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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| Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
| 2001 | 11^246167-90 | 256357 | Enzo Doria | 12/2012 |
| 2002 | (85*10^256301-1)/3 | 256303 | Robert Price | 12/2022 |
| 2003 | (10^256187+7)/63443/148782853 | 256175 | Alfred Reich | 10/2021 |
| 2004 | 2^850700-569049 | 256087 | Enzo Doria | 11/2013 |
| 2005 | 2^850675+153 | 256079 | Stefano Morozzi | 05/2021 |
| 2006 | 21^193601-20^193601 | 255983 | Jean-Louis Charton | 02/2015 |
| 2007 | (37^163193+1)/38 | 255918 | Paul Bourdelais | 07/2019 |
| 2008 | (14*10^255805-83)/3 | 255806 | Robert Price | 11/2022 |
| 2009 | 2^849316+25861 | 255670 | Enzo Doria | 12/2023 |
| 2010 | 2^849177-114025 | 255628 | Enzo Doria | 12/2014 |
| 2011 | 2*10^255442-21 | 255443 | Robert Price | 08/2023 |
| 2012 | 2^848502-3173 | 255425 | Yves Minet | 07/2016 |
| 2013 | 2^848178-140291 | 255328 | Enzo Doria | 01/2014 |
| 2014 | 7*10^255167+87 | 255168 | Robert Price | 11/2022 |
| 2015 | 2^847622-2441 | 255160 | Yves Minet | 02/2016 |
| 2016 | 2^847291+182843 | 255061 | Enzo Doria | 11/2016 |
| 2017 | 2^847174+1879429 | 255025 | Enzo Doria | 09/2016 |
| 2018 | 2^846881+215837 | 254937 | Enzo Doria | 12/2023 |
| 2019 | Phi(475779,2^3) | 254889 | Henri Lifchitz | 12/2025 |
| 2020 | 24*29^174239+13361 | 254809 | Curtis Bright | 04/2015 |
| 2021 | 22*10^254639+7 | 254641 | Robert Price | 10/2022 |
| 2022 | 2^845633-933075 | 254561 | Paul Bourdelais | 11/2021 |
| 2023 | 2^845610-1868591 | 254554 | Enzo Doria | 04/2016 |
| 2024 | 2^845484+81931 | 254517 | Enzo Doria | 08/2016 |
| 2025 | 2^845402-114761 | 254492 | Enzo Doria | 05/2015 |
| 2026 | Phi(115655,561) | 254335 | Henri Lifchitz | 12/2025 |
| 2027 | 98*10^254173-9 | 254175 | Robert Price | 05/2023 |
| 2028 | 2^844334-2792441 | 254170 | Enzo Doria | 02/2016 |
| 2029 | 2*10^254162+69 | 254163 | Robert Price | 08/2023 |
| 2030 | (4*10^254107+11)/3 | 254108 | Tyler Busby | 02/2023 |
| 2031 | 11^243796-90 | 253888 | Enzo Doria | 12/2012 |
| 2032 | (10^253891+7)/44777/79843/16940711 | 253875 | Alfred Reich | 10/2021 |
| 2033 | 30^171733-29^171733 | 253671 | Jean-Louis Charton | 10/2018 |
| 2034 | 2^842325+25907 | 253566 | Enzo Doria | 11/2023 |
| 2035 | Sm(52936)/27320754423352 | 253560 | Youcef Lemsafer | 06/2026 |
| 2036 | 2^842209+1876037 | 253531 | Enzo Doria | 07/2016 |
| 2037 | 2^842123-59197 | 253505 | Enzo Doria | 10/2015 |
| 2038 | (8*10^253313-53)/9 | 253313 | Serge Batalov | 11/2022 |
| 2039 | (28*10^253210+191)/3 | 253211 | Robert Price | 07/2023 |
