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 | 10^215802+33 | 215803 | Robert Price | 08/2023 |
| 2002 | 30^146021-29^146021 | 215691 | Jean-Louis Charton | 09/2018 |
| 2003 | 277^88301-276^88301 | 215674 | Jean-Louis Charton | 06/2012 |
| 2004 | 2^716428+215011 | 215667 | Enzo Doria | 11/2023 |
| 2005 | (13*10^215592-43)/3 | 215593 | Robert Price | 08/2023 |
| 2006 | p(41292)#+p(41292+1) | 215450 | Henri Lifchitz | 11/2024 |
| 2007 | 227^91413-40 | 215372 | Enzo Doria | 04/2015 |
| 2008 | (2^715008-21)/5 | 215239 | Stefano Morozzi | 08/2022 |
| 2009 | 2^714717+782897 | 215152 | Enzo Doria | 11/2016 |
| 2010 | tau(373^15186) | 214796 | Nik Lygeros / Olivier Rozier / LR team | 10/2013 |
| 2011 | 2^713241+1879157 | 214707 | Enzo Doria | 08/2016 |
| 2012 | (23*10^214633+91)/3 | 214634 | Robert Price | 03/2023 |
| 2013 | 11^206081-10^206081 | 214612 | Jean-Louis Charton | 10/2011 |
| 2014 | 2^712801-69553 | 214575 | Enzo Doria | 01/2016 |
| 2015 | 2^712603-25357 | 214515 | Enzo Doria | 09/2013 |
| 2016 | 2^711721-1846723 | 214250 | Enzo Doria | 07/2015 |
| 2017 | 2^710730-396765 | 213952 | Enzo Doria | 09/2013 |
| 2018 | (19*10^213934-37)/9 | 213935 | Alfred Reich | 12/2023 |
| 2019 | (19*10^213730-37)/9 | 213731 | Alfred Reich | 12/2023 |
| 2020 | (713^74897-1)/712 | 213685 | Jinyuan Wang | 08/2023 |
| 2021 | 2^709773+25907 | 213663 | Enzo Doria | 12/2023 |
| 2022 | 2^708468-114329 | 213271 | Enzo Doria | 02/2015 |
| 2023 | 2^708293+27557 | 213218 | Enzo Doria | 01/2024 |
| 2024 | 379*10^213199+9 | 213202 | Jason Yuen | 01/2025 |
| 2025 | 2^707277+28997 | 212912 | Enzo Doria | 02/2024 |
| 2026 | (163*10^212779-1)/9 | 212781 | Serge Batalov | 12/2014 |
| 2027 | 2^706838-69041 | 212780 | Enzo Doria | 11/2015 |
| 2028 | 2^705653+25907 | 212423 | Enzo Doria | 12/2023 |
| 2029 | 22*10^212339+7 | 212341 | Robert Price | 10/2022 |
| 2030 | 2^704577-113871 | 212099 | Enzo Doria | 10/2014 |
| 2031 | (2^704548-19)/3 | 212090 | Stefano Morozzi | 08/2022 |
| 2032 | 2^704110-2792441 | 211959 | Enzo Doria | 02/2016 |
| 2033 | 2^704084+28531 | 211951 | Enzo Doria | 02/2024 |
| 2034 | 2^703943-1862947 | 211908 | Enzo Doria | 12/2015 |
| 2035 | (60^119083+1)/61 | 211746 | Paul Bourdelais | 10/2018 |
| 2036 | (184*10^211682-1)/3 | 211684 | Robert Price | 12/2022 |
| 2037 | (10^211610-91)/9 | 211610 | Serge Batalov | 12/2014 |
| 2038 | 227^89797+2 | 211565 | Lelio R Paula | 08/2012 |
| 2039 | 2^702194-3 | 211382 | Paul Bourdelais | 03/2012 |
| 2040 | 2^702064+1874911 | 211343 | Enzo Doria | 07/2016 |
| 2041 | 2^701968-113873 | 211314 | Enzo Doria | 10/2014 |
| 2042 | (14*10^211262-41)/9 | 211263 | Serge Batalov | 01/2023 |
