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 | 23*10^234025-7 | 234027 | Robert Price | 10/2022 |
| 2002 | 2^777170+21489 | 233952 | Enzo Doria | 05/2024 |
| 2003 | Phi(78125,5517) | 233857 | Anonymous | 09/2022 |
| 2004 | 5^334359-3^334359-1 | 233707 | Jon Grantham | 08/2023 |
| 2005 | 2^776245-2792353 | 233674 | Enzo Doria | 02/2016 |
| 2006 | 49748^49748+49735^49735 | 233656 | Henri Lifchitz | 11/2024 |
| 2007 | 2^776060-114029 | 233618 | Enzo Doria | 11/2014 |
| 2008 | 2^775987-2789557 | 233596 | Enzo Doria | 12/2015 |
| 2009 | 2*10^233564-91 | 233565 | Robert Price | 02/2023 |
| 2010 | 2^775865+21489 | 233559 | Enzo Doria | 05/2024 |
| 2011 | 2^775672+1866721 | 233501 | Enzo Doria | 03/2016 |
| 2012 | 2^775238+57 | 233370 | Stefano Morozzi | 05/2021 |
| 2013 | (11^223999+1)/12 | 233270 | Paul Bourdelais | 02/2010 |
| 2014 | U(1302049) | 233238 | Serge Batalov | 07/2024 |
| 2015 | 2^774118+1885789 | 233033 | Enzo Doria | 04/2017 |
| 2016 | 21^176191-20^176191 | 232964 | Jean-Louis Charton | 01/2015 |
| 2017 | 2^773723+217523 | 232914 | Enzo Doria | 01/2024 |
| 2018 | 2^773679-113425 | 232901 | Enzo Doria | 08/2014 |
| 2019 | (7*10^232620+23)/3 | 232621 | Robert Price | 05/2023 |
| 2020 | 10^232599+192489 | 232600 | Patrick De Geest | 12/2013 |
| 2021 | 10^232599-3 | 232599 | Markus Tervooren | 10/2010 |
| 2022 | 2^772552-458879 | 232562 | Enzo Doria | 04/2015 |
| 2023 | 2^772214+1874899 | 232460 | Enzo Doria | 06/2016 |
| 2024 | 2^771994-1862771 | 232394 | Enzo Doria | 12/2015 |
| 2025 | 2^771889+1876037 | 232362 | Enzo Doria | 07/2016 |
| 2026 | 2^771660+1866511 | 232293 | Enzo Doria | 02/2016 |
| 2027 | 5^332150-18188 | 232163 | Enzo Doria | 06/2014 |
| 2028 | 2^771227+61121 | 232163 | Boyan Hu | 05/2024 |
| 2029 | 2^770623+212543 | 231981 | Enzo Doria | 09/2023 |
| 2030 | 3^485977-2^485977 | 231870 | Mike Oakes | 09/2009 |
| 2031 | 2^770082-114161 | 231818 | Enzo Doria | 01/2015 |
| 2032 | 2^769791+25523 | 231731 | Enzo Doria | 11/2023 |
| 2033 | 7^274120-2 | 231659 | Paul Bourdelais | 08/2023 |
| 2034 | (20^177967+1)/21 | 231540 | Paul Bourdelais | 05/2013 |
| 2035 | 2^769011+81 | 231496 | Henri Lifchitz | 01/2025 |
| 2036 | (71^125029-1)/105024430 | 231453 | Paul Vanderveen | 06/2025 |
| 2037 | (4*10^231254+23)/9 | 231254 | Serge Batalov | 11/2022 |
| 2038 | 2^768205+22217 | 231253 | Enzo Doria | 09/2023 |
| 2039 | 49262^49262-49247^49247 | 231163 | Henri Lifchitz | 11/2024 |
| 2040 | 2^767622-9221 | 231078 | Lelio R Paula | 01/2016 |
| 2041 | 2^767344+1880311 | 230994 | Enzo Doria | 09/2016 |
| 2042 | 8*10^230921-13 | 230922 | Robert Price | 08/2023 |