| 2040 | 2^840797-3 | 253106 | Paul Bourdelais | 06/2019 |
| 2041 | 2^840716-2969 | 253081 | Yves Minet | 05/2016 |
| 2042 | 2^840358-462491 | 252973 | Enzo Doria | 08/2015 |
| 2043 | 2^840310+1878379 | 252959 | Enzo Doria | 08/2016 |
| 2044 | 2^840203-21 | 252927 | Stefano Morozzi | 07/2022 |
| 2045 | 11^242579-60 | 252620 | Enzo Doria | 10/2012 |
| 2046 | 45^152659+2 | 252378 | Robert Price | 09/2015 |
| 2047 | (95^127583+1)/96 | 252322 | Paul Bourdelais | 07/2019 |
| 2048 | 7*10^252209-17 | 252210 | Robert Price | 12/2022 |
| 2049 | 2^837725+1869377 | 252181 | Enzo Doria | 05/2016 |
| 2050 | 2^837536-311039 | 252124 | Enzo Doria | 06/2015 |
| 2051 | 21^190632-2 | 252058 | Robert Price | 07/2015 |
| 2052 | 2^837242+1873297 | 252035 | Enzo Doria | 06/2016 |
| 2053 | 2^836995+226575 | 251961 | Enzo Doria | 10/2024 |
| 2054 | 2^836656-2787929 | 251859 | Enzo Doria | 11/2015 |
| 2055 | 2^836548+219061 | 251827 | Enzo Doria | 02/2024 |
| 2056 | 2^836380+1875541 | 251776 | Enzo Doria | 07/2016 |
| 2057 | (359^98327-1)/358 | 251233 | Alexander Zhirkov | 11/2017 |
| 2058 | tau(41^28288) | 250924 | Nik Lygeros / Olivier Rozier | 10/2013 |
| 2059 | Phi(137951,-100) | 250801 | Henri Lifchitz | 12/2025 |
| 2060 | 406^96126+405 | 250748 | Alfred Reich | 05/2026 |
| 2061 | Phi(74531,11#) | 250691 | Henri Lifchitz | 12/2025 |
| 2062 | (28*10^250655+113)/3 | 250656 | Robert Price | 06/2023 |
| 2063 | 2^832511-461197 | 250611 | Enzo Doria | 07/2015 |
| 2064 | 2^832505+1881137 | 250609 | Enzo Doria | 11/2016 |
| 2065 | 2^832363+583295 | 250567 | Enzo Doria | 12/2016 |
| 2066 | 2^832244-403635 | 250531 | Enzo Doria | 01/2014 |
| 2067 | (14*10^250336-41)/9 | 250337 | Serge Batalov | 01/2023 |
| 2068 | 2^831528+24811 | 250315 | Enzo Doria | 11/2023 |
| 2069 | 2^831157+1880657 | 250204 | Enzo Doria | 11/2016 |
| 2070 | 2^831088-7200899 | 250183 | Enzo Doria | 01/2015 |
| 2071 | 2^830956-1349 | 250143 | Yves Minet | 07/2015 |
| 2072 | 2^830699+220583 | 250066 | Enzo Doria | 03/2024 |
| 2073 | 2^830037+282317 | 249867 | Enzo Doria | 09/2016 |
| 2074 | 2^829589-113653 | 249732 | Enzo Doria | 09/2014 |
| 2075 | (4*10^249550-7)/3 | 249551 | Serge Batalov | 01/2023 |
| 2076 | (103*10^249399+17)/3 | 249401 | Robert Price | 04/2023 |
| 2077 | 2^828281-3193 | 249338 | Yves Minet | 08/2016 |
| 2078 | (2^828140-19)/3 | 249295 | Stefano Morozzi | 08/2022 |
| 2079 | 2^828064-2785619 | 249273 | Enzo Doria | 10/2015 |
| 2080 | 2^827602+60409 | 249134 | Enzo Doria | 03/2016 |
| 2081 | 2^827306+212419 | 249044 | Enzo Doria | 09/2023 |
| 2082 | 10^249010+348861 | 249011 | Patrick De Geest | 04/2016 |
