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 (> 30000) |
Who ? |
When ? |
1751 | (11*2^435879+1)/3337 | 131211 | Lelio R Paula | 06/2015 |
1753 | (2^435808+1)/641/6700417 | 131182 | Lelio R Paula | 02/2012 |
1752 | (2^435808+1)/4294967297 | 131182 | Serge Batalov | 12/2016 |
1754 | 2^435773+1875557 | 131181 | Enzo Doria | 06/2016 |
1755 | 2^435612-2789939 | 131133 | Enzo Doria | 12/2015 |
1756 | 66^72047-65^72047 | 131093 | Robert Price | 09/2013 |
1757 | (5*10^131090+37)/3 | 131091 | Robert Price | 03/2018 |
1758 | 2^435468+75631 | 131089 | Enzo Doria | 04/2016 |
1759 | 37^83588-2 | 131083 | Lelio R Paula | 08/2015 |
1760 | (4^217720+11)/3 | 131081 | Robert Price | 02/2017 |
1761 | 2^435202-113193 | 131009 | Enzo Doria | 07/2014 |
1762 | floor((sqrt(5)-1)/2*10^130911) | 130911 | Serge Batalov | 06/2017 |
1763 | 2^434835-111937 | 130899 | Enzo Doria | 05/2014 |
1764 | 2^434685+72257 | 130854 | Enzo Doria | 04/2016 |
1765 | (7*10^130825+113)/3 | 130826 | Robert Price | 02/2018 |
1766 | 2^434539-29317 | 130810 | Enzo Doria | 07/2015 |
1767 | 2^434469-114259 | 130789 | Enzo Doria | 01/2015 |
1768 | 2^434246+33 | 130722 | Robert Price | 11/2015 |
1769 | 2^433911-91 | 130621 | Lelio R Paula | 06/2017 |
1770 | 2^433744-114419 | 130570 | Enzo Doria | 02/2015 |
1771 | 2^433708+1869451 | 130560 | Enzo Doria | 05/2016 |
1772 | 2^433710+93 | 130560 | Lelio R Paula | 06/2017 |
1773 | (29*2^433547-1)/27 | 130511 | Lelio R Paula | 06/2015 |
1774 | 4*10^130480+9 | 130481 | Robert Price | 05/2015 |
1775 | (23*2^433449-1)/75 | 130481 | Lelio R Paula | 06/2015 |
1776 | (23*2^433334-1)/3731 | 130445 | Lelio R Paula | 06/2015 |
1777 | 2^433023-113497 | 130353 | Enzo Doria | 08/2014 |
1778 | 2^433002+1179379 | 130347 | Enzo Doria | 06/2016 |
1779 | 2^432974+19 | 130339 | Robert Price | 08/2015 |
1780 | (2^432457-1)/1672739247834685086279697 | 130159 | Tony Prest / Never Odd Or Even | 09/2013 |
1781 | 2^432217+41 | 130111 | Lelio R Paula | 06/2017 |
1782 | (2^216089*(2^216091-1)-339)/25 | 130098 | Makoto Morimoto | 03/2017 |
1783 | ((2^216091+1066)^2+(2^216091+1066)+41)/47/2069 | 130095 | Makoto Morimoto | 05/2016 |
1784 | 97^65480-2 | 130094 | Lelio R Paula | 05/2017 |
1785 | 2^432117-113215 | 130081 | Enzo Doria | 07/2014 |
1786 | 2^431804+72511 | 129986 | Enzo Doria | 04/2016 |
1787 | (3^272141-3^136071+1)/7 | 129844 | Serge Batalov | 03/2014 |
1788 | (9*2^431141+1)/17 | 129787 | Lelio R Paula | 06/2015 |
1789 | (29*2^430881-1)/21 | 129709 | Lelio R Paula | 06/2015 |
