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
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See the Latest PRPs
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Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
2001 | (238*10^209715-1)/3 | 209717 | Robert Price | 09/2023 |
2002 | 6^269407+5 | 209640 | Paul Bourdelais | 02/2021 |
2003 | (2^696343-1)/11141489/36009913139329 | 209600 | Tony Prest / Never Odd Or Even | 02/2014 |
2004 | 2^696254-115151 | 209594 | Enzo Doria | 06/2015 |
2005 | 2^695841+225 | 209470 | Henri Lifchitz | 01/2025 |
2006 | (35^135623+1)/36 | 209410 | Paul Bourdelais | 07/2018 |
2007 | 7*10^209161+39 | 209162 | Robert Price | 01/2023 |
2008 | 2^694633+1887257 | 209106 | Enzo Doria | 05/2017 |
2009 | fibonacci(999790)-4 | 208944 | Jon Grantham | 08/2023 |
2010 | 2^693959+180923 | 208903 | Enzo Doria | 07/2016 |
2011 | (2^693747-11)/3 | 208839 | Stefano Morozzi | 08/2022 |
2012 | 2^693462-1847561 | 208753 | Enzo Doria | 07/2015 |
2013 | 2^690890-59981 | 207979 | Enzo Doria | 11/2015 |
2014 | (38^131591+1)/39 | 207884 | Paul Bourdelais | 07/2018 |
2015 | 3*2^690484+5 | 207857 | Jon Grantham | 07/2023 |
2016 | 2^690163+1877063 | 207760 | Enzo Doria | 07/2016 |
2017 | 7^245608-2 | 207563 | Paul Bourdelais | 01/2021 |
2018 | (67*10^207556+23)/9 | 207557 | Serge Batalov | 01/2023 |
2019 | 2^689286-29381 | 207496 | Enzo Doria | 08/2015 |
2020 | 2^689122-114521 | 207447 | Enzo Doria | 04/2015 |
2021 | 9*10^207254-89 | 207255 | Robert Price | 02/2023 |
2022 | 2^688373+6077 | 207221 | Enzo Doria | 02/2016 |
2023 | 2^688201+1875527 | 207170 | Enzo Doria | 07/2016 |
2024 | (42^127609+1)/43 | 207140 | Paul Bourdelais | 07/2018 |
2025 | 2^687938+213589 | 207090 | Enzo Doria | 10/2023 |
2026 | 2^687619+81563 | 206994 | Enzo Doria | 08/2016 |
2027 | 3*10^206927+37 | 206928 | Robert Price | 08/2023 |
2028 | 2^687383+21803 | 206923 | Enzo Doria | 09/2023 |
2029 | (11*10^206688+19)/3 | 206689 | Robert Price | 07/2024 |
2030 | 2^686572-1845299 | 206679 | Enzo Doria | 07/2015 |
2031 | (21^156217-1)/20 | 206552 | Paul Bourdelais | 04/2010 |
2032 | 2^685970+39415 | 206498 | Enzo Doria | 11/2024 |
2033 | (2^685739+1)/(3*87774593) | 206420 | Gord Palameta | 08/2018 |
2034 | 2^685578+3 | 206380 | Paul Bourdelais | 04/2012 |
2035 | 2^685078+218599 | 206230 | Enzo Doria | 01/2024 |
2036 | 2^684836-49349 | 206157 | Enzo Doria | 10/2015 |
2037 | (73^110603-1)/72 | 206088 | Paul Bourdelais | 06/2018 |
2038 | 2^684163-2790967 | 205954 | Enzo Doria | 12/2015 |
2039 | 326^81943-325^81943 | 205941 | Jean-Louis Charton | 07/2012 |
2040 | (2^684127-1)/23765203727 | 205933 | Jens K. Andersen | 04/2009 |
