 |
5880 | 66*10^118155+7 | 118157 | Robert Price | 07/2020 |
5881 | Phi(177231,10) | 118152 | Maksym Voznyy | 09/2015 |
5882 | 2^392413-112123 | 118129 | Enzo Doria | 06/2014 |
5883 | 27491^19798+19798^27491 | 118119 | Hans Havermann | 02/2021 |
5884 | (49*10^118109-319)/9 | 118110 | Robert Price | 10/2021 |
5885 | (2^392342+5)/27 | 118106 | Lelio R Paula | 04/2014 |
5886 | (2^392333+1782)/2 | 118104 | Stefano Morozzi | 01/2021 |
5887 | 2^392300-1841429 | 118095 | Enzo Doria | 06/2015 |
5888 | 3*2^392260-5 | 118083 | Jon Grantham | 07/2023 |
5889 | 2^392220+75241 | 118070 | Enzo Doria | 04/2016 |
5890 | 27836^17409+17409^27836 | 118047 | Hans Havermann | 02/2021 |
5891 | 10^118009+664447 | 118010 | Patrick De Geest | 07/2018 |
5892 | 10^118009-20001 | 118009 | Robert Price | 01/2018 |
5893 | (14*10^117991+61)/3 | 117992 | Robert Price | 12/2018 |
5894 | 2^391933+5897 | 117984 | Yves Minet | 02/2011 |
5895 | 2^391912-1849259 | 117978 | Enzo Doria | 08/2015 |
5896 | (2*34^77029+1043)/11 | 117968 | Eric Chen | 08/2023 |
5897 | 5*2^391836-3 | 117956 | Jon Grantham | 07/2023 |
5898 | 28357^14440+14440^28357 | 117953 | Hans Havermann | 02/2021 |
5899 | (2^391812+5)/14181 | 117944 | Lelio R Paula | 04/2014 |
5900 | 85^61124-61124^85 | 117934 | Norman Luhn | 09/2024 |
5901 | (7*10^117930-79)/9 | 117930 | Robert Price | 01/2021 |
5902 | 27531^19168+19168^27531 | 117904 | Hans Havermann | 02/2021 |
5903 | (46*10^117902+683)/9 | 117903 | Robert Price | 03/2019 |
5904 | 26349^26668-26668^26349 | 117893 | Frank Doornink | 03/2024 |
5905 | 27670^18189+18189^27670 | 117869 | Hans Havermann | 02/2021 |
5906 | (7*2^391521+1)/285 | 117858 | Lelio R Paula | 04/2014 |
5907 | (56*10^117856+583)/9 | 117857 | Robert Price | 08/2021 |
5908 | 32169^4606+4606^32169 | 117846 | Hans Havermann | 02/2021 |
5909 | (71*10^117803-143)/9 | 117804 | Robert Price | 10/2021 |
5910 | 2^391324+90901 | 117801 | Yves Minet | 02/2011 |
5911 | 2^391301-1859923 | 117794 | Enzo Doria | 03/2016 |
5912 | 2^391261-4131 | 117782 | Yves Minet | 02/2018 |
5913 | (2^391211+554)/2 | 117766 | Stefano Morozzi | 09/2020 |
5914 | 816^40445-40445^816 | 117764 | Norman Luhn | 09/2024 |
5915 | 38434^1157+1157^38434 | 117737 | Hans Havermann | 01/2021 |
5916 | (2^391115-7)/11791 | 117734 | Lelio R Paula | 04/2014 |
5917 | (85*10^117719+473)/9 | 117720 | Robert Price | 01/2020 |
5918 | (2^391049+582)/2 | 117718 | Stefano Morozzi | 09/2020 |
5919 | (21*23^86445-197)/22 | 117715 | Eric Chen | 08/2023 |
5920 | 31083^6122+6122^31083 | 117709 | Hans Havermann | 02/2021 |
5921 | 2^390960+1880881 | 117691 | Enzo Doria | 11/2016 |
5922 | (71*10^117685+91)/9 | 117686 | Robert Price | 04/2022 |
5924 | 2^390897-1860553 | 117672 | Enzo Doria | 11/2015 |
5923 | (61*10^117671+47)/9 | 117672 | Robert Price | 07/2022 |
5925 | 2^390889-115003 | 117670 | Enzo Doria | 06/2015 |
5926 | 12^109010+35 | 117642 | Riley Fisher | 08/2023 |
5927 | 2^390779-30337 | 117637 | Paul Bourdelais | 02/2012 |
5928 | (2^390735+378)/2 | 117623 | Stefano Morozzi | 02/2021 |
5929 | 11^112916-780 | 117590 | Enzo Doria | 12/2012 |
5930 | 27641^17916+17916^27641 | 117564 | Hans Havermann | 02/2021 |
5931 | 27906^16321+16321^27906 | 117561 | Hans Havermann | 02/2021 |
5932 | 27294^20275+20275^27294 | 117555 | Hans Havermann | 02/2021 |
5933 | (2^390473+1002)/2 | 117544 | Stefano Morozzi | 09/2020 |
5934 | 35912^1875+1875^35912 | 117541 | Hans Havermann | 02/2021 |
5935 | (16^97613-5^97613)/11 | 117537 | Robert Price | 07/2013 |
5936 | (2^390438+1774)/2 | 117534 | Stefano Morozzi | 01/2021 |
5937 | (2^390418+1722)/2 | 117528 | Stefano Morozzi | 09/2020 |
5938 | (2^390403+654)/2 | 117523 | Stefano Morozzi | 09/2020 |
5939 | (2^390343+2246)/2 | 117505 | Stefano Morozzi | 01/2021 |