1790 | 2^430807+1869563 | 129686 | Enzo Doria | 05/2016 |
1791 | 2^430721-21429 | 129660 | Enzo Doria | 07/2013 |
1792 | 2^430415-276271 | 129568 | Enzo Doria | 07/2015 |
1793 | 2^430142-2791721 | 129486 | Enzo Doria | 03/2016 |
1794 | 2^429568-21017 | 129313 | Enzo Doria | 07/2013 |
1795 | 2^429194-112685 | 129201 | Enzo Doria | 06/2014 |
1796 | 2^429145-2780449 | 129186 | Enzo Doria | 04/2016 |
1797 | 2^428892-113453 | 129110 | Enzo Doria | 07/2014 |
1798 | (11*2^428881-7)/15 | 129106 | Renaud Lifchitz | 03/2011 |
1799 | 2^428727-113959 | 129060 | Enzo Doria | 10/2014 |
1800 | (7*2^428725-1)/13 | 129059 | Lelio R Paula | 05/2014 |
1801 | (10^129051-31)/3 | 129051 | Serge Batalov | 12/2014 |
1802 | 2^428564+71161 | 129011 | Enzo Doria | 04/2016 |
1803 | 2^428502-113285 | 128992 | Enzo Doria | 07/2014 |
1804 | 2^428421-21373 | 128968 | Enzo Doria | 06/2013 |
1805 | L(616787) | 128901 | Henri Lifchitz | 09/2008 |
1806 | 91^65772-2 | 128851 | Lelio R Paula | 05/2017 |
1807 | 2^428022+43 | 128848 | Lelio R Paula | 05/2017 |
1808 | 2^427999-459397 | 128841 | Enzo Doria | 05/2015 |
1809 | 2^427993+76847 | 128839 | Enzo Doria | 05/2016 |
1810 | 2^427824-1851507 | 128788 | Enzo Doria | 08/2015 |
1811 | 2^427807-21469 | 128783 | Enzo Doria | 07/2013 |
1812 | 11^123594-240 | 128710 | Enzo Doria | 09/2012 |
1813 | 2^427504-21503 | 128692 | Enzo Doria | 07/2013 |
1814 | 2^427420+91 | 128667 | Lelio R Paula | 05/2017 |
1815 | 2^427269-113635 | 128621 | Enzo Doria | 08/2014 |
1816 | 2^427130+1877569 | 128579 | Enzo Doria | 08/2016 |
1817 | 2^427016-115349 | 128545 | Enzo Doria | 07/2015 |
1818 | (4*10^128510+137)/3 | 128511 | Robert Price | 03/2018 |
1819 | 2^426889-112879 | 128507 | Enzo Doria | 06/2014 |
1820 | 2^426804+1869931 | 128481 | Enzo Doria | 05/2016 |
1821 | 2^426750+77635 | 128465 | Enzo Doria | 05/2016 |
1822 | 2^426425-91 | 128367 | Lelio R Paula | 05/2017 |
1823 | (15*2^426398-1)/11 | 128359 | Lelio R Paula | 05/2014 |
1824 | 2^426352+74971 | 128345 | Enzo Doria | 04/2016 |
1825 | 2^426300-1863689 | 128330 | Enzo Doria | 03/2016 |
1826 | 2^426293+1881017 | 128327 | Enzo Doria | 11/2016 |
1827 | 2^426043+35 | 128252 | Robert Price | 11/2015 |
1828 | (4*10^128244-19)/3 | 128245 | Robert Price | 03/2018 |
1829 | 2^425808-459959 | 128181 | Enzo Doria | 06/2015 |
1830 | 2^425627-113605 | 128127 | Enzo Doria | 08/2014 |
1831 | 18565^30002-30002^18565 | 128070 | Norbert Schneider | 01/2015 |
1832 | (2^425287-9)/2737 | 128021 | Lelio R Paula | 05/2015 |
