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
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| Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
| 2001 | 2^805843-113611 | 242583 | Enzo Doria | 08/2014 |
| 2002 | 2^805745-459763 | 242554 | Enzo Doria | 05/2015 |
| 2003 | 2^805353+782687 | 242436 | Enzo Doria | 11/2016 |
| 2004 | (19*10^242362-7)/3 | 242363 | Robert Price | 12/2023 |
| 2005 | 2^804895+29963 | 242298 | Enzo Doria | 03/2024 |
| 2006 | 2^804725+28229 | 242247 | Enzo Doria | 01/2024 |
| 2007 | 6^311257+5 | 242206 | Paul Bourdelais | 02/2021 |
| 2008 | (21^242194)%(10^242194) | 242194 | Henri Lifchitz | 06/2025 |
| 2009 | 2^804277-417933 | 242112 | Enzo Doria | 01/2014 |
| 2010 | 2^803468-269039 | 241868 | Enzo Doria | 10/2013 |
| 2011 | 2^803172+80851 | 241779 | Enzo Doria | 07/2016 |
| 2012 | 2^803011+220073 | 241731 | Enzo Doria | 03/2024 |
| 2013 | 3^506233-2 | 241535 | Robert Price | 11/2013 |
| 2014 | 2^802025-25999 | 241434 | Enzo Doria | 10/2013 |
| 2015 | (3^505823+3^252912+1)/7 | 241339 | Serge Batalov | 03/2014 |
| 2016 | 2^801575+25073 | 241299 | Enzo Doria | 11/2023 |
| 2017 | 2^801303+1872923 | 241217 | Enzo Doria | 05/2016 |
| 2018 | 2^801105+216977 | 241157 | Enzo Doria | 12/2023 |
| 2019 | (23*10^241048-143)/3 | 241049 | Robert Price | 12/2023 |
| 2020 | 2^800579-1862947 | 240999 | Enzo Doria | 12/2015 |
| 2021 | 2^799999+16205 | 240824 | Norman Luhn | 09/2023 |
| 2022 | 3^504206+2 | 240568 | Luke W. Richards | 03/2018 |
| 2023 | 2^798973-26283 | 240515 | Enzo Doria | 10/2013 |
| 2024 | Phi(114205,3^7) | 240470 | Henri Lifchitz | 12/2025 |
| 2025 | 2^798671-69487 | 240424 | Enzo Doria | 12/2015 |
| 2026 | 2^797220+79831 | 239988 | Enzo Doria | 06/2016 |
| 2027 | 2^796910-26001 | 239894 | Enzo Doria | 10/2013 |
| 2028 | (97^120721-1)/811245216 | 239837 | Paul Vanderveen | 06/2025 |
| 2029 | 2^796598+653119 | 239800 | Enzo Doria | 12/2016 |
| 2030 | 2^796432-1859729 | 239750 | Enzo Doria | 11/2015 |
| 2031 | 2^796002-1852211 | 239621 | Enzo Doria | 08/2015 |
| 2032 | 2^795884+214081 | 239585 | Enzo Doria | 10/2023 |
| 2033 | 2^795709+75767 | 239533 | Enzo Doria | 04/2016 |
| 2034 | 2^795708+81721 | 239532 | Enzo Doria | 08/2016 |
| 2035 | 2^795468-2786249 | 239460 | Enzo Doria | 10/2015 |
| 2036 | 2^795442+80779 | 239452 | Enzo Doria | 07/2016 |
| 2037 | 2^795075-1852057 | 239342 | Enzo Doria | 08/2015 |
| 2038 | (86^123677+1)/87 | 239252 | Paul Bourdelais | 01/2019 |
| 2039 | 2^794043+1875023 | 239031 | Enzo Doria | 06/2016 |
| 2040 | 2^793347-69577 | 238822 | Enzo Doria | 01/2016 |
| 2041 | 5*2^793288+3 | 238805 | Jon Grantham | 07/2023 |