2041 | (68*10^205510+13)/9 | 205511 | Serge Batalov | 01/2023 |
2042 | 4^341233-3^341233 | 205443 | Jean-Louis Charton | 01/2006 |
2043 | 2^682414+215029 | 205428 | Enzo Doria | 11/2023 |
2044 | (963^68821-1)/962 | 205334 | Jinyuan Wang | 01/2024 |
2045 | (43*10^205183-421)/9 | 205184 | Robert Price | 10/2023 |
2046 | 2^681545+467 | 205166 | Lelio R Paula | 11/2013 |
2047 | 2^681306+81049 | 205094 | Enzo Doria | 07/2016 |
2048 | 2^680697+1877057 | 204911 | Enzo Doria | 07/2016 |
2049 | 2^680415+71783 | 204826 | Enzo Doria | 04/2016 |
2050 | 10^204764-8001 | 204764 | Robert Price | 03/2023 |
2051 | (26*10^204730-77)/3 | 204731 | Robert Price | 03/2023 |
2052 | 2^679860-459995 | 204659 | Enzo Doria | 06/2015 |
2053 | 2^679593+1879547 | 204578 | Enzo Doria | 09/2016 |
2054 | 2^678899+220073 | 204369 | Enzo Doria | 03/2024 |
2055 | 2^678753+21677 | 204326 | Enzo Doria | 08/2023 |
2056 | 2^678651+1875023 | 204295 | Enzo Doria | 07/2016 |
2057 | 2^678561+678561 | 204268 | Henri Lifchitz | 05/2006 |
2058 | 5*3^427884+2^427884 | 204154 | Jon Grantham | 08/2023 |
2059 | 2^678101-114043 | 204129 | Enzo Doria | 11/2014 |
2060 | 2^678028+1875631 | 204107 | Enzo Doria | 06/2016 |
2061 | 2^677721+28607 | 204015 | Enzo Doria | 01/2024 |
2062 | (19*10^203798-7)/3 | 203799 | Robert Price | 12/2023 |
2063 | 2^676992-59783 | 203795 | Enzo Doria | 10/2015 |
2064 | 2^676972+1866871 | 203789 | Enzo Doria | 03/2016 |
2065 | 2^676815+22583 | 203742 | Enzo Doria | 09/2023 |
2066 | 2^676761-9 | 203726 | Robert Price | 01/2017 |
2067 | 2^676592-23 | 203675 | Stefano Morozzi | 07/2022 |
2068 | 2^676563-2792407 | 203666 | Enzo Doria | 02/2016 |
2069 | 2^676306-114713 | 203589 | Enzo Doria | 04/2015 |
2070 | (2^675977-1)/(1686378749257*7171117283326998925471) | 203456 | Dario Alpern | 07/2015 |
2071 | 6*10^203365+53 | 203366 | Robert Price | 09/2023 |
2072 | 10247^50678-50678^10247 | 203250 | Norbert Schneider | 03/2022 |
2073 | 2^675106-73241 | 203228 | Stefano Morozzi | 02/2025 |
2074 | 2^675103-188727 | 203227 | Stefano Morozzi | 02/2025 |
2075 | 2^675104-16199 | 203227 | Stefano Morozzi | 02/2025 |
2076 | 2^675104-195303 | 203227 | Stefano Morozzi | 02/2025 |
2077 | 2^675105-94521 | 203227 | Stefano Morozzi | 02/2025 |
2078 | 2^675100-2775 | 203226 | Stefano Morozzi | 02/2025 |
2079 | 2^675098-170703 | 203225 | Stefano Morozzi | 02/2025 |
2080 | 2^675093-162123 | 203224 | Stefano Morozzi | 02/2025 |
2081 | 2^675093-48955 | 203224 | Stefano Morozzi | 02/2025 |
2082 | 2^675095-73591 | 203224 | Stefano Morozzi | 02/2025 |
2083 | 2^675095-89937 | 203224 | Stefano Morozzi | 02/2025 |
2084 | 2^675092-144539 | 203223 | Stefano Morozzi | 02/2025 |
