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 | 2^744211-1845787 | 224030 | Enzo Doria | 07/2015 |
| 2002 | 2^743773+37757 | 223898 | Enzo Doria | 10/2024 |
| 2003 | 2^743592-134579 | 223844 | Hans Havermann | 10/2018 |
| 2004 | 2^742452+3 | 223501 | Paul Bourdelais | 06/2019 |
| 2005 | 234178^9+9^234178 | 223463 | Anatoly F. Selevich | 07/2011 |
| 2006 | 47747^47747-2512^2512 | 223406 | Henri Lifchitz | 10/2024 |
| 2007 | 2^741651-461197 | 223260 | Enzo Doria | 07/2015 |
| 2008 | 10^223236-1001 | 223236 | Robert Price | 10/2022 |
| 2009 | 2^741362-1845251 | 223173 | Enzo Doria | 07/2015 |
| 2010 | 3^467546-5*2^467546 | 223077 | Jon Grantham | 08/2023 |
| 2011 | 2^740455-1863877 | 222900 | Enzo Doria | 12/2015 |
| 2012 | 2^740274+217519 | 222845 | Enzo Doria | 01/2024 |
| 2013 | (14*10^222718-41)/9 | 222719 | Serge Batalov | 01/2023 |
| 2014 | 2^739636-2792219 | 222653 | Enzo Doria | 02/2016 |
| 2015 | 11^213654-180 | 222498 | Enzo Doria | 01/2013 |
| 2016 | 2^738957-1859743 | 222449 | Enzo Doria | 11/2015 |
| 2017 | 4*10^222253-21 | 222254 | Robert Price | 12/2022 |
| 2018 | 2^737825+57 | 222108 | Stefano Morozzi | 05/2021 |
| 2019 | (54^128189+1)/55 | 222073 | Paul Bourdelais | 11/2018 |
| 2020 | 3^232689+1^232689+4^232689+1^232689+5^232689+9^232689 | 222042 | Henri Lifchitz | 03/2025 |
| 2021 | 2^737166+220099 | 221910 | Enzo Doria | 03/2024 |
| 2022 | (10^221654+179)/9 | 221654 | Serge Batalov | 12/2014 |
| 2023 | 2^736281+79817 | 221643 | Enzo Doria | 06/2016 |
| 2024 | 10^221631+247617 | 221632 | Patrick De Geest | 10/2013 |
| 2025 | 10^221631-9 | 221631 | Alexander Gramolin | 02/2011 |
| 2026 | 10^221628+7 | 221629 | Alfred Reich | 04/2021 |
| 2027 | 2^735970-1839821 | 221550 | Enzo Doria | 06/2015 |
| 2028 | 2^735367+60293 | 221368 | Enzo Doria | 03/2016 |
| 2029 | 77*10^221343+3 | 221345 | Robert Price | 11/2023 |
| 2030 | 299^299^299-582 | 221328 | Henri Lifchitz | 03/2025 |
| 2031 | (241^92821-1)/240 | 221099 | Anonymous | 04/2024 |
| 2032 | (202*10^221092-1)/3 | 221094 | Robert Price | 06/2023 |
| 2033 | (5^316297-1)/220142716 | 221074 | Paul Vanderveen | 05/2025 |
| 2034 | (29^151153+1)/30 | 221045 | Paul Bourdelais | 09/2017 |
| 2035 | 2^734228+24751 | 221025 | Enzo Doria | 10/2023 |
| 2036 | (28*10^220800+173)/3 | 220801 | Robert Price | 07/2024 |
| 2037 | 2^733264-2784089 | 220735 | Enzo Doria | 10/2015 |
| 2038 | 2^733114-24555 | 220690 | Enzo Doria | 09/2013 |
| 2039 | 2^731891-636259 | 220322 | Enzo Doria | 12/2013 |
| 2040 | 98*10^220185-9 | 220187 | Robert Price | 05/2023 |
| 2041 | 418319^39164+418318 | 220161 | Alfred Reich | 11/2023 |