| 2043 | (3^483611-1)/2 | 230741 | Paul Bourdelais | 02/2010 |
| 2044 | (10^230706+179)/9 | 230706 | Serge Batalov | 12/2014 |
| 2045 | 2^766309+1875257 | 230682 | Enzo Doria | 06/2016 |
| 2046 | (26131^52441-1)/(26131^229-1) | 230629 | Ryan Propper | 11/2023 |
| 2047 | 2^765635+1879883 | 230480 | Enzo Doria | 09/2016 |
| 2048 | 43^141090+141090 | 230467 | Kellen Shenton | 06/2023 |
| 2049 | (26*10^230394-119)/3 | 230395 | Robert Price | 07/2023 |
| 2050 | 2^764348-113697 | 230092 | Enzo Doria | 09/2014 |
| 2051 | 2^764131+78863 | 230027 | Enzo Doria | 05/2016 |
| 2052 | 2^763701+60197 | 229897 | Enzo Doria | 03/2016 |
| 2053 | 4*10^229836+21 | 229837 | Robert Price | 12/2022 |
| 2054 | 2^763362+27799 | 229795 | Enzo Doria | 01/2024 |
| 2055 | 2^762841-25905 | 229639 | Enzo Doria | 10/2013 |
| 2056 | 2^762659+212633 | 229584 | Enzo Doria | 09/2023 |
| 2057 | 77*10^229211+3 | 229213 | Robert Price | 11/2023 |
| 2058 | 2^761117-113569 | 229120 | Enzo Doria | 08/2014 |
| 2059 | (29022^51529-1)/(29022^227-1) | 228947 | Ryan Propper | 11/2023 |
| 2060 | (98^114859+1)/99 | 228709 | Paul Bourdelais | 12/2018 |
| 2061 | 5*3^479067-2^479067 | 228574 | Jon Grantham | 08/2023 |
| 2062 | 2^758645+216011 | 228375 | Enzo Doria | 12/2023 |
| 2063 | (2^758231+1)/(3*27146942976539*73236839266867) | 228223 | Gord Palameta | 12/2018 |
| 2064 | 10^228208+111 | 228209 | Boyan Hu | 10/2024 |
| 2065 | (298*10^228177-7)/3 | 228179 | Robert Price | 02/2023 |
| 2066 | 2^757985-2790013 | 228177 | Enzo Doria | 12/2015 |
| 2067 | 34*10^228129-9 | 228131 | Robert Price | 05/2023 |
| 2068 | 2^757038-1862081 | 227892 | Enzo Doria | 12/2015 |
| 2069 | 2^756839+95849 | 227832 | Makoto Morimoto | 10/2013 |
| 2071 | (2^756839+6989)/756091 | 227826 | Makoto Morimoto | 09/2016 |
| 2070 | (2^756839-50211)/(137*3203) | 227826 | Makoto Morimoto | 08/2019 |
| 2072 | 2^756773-112723 | 227812 | Enzo Doria | 07/2014 |
| 2073 | (7*10^(2*113887+1)+9*10^113887-7)/9 | 227775 | Robert Price | 08/2024 |
| 2074 | (10^227542)/(227542^10) | 227489 | Henri Lifchitz | 05/2025 |
| 2075 | 524309#+616367 | 227431 | Makoto Morimoto | 02/2016 |
| 2076 | 2^755404+226575 | 227400 | Enzo Doria | 09/2024 |
| 2077 | 2^755116+81 | 227313 | Henri Lifchitz | 11/2024 |
| 2078 | 2^755097-114193 | 227307 | Enzo Doria | 12/2014 |
| 2079 | 7*10^227178+39 | 227179 | Robert Price | 01/2023 |
| 2080 | 9*10^227153-89 | 227154 | Robert Price | 02/2023 |
| 2081 | 2^754473-2791513 | 227120 | Enzo Doria | 01/2016 |
| 2082 | 2^754376+25 | 227090 | Stefano Morozzi | 05/2021 |
| 2083 | 2^754138+213289 | 227019 | Enzo Doria | 09/2023 |
| 2084 | 2^754038+25 | 226989 | Stefano Morozzi | 05/2021 |