2085 | 2^675086-186387 | 203222 | Stefano Morozzi | 02/2025 |
2086 | 2^675088-68505 | 203222 | Stefano Morozzi | 02/2025 |
2087 | 2^675083-149199 | 203221 | Stefano Morozzi | 02/2025 |
2088 | 2^675081-91425 | 203220 | Stefano Morozzi | 02/2025 |
2089 | 2^675082-80213 | 203220 | Stefano Morozzi | 02/2025 |
2090 | 2^675077-152683 | 203219 | Stefano Morozzi | 02/2025 |
2091 | 2^675077-79213 | 203219 | Stefano Morozzi | 02/2025 |
2092 | 2^675073-149065 | 203218 | Stefano Morozzi | 02/2025 |
2093 | 2^675073-19663 | 203218 | Stefano Morozzi | 02/2025 |
2094 | 2^675069-147135 | 203217 | Stefano Morozzi | 02/2025 |
2095 | 2^675069-161461 | 203217 | Stefano Morozzi | 02/2025 |
2096 | 2^675071-175189 | 203217 | Stefano Morozzi | 02/2025 |
2097 | 2^675060+119983 | 203214 | Stefano Morozzi | 02/2025 |
2098 | 2^675060+161301 | 203214 | Stefano Morozzi | 02/2025 |
2099 | 2^675061-187773 | 203214 | Stefano Morozzi | 02/2025 |
2100 | 2^675062-92193 | 203214 | Stefano Morozzi | 02/2025 |
2101 | 2^675058-10403 | 203213 | Stefano Morozzi | 01/2025 |
2102 | 2^675058-40337 | 203213 | Stefano Morozzi | 01/2025 |
2103 | 2^675057+123557 | 203213 | Stefano Morozzi | 02/2025 |
2104 | 2^675057+172475 | 203213 | Stefano Morozzi | 02/2025 |
2105 | 2^675053-4801 | 203212 | Stefano Morozzi | 01/2025 |
2106 | 2^675054-174341 | 203212 | Stefano Morozzi | 01/2025 |
2107 | 2^675054-53697 | 203212 | Stefano Morozzi | 01/2025 |
2108 | 2^675054+24825 | 203212 | Stefano Morozzi | 02/2025 |
2109 | 2^675055+160265 | 203212 | Stefano Morozzi | 02/2025 |
2110 | 2^675050-30015 | 203211 | Stefano Morozzi | 01/2025 |
2111 | 2^675051-85941 | 203211 | Stefano Morozzi | 01/2025 |
2112 | 2^675051+30885 | 203211 | Stefano Morozzi | 02/2025 |
2113 | 2^675052+12537 | 203211 | Stefano Morozzi | 02/2025 |
2114 | 2^675047-100299 | 203210 | Stefano Morozzi | 01/2025 |
2115 | 2^675048-97313 | 203210 | Stefano Morozzi | 01/2025 |
2116 | 2^675046+118119 | 203210 | Stefano Morozzi | 02/2025 |
2117 | 2^675048+128941 | 203210 | Stefano Morozzi | 02/2025 |
2118 | 2^675049+136359 | 203210 | Stefano Morozzi | 02/2025 |
2119 | 2^675044-81087 | 203209 | Stefano Morozzi | 01/2025 |
2120 | 2^675042-179811 | 203208 | Stefano Morozzi | 01/2025 |
2121 | 2^675036-192939 | 203207 | Stefano Morozzi | 01/2025 |
2122 | 2^675037-17853 | 203207 | Stefano Morozzi | 01/2025 |
2123 | 2^675036+47101 | 203207 | Stefano Morozzi | 02/2025 |
2124 | 2^675038+189589 | 203207 | Stefano Morozzi | 02/2025 |
2125 | 2^675034-169727 | 203206 | Stefano Morozzi | 01/2025 |
2126 | 2^675035-173055 | 203206 | Stefano Morozzi | 01/2025 |
2127 | 2^675035-73551 | 203206 | Stefano Morozzi | 01/2025 |
