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) !!!
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Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
2001 | 2^427824-1851507 | 128788 | Enzo Doria | 08/2015 |
2002 | 2^427807-21469 | 128783 | Enzo Doria | 07/2013 |
2003 | 11^123594-240 | 128710 | Enzo Doria | 09/2012 |
2004 | 2^427504-21503 | 128692 | Enzo Doria | 07/2013 |
2005 | 2^427420+91 | 128667 | Lelio R Paula | 05/2017 |
2006 | 2^427269-113635 | 128621 | Enzo Doria | 08/2014 |
2007 | 2^427130+1877569 | 128579 | Enzo Doria | 08/2016 |
2008 | 2^427016-115349 | 128545 | Enzo Doria | 07/2015 |
2009 | (4*10^128510+137)/3 | 128511 | Robert Price | 03/2018 |
2010 | 2^426889-112879 | 128507 | Enzo Doria | 06/2014 |
2011 | 2^426804+1869931 | 128481 | Enzo Doria | 05/2016 |
2012 | 2^426750+77635 | 128465 | Enzo Doria | 05/2016 |
2013 | 2^426425-91 | 128367 | Lelio R Paula | 05/2017 |
2014 | (15*2^426398-1)/11 | 128359 | Lelio R Paula | 05/2014 |
2015 | 2^426352+74971 | 128345 | Enzo Doria | 04/2016 |
2016 | 4*10^128343-21 | 128344 | Robert Price | 09/2018 |
2017 | 2^426300-1863689 | 128330 | Enzo Doria | 03/2016 |
2018 | 2^426293+1881017 | 128327 | Enzo Doria | 11/2016 |
2019 | 2^426043+35 | 128252 | Robert Price | 11/2015 |
2020 | (4*10^128244-19)/3 | 128245 | Robert Price | 03/2018 |
2021 | 2^425808-459959 | 128181 | Enzo Doria | 06/2015 |
2022 | 2^425627-113605 | 128127 | Enzo Doria | 08/2014 |
2023 | 18565^30002-30002^18565 | 128070 | Norbert Schneider | 01/2015 |
2024 | (2^425287-9)/2737 | 128021 | Lelio R Paula | 05/2015 |
2025 | (3*2^425233-1)/25 | 128007 | Lelio R Paula | 05/2014 |
2026 | 2^425205+4911 | 128000 | Marek Hubal | 02/2017 |
2027 | 2^425118-113663 | 127974 | Enzo Doria | 08/2014 |
2028 | 2^425061+1869761 | 127957 | Enzo Doria | 05/2016 |
2029 | 2^424918-21141 | 127914 | Enzo Doria | 07/2013 |
2030 | 2^424864-29489 | 127897 | Enzo Doria | 08/2015 |
2031 | (97*10^127858-1)/3 | 127860 | Serge Batalov | 12/2014 |
2032 | 2^424632-2786639 | 127827 | Enzo Doria | 03/2016 |
2033 | 2^424577-113755 | 127811 | Enzo Doria | 09/2014 |
2034 | (7*2^424512-1)/3 | 127792 | Lelio R Paula | 05/2014 |
2035 | 11^122629-720 | 127705 | Enzo Doria | 11/2012 |
2036 | 2^423696-21429 | 127546 | Enzo Doria | 07/2013 |
2037 | 2^423664-1864559 | 127536 | Enzo Doria | 03/2016 |
2038 | 3^267267-4 | 127519 | Henri Lifchitz | 10/2014 |
2039 | (19^99689+5^99689)/24 | 127477 | Robert Price | 09/2013 |
2040 | (21*2^423372+1)/101 | 127447 | Lelio R Paula | 05/2014 |
2041 | 2^423328-21537 | 127435 | Enzo Doria | 07/2013 |
2042 | (2^423165-7)/25 | 127384 | Lelio R Paula | 05/2015 |
2043 | (F(5)^182099-F(4)^182099)/F(3) | 127282 | Wayne Halsdorf | 08/2013 |