| 2083 | 10^249010-21 | 249010 | Serge Batalov | 12/2014 |
| 2084 | 2^826733+1882907 | 248872 | Enzo Doria | 12/2016 |
| 2085 | 2^825800+22441 | 248591 | Enzo Doria | 10/2023 |
| 2086 | 2^825682+1876549 | 248556 | Enzo Doria | 07/2016 |
| 2087 | 2^824991-114121 | 248348 | Enzo Doria | 12/2014 |
| 2088 | 2^824642-362727 | 248242 | Enzo Doria | 12/2013 |
| 2089 | 2^824565-114265 | 248219 | Enzo Doria | 01/2015 |
| 2090 | 2^824325-25 | 248147 | Boyan Hu | 12/2024 |
| 2091 | (73*10^248145-1)/9 | 248146 | Robert Price | 01/2015 |
| 2092 | 2^823321+219407 | 247845 | Enzo Doria | 02/2024 |
| 2093 | (2^823337+1)/(3*362268281) | 247841 | Gord Palameta | 08/2018 |
| 2094 | (13*10^247793-43)/3 | 247794 | Robert Price | 08/2023 |
| 2095 | (2^822971-1)/6583769/28211445881/21255852651726486149207 | 247700 | Robert Kinser | 09/2016 |
| 2096 | 2^822296+76501 | 247536 | Enzo Doria | 05/2016 |
| 2097 | 2^821590-114167 | 247324 | Enzo Doria | 12/2014 |
| 2098 | 2^821512-2790659 | 247300 | Enzo Doria | 12/2015 |
| 2099 | (21996^57121-1)/(21996^239-1) | 247002 | Ryan Propper | 11/2023 |
| 2100 | 2^820356+7 | 246952 | Jon Grantham | 08/2023 |
| 2101 | 2^820077+382847 | 246868 | Enzo Doria | 11/2016 |
| 2102 | 2^820008+81 | 246848 | Henri Lifchitz | 01/2025 |
| 2103 | 2^820001+81269 | 246845 | Enzo Doria | 07/2016 |
| 2104 | 2^819463-59197 | 246683 | Enzo Doria | 10/2015 |
| 2105 | 2^819296+80581 | 246633 | Enzo Doria | 07/2016 |
| 2106 | 2^818764+21573 | 246473 | Enzo Doria | 11/2023 |
| 2107 | 2^817852+215491 | 246198 | Enzo Doria | 11/2023 |
| 2108 | 2^817160-350369 | 245990 | Enzo Doria | 06/2015 |
| 2109 | 2^816039-19 | 245653 | Stefano Morozzi | 07/2022 |
| 2110 | 2^816029+219407 | 245650 | Enzo Doria | 02/2024 |
| 2111 | (71*10^245558-17)/9 | 245559 | Serge Batalov | 01/2023 |
| 2112 | 5*3^514648+2^514648 | 245551 | Jon Grantham | 08/2023 |
| 2113 | 88093#+(653879#)/(88093#) | 245374 | Makoto Morimoto | 11/2017 |
| 2114 | 2^815111-113857 | 245373 | Enzo Doria | 10/2014 |
| 2115 | (34555^54289-1)/(34555^233-1) | 245334 | Ryan Propper | 11/2023 |
| 2116 | 2^814914-4001 | 245314 | Yves Minet | 05/2017 |
| 2117 | 846^83761-845^83761 | 245200 | Jean-Louis Charton | 12/2012 |
| 2118 | 2^814356-2790449 | 245146 | Enzo Doria | 12/2015 |
| 2119 | 2^814276-459029 | 245122 | Enzo Doria | 04/2015 |
| 2120 | 2^814023+180923 | 245046 | Enzo Doria | 07/2016 |
| 2121 | 2^813496+216751 | 244887 | Enzo Doria | 12/2023 |
| 2122 | (3^513059-2^513059)/(1026119*5430216457) | 244776 | Mike Oakes | 03/2017 |
| 2123 | 3^513007+16 | 244767 | Robert Price | 04/2020 |
| 2124 | (46^147197-31^147197)/15 | 244752 | Aurel Gibier | 06/2024 |