| 2042 | 2^4^182829+182829^4^2 | 220149 | Henri Lifchitz | 03/2025 |
| 2043 | 2^731124-25539 | 220091 | Enzo Doria | 09/2013 |
| 2044 | 2^730972-462029 | 220045 | Enzo Doria | 07/2015 |
| 2045 | 2^730833+1868627 | 220003 | Enzo Doria | 04/2016 |
| 2046 | 2^730645-2787133 | 219947 | Enzo Doria | 11/2015 |
| 2047 | 2^730547-25581 | 219917 | Enzo Doria | 09/2013 |
| 2048 | (113*13^197420-5)/12 | 219916 | Anonymous | 11/2022 |
| 2049 | (13^197420*113-5)/12 | 219916 | Eric Chen | 10/2023 |
| 2050 | 2^730460+82291 | 219891 | Enzo Doria | 09/2016 |
| 2051 | (5*10^219847-101)/3 | 219848 | Robert Price | 08/2023 |
| 2052 | (2^730339+1)/(3*27839062003*7943469324347) | 219831 | Gord Palameta | 12/2018 |
| 2053 | L(1051849) | 219824 | Renaud Lifchitz | 03/2009 |
| 2054 | 3*2^730149+5 | 219798 | Jon Grantham | 07/2023 |
| 2055 | 8*10^219740-3 | 219741 | Serge Batalov | 01/2023 |
| 2056 | 11^210961-240 | 219694 | Enzo Doria | 01/2013 |
| 2057 | (26*10^219639-77)/3 | 219640 | Robert Price | 03/2023 |
| 2058 | 2^729611-113437 | 219635 | Enzo Doria | 08/2014 |
| 2059 | 7^259710-2 | 219481 | Paul Bourdelais | 01/2021 |
| 2060 | F(1049897) | 219416 | Henri Lifchitz | 10/2008 |
| 2061 | (1488^69151-1)/1487 | 219386 | Alexander Zhirkov | 02/2023 |
| 2062 | 2^728604+1879321 | 219332 | Enzo Doria | 10/2016 |
| 2063 | 33^144412+2 | 219292 | Robert Price | 04/2015 |
| 2064 | 2^728277-183313 | 219234 | Hans Havermann | 10/2018 |
| 2065 | 2^727998-1862711 | 219150 | Enzo Doria | 12/2015 |
| 2066 | (29*10^219124+91)/3 | 219125 | Robert Price | 12/2022 |
| 2067 | 2^727729-114073 | 219069 | Enzo Doria | 12/2014 |
| 2068 | 2^727496-1851809 | 218999 | Enzo Doria | 08/2015 |
| 2069 | 2^727025+25907 | 218857 | Enzo Doria | 12/2023 |
| 2070 | 2^726591+2793143 | 218726 | Enzo Doria | 02/2016 |
| 2071 | (7*10^218644+17)/3 | 218645 | Robert Price | 06/2023 |
| 2072 | 2^725534-2791931 | 218408 | Enzo Doria | 02/2016 |
| 2073 | Phi(220531,10)/2686456812680882641 | 217774 | Makoto Kamada | 10/2020 |
| 2074 | 2^722184+1877821 | 217400 | Enzo Doria | 08/2016 |
| 2075 | (109*10^217360-1)/9 | 217362 | Serge Batalov | 12/2014 |
| 2076 | 2^721721-4453 | 217260 | Yves Minet | 03/2021 |
| 2077 | 10^216950+49 | 216951 | Robert Price | 02/2023 |
| 2078 | 281*499979#/46410-2702372 | 216849 | Robert Smith | 08/2016 |
| 2079 | 281*499979#/46410+2400766 | 216849 | Robert Smith | 08/2016 |
| 2080 | tau(311^15786) | 216429 | Nik Lygeros / Olivier Rozier / LR team | 10/2013 |
| 2081 | 2^718756-114107 | 216368 | Enzo Doria | 12/2014 |
| 2082 | 2^717672+121 | 216041 | Stefano Morozzi | 05/2021 |
| 2083 | 2^717305+80327 | 215931 | Enzo Doria | 07/2016 |