2044 | (234483*27^88884-145)/26 | 127230 | Curtis Bright | 05/2015 |
2045 | 2^422515-114997 | 127190 | Enzo Doria | 06/2015 |
2046 | 5*10^127179-3 | 127180 | Robert Price | 07/2015 |
2047 | (44*10^127169-233)/9 | 127170 | Robert Price | 01/2019 |
2048 | 5*10^127153+77 | 127154 | Robert Price | 12/2018 |
2049 | -516776642557847117490*Bern(37960)/34256837217082767928421792453 | 127042 | Thomas Ritschel | 06/2017 |
2050 | (78^67141-1)/77 | 127036 | Paul Bourdelais | 09/2017 |
2051 | 2^421860-113285 | 126993 | Enzo Doria | 07/2014 |
2052 | (2^421827-7)/11 | 126982 | Lelio R Paula | 05/2015 |
2053 | 11^121910-840 | 126957 | Enzo Doria | 12/2012 |
2054 | (71^68539+1)/72 | 126882 | Paul Bourdelais | 09/2017 |
2055 | (5*10^126871-119)/3 | 126872 | Robert Price | 03/2018 |
2056 | 331^50339-10004 | 126846 | Enzo Doria | 07/2012 |
2057 | 2^421363-2790757 | 126843 | Enzo Doria | 03/2016 |
2058 | (106*10^126839-1)/3 | 126841 | Serge Batalov | 12/2014 |
2059 | (7*2^421243+1)/39 | 126807 | Lelio R Paula | 05/2014 |
2060 | (14*10^126784-83)/3 | 126785 | Robert Price | 12/2018 |
2061 | 2^421161-286183 | 126783 | Enzo Doria | 06/2015 |
2062 | 2^420939-113935 | 126716 | Enzo Doria | 10/2014 |
2063 | 177^56363-2 | 126703 | Lelio R Paula | 10/2017 |
2064 | 2^420741-113659 | 126656 | Enzo Doria | 08/2014 |
2065 | 2^420694-21 | 126642 | Lelio R Paula | 05/2017 |
2066 | (13*10^126638+437)/9 | 126639 | Robert Price | 04/2018 |
2067 | 4*10^126625+87 | 126626 | Robert Price | 08/2018 |
2068 | (31*2^420556+1)/7 | 126601 | Lelio R Paula | 05/2014 |
2069 | 2^420424-59189 | 126561 | Enzo Doria | 10/2015 |
2070 | 2^420126+71893 | 126471 | Enzo Doria | 04/2016 |
2071 | (43*10^126441+47)/9 | 126442 | Robert Price | 12/2018 |
2072 | 2^419866+1877059 | 126393 | Enzo Doria | 07/2016 |
2073 | F(604711) | 126377 | Henri Lifchitz | 02/2005 |
2074 | 2^419757+72707 | 126360 | Enzo Doria | 04/2016 |
2075 | 2^419720-21569 | 126349 | Enzo Doria | 07/2013 |
2076 | 2^419637+29 | 126324 | Henri Lifchitz | 02/2006 |
2077 | 2^419612+1876741 | 126316 | Enzo Doria | 07/2016 |
2078 | 2^419520+2793271 | 126289 | Enzo Doria | 03/2016 |
2079 | (2^419447-5)/369 | 126264 | Lelio R Paula | 05/2014 |
2080 | 2^419328-1859939 | 126231 | Enzo Doria | 03/2016 |
2081 | 2^419282-1851507 | 126217 | Enzo Doria | 08/2015 |
2082 | 2^419251+1866143 | 126208 | Enzo Doria | 03/2016 |
2083 | 11^121185+2 | 126202 | Robert Price | 05/2014 |
2084 | (23*2^419036-1)/1393 | 126141 | Lelio R Paula | 05/2014 |
2085 | 2^418851+23 | 126087 | Robert Price | 09/2015 |
2086 | (2^418849-9)/2681 | 126083 | Lelio R Paula | 05/2014 |
2087 | 2^418829+167 | 126081 | Lelio R Paula | 01/2012 |
2088 | (31*2^418782-1)/75891 | 126063 | Lelio R Paula | 05/2014 |