| 2085 | 2^753263+217133 | 226755 | Enzo Doria | 12/2023 |
| 2086 | 7*10^226479-9 | 226480 | Robert Price | 02/2023 |
| 2087 | (10^226381+1)/14973418875371 | 226368 | Alfred Reich | 06/2025 |
| 2088 | 2^751655+33893 | 226271 | Enzo Doria | 06/2024 |
| 2089 | 2^751426-764321 | 226202 | Enzo Doria | 12/2013 |
| 2090 | (18^180181-1)/17 | 226176 | Andy Steward | 04/2007 |
| 2091 | 2^750740-3 | 225996 | Paul Bourdelais | 03/2012 |
| 2092 | 2^750725+60227 | 225991 | Enzo Doria | 02/2016 |
| 2093 | 2^750525-113743 | 225931 | Enzo Doria | 09/2014 |
| 2094 | (2^750151-1)/(429934042631*7590093831289*397764574647511*8361437834787151*17383638888678527263) | 225744 | Dario Alpern | 10/2014 |
| 2095 | 2^749444-1861889 | 225606 | Enzo Doria | 12/2015 |
| 2096 | tau(311^16452) | 225560 | Nik Lygeros / Olivier Rozier / LR team | 10/2013 |
| 2097 | (3^472721+1)/9422189991086734893916 | 225524 | Paul Vanderveen | 06/2025 |
| 2098 | 2^749096+1876861 | 225501 | Enzo Doria | 07/2016 |
| 2099 | 2^748895+26213 | 225440 | Enzo Doria | 12/2023 |
| 2100 | (519643#+43033)/(23*1871*2706283) | 225379 | Makoto Morimoto | 08/2019 |
| 2101 | 2^748657+79607 | 225369 | Enzo Doria | 06/2016 |
| 2102 | (2^746920-11)/5 | 224845 | Stefano Morozzi | 08/2022 |
| 2103 | 2^746653-291583 | 224765 | Enzo Doria | 07/2015 |
| 2104 | 2^746461-114043 | 224708 | Enzo Doria | 11/2014 |
| 2105 | 2^746302+25 | 224660 | Stefano Morozzi | 05/2021 |
| 2106 | (202*10^224545-1)/3 | 224547 | Robert Price | 06/2023 |
| 2107 | (19*10^224533-37)/9 | 224534 | Alfred Reich | 12/2023 |
| 2108 | 2^745674+213949 | 224471 | Enzo Doria | 10/2023 |
| 2109 | 2^745098-350471 | 224297 | Enzo Doria | 06/2015 |
| 2110 | 2^745039-4897 | 224280 | Yves Minet | 03/2021 |
| 2111 | 23*10^224232-7 | 224234 | Robert Price | 10/2022 |
| 2112 | (154*10^224061-1)/9 | 224063 | Serge Batalov | 12/2014 |
| 2113 | 2^744211-1845787 | 224030 | Enzo Doria | 07/2015 |
| 2114 | 2^743773+37757 | 223898 | Enzo Doria | 10/2024 |
| 2115 | 2^743592-134579 | 223844 | Hans Havermann | 10/2018 |
| 2116 | 2^742452+3 | 223501 | Paul Bourdelais | 06/2019 |
| 2117 | 234178^9+9^234178 | 223463 | Anatoly F. Selevich | 07/2011 |
| 2118 | 47747^47747-2512^2512 | 223406 | Henri Lifchitz | 10/2024 |
| 2119 | 2^741651-461197 | 223260 | Enzo Doria | 07/2015 |
| 2120 | 10^223236-1001 | 223236 | Robert Price | 10/2022 |
| 2121 | 2^741362-1845251 | 223173 | Enzo Doria | 07/2015 |
| 2122 | 3^467546-5*2^467546 | 223077 | Jon Grantham | 08/2023 |
| 2123 | 2^740455-1863877 | 222900 | Enzo Doria | 12/2015 |
| 2124 | 2^740274+217519 | 222845 | Enzo Doria | 01/2024 |