| 2125 | (2543*17^198855-15)/16 | 244684 | Eric Chen | 01/2026 |
| 2126 | 2^811882+27289 | 244401 | Enzo Doria | 12/2023 |
| 2127 | 2^811842-113675 | 244389 | Enzo Doria | 09/2014 |
| 2128 | 2^811132-2787929 | 244176 | Enzo Doria | 11/2015 |
| 2129 | (47*21^184501+953)/20 | 243952 | Eric Chen | 03/2026 |
| 2130 | 2^809746-2790971 | 243758 | Enzo Doria | 01/2016 |
| 2131 | (14*10^243724-197)/3 | 243725 | Robert Price | 03/2023 |
| 2132 | 2^808767-3295 | 243464 | Yves Minet | 12/2016 |
| 2133 | 2^808621-113809 | 243420 | Enzo Doria | 09/2014 |
| 2134 | 2^808199+29693 | 243293 | Enzo Doria | 03/2024 |
| 2135 | 2^807724+1879621 | 243150 | Enzo Doria | 09/2016 |
| 2136 | 2^807417+217787 | 243057 | Enzo Doria | 01/2024 |
| 2137 | (23*10^242909+91)/3 | 242910 | Robert Price | 03/2023 |
| 2138 | 2^806708+20371 | 242844 | Enzo Doria | 08/2023 |
| 2139 | 2*10^242822-91 | 242823 | Robert Price | 02/2023 |
| 2140 | 20^186554-3 | 242713 | Paul Bourdelais | 12/2020 |
| 2141 | 2^805843-113611 | 242583 | Enzo Doria | 08/2014 |
| 2142 | 2^805745-459763 | 242554 | Enzo Doria | 05/2015 |
| 2143 | 2^805353+782687 | 242436 | Enzo Doria | 11/2016 |
| 2144 | (19*10^242362-7)/3 | 242363 | Robert Price | 12/2023 |
| 2145 | 2^804895+29963 | 242298 | Enzo Doria | 03/2024 |
| 2146 | 2^804725+28229 | 242247 | Enzo Doria | 01/2024 |
| 2147 | 6^311257+5 | 242206 | Paul Bourdelais | 02/2021 |
| 2148 | (21^242194)%(10^242194) | 242194 | Henri Lifchitz | 06/2025 |
| 2149 | 2^804277-417933 | 242112 | Enzo Doria | 01/2014 |
| 2150 | 7*(10^(2*121002+1)-1)/9-3*10^121002 | 242005 | Robert Price | 06/2026 |
| 2151 | 2^803468-269039 | 241868 | Enzo Doria | 10/2013 |
| 2152 | 2^803172+80851 | 241779 | Enzo Doria | 07/2016 |
| 2153 | 2^803011+220073 | 241731 | Enzo Doria | 03/2024 |
| 2154 | 3^506233-2 | 241535 | Robert Price | 11/2013 |
| 2155 | 2^802025-25999 | 241434 | Enzo Doria | 10/2013 |
| 2156 | (3^505823+3^252912+1)/7 | 241339 | Serge Batalov | 03/2014 |
| 2157 | 2^801575+25073 | 241299 | Enzo Doria | 11/2023 |
| 2158 | 2^801303+1872923 | 241217 | Enzo Doria | 05/2016 |
| 2159 | 2^801105+216977 | 241157 | Enzo Doria | 12/2023 |
| 2160 | (23*10^241048-143)/3 | 241049 | Robert Price | 12/2023 |
| 2161 | 2^800579-1862947 | 240999 | Enzo Doria | 12/2015 |
| 2162 | 2^799999+16205 | 240824 | Norman Luhn | 09/2023 |
| 2163 | 3^504206+2 | 240568 | Luke W. Richards | 03/2018 |
| 2164 | 2^798973-26283 | 240515 | Enzo Doria | 10/2013 |
| 2165 | Phi(114205,3^7) | 240470 | Henri Lifchitz | 12/2025 |
| 2166 | 2^798671-69487 | 240424 | Enzo Doria | 12/2015 |