2089 | (19*2^418754-1)/15 | 126058 | Lelio R Paula | 05/2014 |
2090 | 2^418319-109501 | 125927 | Enzo Doria | 04/2014 |
2091 | 2^418316-112373 | 125926 | Enzo Doria | 06/2014 |
2092 | (8*10^125894-29)/3 | 125895 | Robert Price | 07/2018 |
2093 | (26*10^125886-413)/9 | 125887 | Robert Price | 05/2018 |
2094 | 2^417968+1869811 | 125821 | Enzo Doria | 06/2016 |
2095 | 2^417902+63 | 125802 | Lelio R Paula | 09/2015 |
2096 | (10^125792-91)/9 | 125792 | Serge Batalov | 12/2014 |
2097 | (35*10^125754-593)/9 | 125755 | Robert Price | 07/2018 |
2098 | (32*10^125751-77)/9 | 125752 | Robert Price | 06/2018 |
2099 | 2^417704+77011 | 125742 | Enzo Doria | 05/2016 |
2100 | (10^125706+149)/3 | 125706 | Serge Batalov | 12/2014 |
2101 | 2^417419-115309 | 125656 | Enzo Doria | 07/2015 |
2102 | 2^417300+77281 | 125620 | Enzo Doria | 05/2016 |
2103 | 2^417095-1657 | 125559 | Yves Minet | 07/2014 |
2104 | 2^416773-25 | 125462 | Lelio R Paula | 09/2015 |
2105 | (289511#+292834)/(2^3*146417) | 125444 | Makoto Morimoto | 10/2017 |
2106 | (11*2^416691+1)/43 | 125436 | Lelio R Paula | 05/2014 |
2107 | 2^416641-2*416641+1 | 125422 | Robert Price | 05/2018 |
2108 | (21*2^416566-1)/17 | 125399 | Lelio R Paula | 05/2014 |
2109 | 2^416530+1870429 | 125389 | Enzo Doria | 05/2016 |
2110 | 2^416490+1875109 | 125376 | Enzo Doria | 09/2016 |
2111 | 2^416416-114929 | 125354 | Enzo Doria | 05/2015 |
2112 | (172*10^125292-1)/9 | 125294 | Serge Batalov | 12/2014 |
2113 | 2^416134+1865899 | 125269 | Enzo Doria | 03/2016 |
2114 | 153^57337-152 | 125264 | Norbert Schneider | 12/2018 |
2115 | (9*2^415992+1)/13560845 | 125220 | Lelio R Paula | 05/2014 |
2116 | (23^91943-1)/22 | 125201 | Robert Price | 01/2012 |
2117 | 43125^27010-106 | 125185 | Enzo Doria | 08/2012 |
2118 | (38*10^125166+349)/9 | 125167 | Robert Price | 10/2018 |
2119 | 2^415765-112603 | 125158 | Enzo Doria | 06/2014 |
2120 | 2^415290-113591 | 125015 | Enzo Doria | 08/2014 |
2121 | 2^415276-460919 | 125011 | Enzo Doria | 06/2015 |
2122 | 2^415259+77243 | 125006 | Enzo Doria | 05/2016 |
2123 | 2^415144-3683 | 124971 | Yves Minet | 10/2011 |
2124 | 2^414874+79 | 124890 | Lelio R Paula | 01/2015 |
2125 | (2^414765+7)/1389 | 124854 | Lelio R Paula | 05/2014 |
2126 | 2^414618+79459 | 124813 | Enzo Doria | 06/2016 |
2127 | 2^414432-1846709 | 124757 | Enzo Doria | 07/2015 |
2128 | 2*10^124751-51 | 124752 | Robert Price | 04/2018 |
2129 | (13*2^414274-1)/153 | 124708 | Lelio R Paula | 05/2014 |
2130 | (7*10^124648+197)/3 | 124649 | Robert Price | 07/2018 |
2131 | 2^414032-5 | 124637 | Henri Lifchitz | 07/2006 |
2132 | 2^414032+1872331 | 124637 | Enzo Doria | 05/2016 |
2133 | 14120^30009-30009^14120 | 124533 | Norbert Schneider | 02/2015 |