1833 | (3*2^425233-1)/25 | 128007 | Lelio R Paula | 05/2014 |
1834 | 2^425205+4911 | 128000 | Marek Hubal | 02/2017 |
1835 | 2^425118-113663 | 127974 | Enzo Doria | 08/2014 |
1836 | 2^425061+1869761 | 127957 | Enzo Doria | 05/2016 |
1837 | 2^424918-21141 | 127914 | Enzo Doria | 07/2013 |
1838 | 2^424864-29489 | 127897 | Enzo Doria | 08/2015 |
1839 | (97*10^127858-1)/3 | 127860 | Serge Batalov | 12/2014 |
1840 | 2^424632-2786639 | 127827 | Enzo Doria | 03/2016 |
1841 | 2^424577-113755 | 127811 | Enzo Doria | 09/2014 |
1842 | (7*2^424512-1)/3 | 127792 | Lelio R Paula | 05/2014 |
1843 | 11^122629-720 | 127705 | Enzo Doria | 11/2012 |
1844 | 2^423696-21429 | 127546 | Enzo Doria | 07/2013 |
1845 | 2^423664-1864559 | 127536 | Enzo Doria | 03/2016 |
1846 | 3^267267-4 | 127519 | Henri Lifchitz | 10/2014 |
1847 | (19^99689+5^99689)/24 | 127477 | Robert Price | 09/2013 |
1848 | (21*2^423372+1)/101 | 127447 | Lelio R Paula | 05/2014 |
1849 | 2^423328-21537 | 127435 | Enzo Doria | 07/2013 |
1850 | (2^423165-7)/25 | 127384 | Lelio R Paula | 05/2015 |
1851 | (F(5)^182099-F(4)^182099)/F(3) | 127282 | Wayne Halsdorf | 08/2013 |
1852 | (234483*27^88884-145)/26 | 127230 | Curtis Bright | 05/2015 |
1853 | 2^422515-114997 | 127190 | Enzo Doria | 06/2015 |
1854 | 5*10^127179-3 | 127180 | Robert Price | 07/2015 |
1855 | -516776642557847117490*Bern(37960)/34256837217082767928421792453 | 127042 | Thomas Ritschel | 06/2017 |
1856 | (78^67141-1)/77 | 127036 | Paul Bourdelais | 09/2017 |
1857 | 2^421860-113285 | 126993 | Enzo Doria | 07/2014 |
1858 | (2^421827-7)/11 | 126982 | Lelio R Paula | 05/2015 |
1859 | 11^121910-840 | 126957 | Enzo Doria | 12/2012 |
1860 | (71^68539+1)/72 | 126882 | Paul Bourdelais | 09/2017 |
1861 | (5*10^126871-119)/3 | 126872 | Robert Price | 03/2018 |
1862 | 331^50339-10004 | 126846 | Enzo Doria | 07/2012 |
1863 | 2^421363-2790757 | 126843 | Enzo Doria | 03/2016 |
1864 | (106*10^126839-1)/3 | 126841 | Serge Batalov | 12/2014 |
1865 | (7*2^421243+1)/39 | 126807 | Lelio R Paula | 05/2014 |
1866 | 2^421161-286183 | 126783 | Enzo Doria | 06/2015 |
1867 | 2^420939-113935 | 126716 | Enzo Doria | 10/2014 |
1868 | 177^56363-2 | 126703 | Lelio R Paula | 10/2017 |
1869 | 2^420741-113659 | 126656 | Enzo Doria | 08/2014 |
1870 | 2^420694-21 | 126642 | Lelio R Paula | 05/2017 |
1871 | (13*10^126638+437)/9 | 126639 | Robert Price | 04/2018 |
1872 | (31*2^420556+1)/7 | 126601 | Lelio R Paula | 05/2014 |
1873 | 2^420424-59189 | 126561 | Enzo Doria | 10/2015 |