2128 | 2^675033+79109 | 203206 | Stefano Morozzi | 02/2025 |
2129 | 2^675034+154057 | 203206 | Stefano Morozzi | 02/2025 |
2130 | 2^675030+109245 | 203205 | Stefano Morozzi | 01/2025 |
2131 | 2^675030-160047 | 203205 | Stefano Morozzi | 01/2025 |
2132 | 2^675027+106733 | 203204 | Stefano Morozzi | 01/2025 |
2133 | 2^675026-67377 | 203204 | Stefano Morozzi | 01/2025 |
2134 | 2^675021+13335 | 203202 | Stefano Morozzi | 01/2025 |
2135 | 2^675020-180497 | 203202 | Stefano Morozzi | 01/2025 |
2136 | 2^675016+174777 | 203201 | Stefano Morozzi | 01/2025 |
2137 | 2^675017+128379 | 203201 | Stefano Morozzi | 01/2025 |
2138 | 2^675017+171249 | 203201 | Stefano Morozzi | 01/2025 |
2139 | 2^675018+86517 | 203201 | Stefano Morozzi | 01/2025 |
2140 | 2^675019+125891 | 203201 | Stefano Morozzi | 01/2025 |
2141 | 2^675019+163251 | 203201 | Stefano Morozzi | 01/2025 |
2142 | 2^675016-170847 | 203201 | Stefano Morozzi | 01/2025 |
2143 | 2^675019-44755 | 203201 | Stefano Morozzi | 01/2025 |
2144 | 2^675015+120225 | 203200 | Stefano Morozzi | 01/2025 |
2145 | 2^675013-69831 | 203200 | Stefano Morozzi | 01/2025 |
2146 | 2^675014-3897 | 203200 | Stefano Morozzi | 01/2025 |
2147 | 2^675006+75357 | 203198 | Stefano Morozzi | 01/2025 |
2148 | 2^675008+112231 | 203198 | Stefano Morozzi | 01/2025 |
2149 | 2^675007-123309 | 203198 | Stefano Morozzi | 01/2025 |
2150 | 2^675003+52529 | 203197 | Stefano Morozzi | 01/2025 |
2151 | 2^675002+50595 | 203196 | Stefano Morozzi | 01/2025 |
2152 | 2^674627-25161 | 203083 | Enzo Doria | 09/2013 |
2153 | 2^674603-69337 | 203076 | Enzo Doria | 12/2015 |
2154 | (182*10^203048+1)/3 | 203050 | Robert Price | 09/2023 |
2155 | 2^674459+74213 | 203033 | Enzo Doria | 04/2016 |
2156 | 2^674116-458879 | 202930 | Enzo Doria | 04/2015 |
2157 | 2^674076-114755 | 202918 | Enzo Doria | 04/2015 |
2158 | 5^289937-4^289937 | 202658 | Jean-Louis Charton | 03/2013 |
2159 | 5^289926-289926^5 | 202650 | Henri Lifchitz | 07/2024 |
2160 | (2^673184-7)/3 | 202649 | Stefano Morozzi | 08/2022 |
2161 | (467617#+14534)/(2^2*13*43) | 202603 | Makoto Morimoto | 06/2019 |
2162 | (155^92479-1)/154 | 202558 | Anonymous | 06/2024 |
2163 | 2^672773+219407 | 202525 | Enzo Doria | 03/2024 |
2164 | 1374^64531-64531^1374 | 202498 | Henri Lifchitz | 10/2024 |
2165 | 2^672556-1835519 | 202460 | Enzo Doria | 04/2015 |
2166 | (7*10^202267+179)/3 | 202268 | Robert Price | 02/2023 |
2167 | 2^671446-351401 | 202126 | Enzo Doria | 07/2015 |
2168 | 2^671373+77747 | 202104 | Enzo Doria | 05/2016 |
2169 | (2*10^202059+7)/9 | 202059 | Rytis Slatkevicius | 01/2023 |
2170 | 98*10^202021-9 | 202023 | Robert Price | 05/2023 |