2134 | 64^68909-63^68909 | 124463 | Robert Price | 07/2013 |
2135 | 2^413387+76253 | 124442 | Enzo Doria | 04/2016 |
2136 | 2^413352+524287 | 124432 | Paul Underwood | 09/2018 |
2137 | 287117#+391613 | 124424 | Nicolas PALAU | 01/2017 |
2138 | (4*10^124420+83)/3 | 124421 | Robert Price | 02/2018 |
2139 | (27*2^413207-1)/108335 | 124385 | Lelio R Paula | 05/2014 |
2140 | (41*10^124335-383)/9 | 124336 | Robert Price | 11/2018 |
2141 | 2^412868-120599 | 124286 | Paul Bourdelais | 02/2012 |
2142 | 45^75145-2 | 124231 | Lelio R Paula | 08/2015 |
2143 | 2^412645-112213 | 124219 | Enzo Doria | 06/2014 |
2144 | 2^412248+74611 | 124100 | Enzo Doria | 04/2016 |
2145 | (22*10^124096-13)/9 | 124097 | Robert Price | 06/2018 |
2146 | 2^412192-3329 | 124083 | Yves Minet | 12/2014 |
2147 | (25*2^412191-1)/23 | 124082 | Lelio R Paula | 05/2014 |
2148 | F(593689) | 124074 | Henri Lifchitz | 01/2005 |
2149 | (11*2^412161+1)/19 | 124073 | Lelio R Paula | 05/2014 |
2150 | 2^411884-113279 | 123990 | Enzo Doria | 07/2014 |
2151 | (2^411832+1)/257 | 123972 | Lelio R Paula | 05/2014 |
2152 | (26*10^123970-89)/9 | 123971 | Robert Price | 06/2018 |
2153 | 2^411790-1853531 | 123962 | Enzo Doria | 08/2015 |
2154 | (5^177337+1)/6 | 123953 | Paul Bourdelais | 11/2008 |
2155 | 2^411711-113257 | 123938 | Enzo Doria | 07/2014 |
2156 | (23*2^411675-1)/3 | 123928 | Lelio R Paula | 05/2014 |
2157 | (11*10^123899-179)/3 | 123900 | Robert Price | 09/2018 |
2158 | 2^411325-351103 | 123822 | Enzo Doria | 06/2015 |
2159 | 2^411052+1872481 | 123739 | Enzo Doria | 05/2016 |
2160 | 2^410997+39 | 123723 | Lelio R Paula | 05/2014 |
2161 | 155^56438+154 | 123618 | Norbert Schneider | 01/2019 |
2162 | 2^410596-39 | 123602 | Lelio R Paula | 05/2014 |
2163 | 2^410540-115079 | 123585 | Enzo Doria | 06/2015 |
2164 | (7*10^123563+107)/3 | 123564 | Robert Price | 02/2018 |
2165 | (3*2^410392-1)/9229 | 123537 | Lelio R Paula | 05/2014 |
2166 | 2^410206-113081 | 123485 | Enzo Doria | 07/2014 |
2167 | (25*2^410192+1)/10397 | 123478 | Lelio R Paula | 04/2014 |
2168 | 2^409909-189 | 123395 | Enzo Doria | 05/2014 |
2169 | 2^409896-109043 | 123391 | Enzo Doria | 04/2014 |
2170 | 2^409890+75409 | 123390 | Enzo Doria | 04/2016 |
2171 | 133^58076-2 | 123345 | Lelio R Paula | 10/2017 |
2172 | F(590041) | 123311 | Henri Lifchitz | 01/2005 |
2173 | 2^409566-113501 | 123292 | Enzo Doria | 08/2014 |
2174 | 2^409533+77747 | 123282 | Enzo Doria | 05/2016 |
2175 | 2^409436-112799 | 123253 | Enzo Doria | 06/2014 |
2176 | 2^409225+1873787 | 123189 | Enzo Doria | 06/2016 |
2177 | 2^409174+73009 | 123174 | Enzo Doria | 04/2016 |
2178 | 2^409058-112685 | 123139 | Enzo Doria | 06/2014 |
2179 | (13*10^123137-61)/3 | 123138 | Robert Price | 11/2018 |