1874 | 2^420126+71893 | 126471 | Enzo Doria | 04/2016 |
1875 | 2^419866+1877059 | 126393 | Enzo Doria | 07/2016 |
1876 | F(604711) | 126377 | Henri Lifchitz | 02/2005 |
1877 | 2^419757+72707 | 126360 | Enzo Doria | 04/2016 |
1878 | 2^419720-21569 | 126349 | Enzo Doria | 07/2013 |
1879 | 2^419637+29 | 126324 | Henri Lifchitz | 02/2006 |
1880 | 2^419612+1876741 | 126316 | Enzo Doria | 07/2016 |
1881 | 2^419520+2793271 | 126289 | Enzo Doria | 03/2016 |
1882 | (2^419447-5)/369 | 126264 | Lelio R Paula | 05/2014 |
1883 | 2^419328-1859939 | 126231 | Enzo Doria | 03/2016 |
1884 | 2^419282-1851507 | 126217 | Enzo Doria | 08/2015 |
1885 | 2^419251+1866143 | 126208 | Enzo Doria | 03/2016 |
1886 | 11^121185+2 | 126202 | Robert Price | 05/2014 |
1887 | (23*2^419036-1)/1393 | 126141 | Lelio R Paula | 05/2014 |
1888 | 2^418851+23 | 126087 | Robert Price | 09/2015 |
1889 | (2^418849-9)/2681 | 126083 | Lelio R Paula | 05/2014 |
1890 | 2^418829+167 | 126081 | Lelio R Paula | 01/2012 |
1891 | (31*2^418782-1)/75891 | 126063 | Lelio R Paula | 05/2014 |
1892 | (19*2^418754-1)/15 | 126058 | Lelio R Paula | 05/2014 |
1893 | 2^418319-109501 | 125927 | Enzo Doria | 04/2014 |
1894 | 2^418316-112373 | 125926 | Enzo Doria | 06/2014 |
1895 | 2^417968+1869811 | 125821 | Enzo Doria | 06/2016 |
1896 | 2^417902+63 | 125802 | Lelio R Paula | 09/2015 |
1897 | (10^125792-91)/9 | 125792 | Serge Batalov | 12/2014 |
1898 | 2^417704+77011 | 125742 | Enzo Doria | 05/2016 |
1899 | (10^125706+149)/3 | 125706 | Serge Batalov | 12/2014 |
1900 | 2^417419-115309 | 125656 | Enzo Doria | 07/2015 |
1901 | 2^417300+77281 | 125620 | Enzo Doria | 05/2016 |
1902 | 2^417095-1657 | 125559 | Yves Minet | 07/2014 |
1903 | 2^416773-25 | 125462 | Lelio R Paula | 09/2015 |
1904 | (289511#+292834)/(2^3*146417) | 125444 | Makoto Morimoto | 10/2017 |
1905 | (11*2^416691+1)/43 | 125436 | Lelio R Paula | 05/2014 |
1906 | (21*2^416566-1)/17 | 125399 | Lelio R Paula | 05/2014 |
1907 | 2^416530+1870429 | 125389 | Enzo Doria | 05/2016 |
1908 | 2^416490+1875109 | 125376 | Enzo Doria | 09/2016 |
1909 | 2^416416-114929 | 125354 | Enzo Doria | 05/2015 |
1910 | (172*10^125292-1)/9 | 125294 | Serge Batalov | 12/2014 |
1911 | 2^416134+1865899 | 125269 | Enzo Doria | 03/2016 |
1912 | (9*2^415992+1)/13560845 | 125220 | Lelio R Paula | 05/2014 |
1913 | (23^91943-1)/22 | 125201 | Robert Price | 01/2012 |
1914 | 43125^27010-106 | 125185 | Enzo Doria | 08/2012 |
1915 | 2^415765-112603 | 125158 | Enzo Doria | 06/2014 |
1916 | 2^415290-113591 | 125015 | Enzo Doria | 08/2014 |