| 2167 | 2^797220+79831 | 239988 | Enzo Doria | 06/2016 |
| 2168 | 2^796910-26001 | 239894 | Enzo Doria | 10/2013 |
| 2169 | (97^120721-1)/811245216 | 239837 | Paul Vanderveen | 06/2025 |
| 2170 | 2^796598+653119 | 239800 | Enzo Doria | 12/2016 |
| 2171 | 2^796432-1859729 | 239750 | Enzo Doria | 11/2015 |
| 2172 | 2^796002-1852211 | 239621 | Enzo Doria | 08/2015 |
| 2173 | 2^795884+214081 | 239585 | Enzo Doria | 10/2023 |
| 2174 | 2^795709+75767 | 239533 | Enzo Doria | 04/2016 |
| 2175 | 2^795708+81721 | 239532 | Enzo Doria | 08/2016 |
| 2176 | 2^795468-2786249 | 239460 | Enzo Doria | 10/2015 |
| 2177 | 2^795442+80779 | 239452 | Enzo Doria | 07/2016 |
| 2178 | 2^795075-1852057 | 239342 | Enzo Doria | 08/2015 |
| 2179 | (86^123677+1)/87 | 239252 | Paul Bourdelais | 01/2019 |
| 2180 | 2^794043+1875023 | 239031 | Enzo Doria | 06/2016 |
| 2181 | 2^793347-69577 | 238822 | Enzo Doria | 01/2016 |
| 2182 | 5*2^793288+3 | 238805 | Jon Grantham | 07/2023 |
| 2183 | 2^792988-344429 | 238714 | Enzo Doria | 08/2015 |
| 2184 | 2^792700-2786369 | 238627 | Enzo Doria | 11/2015 |
| 2185 | 2^792663-1844797 | 238616 | Enzo Doria | 06/2015 |
| 2186 | 2^792605-291943 | 238598 | Enzo Doria | 07/2015 |
| 2187 | 2^792366+218599 | 238526 | Enzo Doria | 01/2024 |
| 2188 | (2^792061-2^396031+1)/5 | 238434 | Thomas Ritschel | 03/2014 |
| 2189 | 2^791321+30077 | 238212 | Enzo Doria | 03/2024 |
| 2190 | 4*10^238163+21 | 238164 | Robert Price | 12/2022 |
| 2191 | (26*10^238157-77)/3 | 238158 | Robert Price | 03/2023 |
| 2192 | 10^237670+9 | 237671 | Robert Price | 08/2023 |
| 2193 | 2^789373+1869377 | 237625 | Enzo Doria | 05/2016 |
| 2194 | ((10^59387+1)^3*(10^59387+1+10^29694)-(10^118774+10^59387)*(10^29694-1)+10^178161)/27961 | 237544 | Serge Batalov | 04/2015 |
| 2195 | Phi(1187740M,10) | 237544 | Anonymous | 03/2025 |
| 2196 | 2^789033+218537 | 237523 | Enzo Doria | 01/2024 |
| 2197 | 2^788942+1866409 | 237496 | Enzo Doria | 02/2016 |
| 2198 | 2^788844-114329 | 237466 | Enzo Doria | 01/2015 |
| 2199 | 2^788705-1859713 | 237424 | Enzo Doria | 11/2015 |
| 2200 | 2^788325+224789 | 237310 | Enzo Doria | 07/2024 |
| 2201 | 15^201475+14 | 236953 | Alfred Reich | 10/2023 |
| 2202 | 2^786663+219173 | 236810 | Enzo Doria | 02/2024 |
| 2203 | 2^786180+1871971 | 236664 | Enzo Doria | 05/2016 |
| 2204 | 11^227092-90 | 236492 | Enzo Doria | 11/2012 |
| 2205 | 2^785260+1866361 | 236387 | Enzo Doria | 02/2016 |
| 2206 | (309*21^178772+71)/20 | 236377 | Eric Chen | 03/2026 |
| 2207 | 2^785220+1880611 | 236375 | Enzo Doria | 10/2016 |
| 2208 | (2^784689-15)/7 | 236215 | Stefano Morozzi | 08/2022 |
