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
See the Top discoverers
See the Latest PRPs
Search by form
Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
2001 | 7*10^161192-9 | 161193 | Robert Price | 10/2015 |
2002 | 2^535269-113803 | 161133 | Enzo Doria | 09/2014 |
2003 | 2^535205-23295 | 161113 | Enzo Doria | 08/2013 |
2004 | (49*10^161105+437)/9 | 161106 | Robert Price | 09/2021 |
2005 | (89^82609+1)/90 | 161036 | Paul Bourdelais | 10/2017 |
2006 | 2^534359-23229 | 160859 | Enzo Doria | 08/2013 |
2007 | 457^60454+60454^457 | 160803 | Norbert Schneider | 07/2021 |
2008 | 8*10^160782+53 | 160783 | Robert Price | 08/2020 |
2009 | 67^88037-66^88037 | 160763 | Robert Price | 10/2013 |
2010 | (88*10^160761-637)/9 | 160762 | Robert Price | 11/2020 |
2011 | 2^533948-1852559 | 160735 | Enzo Doria | 08/2015 |
2012 | 2^533665-23335 | 160650 | Enzo Doria | 08/2013 |
2013 | (19*10^160619+77)/3 | 160620 | Robert Price | 05/2019 |
2014 | (38*10^160508+151)/9 | 160509 | Robert Price | 03/2022 |
2015 | 3^336353-2^336353 | 160482 | Mike Oakes | 10/2007 |
2016 | 2*10^160339-63 | 160340 | Robert Price | 01/2022 |
2017 | (91*10^160249+11)/3 | 160251 | Robert Price | 02/2020 |
2018 | (772*10^160239-7)/9 | 160241 | Robert Price | 06/2022 |
2019 | (2*10^160226+187)/9 | 160226 | Robert Price | 06/2022 |
2020 | 2^532253+1868417 | 160225 | Enzo Doria | 04/2016 |
2021 | 2^532108-291989 | 160181 | Enzo Doria | 07/2015 |
2022 | (28*10^160171-79)/3 | 160172 | Robert Price | 02/2021 |
2023 | (26*10^160166-131)/3 | 160167 | Robert Price | 10/2019 |
2024 | 55*10^160145+9 | 160147 | Robert Price | 03/2022 |
2025 | (17*10^160143+67)/3 | 160144 | Robert Price | 01/2019 |
2026 | (19*10^159921-49)/3 | 159922 | Robert Price | 05/2019 |
2027 | 2^531110-1853771 | 159881 | Enzo Doria | 09/2015 |
2028 | (275^65536+53^65536)/2 | 159864 | Kellen Shenton | 11/2020 |
2029 | 2^530992-1845299 | 159845 | Enzo Doria | 07/2015 |
2030 | 2^530810+25 | 159790 | Stefano Morozzi | 04/2021 |
2031 | (136*10^159736-1)/9 | 159738 | Serge Batalov | 12/2014 |
2032 | 2^530417-113833 | 159672 | Enzo Doria | 09/2014 |
2033 | 2^530406-69701 | 159669 | Enzo Doria | 02/2016 |
2034 | 5*10^159656+41 | 159657 | Robert Price | 03/2019 |
2035 | 8*10^159614+29 | 159615 | Robert Price | 11/2021 |
2036 | 7^188858-188858^7 | 159604 | Norbert Schneider | 05/2018 |
2037 | (24^115597-1)/23 | 159547 | Paul Bourdelais | 09/2017 |
2038 | (17*10^159438-377)/9 | 159439 | Robert Price | 03/2018 |
2039 | (203*10^159381+1)/3 | 159383 | Robert Price | 03/2020 |
2040 | 89*10^159258-9 | 159260 | Robert Price | 05/2020 |
2041 | 2^528944-461315 | 159229 | Enzo Doria | 07/2015 |
2042 | (13*10^159147+161)/3 | 159148 | Robert Price | 11/2018 |
2043 | 2^528620-113879 | 159131 | Enzo Doria | 10/2014 |
2044 | (47*10^159083+259)/9 | 159084 | Robert Price | 03/2022 |
2045 | 2^528000-23307 | 158944 | Enzo Doria | 08/2013 |
2046 | (29*10^158909+61)/9 | 158910 | Robert Price | 08/2018 |
2047 | 2^527817+1876817 | 158889 | Enzo Doria | 07/2016 |
2048 | 2^527774-49451 | 158876 | Enzo Doria | 10/2015 |