| 2043 | 2^701713-113779 | 211237 | Enzo Doria | 09/2014 |
| 2044 | 2^701616-216803 | 211208 | Enzo Doria | 01/2024 |
| 2045 | 2^701449-25201 | 211158 | Enzo Doria | 09/2013 |
| 2046 | 2^701403-2786977 | 211144 | Enzo Doria | 11/2015 |
| 2047 | 2^701189-25423 | 211079 | Enzo Doria | 09/2013 |
| 2048 | 2^701162-459161 | 211071 | Enzo Doria | 05/2015 |
| 2049 | 2^700793+219407 | 210960 | Enzo Doria | 03/2024 |
| 2050 | (24^152783-1)/23 | 210872 | Paul Bourdelais | 04/2018 |
| 2051 | 2^700400+9385 | 210842 | Lelio R Paula | 01/2014 |
| 2052 | 2^700304-17 | 210813 | Stefano Morozzi | 07/2022 |
| 2053 | 2^700131+1874693 | 210761 | Enzo Doria | 06/2016 |
| 2054 | (2^700095+225414)/2 | 210750 | Stefano Morozzi | 04/2020 |
| 2055 | (2^700090+278254)/2 | 210748 | Stefano Morozzi | 04/2020 |
| 2056 | (2^700075+303666)/2 | 210744 | Stefano Morozzi | 04/2020 |
| 2057 | (2^700073+75882)/2 | 210743 | Stefano Morozzi | 04/2020 |
| 2058 | (2^700074+328890)/2 | 210743 | Stefano Morozzi | 04/2020 |
| 2059 | (2^700052+79162)/2 | 210737 | Stefano Morozzi | 04/2020 |
| 2060 | (2^700052+304458)/2 | 210737 | Stefano Morozzi | 04/2020 |
| 2061 | (2^700048+376578)/2 | 210736 | Stefano Morozzi | 04/2020 |
| 2062 | 11^202357-1140 | 210734 | Enzo Doria | 12/2012 |
| 2063 | (2^700021+25874)/2 | 210728 | Stefano Morozzi | 04/2020 |
| 2064 | (2^700018+377518)/2 | 210727 | Stefano Morozzi | 04/2020 |
| 2065 | 2^699999+300729 | 210721 | Norman Luhn | 09/2023 |
| 2066 | (238*10^210712-1)/3 | 210714 | Robert Price | 09/2023 |
| 2067 | 2^699740+25 | 210643 | Stefano Morozzi | 05/2021 |
| 2068 | (23*10^210525-143)/3 | 210526 | Robert Price | 12/2023 |
| 2069 | 2^698929-2788423 | 210399 | Enzo Doria | 11/2015 |
| 2070 | (5^300893+4^300893)/9 | 210315 | Jean-Louis Charton | 11/2011 |
| 2071 | 2^698316+1878601 | 210215 | Enzo Doria | 08/2016 |
| 2072 | 34*10^210097-9 | 210099 | Robert Price | 05/2023 |
| 2073 | (19*10^210011-49)/3 | 210012 | Robert Price | 06/2023 |
| 2074 | 6*10^209846-91 | 209847 | Robert Price | 05/2023 |
| 2075 | 2^697036+1878751 | 209829 | Enzo Doria | 08/2016 |
| 2076 | 2^696813+28607 | 209762 | Enzo Doria | 02/2024 |
| 2077 | (238*10^209715-1)/3 | 209717 | Robert Price | 09/2023 |
| 2078 | 6^269407+5 | 209640 | Paul Bourdelais | 02/2021 |
| 2079 | (2^696343-1)/11141489/36009913139329 | 209600 | Tony Prest / Never Odd Or Even | 02/2014 |
| 2080 | 2^696254-115151 | 209594 | Enzo Doria | 06/2015 |
| 2081 | 2^695841+225 | 209470 | Henri Lifchitz | 01/2025 |
| 2082 | (35^135623+1)/36 | 209410 | Paul Bourdelais | 07/2018 |
| 2083 | 7*10^209161+39 | 209162 | Robert Price | 01/2023 |