| 2042 | 2^792988-344429 | 238714 | Enzo Doria | 08/2015 |
| 2043 | 2^792700-2786369 | 238627 | Enzo Doria | 11/2015 |
| 2044 | 2^792663-1844797 | 238616 | Enzo Doria | 06/2015 |
| 2045 | 2^792605-291943 | 238598 | Enzo Doria | 07/2015 |
| 2046 | 2^792366+218599 | 238526 | Enzo Doria | 01/2024 |
| 2047 | (2^792061-2^396031+1)/5 | 238434 | Thomas Ritschel | 03/2014 |
| 2048 | 2^791321+30077 | 238212 | Enzo Doria | 03/2024 |
| 2049 | 4*10^238163+21 | 238164 | Robert Price | 12/2022 |
| 2050 | (26*10^238157-77)/3 | 238158 | Robert Price | 03/2023 |
| 2051 | 10^237670+9 | 237671 | Robert Price | 08/2023 |
| 2052 | 2^789373+1869377 | 237625 | Enzo Doria | 05/2016 |
| 2053 | ((10^59387+1)^3*(10^59387+1+10^29694)-(10^118774+10^59387)*(10^29694-1)+10^178161)/27961 | 237544 | Serge Batalov | 04/2015 |
| 2054 | Phi(1187740M,10) | 237544 | Anonymous | 03/2025 |
| 2055 | 2^789033+218537 | 237523 | Enzo Doria | 01/2024 |
| 2056 | 2^788942+1866409 | 237496 | Enzo Doria | 02/2016 |
| 2057 | 2^788844-114329 | 237466 | Enzo Doria | 01/2015 |
| 2058 | 2^788705-1859713 | 237424 | Enzo Doria | 11/2015 |
| 2059 | 2^788325+224789 | 237310 | Enzo Doria | 07/2024 |
| 2060 | 15^201475+14 | 236953 | Alfred Reich | 10/2023 |
| 2061 | 2^786663+219173 | 236810 | Enzo Doria | 02/2024 |
| 2062 | 2^786180+1871971 | 236664 | Enzo Doria | 05/2016 |
| 2063 | 11^227092-90 | 236492 | Enzo Doria | 11/2012 |
| 2064 | 2^785260+1866361 | 236387 | Enzo Doria | 02/2016 |
| 2065 | (309*21^178772+71)/20 | 236377 | Eric Chen | 03/2026 |
| 2066 | 2^785220+1880611 | 236375 | Enzo Doria | 10/2016 |
| 2067 | (2^784689-15)/7 | 236215 | Stefano Morozzi | 08/2022 |
| 2068 | 19^184650-2 | 236122 | Robert Price | 10/2014 |
| 2069 | 10^236059+216513 | 236060 | Patrick De Geest | 04/2016 |
| 2070 | 10^236059-20909 | 236059 | Robert Price | 09/2015 |
| 2071 | 2^783988+38011 | 236004 | Enzo Doria | 10/2024 |
| 2072 | 2^783893-21 | 235976 | Stefano Morozzi | 07/2022 |
| 2073 | (47^140983-1)/2792206142311142462 | 235719 | Paul Vanderveen | 06/2025 |
| 2074 | 2^782821+37577 | 235653 | Enzo Doria | 10/2024 |
| 2075 | (87^121487-1)/86 | 235625 | Paul Bourdelais | 12/2018 |
| 2076 | 2^782634-113981 | 235597 | Enzo Doria | 11/2014 |
| 2077 | 2^782423+1879733 | 235533 | Enzo Doria | 09/2016 |
| 2078 | (10^(2*117707+1)+12*10^117707-1)/3 | 235415 | Robert Price | 10/2023 |
| 2079 | (2^781970)/(781970^2) | 235385 | Henri Lifchitz | 06/2025 |
| 2080 | 2^781682-2789543 | 235310 | Enzo Doria | 12/2015 |
| 2081 | 2^780481+21489 | 234949 | Enzo Doria | 05/2024 |
| 2082 | 2^780408-113453 | 234927 | Enzo Doria | 08/2014 |
| 2083 | 7*10^234915+9 | 234916 | Robert Price | 04/2023 |