| 2084 | 2^717069-59773 | 215860 | Enzo Doria | 10/2015 |
| 2085 | 10^215802+33 | 215803 | Robert Price | 08/2023 |
| 2086 | 30^146021-29^146021 | 215691 | Jean-Louis Charton | 09/2018 |
| 2087 | 277^88301-276^88301 | 215674 | Jean-Louis Charton | 06/2012 |
| 2088 | 2^716428+215011 | 215667 | Enzo Doria | 11/2023 |
| 2089 | (13*10^215592-43)/3 | 215593 | Robert Price | 08/2023 |
| 2090 | p(41292)#+p(41292+1) | 215450 | Henri Lifchitz | 11/2024 |
| 2091 | (29^147319-1)/466757843690852 | 215425 | Paul Vanderveen | 06/2025 |
| 2092 | 227^91413-40 | 215372 | Enzo Doria | 04/2015 |
| 2093 | (2^715008-21)/5 | 215239 | Stefano Morozzi | 08/2022 |
| 2094 | 2^714717+782897 | 215152 | Enzo Doria | 11/2016 |
| 2095 | (19^168013-1)/80910356454 | 214837 | Paul Vanderveen | 05/2025 |
| 2096 | tau(373^15186) | 214796 | Nik Lygeros / Olivier Rozier / LR team | 10/2013 |
| 2097 | 2^713241+1879157 | 214707 | Enzo Doria | 08/2016 |
| 2098 | (23*10^214633+91)/3 | 214634 | Robert Price | 03/2023 |
| 2099 | 11^206081-10^206081 | 214612 | Jean-Louis Charton | 10/2011 |
| 2100 | 2^712801-69553 | 214575 | Enzo Doria | 01/2016 |
| 2101 | 2^712603-25357 | 214515 | Enzo Doria | 09/2013 |
| 2102 | 2^711721-1846723 | 214250 | Enzo Doria | 07/2015 |
| 2103 | 2^710730-396765 | 213952 | Enzo Doria | 09/2013 |
| 2104 | (19*10^213934-37)/9 | 213935 | Alfred Reich | 12/2023 |
| 2105 | (19*10^213730-37)/9 | 213731 | Alfred Reich | 12/2023 |
| 2106 | (713^74897-1)/712 | 213685 | Jinyuan Wang | 08/2023 |
| 2107 | 2^709773+25907 | 213663 | Enzo Doria | 12/2023 |
| 2108 | 2^708468-114329 | 213271 | Enzo Doria | 02/2015 |
| 2109 | 2^708293+27557 | 213218 | Enzo Doria | 01/2024 |
| 2110 | 379*10^213199+9 | 213202 | Jason Yuen | 01/2025 |
| 2111 | 2^707277+28997 | 212912 | Enzo Doria | 02/2024 |
| 2112 | (163*10^212779-1)/9 | 212781 | Serge Batalov | 12/2014 |
| 2113 | 2^706838-69041 | 212780 | Enzo Doria | 11/2015 |
| 2114 | 2^705653+25907 | 212423 | Enzo Doria | 12/2023 |
| 2115 | 22*10^212339+7 | 212341 | Robert Price | 10/2022 |
| 2116 | 2^704577-113871 | 212099 | Enzo Doria | 10/2014 |
| 2117 | (2^704548-19)/3 | 212090 | Stefano Morozzi | 08/2022 |
| 2118 | 2^704110-2792441 | 211959 | Enzo Doria | 02/2016 |
| 2119 | 2^704084+28531 | 211951 | Enzo Doria | 02/2024 |
| 2120 | 2^703943-1862947 | 211908 | Enzo Doria | 12/2015 |
| 2121 | (60^119083+1)/61 | 211746 | Paul Bourdelais | 10/2018 |
| 2122 | (184*10^211682-1)/3 | 211684 | Robert Price | 12/2022 |
| 2123 | (10^211610-91)/9 | 211610 | Serge Batalov | 12/2014 |
| 2124 | 227^89797+2 | 211565 | Lelio R Paula | 08/2012 |