| 2084 | 2^694633+1887257 | 209106 | Enzo Doria | 05/2017 |
| 2085 | fibonacci(999790)-4 | 208944 | Jon Grantham | 08/2023 |
| 2086 | 2^693959+180923 | 208903 | Enzo Doria | 07/2016 |
| 2087 | (2^693747-11)/3 | 208839 | Stefano Morozzi | 08/2022 |
| 2088 | 2^693462-1847561 | 208753 | Enzo Doria | 07/2015 |
| 2089 | 2^690890-59981 | 207979 | Enzo Doria | 11/2015 |
| 2090 | (38^131591+1)/39 | 207884 | Paul Bourdelais | 07/2018 |
| 2091 | 3*2^690484+5 | 207857 | Jon Grantham | 07/2023 |
| 2092 | 2^690163+1877063 | 207760 | Enzo Doria | 07/2016 |
| 2093 | 7^245608-2 | 207563 | Paul Bourdelais | 01/2021 |
| 2094 | (67*10^207556+23)/9 | 207557 | Serge Batalov | 01/2023 |
| 2095 | 2^689286-29381 | 207496 | Enzo Doria | 08/2015 |
| 2096 | 2^689122-114521 | 207447 | Enzo Doria | 04/2015 |
| 2097 | 9*10^207254-89 | 207255 | Robert Price | 02/2023 |
| 2098 | 2^688373+6077 | 207221 | Enzo Doria | 02/2016 |
| 2099 | 2^688201+1875527 | 207170 | Enzo Doria | 07/2016 |
| 2100 | (42^127609+1)/43 | 207140 | Paul Bourdelais | 07/2018 |
| 2101 | 2^687938+213589 | 207090 | Enzo Doria | 10/2023 |
| 2102 | 2^687619+81563 | 206994 | Enzo Doria | 08/2016 |
| 2103 | 3*10^206927+37 | 206928 | Robert Price | 08/2023 |
| 2104 | 2^687383+21803 | 206923 | Enzo Doria | 09/2023 |
| 2105 | (11*10^206688+19)/3 | 206689 | Robert Price | 07/2024 |
| 2106 | 2^686572-1845299 | 206679 | Enzo Doria | 07/2015 |
| 2107 | (21^156217-1)/20 | 206552 | Paul Bourdelais | 04/2010 |
| 2108 | 2^685970+39415 | 206498 | Enzo Doria | 11/2024 |
| 2109 | (2^685739+1)/(3*87774593) | 206420 | Gord Palameta | 08/2018 |
| 2110 | 2^685578+3 | 206380 | Paul Bourdelais | 04/2012 |
| 2111 | 2^685078+218599 | 206230 | Enzo Doria | 01/2024 |
| 2112 | 2^684836-49349 | 206157 | Enzo Doria | 10/2015 |
| 2113 | (73^110603-1)/72 | 206088 | Paul Bourdelais | 06/2018 |
| 2114 | 2^684163-2790967 | 205954 | Enzo Doria | 12/2015 |
| 2115 | 326^81943-325^81943 | 205941 | Jean-Louis Charton | 07/2012 |
| 2116 | (2^684127-1)/23765203727 | 205933 | Jens K. Andersen | 04/2009 |
| 2117 | (68*10^205510+13)/9 | 205511 | Serge Batalov | 01/2023 |
| 2118 | 4^341233-3^341233 | 205443 | Jean-Louis Charton | 01/2006 |
| 2119 | 2^682414+215029 | 205428 | Enzo Doria | 11/2023 |
| 2120 | (963^68821-1)/962 | 205334 | Jinyuan Wang | 01/2024 |
| 2121 | (43*10^205183-421)/9 | 205184 | Robert Price | 10/2023 |
| 2122 | 2^681545+467 | 205166 | Lelio R Paula | 11/2013 |
| 2123 | 2^681306+81049 | 205094 | Enzo Doria | 07/2016 |
| 2124 | 2^680697+1877057 | 204911 | Enzo Doria | 07/2016 |
| 2125 | 2^680415+71783 | 204826 | Enzo Doria | 04/2016 |