| 2084 | 2^780368-1864829 | 234915 | Enzo Doria | 01/2016 |
| 2085 | 2^780284+7 | 234889 | Jon Grantham | 08/2023 |
| 2086 | 2^779593-1836559 | 234681 | Enzo Doria | 05/2015 |
| 2087 | (8713#+(549391#)/(8713#))/360295171 | 234487 | Makoto Morimoto | 11/2017 |
| 2088 | (5^335429+1)/6 | 234455 | Paul Bourdelais | 08/2010 |
| 2089 | 2^778788+22201 | 234439 | Enzo Doria | 09/2023 |
| 2090 | 2^778395-113617 | 234321 | Enzo Doria | 08/2014 |
| 2091 | 5*2^778090+3 | 234230 | Jon Grantham | 07/2023 |
| 2092 | (21430^54289-1)/(21430^233-1) | 234118 | Ryan Propper | 11/2023 |
| 2093 | (5*10^234054-101)/3 | 234055 | Robert Price | 08/2023 |
| 2094 | 23*10^234025-7 | 234027 | Robert Price | 10/2022 |
| 2095 | 2^777170+21489 | 233952 | Enzo Doria | 05/2024 |
| 2096 | Phi(78125,5517) | 233857 | Anonymous | 09/2022 |
| 2097 | 5^334359-3^334359-1 | 233707 | Jon Grantham | 08/2023 |
| 2098 | 2^776245-2792353 | 233674 | Enzo Doria | 02/2016 |
| 2099 | 49748^49748+49735^49735 | 233656 | Henri Lifchitz | 11/2024 |
| 2100 | 2^776060-114029 | 233618 | Enzo Doria | 11/2014 |
| 2101 | 2^775987-2789557 | 233596 | Enzo Doria | 12/2015 |
| 2102 | 2*10^233564-91 | 233565 | Robert Price | 02/2023 |
| 2103 | 2^775865+21489 | 233559 | Enzo Doria | 05/2024 |
| 2104 | 2^775672+1866721 | 233501 | Enzo Doria | 03/2016 |
| 2105 | 2^775238+57 | 233370 | Stefano Morozzi | 05/2021 |
| 2106 | (11^223999+1)/12 | 233270 | Paul Bourdelais | 02/2010 |
| 2107 | U(1302049) | 233238 | Serge Batalov | 07/2024 |
| 2108 | 2^774118+1885789 | 233033 | Enzo Doria | 04/2017 |
| 2109 | 21^176191-20^176191 | 232964 | Jean-Louis Charton | 01/2015 |
| 2110 | 2^773723+217523 | 232914 | Enzo Doria | 01/2024 |
| 2111 | 2^773679-113425 | 232901 | Enzo Doria | 08/2014 |
| 2112 | 11*17^189085+232 | 232661 | Eric Chen | 01/2026 |
| 2113 | (7*10^232620+23)/3 | 232621 | Robert Price | 05/2023 |
| 2114 | 10^232599+192489 | 232600 | Patrick De Geest | 12/2013 |
| 2115 | 10^232599-3 | 232599 | Markus Tervooren | 10/2010 |
| 2116 | 2^772552-458879 | 232562 | Enzo Doria | 04/2015 |
| 2117 | 2^772214+1874899 | 232460 | Enzo Doria | 06/2016 |
| 2118 | 2^771994-1862771 | 232394 | Enzo Doria | 12/2015 |
| 2119 | 2^771889+1876037 | 232362 | Enzo Doria | 07/2016 |
| 2120 | 2^771660+1866511 | 232293 | Enzo Doria | 02/2016 |
| 2121 | 5^332150-18188 | 232163 | Enzo Doria | 06/2014 |
| 2122 | 2^771227+61121 | 232163 | Boyan Hu | 05/2024 |
| 2123 | 2^770623+212543 | 231981 | Enzo Doria | 09/2023 |
| 2124 | 3^485977-2^485977 | 231870 | Mike Oakes | 09/2009 |
| 2125 | 2^770082-114161 | 231818 | Enzo Doria | 01/2015 |
| 2126 | 2^769791+25523 | 231731 | Enzo Doria | 11/2023 |