2171 | 2^670726-114845 | 201909 | Enzo Doria | 05/2015 |
2172 | 2^670539-25045 | 201853 | Enzo Doria | 09/2013 |
2173 | 10^201801-93 | 201801 | Robert Price | 02/2023 |
2174 | 43284^43519-43519^43284 | 201769 | Norbert Schneider | 08/2018 |
2175 | 2^670213+282317 | 201755 | Enzo Doria | 09/2016 |
2176 | 2^670133+89 | 201731 | Stefano Morozzi | 05/2021 |
2177 | 2^669854-113501 | 201647 | Enzo Doria | 08/2014 |
2178 | 2^669718+81619 | 201606 | Enzo Doria | 08/2016 |
2179 | (299*10^201547-17)/3 | 201549 | Robert Price | 02/2023 |
2180 | (145*10^201504-1)/9 | 201506 | Serge Batalov | 12/2014 |
2181 | 2^668938-1839821 | 201371 | Enzo Doria | 06/2015 |
2182 | (198^87623-1)/197 | 201239 | Anonymous | 06/2024 |
2183 | 2^668492+1879303 | 201237 | Enzo Doria | 08/2016 |
2184 | 7*10^201140-87 | 201141 | Robert Price | 03/2023 |
2185 | 6^258413-5^258413 | 201085 | Jean-Louis Charton | 03/2013 |
2186 | 10194^50161-50161^10194 | 201063 | Norbert Schneider | 09/2020 |
2187 | 2^667894+1875589 | 201057 | Enzo Doria | 06/2016 |
2188 | 2^667569-1836559 | 200959 | Enzo Doria | 05/2015 |
2189 | (172*10^200746-1)/9 | 200748 | Serge Batalov | 12/2014 |
2190 | (166^90407-1)/165 | 200712 | Anonymous | 06/2024 |
2191 | 2^666430+782569 | 200616 | Enzo Doria | 10/2016 |
2192 | (13*10^200610-43)/3 | 200611 | Robert Price | 08/2023 |
2193 | (8*10^200408-11)/3 | 200409 | Robert Price | 07/2023 |
2194 | p(38635)#-p(38635+1) | 200356 | Henri Lifchitz | 11/2024 |
2195 | (19*10^200260+101)/3 | 200261 | Robert Price | 06/2023 |
2196 | 43183^43183+4^4 | 200167 | Serge Batalov | 04/2024 |
2197 | (86^103471+1)/87 | 200163 | Paul Bourdelais | 05/2018 |
2198 | (10^(2*100072+1)+36*10^100072-1)/9 | 200145 | Robert Price | 09/2023 |
2199 | 2^664778+34789 | 200119 | Enzo Doria | 07/2024 |
2200 | 103*(10^100000+20110)^2-4707*(10^100000+20110)+50383 | 200003 | Robert Price | 05/2017 |
2201 | 103*(10^100000+33798)^2-4707*(10^100000+33798)+50383 | 200003 | Robert Price | 01/2018 |
2202 | numbpart(32235776596) | 200002 | Serge Batalov | 04/2017 |
2203 | (10^200001+149)/3 | 200001 | Serge Batalov | 12/2014 |
2204 | 10^200000+571791 | 200001 | Patrick De Geest | 08/2019 |
2205 | (3^419180-621444)/3 | 200000 | Stefano Morozzi | 06/2019 |
2206 | (3^419180-1941384)/3 | 200000 | Stefano Morozzi | 08/2019 |
2207 | 10^200000-45557 | 200000 | Patrick De Geest | 08/2019 |
2208 | (10^200000-1)/9-10^58838 | 200000 | Akihiko Yoshida | 04/2020 |
2209 | 2593604092947240127723272^8192+2593604092947240127722755^8192 | 200000 | Youcef Lemsafer | 01/2023 |
2210 | (2593604092947240127723019^8192+2593604092947240127723011^8192)/2 | 199999 | Youcef Lemsafer | 01/2023 |