2049 | 2^527745-291553 | 158868 | Enzo Doria | 07/2015 |
2050 | (91*10^158862+11)/3 | 158864 | Robert Price | 02/2020 |
2051 | 2^527644-1856999 | 158837 | Enzo Doria | 10/2015 |
2052 | (37200^37199-37198^37199)/(2^37199) | 158822 | Henri Lifchitz | 06/2013 |
2053 | 2^527573-1863253 | 158816 | Enzo Doria | 12/2015 |
2054 | 2^527553-23401 | 158810 | Enzo Doria | 08/2013 |
2055 | (49*10^158783+437)/9 | 158784 | Robert Price | 09/2021 |
2056 | 10^158755+310207 | 158756 | Patrick De Geest | 08/2021 |
2057 | 10^158755-50001 | 158755 | Robert Price | 08/2020 |
2058 | (61*10^158748-619)/9 | 158749 | Robert Price | 03/2022 |
2059 | 11^152420-210 | 158730 | Enzo Doria | 09/2012 |
2060 | (13*10^158694+401)/9 | 158695 | Robert Price | 01/2018 |
2061 | 2^527052-69059 | 158659 | Enzo Doria | 11/2015 |
2062 | 2^526849-113233 | 158598 | Enzo Doria | 07/2014 |
2063 | (2^526763-lucasV(1,2,526763)+1)/2 | 158572 | Mike Oakes | 11/2016 |
2064 | (299*10^158544-17)/3 | 158546 | Robert Price | 04/2020 |
2065 | 2^526658-3551 | 158540 | Yves Minet | 03/2017 |
2066 | 7*10^158465-11 | 158466 | Robert Price | 06/2019 |
2067 | 2^526375-23115 | 158455 | Enzo Doria | 08/2013 |
2068 | (77*10^158407-293)/9 | 158408 | Robert Price | 09/2019 |
2069 | 2^526028-112793 | 158351 | Enzo Doria | 07/2014 |
2070 | (229*10^158339-1)/3 | 158341 | Robert Price | 07/2020 |
2071 | 2^525690-9221 | 158249 | Lelio R Paula | 01/2013 |
2072 | 2*10^158242-7 | 158243 | Robert Price | 10/2015 |
2073 | 2^525667-525667^2 | 158242 | Henri Lifchitz | 12/2017 |
2074 | (56*10^158230+187)/9 | 158231 | Robert Price | 10/2021 |
2075 | 10^158209-7000000001 | 158209 | Robert Price | 12/2021 |
2076 | 2^525186-1857431 | 158097 | Enzo Doria | 10/2015 |
2077 | 2^524515-23245 | 157895 | Enzo Doria | 08/2013 |
2078 | 2^524499-109087 | 157890 | Enzo Doria | 04/2014 |
2079 | 2^18067*(2^506221+1)-1 | 157827 | Makoto Morimoto | 05/2014 |
2080 | 2^524288+189093 | 157827 | Makoto Morimoto | 01/2016 |
2081 | 2^524288-164073 | 157827 | Matthias Baur | 03/2020 |
2082 | (2^(2^19)-9333)/(19*23*463*1213*31973) | 157814 | Makoto Morimoto | 09/2017 |
2083 | (10^157792+359)/9 | 157792 | Serge Batalov | 12/2014 |
2084 | 2^524154+25 | 157787 | Stefano Morozzi | 04/2021 |
2085 | 2^523924+1876591 | 157717 | Enzo Doria | 07/2016 |
2086 | (17*10^157705+67)/3 | 157706 | Robert Price | 01/2019 |
2087 | (46^94841+1)/47 | 157696 | Robert Price | 01/2014 |
2088 | 2^523774+77839 | 157672 | Enzo Doria | 05/2016 |
2089 | 2^523587+2799143 | 157616 | Enzo Doria | 04/2016 |
2090 | 2^523371+1872113 | 157551 | Enzo Doria | 05/2016 |
2091 | 8*10^157477+27 | 157478 | Robert Price | 09/2021 |
2092 | (8*10^157368+49)/3 | 157369 | Robert Price | 05/2020 |
2093 | (82*10^157319+449)/9 | 157320 | Robert Price | 11/2019 |
2094 | 2^522535-351457 | 157299 | Enzo Doria | 07/2015 |
2095 | 2^522226+2799079 | 157206 | Enzo Doria | 04/2016 |
2096 | (134*10^157191-11)/3 | 157193 | Robert Price | 01/2022 |
2097 | 2^522134-1849451 | 157178 | Enzo Doria | 08/2015 |
2098 | 9*10^157152+71 | 157153 | Robert Price | 08/2020 |