| 2127 | 7^274120-2 | 231659 | Paul Bourdelais | 08/2023 |
| 2128 | (20^177967+1)/21 | 231540 | Paul Bourdelais | 05/2013 |
| 2129 | 2^769011+81 | 231496 | Henri Lifchitz | 01/2025 |
| 2130 | (71^125029-1)/105024430 | 231453 | Paul Vanderveen | 06/2025 |
| 2131 | (4*10^231254+23)/9 | 231254 | Serge Batalov | 11/2022 |
| 2132 | 2^768205+22217 | 231253 | Enzo Doria | 09/2023 |
| 2133 | 49262^49262-49247^49247 | 231163 | Henri Lifchitz | 11/2024 |
| 2134 | 2^767622-9221 | 231078 | Lelio R Paula | 01/2016 |
| 2135 | 2^767344+1880311 | 230994 | Enzo Doria | 09/2016 |
| 2136 | 8*10^230921-13 | 230922 | Robert Price | 08/2023 |
| 2137 | (3^483611-1)/2 | 230741 | Paul Bourdelais | 02/2010 |
| 2138 | (10^230706+179)/9 | 230706 | Serge Batalov | 12/2014 |
| 2139 | 2^766309+1875257 | 230682 | Enzo Doria | 06/2016 |
| 2140 | (26131^52441-1)/(26131^229-1) | 230629 | Ryan Propper | 11/2023 |
| 2141 | 2^765635+1879883 | 230480 | Enzo Doria | 09/2016 |
| 2142 | 43^141090+141090 | 230467 | Kellen Shenton | 06/2023 |
| 2143 | (26*10^230394-119)/3 | 230395 | Robert Price | 07/2023 |
| 2144 | 2^764348-113697 | 230092 | Enzo Doria | 09/2014 |
| 2145 | 2^764131+78863 | 230027 | Enzo Doria | 05/2016 |
| 2146 | 2^763701+60197 | 229897 | Enzo Doria | 03/2016 |
| 2147 | 4*10^229836+21 | 229837 | Robert Price | 12/2022 |
| 2148 | 2^763362+27799 | 229795 | Enzo Doria | 01/2024 |
| 2149 | 2^762841-25905 | 229639 | Enzo Doria | 10/2013 |
| 2150 | 2^762659+212633 | 229584 | Enzo Doria | 09/2023 |
| 2151 | 77*10^229211+3 | 229213 | Robert Price | 11/2023 |
| 2152 | 2^761117-113569 | 229120 | Enzo Doria | 08/2014 |
| 2153 | (29022^51529-1)/(29022^227-1) | 228947 | Ryan Propper | 11/2023 |
| 2154 | (98^114859+1)/99 | 228709 | Paul Bourdelais | 12/2018 |
| 2155 | 5*3^479067-2^479067 | 228574 | Jon Grantham | 08/2023 |
| 2156 | 2^758645+216011 | 228375 | Enzo Doria | 12/2023 |
| 2157 | (2^758231+1)/(3*27146942976539*73236839266867) | 228223 | Gord Palameta | 12/2018 |
| 2158 | 10^228208+111 | 228209 | Boyan Hu | 10/2024 |
| 2159 | (298*10^228177-7)/3 | 228179 | Robert Price | 02/2023 |
| 2160 | 2^757985-2790013 | 228177 | Enzo Doria | 12/2015 |
| 2161 | 34*10^228129-9 | 228131 | Robert Price | 05/2023 |
| 2162 | 2^757038-1862081 | 227892 | Enzo Doria | 12/2015 |
| 2163 | 2^756839+95849 | 227832 | Makoto Morimoto | 10/2013 |
| 2165 | (2^756839+6989)/756091 | 227826 | Makoto Morimoto | 09/2016 |
| 2164 | (2^756839-50211)/(137*3203) | 227826 | Makoto Morimoto | 08/2019 |
| 2166 | 2^756773-112723 | 227812 | Enzo Doria | 07/2014 |
| 2167 | (7*10^(2*113887+1)+9*10^113887-7)/9 | 227775 | Robert Price | 08/2024 |