| 2209 | 19^184650-2 | 236122 | Robert Price | 10/2014 |
| 2210 | 10^236059+216513 | 236060 | Patrick De Geest | 04/2016 |
| 2211 | 10^236059-20909 | 236059 | Robert Price | 09/2015 |
| 2212 | 2^783988+38011 | 236004 | Enzo Doria | 10/2024 |
| 2213 | 2^783893-21 | 235976 | Stefano Morozzi | 07/2022 |
| 2214 | (47^140983-1)/2792206142311142462 | 235719 | Paul Vanderveen | 06/2025 |
| 2215 | 2^782821+37577 | 235653 | Enzo Doria | 10/2024 |
| 2216 | (87^121487-1)/86 | 235625 | Paul Bourdelais | 12/2018 |
| 2217 | 2^782634-113981 | 235597 | Enzo Doria | 11/2014 |
| 2218 | 2^782423+1879733 | 235533 | Enzo Doria | 09/2016 |
| 2219 | (10^(2*117707+1)+12*10^117707-1)/3 | 235415 | Robert Price | 10/2023 |
| 2220 | (2^781970)/(781970^2) | 235385 | Henri Lifchitz | 06/2025 |
| 2221 | 2^781682-2789543 | 235310 | Enzo Doria | 12/2015 |
| 2222 | 2^780481+21489 | 234949 | Enzo Doria | 05/2024 |
| 2223 | 2^780408-113453 | 234927 | Enzo Doria | 08/2014 |
| 2224 | 7*10^234915+9 | 234916 | Robert Price | 04/2023 |
| 2225 | 2^780368-1864829 | 234915 | Enzo Doria | 01/2016 |
| 2226 | 2^780284+7 | 234889 | Jon Grantham | 08/2023 |
| 2227 | 2^779593-1836559 | 234681 | Enzo Doria | 05/2015 |
| 2228 | (8713#+(549391#)/(8713#))/360295171 | 234487 | Makoto Morimoto | 11/2017 |
| 2229 | (5^335429+1)/6 | 234455 | Paul Bourdelais | 08/2010 |
| 2230 | 2^778788+22201 | 234439 | Enzo Doria | 09/2023 |
| 2231 | 2^778395-113617 | 234321 | Enzo Doria | 08/2014 |
| 2232 | 5*2^778090+3 | 234230 | Jon Grantham | 07/2023 |
| 2233 | (21430^54289-1)/(21430^233-1) | 234118 | Ryan Propper | 11/2023 |
| 2234 | (5*10^234054-101)/3 | 234055 | Robert Price | 08/2023 |
| 2235 | 23*10^234025-7 | 234027 | Robert Price | 10/2022 |
| 2236 | 2^777170+21489 | 233952 | Enzo Doria | 05/2024 |
| 2237 | Phi(78125,5517) | 233857 | Anonymous | 09/2022 |
| 2238 | 5^334359-3^334359-1 | 233707 | Jon Grantham | 08/2023 |
| 2239 | 2^776245-2792353 | 233674 | Enzo Doria | 02/2016 |
| 2240 | 49748^49748+49735^49735 | 233656 | Henri Lifchitz | 11/2024 |
| 2241 | 2^776060-114029 | 233618 | Enzo Doria | 11/2014 |
| 2242 | 2^775987-2789557 | 233596 | Enzo Doria | 12/2015 |
| 2243 | 2*10^233564-91 | 233565 | Robert Price | 02/2023 |
| 2244 | 2^775865+21489 | 233559 | Enzo Doria | 05/2024 |
| 2245 | 2^775672+1866721 | 233501 | Enzo Doria | 03/2016 |
| 2246 | 2^775238+57 | 233370 | Stefano Morozzi | 05/2021 |
| 2247 | (11^223999+1)/12 | 233270 | Paul Bourdelais | 02/2010 |
| 2248 | U(1302049) | 233238 | Serge Batalov | 07/2024 |
| 2249 | 2^774118+1885789 | 233033 | Enzo Doria | 04/2017 |
| 2250 | 21^176191-20^176191 | 232964 | Jean-Louis Charton | 01/2015 |