| 2126 | 10^204764-8001 | 204764 | Robert Price | 03/2023 |
| 2127 | (26*10^204730-77)/3 | 204731 | Robert Price | 03/2023 |
| 2128 | 2^679860-459995 | 204659 | Enzo Doria | 06/2015 |
| 2129 | 2^679593+1879547 | 204578 | Enzo Doria | 09/2016 |
| 2130 | 2^678899+220073 | 204369 | Enzo Doria | 03/2024 |
| 2131 | 2^678753+21677 | 204326 | Enzo Doria | 08/2023 |
| 2132 | 2^678651+1875023 | 204295 | Enzo Doria | 07/2016 |
| 2133 | 2^678561+678561 | 204268 | Henri Lifchitz | 05/2006 |
| 2134 | 5*3^427884+2^427884 | 204154 | Jon Grantham | 08/2023 |
| 2135 | 2^678101-114043 | 204129 | Enzo Doria | 11/2014 |
| 2136 | 2^678028+1875631 | 204107 | Enzo Doria | 06/2016 |
| 2137 | 2^677721+28607 | 204015 | Enzo Doria | 01/2024 |
| 2138 | (19*10^203798-7)/3 | 203799 | Robert Price | 12/2023 |
| 2139 | 2^676992-59783 | 203795 | Enzo Doria | 10/2015 |
| 2140 | 2^676972+1866871 | 203789 | Enzo Doria | 03/2016 |
| 2141 | 2^676815+22583 | 203742 | Enzo Doria | 09/2023 |
| 2142 | 2^676761-9 | 203726 | Robert Price | 01/2017 |
| 2143 | 2^676592-23 | 203675 | Stefano Morozzi | 07/2022 |
| 2144 | 2^676563-2792407 | 203666 | Enzo Doria | 02/2016 |
| 2145 | 2^676306-114713 | 203589 | Enzo Doria | 04/2015 |
| 2146 | (2^675977-1)/(1686378749257*7171117283326998925471) | 203456 | Dario Alpern | 07/2015 |
| 2147 | 6*10^203365+53 | 203366 | Robert Price | 09/2023 |
| 2148 | 2^675211-198405 | 203259 | Stefano Morozzi | 04/2025 |
| 2149 | 2^675208-131505 | 203258 | Stefano Morozzi | 04/2025 |
| 2150 | 2^675202-14823 | 203257 | Stefano Morozzi | 04/2025 |
| 2151 | 2^675202-35967 | 203257 | Stefano Morozzi | 04/2025 |
| 2152 | 2^675202-54681 | 203257 | Stefano Morozzi | 04/2025 |
| 2153 | 2^675205-107845 | 203257 | Stefano Morozzi | 04/2025 |
| 2154 | 2^675199-131397 | 203256 | Stefano Morozzi | 04/2025 |
| 2155 | 2^675199-34219 | 203256 | Stefano Morozzi | 04/2025 |
| 2156 | 2^675199-56175 | 203256 | Stefano Morozzi | 04/2025 |
| 2157 | 2^675198-106925 | 203255 | Stefano Morozzi | 04/2025 |
| 2158 | 2^675192-192243 | 203254 | Stefano Morozzi | 04/2025 |
| 2159 | 2^675189-37383 | 203253 | Stefano Morozzi | 04/2025 |
| 2160 | 2^675190-68711 | 203253 | Stefano Morozzi | 04/2025 |
| 2161 | 2^675191-114549 | 203253 | Stefano Morozzi | 04/2025 |
| 2162 | 2^675191-29445 | 203253 | Stefano Morozzi | 04/2025 |
| 2163 | 2^675186-24563 | 203252 | Stefano Morozzi | 04/2025 |
| 2164 | 2^675187-185041 | 203252 | Stefano Morozzi | 04/2025 |
| 2165 | 2^675188-121613 | 203252 | Stefano Morozzi | 04/2025 |
| 2166 | 2^675183-43587 | 203251 | Stefano Morozzi | 04/2025 |
| 2167 | 2^675184-60563 | 203251 | Stefano Morozzi | 04/2025 |