| 2168 | (10^227542)/(227542^10) | 227489 | Henri Lifchitz | 05/2025 |
| 2169 | 524309#+616367 | 227431 | Makoto Morimoto | 02/2016 |
| 2170 | 2^755404+226575 | 227400 | Enzo Doria | 09/2024 |
| 2171 | 2^755116+81 | 227313 | Henri Lifchitz | 11/2024 |
| 2172 | 2^755097-114193 | 227307 | Enzo Doria | 12/2014 |
| 2173 | 7*10^227178+39 | 227179 | Robert Price | 01/2023 |
| 2174 | 9*10^227153-89 | 227154 | Robert Price | 02/2023 |
| 2175 | 2^754473-2791513 | 227120 | Enzo Doria | 01/2016 |
| 2176 | 2^754376+25 | 227090 | Stefano Morozzi | 05/2021 |
| 2177 | 2^754138+213289 | 227019 | Enzo Doria | 09/2023 |
| 2178 | 2^754038+25 | 226989 | Stefano Morozzi | 05/2021 |
| 2179 | 2^753263+217133 | 226755 | Enzo Doria | 12/2023 |
| 2180 | 7*10^226479-9 | 226480 | Robert Price | 02/2023 |
| 2181 | (10^226381+1)/14973418875371 | 226368 | Alfred Reich | 06/2025 |
| 2182 | 2^751655+33893 | 226271 | Enzo Doria | 06/2024 |
| 2183 | 2^751426-764321 | 226202 | Enzo Doria | 12/2013 |
| 2184 | (18^180181-1)/17 | 226176 | Andy Steward | 04/2007 |
| 2185 | 2^750740-3 | 225996 | Paul Bourdelais | 03/2012 |
| 2186 | 2^750725+60227 | 225991 | Enzo Doria | 02/2016 |
| 2187 | 2^750525-113743 | 225931 | Enzo Doria | 09/2014 |
| 2188 | (2^750151-1)/(429934042631*7590093831289*397764574647511*8361437834787151*17383638888678527263) | 225744 | Dario Alpern | 10/2014 |
| 2189 | 2^749444-1861889 | 225606 | Enzo Doria | 12/2015 |
| 2190 | tau(311^16452) | 225560 | Nik Lygeros / Olivier Rozier / LR team | 10/2013 |
| 2191 | (3^472721+1)/9422189991086734893916 | 225524 | Paul Vanderveen | 06/2025 |
| 2192 | 2^749096+1876861 | 225501 | Enzo Doria | 07/2016 |
| 2193 | 2^748895+26213 | 225440 | Enzo Doria | 12/2023 |
| 2194 | (519643#+43033)/(23*1871*2706283) | 225379 | Makoto Morimoto | 08/2019 |
| 2195 | 2^748657+79607 | 225369 | Enzo Doria | 06/2016 |
| 2196 | (2^746920-11)/5 | 224845 | Stefano Morozzi | 08/2022 |
| 2197 | 2^746653-291583 | 224765 | Enzo Doria | 07/2015 |
| 2198 | 2^746461-114043 | 224708 | Enzo Doria | 11/2014 |
| 2199 | 2^746302+25 | 224660 | Stefano Morozzi | 05/2021 |
| 2200 | (202*10^224545-1)/3 | 224547 | Robert Price | 06/2023 |
| 2201 | (19*10^224533-37)/9 | 224534 | Alfred Reich | 12/2023 |
| 2202 | 2^745674+213949 | 224471 | Enzo Doria | 10/2023 |
| 2203 | 2^745098-350471 | 224297 | Enzo Doria | 06/2015 |
| 2204 | 2^745039-4897 | 224280 | Yves Minet | 03/2021 |
| 2205 | 23*10^224232-7 | 224234 | Robert Price | 10/2022 |
| 2206 | (154*10^224061-1)/9 | 224063 | Serge Batalov | 12/2014 |
| 2207 | 2^744211-1845787 | 224030 | Enzo Doria | 07/2015 |
| 2208 | 2^743773+37757 | 223898 | Enzo Doria | 10/2024 |