| 2125 | (14*10^222718-41)/9 | 222719 | Serge Batalov | 01/2023 |
| 2126 | 2^739636-2792219 | 222653 | Enzo Doria | 02/2016 |
| 2127 | 11^213654-180 | 222498 | Enzo Doria | 01/2013 |
| 2128 | 2^738957-1859743 | 222449 | Enzo Doria | 11/2015 |
| 2129 | 4*10^222253-21 | 222254 | Robert Price | 12/2022 |
| 2130 | 2^737825+57 | 222108 | Stefano Morozzi | 05/2021 |
| 2131 | (54^128189+1)/55 | 222073 | Paul Bourdelais | 11/2018 |
| 2132 | 3^232689+1^232689+4^232689+1^232689+5^232689+9^232689 | 222042 | Henri Lifchitz | 03/2025 |
| 2133 | 2^737166+220099 | 221910 | Enzo Doria | 03/2024 |
| 2134 | (10^221654+179)/9 | 221654 | Serge Batalov | 12/2014 |
| 2135 | 2^736281+79817 | 221643 | Enzo Doria | 06/2016 |
| 2136 | 10^221631+247617 | 221632 | Patrick De Geest | 10/2013 |
| 2137 | 10^221631-9 | 221631 | Alexander Gramolin | 02/2011 |
| 2138 | 10^221628+7 | 221629 | Alfred Reich | 04/2021 |
| 2139 | 2^735970-1839821 | 221550 | Enzo Doria | 06/2015 |
| 2140 | 2^735367+60293 | 221368 | Enzo Doria | 03/2016 |
| 2141 | 77*10^221343+3 | 221345 | Robert Price | 11/2023 |
| 2142 | 299^299^299-582 | 221328 | Henri Lifchitz | 03/2025 |
| 2143 | (241^92821-1)/240 | 221099 | Anonymous | 04/2024 |
| 2144 | (202*10^221092-1)/3 | 221094 | Robert Price | 06/2023 |
| 2145 | (5^316297-1)/220142716 | 221074 | Paul Vanderveen | 05/2025 |
| 2146 | (29^151153+1)/30 | 221045 | Paul Bourdelais | 09/2017 |
| 2147 | 2^734228+24751 | 221025 | Enzo Doria | 10/2023 |
| 2148 | (28*10^220800+173)/3 | 220801 | Robert Price | 07/2024 |
| 2149 | 2^733264-2784089 | 220735 | Enzo Doria | 10/2015 |
| 2150 | 2^733114-24555 | 220690 | Enzo Doria | 09/2013 |
| 2151 | 2^731891-636259 | 220322 | Enzo Doria | 12/2013 |
| 2152 | 98*10^220185-9 | 220187 | Robert Price | 05/2023 |
| 2153 | 418319^39164+418318 | 220161 | Alfred Reich | 11/2023 |
| 2154 | 2^4^182829+182829^4^2 | 220149 | Henri Lifchitz | 03/2025 |
| 2155 | 2^731124-25539 | 220091 | Enzo Doria | 09/2013 |
| 2156 | 2^730972-462029 | 220045 | Enzo Doria | 07/2015 |
| 2157 | 2^730833+1868627 | 220003 | Enzo Doria | 04/2016 |
| 2158 | 2^730645-2787133 | 219947 | Enzo Doria | 11/2015 |
| 2159 | 2^730547-25581 | 219917 | Enzo Doria | 09/2013 |
| 2160 | (113*13^197420-5)/12 | 219916 | Anonymous | 11/2022 |
| 2161 | (13^197420*113-5)/12 | 219916 | Eric Chen | 10/2023 |
| 2162 | 2^730460+82291 | 219891 | Enzo Doria | 09/2016 |
| 2163 | (5*10^219847-101)/3 | 219848 | Robert Price | 08/2023 |
| 2164 | (2^730339+1)/(3*27839062003*7943469324347) | 219831 | Gord Palameta | 12/2018 |
| 2165 | L(1051849) | 219824 | Renaud Lifchitz | 03/2009 |
| 2166 | 3*2^730149+5 | 219798 | Jon Grantham | 07/2023 |