| 2125 | 2^702194-3 | 211382 | Paul Bourdelais | 03/2012 |
| 2126 | 2^702064+1874911 | 211343 | Enzo Doria | 07/2016 |
| 2127 | 2^701968-113873 | 211314 | Enzo Doria | 10/2014 |
| 2128 | (14*10^211262-41)/9 | 211263 | Serge Batalov | 01/2023 |
| 2129 | 2^701713-113779 | 211237 | Enzo Doria | 09/2014 |
| 2130 | 2^701616-216803 | 211208 | Enzo Doria | 01/2024 |
| 2131 | 2^701449-25201 | 211158 | Enzo Doria | 09/2013 |
| 2132 | 2^701403-2786977 | 211144 | Enzo Doria | 11/2015 |
| 2133 | 2^701189-25423 | 211079 | Enzo Doria | 09/2013 |
| 2134 | 2^701162-459161 | 211071 | Enzo Doria | 05/2015 |
| 2135 | 2^700793+219407 | 210960 | Enzo Doria | 03/2024 |
| 2136 | (24^152783-1)/23 | 210872 | Paul Bourdelais | 04/2018 |
| 2137 | 2^700400+9385 | 210842 | Lelio R Paula | 01/2014 |
| 2138 | 2^700304-17 | 210813 | Stefano Morozzi | 07/2022 |
| 2139 | 2^700131+1874693 | 210761 | Enzo Doria | 06/2016 |
| 2140 | (2^700095+225414)/2 | 210750 | Stefano Morozzi | 04/2020 |
| 2141 | (2^700090+278254)/2 | 210748 | Stefano Morozzi | 04/2020 |
| 2142 | (2^700075+303666)/2 | 210744 | Stefano Morozzi | 04/2020 |
| 2143 | (2^700073+75882)/2 | 210743 | Stefano Morozzi | 04/2020 |
| 2144 | (2^700074+328890)/2 | 210743 | Stefano Morozzi | 04/2020 |
| 2145 | (2^700052+79162)/2 | 210737 | Stefano Morozzi | 04/2020 |
| 2146 | (2^700052+304458)/2 | 210737 | Stefano Morozzi | 04/2020 |
| 2147 | (2^700048+376578)/2 | 210736 | Stefano Morozzi | 04/2020 |
| 2148 | 11^202357-1140 | 210734 | Enzo Doria | 12/2012 |
| 2149 | (2^700021+25874)/2 | 210728 | Stefano Morozzi | 04/2020 |
| 2150 | (2^700018+377518)/2 | 210727 | Stefano Morozzi | 04/2020 |
| 2151 | 2^699999+300729 | 210721 | Norman Luhn | 09/2023 |
| 2152 | (238*10^210712-1)/3 | 210714 | Robert Price | 09/2023 |
| 2153 | 2^699740+25 | 210643 | Stefano Morozzi | 05/2021 |
| 2154 | (23*10^210525-143)/3 | 210526 | Robert Price | 12/2023 |
| 2155 | 2^698929-2788423 | 210399 | Enzo Doria | 11/2015 |
| 2156 | (5^300893+4^300893)/9 | 210315 | Jean-Louis Charton | 11/2011 |
| 2157 | 2^698316+1878601 | 210215 | Enzo Doria | 08/2016 |
| 2158 | 34*10^210097-9 | 210099 | Robert Price | 05/2023 |
| 2159 | (19*10^210011-49)/3 | 210012 | Robert Price | 06/2023 |
| 2160 | 6*10^209846-91 | 209847 | Robert Price | 05/2023 |
| 2161 | 2^697036+1878751 | 209829 | Enzo Doria | 08/2016 |
| 2162 | 2^696813+28607 | 209762 | Enzo Doria | 02/2024 |
| 2163 | (238*10^209715-1)/3 | 209717 | Robert Price | 09/2023 |
| 2164 | 6^269407+5 | 209640 | Paul Bourdelais | 02/2021 |
| 2165 | (2^696343-1)/11141489/36009913139329 | 209600 | Tony Prest / Never Odd Or Even | 02/2014 |
| 2166 | 2^696254-115151 | 209594 | Enzo Doria | 06/2015 |