| 2209 | 2^743592-134579 | 223844 | Hans Havermann | 10/2018 |
| 2210 | 2^742452+3 | 223501 | Paul Bourdelais | 06/2019 |
| 2211 | 234178^9+9^234178 | 223463 | Anatoly F. Selevich | 07/2011 |
| 2212 | 47747^47747-2512^2512 | 223406 | Henri Lifchitz | 10/2024 |
| 2213 | 2^741651-461197 | 223260 | Enzo Doria | 07/2015 |
| 2214 | 10^223236-1001 | 223236 | Robert Price | 10/2022 |
| 2215 | 2^741362-1845251 | 223173 | Enzo Doria | 07/2015 |
| 2216 | 3^467546-5*2^467546 | 223077 | Jon Grantham | 08/2023 |
| 2217 | 2^740455-1863877 | 222900 | Enzo Doria | 12/2015 |
| 2218 | 2^740274+217519 | 222845 | Enzo Doria | 01/2024 |
| 2219 | (14*10^222718-41)/9 | 222719 | Serge Batalov | 01/2023 |
| 2220 | 2^739636-2792219 | 222653 | Enzo Doria | 02/2016 |
| 2221 | 11^213654-180 | 222498 | Enzo Doria | 01/2013 |
| 2222 | 2^738957-1859743 | 222449 | Enzo Doria | 11/2015 |
| 2223 | 4*10^222253-21 | 222254 | Robert Price | 12/2022 |
| 2224 | 2^737825+57 | 222108 | Stefano Morozzi | 05/2021 |
| 2225 | (54^128189+1)/55 | 222073 | Paul Bourdelais | 11/2018 |
| 2226 | 3^232689+1^232689+4^232689+1^232689+5^232689+9^232689 | 222042 | Henri Lifchitz | 03/2025 |
| 2227 | 2^737166+220099 | 221910 | Enzo Doria | 03/2024 |
| 2228 | (10^221654+179)/9 | 221654 | Serge Batalov | 12/2014 |
| 2229 | 2^736281+79817 | 221643 | Enzo Doria | 06/2016 |
| 2230 | 10^221631+247617 | 221632 | Patrick De Geest | 10/2013 |
| 2231 | 10^221631-9 | 221631 | Alexander Gramolin | 02/2011 |
| 2232 | 10^221628+7 | 221629 | Alfred Reich | 04/2021 |
| 2233 | 2^735970-1839821 | 221550 | Enzo Doria | 06/2015 |
| 2234 | 2^735367+60293 | 221368 | Enzo Doria | 03/2016 |
| 2235 | 77*10^221343+3 | 221345 | Robert Price | 11/2023 |
| 2236 | 299^299^299-582 | 221328 | Henri Lifchitz | 03/2025 |
| 2237 | (241^92821-1)/240 | 221099 | Anonymous | 04/2024 |
| 2238 | (202*10^221092-1)/3 | 221094 | Robert Price | 06/2023 |
| 2239 | (5^316297-1)/220142716 | 221074 | Paul Vanderveen | 05/2025 |
| 2240 | (29^151153+1)/30 | 221045 | Paul Bourdelais | 09/2017 |
| 2241 | 2^734228+24751 | 221025 | Enzo Doria | 10/2023 |
| 2242 | (28*10^220800+173)/3 | 220801 | Robert Price | 07/2024 |
| 2243 | 2^733264-2784089 | 220735 | Enzo Doria | 10/2015 |
| 2244 | 2^733114-24555 | 220690 | Enzo Doria | 09/2013 |
| 2245 | 2^731891-636259 | 220322 | Enzo Doria | 12/2013 |
| 2246 | 98*10^220185-9 | 220187 | Robert Price | 05/2023 |
| 2247 | 418319^39164+418318 | 220161 | Alfred Reich | 11/2023 |
| 2248 | 2^4^182829+182829^4^2 | 220149 | Henri Lifchitz | 03/2025 |
| 2249 | 2^731124-25539 | 220091 | Enzo Doria | 09/2013 |
| 2250 | 2^730972-462029 | 220045 | Enzo Doria | 07/2015 |