| 2167 | 8*10^219740-3 | 219741 | Serge Batalov | 01/2023 |
| 2168 | 11^210961-240 | 219694 | Enzo Doria | 01/2013 |
| 2169 | (26*10^219639-77)/3 | 219640 | Robert Price | 03/2023 |
| 2170 | 2^729611-113437 | 219635 | Enzo Doria | 08/2014 |
| 2171 | 7^259710-2 | 219481 | Paul Bourdelais | 01/2021 |
| 2172 | F(1049897) | 219416 | Henri Lifchitz | 10/2008 |
| 2173 | (1488^69151-1)/1487 | 219386 | Alexander Zhirkov | 02/2023 |
| 2174 | 2^728604+1879321 | 219332 | Enzo Doria | 10/2016 |
| 2175 | 33^144412+2 | 219292 | Robert Price | 04/2015 |
| 2176 | 2^728277-183313 | 219234 | Hans Havermann | 10/2018 |
| 2177 | 2^727998-1862711 | 219150 | Enzo Doria | 12/2015 |
| 2178 | (29*10^219124+91)/3 | 219125 | Robert Price | 12/2022 |
| 2179 | 2^727729-114073 | 219069 | Enzo Doria | 12/2014 |
| 2180 | 2^727496-1851809 | 218999 | Enzo Doria | 08/2015 |
| 2181 | 2^727025+25907 | 218857 | Enzo Doria | 12/2023 |
| 2182 | 2^726591+2793143 | 218726 | Enzo Doria | 02/2016 |
| 2183 | (7*10^218644+17)/3 | 218645 | Robert Price | 06/2023 |
| 2184 | 2^725534-2791931 | 218408 | Enzo Doria | 02/2016 |
| 2185 | Phi(220531,10)/2686456812680882641 | 217774 | Makoto Kamada | 10/2020 |
| 2186 | 2^722184+1877821 | 217400 | Enzo Doria | 08/2016 |
| 2187 | (109*10^217360-1)/9 | 217362 | Serge Batalov | 12/2014 |
| 2188 | 2^721721-4453 | 217260 | Yves Minet | 03/2021 |
| 2189 | 10^216950+49 | 216951 | Robert Price | 02/2023 |
| 2190 | 281*499979#/46410-2702372 | 216849 | Robert Smith | 08/2016 |
| 2191 | 281*499979#/46410+2400766 | 216849 | Robert Smith | 08/2016 |
| 2192 | tau(311^15786) | 216429 | Nik Lygeros / Olivier Rozier / LR team | 10/2013 |
| 2193 | 2^718756-114107 | 216368 | Enzo Doria | 12/2014 |
| 2194 | 2^717672+121 | 216041 | Stefano Morozzi | 05/2021 |
| 2195 | 2^717305+80327 | 215931 | Enzo Doria | 07/2016 |
| 2196 | 2^717069-59773 | 215860 | Enzo Doria | 10/2015 |
| 2197 | 10^215802+33 | 215803 | Robert Price | 08/2023 |
| 2198 | 30^146021-29^146021 | 215691 | Jean-Louis Charton | 09/2018 |
| 2199 | 277^88301-276^88301 | 215674 | Jean-Louis Charton | 06/2012 |
| 2200 | 2^716428+215011 | 215667 | Enzo Doria | 11/2023 |
| 2201 | (13*10^215592-43)/3 | 215593 | Robert Price | 08/2023 |
| 2202 | p(41292)#+p(41292+1) | 215450 | Henri Lifchitz | 11/2024 |
| 2203 | (29^147319-1)/466757843690852 | 215425 | Paul Vanderveen | 06/2025 |
| 2204 | 227^91413-40 | 215372 | Enzo Doria | 04/2015 |
| 2205 | (2^715008-21)/5 | 215239 | Stefano Morozzi | 08/2022 |
| 2206 | 2^714717+782897 | 215152 | Enzo Doria | 11/2016 |
| 2207 | (19^168013-1)/80910356454 | 214837 | Paul Vanderveen | 05/2025 |