| 2167 | 2^695841+225 | 209470 | Henri Lifchitz | 01/2025 |
| 2168 | (35^135623+1)/36 | 209410 | Paul Bourdelais | 07/2018 |
| 2169 | 7*10^209161+39 | 209162 | Robert Price | 01/2023 |
| 2170 | 2^694633+1887257 | 209106 | Enzo Doria | 05/2017 |
| 2171 | fibonacci(999790)-4 | 208944 | Jon Grantham | 08/2023 |
| 2172 | 2^693959+180923 | 208903 | Enzo Doria | 07/2016 |
| 2173 | (2^693747-11)/3 | 208839 | Stefano Morozzi | 08/2022 |
| 2174 | 2^693462-1847561 | 208753 | Enzo Doria | 07/2015 |
| 2175 | 2^690890-59981 | 207979 | Enzo Doria | 11/2015 |
| 2176 | (38^131591+1)/39 | 207884 | Paul Bourdelais | 07/2018 |
| 2177 | 3*2^690484+5 | 207857 | Jon Grantham | 07/2023 |
| 2178 | 2^690163+1877063 | 207760 | Enzo Doria | 07/2016 |
| 2179 | Phi(64773,-64773) | 207680 | Henri Lifchitz | 06/2025 |
| 2180 | 7^245608-2 | 207563 | Paul Bourdelais | 01/2021 |
| 2181 | (67*10^207556+23)/9 | 207557 | Serge Batalov | 01/2023 |
| 2182 | 2^689286-29381 | 207496 | Enzo Doria | 08/2015 |
| 2183 | 2^689122-114521 | 207447 | Enzo Doria | 04/2015 |
| 2184 | 9*10^207254-89 | 207255 | Robert Price | 02/2023 |
| 2185 | 2^688373+6077 | 207221 | Enzo Doria | 02/2016 |
| 2186 | 2^688201+1875527 | 207170 | Enzo Doria | 07/2016 |
| 2187 | (42^127609+1)/43 | 207140 | Paul Bourdelais | 07/2018 |
| 2188 | 2^687938+213589 | 207090 | Enzo Doria | 10/2023 |
| 2189 | 2^687619+81563 | 206994 | Enzo Doria | 08/2016 |
| 2190 | 3*10^206927+37 | 206928 | Robert Price | 08/2023 |
| 2191 | 2^687383+21803 | 206923 | Enzo Doria | 09/2023 |
| 2192 | (11*10^206688+19)/3 | 206689 | Robert Price | 07/2024 |
| 2193 | 2^686572-1845299 | 206679 | Enzo Doria | 07/2015 |
| 2194 | (21^156217-1)/20 | 206552 | Paul Bourdelais | 04/2010 |
| 2195 | 2^685970+39415 | 206498 | Enzo Doria | 11/2024 |
| 2196 | (2^685739+1)/(3*87774593) | 206420 | Gord Palameta | 08/2018 |
| 2197 | 2^685578+3 | 206380 | Paul Bourdelais | 04/2012 |
| 2198 | 2^685078+218599 | 206230 | Enzo Doria | 01/2024 |
| 2199 | 2^684836-49349 | 206157 | Enzo Doria | 10/2015 |
| 2200 | (73^110603-1)/72 | 206088 | Paul Bourdelais | 06/2018 |
| 2201 | 2^684163-2790967 | 205954 | Enzo Doria | 12/2015 |
| 2202 | 326^81943-325^81943 | 205941 | Jean-Louis Charton | 07/2012 |
| 2203 | (2^684127-1)/23765203727 | 205933 | Jens K. Andersen | 04/2009 |
| 2204 | (68*10^205510+13)/9 | 205511 | Serge Batalov | 01/2023 |
| 2205 | 4^341233-3^341233 | 205443 | Jean-Louis Charton | 01/2006 |
| 2206 | 2^682414+215029 | 205428 | Enzo Doria | 11/2023 |
| 2207 | (963^68821-1)/962 | 205334 | Jinyuan Wang | 01/2024 |
| 2208 | (43*10^205183-421)/9 | 205184 | Robert Price | 10/2023 |