1917 | 2^415276-460919 | 125011 | Enzo Doria | 06/2015 |
1918 | 2^415259+77243 | 125006 | Enzo Doria | 05/2016 |
1919 | 2^415144-3683 | 124971 | Yves Minet | 10/2011 |
1920 | 2^414874+79 | 124890 | Lelio R Paula | 01/2015 |
1921 | (2^414765+7)/1389 | 124854 | Lelio R Paula | 05/2014 |
1922 | 2^414618+79459 | 124813 | Enzo Doria | 06/2016 |
1923 | 2^414432-1846709 | 124757 | Enzo Doria | 07/2015 |
1924 | 2*10^124751-51 | 124752 | Robert Price | 04/2018 |
1925 | (13*2^414274-1)/153 | 124708 | Lelio R Paula | 05/2014 |
1927 | 2^414032-5 | 124637 | Henri Lifchitz | 07/2006 |
1926 | 2^414032+1872331 | 124637 | Enzo Doria | 05/2016 |
1928 | 14120^30009-30009^14120 | 124533 | Norbert Schneider | 02/2015 |
1929 | 64^68909-63^68909 | 124463 | Robert Price | 07/2013 |
1930 | 2^413387+76253 | 124442 | Enzo Doria | 04/2016 |
1931 | 287117#+391613 | 124424 | Nicolas PALAU | 01/2017 |
1932 | (4*10^124420+83)/3 | 124421 | Robert Price | 02/2018 |
1933 | (27*2^413207-1)/108335 | 124385 | Lelio R Paula | 05/2014 |
1934 | 2^412868-120599 | 124286 | Paul Bourdelais | 02/2012 |
1935 | 45^75145-2 | 124231 | Lelio R Paula | 08/2015 |
1936 | 2^412645-112213 | 124219 | Enzo Doria | 06/2014 |
1937 | 2^412248+74611 | 124100 | Enzo Doria | 04/2016 |
1938 | 2^412192-3329 | 124083 | Yves Minet | 12/2014 |
1939 | (25*2^412191-1)/23 | 124082 | Lelio R Paula | 05/2014 |
1940 | F(593689) | 124074 | Henri Lifchitz | 01/2005 |
1941 | (11*2^412161+1)/19 | 124073 | Lelio R Paula | 05/2014 |
1942 | 2^411884-113279 | 123990 | Enzo Doria | 07/2014 |
1943 | (2^411832+1)/257 | 123972 | Lelio R Paula | 05/2014 |
1944 | 2^411790-1853531 | 123962 | Enzo Doria | 08/2015 |
1945 | (5^177337+1)/6 | 123953 | Paul Bourdelais | 11/2008 |
1946 | 2^411711-113257 | 123938 | Enzo Doria | 07/2014 |
1947 | (23*2^411675-1)/3 | 123928 | Lelio R Paula | 05/2014 |
1948 | 2^411325-351103 | 123822 | Enzo Doria | 06/2015 |
1949 | 2^411052+1872481 | 123739 | Enzo Doria | 05/2016 |
1950 | 2^410997+39 | 123723 | Lelio R Paula | 05/2014 |
1951 | 2^410596-39 | 123602 | Lelio R Paula | 05/2014 |
1952 | 2^410540-115079 | 123585 | Enzo Doria | 06/2015 |
1953 | (7*10^123563+107)/3 | 123564 | Robert Price | 02/2018 |
1954 | (3*2^410392-1)/9229 | 123537 | Lelio R Paula | 05/2014 |
1955 | 2^410206-113081 | 123485 | Enzo Doria | 07/2014 |
1956 | (25*2^410192+1)/10397 | 123478 | Lelio R Paula | 04/2014 |
1957 | 2^409909-189 | 123395 | Enzo Doria | 05/2014 |
1958 | 2^409896-109043 | 123391 | Enzo Doria | 04/2014 |