| 2208 | tau(373^15186) | 214796 | Nik Lygeros / Olivier Rozier / LR team | 10/2013 |
| 2209 | 2^713241+1879157 | 214707 | Enzo Doria | 08/2016 |
| 2210 | (23*10^214633+91)/3 | 214634 | Robert Price | 03/2023 |
| 2211 | 11^206081-10^206081 | 214612 | Jean-Louis Charton | 10/2011 |
| 2212 | 2^712801-69553 | 214575 | Enzo Doria | 01/2016 |
| 2213 | 2^712603-25357 | 214515 | Enzo Doria | 09/2013 |
| 2214 | 2^711721-1846723 | 214250 | Enzo Doria | 07/2015 |
| 2215 | 2^710730-396765 | 213952 | Enzo Doria | 09/2013 |
| 2216 | (19*10^213934-37)/9 | 213935 | Alfred Reich | 12/2023 |
| 2217 | (19*10^213730-37)/9 | 213731 | Alfred Reich | 12/2023 |
| 2218 | (713^74897-1)/712 | 213685 | Jinyuan Wang | 08/2023 |
| 2219 | 2^709773+25907 | 213663 | Enzo Doria | 12/2023 |
| 2220 | 2^708468-114329 | 213271 | Enzo Doria | 02/2015 |
| 2221 | 2^708293+27557 | 213218 | Enzo Doria | 01/2024 |
| 2222 | 379*10^213199+9 | 213202 | Jason Yuen | 01/2025 |
| 2223 | 2^707277+28997 | 212912 | Enzo Doria | 02/2024 |
| 2224 | (163*10^212779-1)/9 | 212781 | Serge Batalov | 12/2014 |
| 2225 | 2^706838-69041 | 212780 | Enzo Doria | 11/2015 |
| 2226 | 2^705653+25907 | 212423 | Enzo Doria | 12/2023 |
| 2227 | 22*10^212339+7 | 212341 | Robert Price | 10/2022 |
| 2228 | 2^704577-113871 | 212099 | Enzo Doria | 10/2014 |
| 2229 | (2^704548-19)/3 | 212090 | Stefano Morozzi | 08/2022 |
| 2230 | 2^704110-2792441 | 211959 | Enzo Doria | 02/2016 |
| 2231 | 2^704084+28531 | 211951 | Enzo Doria | 02/2024 |
| 2232 | 2^703943-1862947 | 211908 | Enzo Doria | 12/2015 |
| 2233 | (60^119083+1)/61 | 211746 | Paul Bourdelais | 10/2018 |
| 2234 | (184*10^211682-1)/3 | 211684 | Robert Price | 12/2022 |
| 2235 | (10^211610-91)/9 | 211610 | Serge Batalov | 12/2014 |
| 2236 | 227^89797+2 | 211565 | Lelio R Paula | 08/2012 |
| 2237 | 2^702194-3 | 211382 | Paul Bourdelais | 03/2012 |
| 2238 | 2^702064+1874911 | 211343 | Enzo Doria | 07/2016 |
| 2239 | 2^701968-113873 | 211314 | Enzo Doria | 10/2014 |
| 2240 | (14*10^211262-41)/9 | 211263 | Serge Batalov | 01/2023 |
| 2241 | 2^701713-113779 | 211237 | Enzo Doria | 09/2014 |
| 2242 | 2^701616-216803 | 211208 | Enzo Doria | 01/2024 |
| 2243 | 2^701449-25201 | 211158 | Enzo Doria | 09/2013 |
| 2244 | 2^701403-2786977 | 211144 | Enzo Doria | 11/2015 |
| 2245 | 2^701189-25423 | 211079 | Enzo Doria | 09/2013 |
| 2246 | 2^701162-459161 | 211071 | Enzo Doria | 05/2015 |
| 2247 | 2^700793+219407 | 210960 | Enzo Doria | 03/2024 |
| 2248 | (24^152783-1)/23 | 210872 | Paul Bourdelais | 04/2018 |
| 2249 | 2^700400+9385 | 210842 | Lelio R Paula | 01/2014 |
| 2250 | 2^700304-17 | 210813 | Stefano Morozzi | 07/2022 |