2211 | (2593604092947240127723087^8192+2593604092947240127722984^8192)/147457 | 199994 | Youcef Lemsafer | 01/2023 |
2212 | (2593604092947240127723229^8192+2593604092947240127723171^8192)/15032745986 | 199989 | Youcef Lemsafer | 01/2023 |
2213 | (2593604092947240127723215^8192+2593604092947240127722938^8192)/12728329863169 | 199986 | Youcef Lemsafer | 01/2023 |
2214 | 92*10^199980-9 | 199982 | Robert Price | 12/2021 |
2215 | (2593604092947240127723216^8192+2593604092947240127723163^8192)/20172788859482903707649 | 199977 | Youcef Lemsafer | 01/2023 |
2216 | (85*10^199951-139)/9 | 199952 | Robert Price | 08/2021 |
2217 | (10^199926+7)/29/373/2339 | 199919 | Alfred Reich | 08/2021 |
2218 | 2^663838+25819 | 199836 | Enzo Doria | 11/2023 |
2219 | 23*10^199833-9 | 199835 | Robert Price | 10/2021 |
2220 | fibonacci(956176)-4 | 199829 | Jon Grantham | 08/2023 |
2221 | (299*10^199801-17)/3 | 199803 | Robert Price | 04/2020 |
2222 | 6*10^199788+77 | 199789 | Robert Price | 06/2020 |
2223 | (2^663604+1)/270750449 | 199757 | Anonymous | 10/2024 |
2224 | (23*10^199615+37)/3 | 199616 | Robert Price | 02/2022 |
2225 | (17*10^199607-167)/3 | 199608 | Robert Price | 05/2022 |
2226 | 2^663020-933075 | 199589 | Paul Bourdelais | 06/2021 |
2227 | 2^663007+29963 | 199585 | Enzo Doria | 03/2024 |
2228 | 3*2^662703-5 | 199494 | Jon Grantham | 07/2023 |
2229 | (14*10^199447+73)/3 | 199448 | Robert Price | 12/2018 |
2230 | (2^662424-15)/7 | 199409 | Stefano Morozzi | 08/2022 |
2231 | 2^662194+22189 | 199341 | Enzo Doria | 09/2023 |
2232 | 2^662103-29287 | 199313 | Enzo Doria | 08/2015 |
2233 | (2*10^199283+457)/9 | 199283 | Robert Price | 01/2018 |
2234 | (10^199248-19)/9 | 199248 | Robert Price | 01/2018 |
2235 | (83*10^199213+529)/9 | 199214 | Robert Price | 12/2021 |
2236 | (194*10^199146-17)/3 | 199148 | Robert Price | 09/2020 |
2237 | (151*10^199003-1)/3 | 199005 | Robert Price | 03/2020 |
2238 | 9*10^198946-73 | 198947 | Robert Price | 01/2021 |
2239 | 45*10^198931-7 | 198933 | Robert Price | 07/2020 |
2240 | 2^660482-2891 | 198825 | Yves Minet | 05/2016 |
2241 | 2^659594+37729 | 198558 | Enzo Doria | 10/2024 |
2242 | 2^659589-21 | 198557 | Stefano Morozzi | 07/2022 |
2243 | 2^659583+1879223 | 198555 | Enzo Doria | 08/2016 |
2244 | (53*10^198529+1)/9 | 198530 | Serge Batalov | 07/2010 |
2245 | (49*10^198403+311)/9 | 198404 | Robert Price | 06/2019 |
2246 | 96*10^198376-7 | 198378 | Robert Price | 03/2021 |
2247 | (10^198375+7)/59/1201/87589 | 198366 | Alfred Reich | 08/2021 |
2248 | 2^658828-29819 | 198327 | Enzo Doria | 08/2015 |
2249 | 2^658776-2791229 | 198312 | Enzo Doria | 01/2016 |
2250 | (35*10^198294-377)/9 | 198295 | Robert Price | 07/2018 |