5940 | 28043^15478+15478^28043 | 117493 | Hans Havermann | 02/2021 |
5941 | (17*2^390272+1)/1983 | 117482 | Lelio R Paula | 04/2014 |
5942 | 37077^1474+1474^37077 | 117479 | Hans Havermann | 01/2021 |
5943 | 31^78759-30 | 117459 | Theodore Burton | 02/2007 |
5944 | (2^390176+1222)/2 | 117455 | Stefano Morozzi | 09/2020 |
5945 | (2^390133+1242)/2 | 117442 | Stefano Morozzi | 09/2020 |
5946 | (2^390013+2634)/2 | 117406 | Stefano Morozzi | 09/2020 |
5947 | 3*10^117402+61 | 117403 | Robert Price | 09/2020 |
5948 | 2^389998+37 | 117402 | Lelio R Paula | 03/2013 |
5949 | (2^389977+314)/2 | 117395 | Stefano Morozzi | 09/2020 |
5950 | (2^389921+342)/2 | 117378 | Stefano Morozzi | 01/2021 |
5951 | 71830^43+43^71830 | 117333 | Hans Havermann | 01/2021 |
5952 | (2^389768+1582)/2 | 117332 | Stefano Morozzi | 09/2020 |
5953 | 33802^2951+2951^33802 | 117292 | Hans Havermann | 02/2021 |
5954 | 26789^23866+23866^26789 | 117277 | Hans Havermann | 02/2021 |
5955 | 29^80192-1*80192^29 | 117273 | Dylan Delgado | 12/2019 |
5956 | (101*10^117260+7)/9 | 117262 | Robert Price | 02/2022 |
5957 | (13*10^117249+161)/3 | 117250 | Robert Price | 11/2018 |
5958 | 2^389478+43 | 117245 | Lelio R Paula | 03/2013 |
5959 | (298*10^117229-7)/3 | 117231 | Robert Price | 06/2020 |
5960 | (2^389416+342)/2 | 117226 | Stefano Morozzi | 01/2021 |
5961 | (29*2^389351-1)/9 | 117207 | Lelio R Paula | 04/2014 |
5962 | 5*10^117205+23 | 117206 | Robert Price | 03/2019 |
5963 | (2^389341-7)/3865 | 117200 | Lelio R Paula | 03/2014 |
5964 | 27272^19827+19827^27272 | 117195 | Hans Havermann | 01/2021 |
5965 | (2^389276+2650)/2 | 117184 | Stefano Morozzi | 09/2020 |
5966 | (844*10^117175-7)/9 | 117177 | Robert Price | 05/2021 |
5967 | 10^117142+209223 | 117143 | Patrick De Geest | 04/2018 |
5969 | 10^117142-1000000001 | 117142 | Robert Price | 03/2018 |
5968 | 10^117142-966057 | 117142 | Patrick De Geest | 04/2018 |
5970 | 10^117135+360577 | 117136 | Patrick De Geest | 07/2018 |
5971 | 10^117135-401 | 117135 | Robert Price | 01/2018 |
5972 | 26415^26488-26488^26415 | 117126 | Norbert Schneider | 05/2021 |
5973 | 4*10^117123+79 | 117124 | Robert Price | 08/2018 |
5974 | 2^389033-12797413 | 117111 | Enzo Doria | 04/2016 |
5975 | (2^388987+2634)/2 | 117097 | Stefano Morozzi | 09/2020 |
5976 | 2^388960-109505 | 117089 | Enzo Doria | 04/2014 |
5977 | 7*10^117082-57 | 117083 | Robert Price | 06/2020 |
5978 | 791^40398-40398^791 | 117081 | Norman Luhn | 09/2024 |
5979 | (2^388928-5)/569 | 117077 | Lelio R Paula | 03/2014 |
5980 | 2^388888-1529 | 117067 | Yves Minet | 01/2013 |
5981 | 10^117059+28879 | 117060 | Patrick De Geest | 05/2016 |
5982 | (10^117059-71)/1 | 117059 | Serge Batalov | 12/2014 |
5983 | (2^388854+3630)/2 | 117057 | Stefano Morozzi | 09/2020 |
5984 | (2^388842+2098)/2 | 117053 | Stefano Morozzi | 09/2020 |
5985 | (2^388789+3150)/2 | 117037 | Stefano Morozzi | 09/2020 |
5986 | (2^388748+378)/2 | 117025 | Stefano Morozzi | 02/2021 |
5987 | (693^41189-1)/692 | 117005 | Michael Stocker | 05/2020 |
5988 | (26*10^116999-503)/9 | 117000 | Robert Price | 07/2018 |
5989 | 20^89917-21 | 116985 | Anonymous | 09/2024 |
5990 | (2^388609+1554)/2 | 116983 | Stefano Morozzi | 09/2020 |
5991 | 38496^1093+1093^38496 | 116975 | Hans Havermann | 02/2021 |
5992 | 3^245154-6256 | 116969 | Enzo Doria | 05/2014 |
5993 | 5*10^116966-43 | 116967 | Robert Price | 01/2019 |
5994 | 2^388536-113495 | 116961 | Enzo Doria | 08/2014 |
5995 | (2^388512+382)/2 | 116954 | Stefano Morozzi | 02/2021 |
5996 | (8*32^77701+271)/31 | 116952 | Eric Chen | 11/2023 |
5997 | 2^388469-43 | 116941 | Lelio R Paula | 03/2013 |
5998 | 27417^18416+18416^27417 | 116939 | Hans Havermann | 02/2021 |
5999 | (2^388438+1842)/2 | 116932 | Stefano Morozzi | 02/2021 |
6000 | (7*2^388372-1)/111 | 116911 | Lelio R Paula | 04/2014 |