2099 | 4*10^157150+93 | 157151 | Robert Price | 08/2018 |
2100 | 2^521401-29593 | 156958 | Enzo Doria | 08/2015 |
2101 | 7*10^156956+87 | 156957 | Robert Price | 07/2019 |
2102 | 2^521348-23397 | 156942 | Enzo Doria | 08/2013 |
2103 | 10^156902+34509 | 156903 | Patrick De Geest | 08/2021 |
2105 | 10^156902-80000001 | 156902 | Robert Price | 04/2021 |
2104 | 10^156902-69789 | 156902 | Patrick De Geest | 08/2021 |
2106 | (98^78797+1)/99 | 156901 | Paul Bourdelais | 12/2017 |
2107 | 65^86522+64 | 156857 | Lelio R Paula | 04/2016 |
2108 | 8^173687-7^173687 | 156855 | Jean-Louis Charton | 09/2004 |
2109 | 2^520977-1858183 | 156830 | Enzo Doria | 10/2015 |
2110 | (8*10^156718-101)/3 | 156719 | Robert Price | 08/2018 |
2111 | (10^156640+7)/53 | 156639 | Alfred Reich | 07/2021 |
2112 | 2^520314-1849481 | 156631 | Enzo Doria | 08/2015 |
2113 | (13*10^156522+89)/3 | 156523 | Robert Price | 09/2018 |
2114 | (2^(6*86654+1)-5)/3 | 156513 | Kevin Acres | 12/2013 |
2115 | (4*10^156501+119)/3 | 156502 | Robert Price | 12/2021 |
2116 | (83*10^156476-101)/9 | 156477 | Robert Price | 08/2021 |
2117 | 3*10^156435-97 | 156436 | Robert Price | 07/2018 |
2118 | (8*10^156371-77)/3 | 156372 | Robert Price | 07/2018 |
2119 | 53^90679-52^90679 | 156356 | Robert Price | 01/2013 |
2120 | (418*10^156309-31)/9 | 156311 | Robert Price | 05/2022 |
2121 | 2^519106-59141 | 156267 | Enzo Doria | 10/2015 |
2122 | 2^519053+6077 | 156251 | Enzo Doria | 02/2016 |
2123 | 2^518968-1860989 | 156225 | Enzo Doria | 11/2015 |
2124 | (25*10^156221-7)/9 | 156222 | Robert Price | 05/2018 |
2125 | 2^518931-2782297 | 156214 | Enzo Doria | 09/2015 |
2126 | 2^518608-2939 | 156117 | Yves Minet | 09/2014 |
2127 | 10*27^109005+697 | 156027 | Curtis Bright | 05/2015 |
2128 | (49*10^155933-319)/9 | 155934 | Robert Price | 10/2021 |
2129 | 2^517967-113485 | 155924 | Enzo Doria | 08/2014 |
2130 | (103*10^155904+17)/3 | 155906 | Robert Price | 08/2020 |
2131 | (8*10^155887-719)/9 | 155887 | Robert Price | 03/2021 |
2132 | 4*10^155853-39 | 155854 | Robert Price | 09/2020 |
2133 | 2^517698+4429 | 155843 | Lelio R Paula | 01/2013 |
2134 | 2^517543-113257 | 155796 | Enzo Doria | 07/2014 |
2135 | (14*10^155740-143)/3 | 155741 | Robert Price | 11/2018 |
2136 | 31^104309-30^104309 | 155563 | Henri Lifchitz | 08/2013 |
2137 | 2^516742-39851 | 155555 | Enzo Doria | 09/2015 |
2138 | (22*10^155543+47)/3 | 155544 | Robert Price | 06/2021 |
2139 | (19*10^155504+131)/3 | 155505 | Robert Price | 06/2020 |
2140 | 7*10^155496+61 | 155497 | Robert Price | 08/2019 |
2141 | 2^516440+1878421 | 155464 | Enzo Doria | 08/2016 |
2142 | 2^515863-1867237 | 155291 | Enzo Doria | 03/2016 |
2143 | 2^515786-461861 | 155268 | Enzo Doria | 07/2015 |
2144 | 2^515644-113247 | 155225 | Enzo Doria | 07/2014 |
2145 | (7*10^155203+107)/3 | 155204 | Robert Price | 02/2018 |
2146 | 10^155163+206871 | 155164 | Patrick De Geest | 05/2021 |
2147 | 10^155163-40001 | 155163 | Robert Price | 01/2021 |
2148 | (17*10^155133-89)/9 | 155134 | Robert Price | 07/2018 |
2149 | 2^515227-114997 | 155099 | Enzo Doria | 06/2015 |