| 2168 | 10247^50678-50678^10247 | 203250 | Norbert Schneider | 03/2022 |
| 2169 | 2^675177-30495 | 203249 | Stefano Morozzi | 04/2025 |
| 2170 | 2^675170-170651 | 203247 | Stefano Morozzi | 04/2025 |
| 2171 | 2^675171-21231 | 203247 | Stefano Morozzi | 04/2025 |
| 2172 | 2^675166-116351 | 203246 | Stefano Morozzi | 04/2025 |
| 2173 | 2^675166-63465 | 203246 | Stefano Morozzi | 04/2025 |
| 2174 | 2^675167-11047 | 203246 | Stefano Morozzi | 04/2025 |
| 2175 | 2^675168-197307 | 203246 | Stefano Morozzi | 04/2025 |
| 2176 | 2^675168-89379 | 203246 | Stefano Morozzi | 04/2025 |
| 2177 | 2^675162-24471 | 203245 | Stefano Morozzi | 04/2025 |
| 2178 | 2^675163-4971 | 203245 | Stefano Morozzi | 04/2025 |
| 2179 | 2^675163-69489 | 203245 | Stefano Morozzi | 04/2025 |
| 2180 | 2^675165-153541 | 203245 | Stefano Morozzi | 04/2025 |
| 2181 | 2^675159-107809 | 203244 | Stefano Morozzi | 04/2025 |
| 2182 | 2^675156-156785 | 203243 | Stefano Morozzi | 04/2025 |
| 2183 | 2^675157-177433 | 203243 | Stefano Morozzi | 04/2025 |
| 2184 | 2^675154-66563 | 203242 | Stefano Morozzi | 04/2025 |
| 2185 | 2^675148-71007 | 203240 | Stefano Morozzi | 04/2025 |
| 2186 | 2^675148-94815 | 203240 | Stefano Morozzi | 04/2025 |
| 2187 | 2^675138-52371 | 203237 | Stefano Morozzi | 04/2025 |
| 2188 | 2^675133-7273 | 203236 | Stefano Morozzi | 04/2025 |
| 2189 | 2^675134-73473 | 203236 | Stefano Morozzi | 04/2025 |
| 2190 | 2^675124-51675 | 203233 | Stefano Morozzi | 04/2025 |
| 2191 | 2^675120-40809 | 203232 | Stefano Morozzi | 04/2025 |
| 2192 | 2^675120-50573 | 203232 | Stefano Morozzi | 04/2025 |
| 2193 | 2^675116-109889 | 203231 | Stefano Morozzi | 04/2025 |
| 2194 | 2^675106-73241 | 203228 | Stefano Morozzi | 02/2025 |
| 2195 | 2^675103-188727 | 203227 | Stefano Morozzi | 02/2025 |
| 2196 | 2^675104-16199 | 203227 | Stefano Morozzi | 02/2025 |
| 2197 | 2^675104-195303 | 203227 | Stefano Morozzi | 02/2025 |
| 2198 | 2^675105-94521 | 203227 | Stefano Morozzi | 02/2025 |
| 2199 | 2^675103+31599 | 203227 | Stefano Morozzi | 04/2025 |
| 2200 | 2^675100-2775 | 203226 | Stefano Morozzi | 02/2025 |
| 2201 | 2^675098-170703 | 203225 | Stefano Morozzi | 02/2025 |
| 2202 | 2^675097+50651 | 203225 | Stefano Morozzi | 04/2025 |
| 2203 | 2^675093-162123 | 203224 | Stefano Morozzi | 02/2025 |
| 2204 | 2^675093-48955 | 203224 | Stefano Morozzi | 02/2025 |
| 2205 | 2^675095-73591 | 203224 | Stefano Morozzi | 02/2025 |
| 2206 | 2^675095-89937 | 203224 | Stefano Morozzi | 02/2025 |
| 2207 | 2^675093+87767 | 203224 | Stefano Morozzi | 04/2025 |
| 2208 | 2^675092-144539 | 203223 | Stefano Morozzi | 02/2025 |
| 2209 | 2^675090+92253 | 203223 | Stefano Morozzi | 04/2025 |