| 2209 | 2^681545+467 | 205166 | Lelio R Paula | 11/2013 |
| 2210 | 2^681306+81049 | 205094 | Enzo Doria | 07/2016 |
| 2211 | 2^680697+1877057 | 204911 | Enzo Doria | 07/2016 |
| 2212 | 2^680415+71783 | 204826 | Enzo Doria | 04/2016 |
| 2213 | 10^204764-8001 | 204764 | Robert Price | 03/2023 |
| 2214 | (26*10^204730-77)/3 | 204731 | Robert Price | 03/2023 |
| 2215 | 2^679860-459995 | 204659 | Enzo Doria | 06/2015 |
| 2216 | 2^679593+1879547 | 204578 | Enzo Doria | 09/2016 |
| 2217 | 2^678899+220073 | 204369 | Enzo Doria | 03/2024 |
| 2218 | 2^678753+21677 | 204326 | Enzo Doria | 08/2023 |
| 2219 | 2^678651+1875023 | 204295 | Enzo Doria | 07/2016 |
| 2220 | 2^678561+678561 | 204268 | Henri Lifchitz | 05/2006 |
| 2221 | 5*3^427884+2^427884 | 204154 | Jon Grantham | 08/2023 |
| 2222 | 2^678101-114043 | 204129 | Enzo Doria | 11/2014 |
| 2223 | 2^678028+1875631 | 204107 | Enzo Doria | 06/2016 |
| 2224 | 2^677721+28607 | 204015 | Enzo Doria | 01/2024 |
| 2225 | (19*10^203798-7)/3 | 203799 | Robert Price | 12/2023 |
| 2226 | 2^676992-59783 | 203795 | Enzo Doria | 10/2015 |
| 2227 | 2^676972+1866871 | 203789 | Enzo Doria | 03/2016 |
| 2228 | 2^676815+22583 | 203742 | Enzo Doria | 09/2023 |
| 2229 | 2^676761-9 | 203726 | Robert Price | 01/2017 |
| 2230 | 2^676592-23 | 203675 | Stefano Morozzi | 07/2022 |
| 2231 | 2^676563-2792407 | 203666 | Enzo Doria | 02/2016 |
| 2232 | 2^676306-114713 | 203589 | Enzo Doria | 04/2015 |
| 2233 | (2^675977-1)/(1686378749257*7171117283326998925471) | 203456 | Dario Alpern | 07/2015 |
| 2234 | 6*10^203365+53 | 203366 | Robert Price | 09/2023 |
| 2235 | 2^675357-45801 | 203303 | Stefano Morozzi | 07/2025 |
| 2236 | 2^675354-109623 | 203302 | Stefano Morozzi | 07/2025 |
| 2237 | 2^675350-124911 | 203301 | Stefano Morozzi | 07/2025 |
| 2238 | 2^675345-83365 | 203300 | Stefano Morozzi | 07/2025 |
| 2239 | 2^675347-160357 | 203300 | Stefano Morozzi | 07/2025 |
| 2240 | 2^675339-178989 | 203298 | Stefano Morozzi | 07/2025 |
| 2241 | 2^675337-135031 | 203297 | Stefano Morozzi | 07/2025 |
| 2242 | 2^675337-21693 | 203297 | Stefano Morozzi | 07/2025 |
| 2243 | 2^675334-194937 | 203296 | Stefano Morozzi | 07/2025 |
| 2244 | 2^675334-34313 | 203296 | Stefano Morozzi | 07/2025 |
| 2245 | 2^675330-167061 | 203295 | Stefano Morozzi | 07/2025 |
| 2246 | 2^675331-148659 | 203295 | Stefano Morozzi | 07/2025 |
| 2247 | 2^675326-178983 | 203294 | Stefano Morozzi | 07/2025 |
| 2248 | 2^675327-107469 | 203294 | Stefano Morozzi | 07/2025 |
| 2249 | 2^675327-55159 | 203294 | Stefano Morozzi | 07/2025 |
| 2250 | 2^675328-92097 | 203294 | Stefano Morozzi | 07/2025 |