2151 | EPrime(155025) | 155025 | Eric W. Weisstein | 10/2010 |
2150 | (14*10^155024-221)/9 | 155025 | Robert Price | 04/2018 |
2152 | (4*10^155022+173)/3 | 155023 | Robert Price | 02/2018 |
2153 | (266*10^154897+1)/3 | 154899 | Robert Price | 04/2020 |
2154 | (115*10^154869-1)/3 | 154871 | Serge Batalov | 12/2014 |
2155 | (86*10^154853-221)/9 | 154854 | Robert Price | 09/2019 |
2156 | 2^514361+78167 | 154839 | Enzo Doria | 05/2016 |
2157 | 2^514281-115033 | 154815 | Enzo Doria | 06/2015 |
2158 | 2^514194-3311 | 154788 | Yves Minet | 12/2014 |
2159 | (14*10^154773+37)/3 | 154774 | Robert Price | 12/2018 |
2160 | (16*10^154748+131)/3 | 154749 | Robert Price | 03/2022 |
2161 | 6*10^154742-31 | 154743 | Robert Price | 07/2020 |
2162 | (14*10^154645+139)/9 | 154646 | Robert Price | 11/2021 |
2163 | 5*10^154618-79 | 154619 | Robert Price | 03/2021 |
2164 | (167*10^154595+1)/3 | 154597 | Robert Price | 04/2021 |
2165 | 2^513437+1879337 | 154560 | Enzo Doria | 09/2016 |
2166 | 2^513306-113201 | 154521 | Enzo Doria | 07/2014 |
2167 | (10^154494-13)/3 | 154494 | Robert Price | 12/2017 |
2168 | 2^513042-113787 | 154442 | Enzo Doria | 09/2014 |
2169 | (151*10^154434-7)/9 | 154436 | Robert Price | 01/2020 |
2170 | (118*10^154428+11)/3 | 154430 | Robert Price | 03/2022 |
2171 | (14*10^154413+139)/9 | 154414 | Robert Price | 11/2021 |
2172 | (77*10^154389-149)/9 | 154390 | Robert Price | 03/2022 |
2173 | 2^512628-114053 | 154317 | Enzo Doria | 11/2014 |
2174 | 2^512529-49783 | 154287 | Enzo Doria | 10/2015 |
2175 | (355573#+6991)/(6991*2031599) | 154285 | Makoto Morimoto | 06/2019 |
2176 | 2^512315-115297 | 154223 | Enzo Doria | 06/2015 |
2177 | (47*10^154221+241)/9 | 154222 | Robert Price | 06/2022 |
2178 | (7*10^154211+173)/9 | 154211 | Robert Price | 01/2022 |
2179 | 2^512168+79561 | 154178 | Enzo Doria | 06/2016 |
2180 | (77*10^154175+67)/9 | 154176 | Robert Price | 12/2021 |
2181 | (5*10^154158-311)/9 | 154158 | Robert Price | 12/2021 |
2182 | (89*10^154103-737)/9 | 154104 | Robert Price | 01/2022 |
2183 | 4*10^154078-57 | 154079 | Robert Price | 10/2018 |
2184 | (355049#+1859)/(11*13*10148891*62587751) | 154051 | Makoto Morimoto | 06/2019 |
2185 | 7*10^154038-57 | 154039 | Robert Price | 06/2020 |
2186 | 2^511658-114371 | 154025 | Enzo Doria | 02/2015 |
2187 | (57^87719+1)/58 | 154022 | Paul Bourdelais | 11/2017 |
2188 | 2^511580-1846679 | 154001 | Enzo Doria | 07/2015 |
2189 | (259*10^153998-1)/3 | 154000 | Robert Price | 12/2020 |
2190 | 2^511541-113713 | 153990 | Enzo Doria | 09/2014 |
2191 | 49958^32768+49957^32768 | 153965 | Kellen Shenton | 11/2020 |
2192 | 10^153935+970801 | 153936 | Patrick De Geest | 05/2021 |
2193 | 10^153935-1000001 | 153935 | Robert Price | 08/2020 |
2194 | (16*10^153868-73)/3 | 153869 | Robert Price | 07/2020 |
2195 | 9*10^153851-67 | 153852 | Robert Price | 11/2020 |
2196 | 2^511077-112723 | 153850 | Enzo Doria | 06/2014 |
2197 | 69^83653-68^83653 | 153826 | Robert Price | 12/2013 |
2198 | 2^510963-113707 | 153816 | Enzo Doria | 09/2014 |
2199 | (154*10^153810-1)/9 | 153812 | Serge Batalov | 12/2014 |