1959 | 2^409890+75409 | 123390 | Enzo Doria | 04/2016 |
1960 | 133^58076-2 | 123345 | Lelio R Paula | 10/2017 |
1961 | F(590041) | 123311 | Henri Lifchitz | 01/2005 |
1962 | 2^409566-113501 | 123292 | Enzo Doria | 08/2014 |
1963 | 2^409533+77747 | 123282 | Enzo Doria | 05/2016 |
1964 | 2^409436-112799 | 123253 | Enzo Doria | 06/2014 |
1965 | 2^409225+1873787 | 123189 | Enzo Doria | 06/2016 |
1966 | 2^409174+73009 | 123174 | Enzo Doria | 04/2016 |
1967 | 2^409058-112685 | 123139 | Enzo Doria | 06/2014 |
1968 | 2^408778+77689 | 123055 | Enzo Doria | 05/2016 |
1969 | 2^408690-75 | 123028 | Lelio R Paula | 11/2013 |
1970 | 2^408574-2787341 | 122994 | Enzo Doria | 03/2016 |
1971 | Phi(157825,10) | 122961 | Maksym Voznyy | 06/2015 |
1972 | (13*2^408283+1)/1665 | 122904 | Lelio R Paula | 05/2014 |
1973 | (11*2^408100-1)/35 | 122850 | Lelio R Paula | 04/2014 |
1974 | (2^407821-lucasV(1,2,407821)+1)/2 | 122767 | Mike Oakes | 11/2016 |
1975 | (21*2^407604-1)/215 | 122701 | Lelio R Paula | 04/2014 |
1976 | (21*2^407433-1)/13 | 122650 | Lelio R Paula | 04/2014 |
1977 | (73*10^122592-1)/9 | 122593 | Robert Price | 01/2015 |
1978 | 2^407179-112075 | 122574 | Enzo Doria | 06/2014 |
1979 | (21*2^407131+1)/207517523 | 122552 | Lelio R Paula | 04/2014 |
1980 | (66^67349+1)/67 | 122543 | Paul Bourdelais | 09/2017 |
1981 | 2^407008-1867919 | 122522 | Enzo Doria | 04/2016 |
1982 | 11^117642-300 | 122512 | Enzo Doria | 10/2012 |
1983 | (F(3*97700+1)^2+L(3*97700+1)^2)/2 | 122509 | Henri Lifchitz | 10/2017 |
1984 | 2^406949+72197 | 122504 | Enzo Doria | 04/2016 |
1985 | 2^406826-65 | 122467 | Lelio R Paula | 11/2013 |
1986 | 2^406821-2797363 | 122466 | Enzo Doria | 04/2016 |
1987 | 2^406758-17 | 122447 | Lelio R Paula | 11/2013 |
1988 | (30^82883-1)/29 | 122427 | Robert Price | 12/2011 |
1989 | (2^406583-1)/813167 | 122388 | Jens K. Andersen | 02/2009 |
1990 | 97^61575-2 | 122336 | Lelio R Paula | 12/2014 |
1991 | 2^406298+2799109 | 122308 | Enzo Doria | 04/2016 |
1992 | (27*2^406241-1)/10277 | 122289 | Lelio R Paula | 04/2014 |
1993 | 2^406229-1849993 | 122288 | Enzo Doria | 08/2015 |
1994 | 3*10^122274+7 | 122275 | Robert Price | 07/2015 |
1995 | 2^406117+1876577 | 122254 | Enzo Doria | 07/2016 |
1996 | 3^256199-2^256199 | 122238 | Mike Oakes | 06/2005 |
1997 | 2^405992-78557 | 122216 | Jorge Menendez | 03/2018 |
1998 | 2^405774+179149 | 122151 | Enzo Doria | 06/2016 |
1999 | 2^405514-3311 | 122072 | Yves Minet | 12/2014 |
2000 | 2^405514-115511 | 122072 | Enzo Doria | 07/2015 |