| 2210 | 2^675086-186387 | 203222 | Stefano Morozzi | 02/2025 |
| 2211 | 2^675088-68505 | 203222 | Stefano Morozzi | 02/2025 |
| 2212 | 2^675083-149199 | 203221 | Stefano Morozzi | 02/2025 |
| 2213 | 2^675081-91425 | 203220 | Stefano Morozzi | 02/2025 |
| 2214 | 2^675082-80213 | 203220 | Stefano Morozzi | 02/2025 |
| 2215 | 2^675080+112651 | 203220 | Stefano Morozzi | 04/2025 |
| 2216 | 2^675082+25435 | 203220 | Stefano Morozzi | 04/2025 |
| 2217 | 2^675082+180613 | 203220 | Stefano Morozzi | 04/2025 |
| 2218 | 2^675077-152683 | 203219 | Stefano Morozzi | 02/2025 |
| 2219 | 2^675077-79213 | 203219 | Stefano Morozzi | 02/2025 |
| 2220 | 2^675077+172221 | 203219 | Stefano Morozzi | 04/2025 |
| 2221 | 2^675073-149065 | 203218 | Stefano Morozzi | 02/2025 |
| 2222 | 2^675073-19663 | 203218 | Stefano Morozzi | 02/2025 |
| 2223 | 2^675074+25755 | 203218 | Stefano Morozzi | 04/2025 |
| 2224 | 2^675075+151203 | 203218 | Stefano Morozzi | 04/2025 |
| 2225 | 2^675069-147135 | 203217 | Stefano Morozzi | 02/2025 |
| 2226 | 2^675069-161461 | 203217 | Stefano Morozzi | 02/2025 |
| 2227 | 2^675071-175189 | 203217 | Stefano Morozzi | 02/2025 |
| 2228 | 2^675071+105575 | 203217 | Stefano Morozzi | 04/2025 |
| 2229 | 2^675071+162299 | 203217 | Stefano Morozzi | 04/2025 |
| 2230 | 2^675067+124541 | 203216 | Stefano Morozzi | 04/2025 |
| 2231 | 2^675068+163695 | 203216 | Stefano Morozzi | 04/2025 |
| 2232 | 2^675064+116445 | 203215 | Stefano Morozzi | 04/2025 |
| 2233 | 2^675065+26045 | 203215 | Stefano Morozzi | 04/2025 |
| 2234 | 2^675060+119983 | 203214 | Stefano Morozzi | 02/2025 |
| 2235 | 2^675060+161301 | 203214 | Stefano Morozzi | 02/2025 |
| 2236 | 2^675061-187773 | 203214 | Stefano Morozzi | 02/2025 |
| 2237 | 2^675062-92193 | 203214 | Stefano Morozzi | 02/2025 |
| 2238 | 2^675058-10403 | 203213 | Stefano Morozzi | 01/2025 |
| 2239 | 2^675058-40337 | 203213 | Stefano Morozzi | 01/2025 |
| 2240 | 2^675057+123557 | 203213 | Stefano Morozzi | 02/2025 |
| 2241 | 2^675057+172475 | 203213 | Stefano Morozzi | 02/2025 |
| 2242 | 2^675053-4801 | 203212 | Stefano Morozzi | 01/2025 |
| 2243 | 2^675054-174341 | 203212 | Stefano Morozzi | 01/2025 |
| 2244 | 2^675054-53697 | 203212 | Stefano Morozzi | 01/2025 |
| 2245 | 2^675054+24825 | 203212 | Stefano Morozzi | 02/2025 |
| 2246 | 2^675055+160265 | 203212 | Stefano Morozzi | 02/2025 |
| 2247 | 2^675050-30015 | 203211 | Stefano Morozzi | 01/2025 |
| 2248 | 2^675051-85941 | 203211 | Stefano Morozzi | 01/2025 |
| 2249 | 2^675051+30885 | 203211 | Stefano Morozzi | 02/2025 |
| 2250 | 2^675052+12537 | 203211 | Stefano Morozzi | 02/2025 |