2200 | (181*25^109991-75077)/8 | 153763 | Curtis Bright | 05/2015 |
2201 | 2*10^153746-3 | 153747 | Robert Price | 07/2015 |
2202 | 2^510626+1179379 | 153714 | Enzo Doria | 05/2016 |
2203 | (7*10^153664+113)/3 | 153665 | Robert Price | 02/2018 |
2204 | 2^510420+81121 | 153652 | Enzo Doria | 07/2016 |
2205 | (197*7^181761-1)/2 | 153608 | Karsten Bonath | 05/2017 |
2206 | 2^509894-459161 | 153494 | Enzo Doria | 05/2015 |
2207 | (74*10^153489+673)/9 | 153490 | Robert Price | 02/2022 |
2208 | (49*10^153484-211)/9 | 153485 | Robert Price | 06/2022 |
2209 | 2^509841+71657 | 153478 | Enzo Doria | 04/2016 |
2210 | 9*10^153446+41 | 153447 | Robert Price | 08/2020 |
2211 | 2^509533-1846723 | 153385 | Enzo Doria | 07/2015 |
2212 | 2^509468-39989 | 153366 | Enzo Doria | 09/2015 |
2213 | 70^83117-69^83117 | 153360 | Robert Price | 01/2014 |
2214 | (112*10^153025-1)/3 | 153027 | Serge Batalov | 12/2014 |
2215 | (19*10^153010+131)/3 | 153011 | Robert Price | 06/2020 |
2216 | 2^508174-1855151 | 152976 | Enzo Doria | 09/2015 |
2217 | 181^67757-2 | 152974 | Lelio R Paula | 12/2017 |
2218 | 2^508160-1864829 | 152972 | Enzo Doria | 01/2016 |
2219 | 10^152960+412563 | 152961 | Patrick De Geest | 05/2021 |
2220 | 10^152960-50000000001 | 152960 | Robert Price | 12/2020 |
2221 | 10^152960-423749 | 152960 | Patrick De Geest | 05/2021 |
2222 | (71*10^152933-143)/9 | 152934 | Robert Price | 10/2021 |
2223 | 2^507857-1848199 | 152881 | Enzo Doria | 07/2015 |
2224 | 2^507638-115361 | 152815 | Enzo Doria | 07/2015 |
2225 | 2^507551-114025 | 152789 | Enzo Doria | 11/2014 |
2226 | (6^196337+1)/7 | 152780 | Paul Bourdelais | 02/2010 |
2227 | (22*10^152670-13)/9 | 152671 | Robert Price | 06/2018 |
2228 | 2^506451-22339 | 152457 | Enzo Doria | 07/2013 |
2229 | 2^505995-113185 | 152320 | Enzo Doria | 07/2014 |
2230 | (4*10^152253+149)/9 | 152253 | Robert Price | 04/2018 |
2231 | 578^55117-577^55117 | 152230 | Jean-Louis Charton | 08/2012 |
2232 | 2^505431-505431 | 152150 | Henri Lifchitz | 04/2005 |
2233 | (203*10^152143+1)/3 | 152145 | Robert Price | 03/2020 |
2234 | 2^505053+73097 | 152037 | Enzo Doria | 04/2016 |
2235 | 22*10^151998+3 | 152000 | Robert Price | 01/2020 |
2236 | (238*10^151979-1)/3 | 151981 | Robert Price | 04/2020 |
2237 | (2^504793-7)/46765 | 151954 | Lelio R Paula | 12/2017 |
2238 | 350377#+797581 | 151937 | Nicolas PALAU | 08/2017 |
2239 | (79*10^151906-529)/9 | 151907 | Robert Price | 01/2022 |
2240 | 2^504618-343991 | 151906 | Enzo Doria | 07/2015 |
2241 | 2^504212-461939 | 151783 | Enzo Doria | 07/2015 |
2242 | 7*10^151772-41 | 151773 | Robert Price | 08/2021 |
2243 | 2^504054-2231 | 151736 | Yves Minet | 10/2011 |
2244 | (28*10^151682+191)/3 | 151683 | Robert Price | 02/2020 |
2245 | 2^503475-933075 | 151562 | Paul Bourdelais | 06/2021 |
2246 | 2^503361-39883 | 151527 | Enzo Doria | 09/2015 |
2247 | 2^503225+382667 | 151486 | Enzo Doria | 10/2016 |
2248 | (206*10^151483-11)/3 | 151485 | Robert Price | 02/2022 |
2249 | (844*10^151396-7)/9 | 151398 | Robert Price | 05/2021 |
2250 | (26*10^151391-503)/9 | 151392 | Robert Price | 07/2018 |