2180 | 4*10^123113+21 | 123114 | Robert Price | 12/2018 |
2181 | 2^408778+77689 | 123055 | Enzo Doria | 05/2016 |
2182 | 2^408690-75 | 123028 | Lelio R Paula | 11/2013 |
2183 | (29*10^122996+673)/9 | 122997 | Robert Price | 12/2018 |
2184 | 2^408574-2787341 | 122994 | Enzo Doria | 03/2016 |
2185 | 3*10^122977+37 | 122978 | Robert Price | 08/2018 |
2186 | Phi(157825,10) | 122961 | Maksym Voznyy | 06/2015 |
2187 | (13*2^408283+1)/1665 | 122904 | Lelio R Paula | 05/2014 |
2188 | (11*2^408100-1)/35 | 122850 | Lelio R Paula | 04/2014 |
2189 | (2^407821-lucasV(1,2,407821)+1)/2 | 122767 | Mike Oakes | 11/2016 |
2190 | (32*10^122733-77)/9 | 122734 | Robert Price | 06/2018 |
2191 | (21*2^407604-1)/215 | 122701 | Lelio R Paula | 04/2014 |
2192 | (21*2^407433-1)/13 | 122650 | Lelio R Paula | 04/2014 |
2193 | (73*10^122592-1)/9 | 122593 | Robert Price | 01/2015 |
2194 | (5*10^122592+91)/3 | 122593 | Robert Price | 04/2018 |
2195 | 2^407179-112075 | 122574 | Enzo Doria | 06/2014 |
2196 | (21*2^407131+1)/207517523 | 122552 | Lelio R Paula | 04/2014 |
2197 | (66^67349+1)/67 | 122543 | Paul Bourdelais | 09/2017 |
2198 | 2^407008-1867919 | 122522 | Enzo Doria | 04/2016 |
2199 | 11^117642-300 | 122512 | Enzo Doria | 10/2012 |
2200 | (F(3*97700+1)^2+L(3*97700+1)^2)/2 | 122509 | Henri Lifchitz | 10/2017 |
2201 | 2^406949+72197 | 122504 | Enzo Doria | 04/2016 |
2202 | 2^406826-65 | 122467 | Lelio R Paula | 11/2013 |
2203 | 2^406821-2797363 | 122466 | Enzo Doria | 04/2016 |
2204 | 2^406758-17 | 122447 | Lelio R Paula | 11/2013 |
2205 | (30^82883-1)/29 | 122427 | Robert Price | 12/2011 |
2206 | (2^406583-1)/813167 | 122388 | Jens K. Andersen | 02/2009 |
2207 | 4*10^122377+19 | 122378 | Robert Price | 10/2018 |
2208 | 3*10^122345-97 | 122346 | Robert Price | 07/2018 |
2209 | 97^61575-2 | 122336 | Lelio R Paula | 12/2014 |
2210 | 2^406298+2799109 | 122308 | Enzo Doria | 04/2016 |
2211 | (27*2^406241-1)/10277 | 122289 | Lelio R Paula | 04/2014 |
2212 | 2^406229-1849993 | 122288 | Enzo Doria | 08/2015 |
2213 | 3*10^122274+7 | 122275 | Robert Price | 07/2015 |
2214 | 2^406117+1876577 | 122254 | Enzo Doria | 07/2016 |
2215 | 3^256199-2^256199 | 122238 | Mike Oakes | 06/2005 |
2216 | 2^405992-78557 | 122216 | Jorge Menendez | 03/2018 |
2217 | (8*10^122203+43)/3 | 122204 | Robert Price | 06/2018 |
2218 | 2^405774+179149 | 122151 | Enzo Doria | 06/2016 |
2219 | 2^405514-3311 | 122072 | Yves Minet | 12/2014 |
2220 | 2^405514-115511 | 122072 | Enzo Doria | 07/2015 |
2221 | 2^405422-113261 | 122045 | Enzo Doria | 07/2014 |
2222 | 2^405173+71237 | 121970 | Enzo Doria | 04/2016 |
2223 | (2^405016+1)/257 | 121920 | Lelio R Paula | 04/2014 |
2224 | 2^404858+71329 | 121875 | Enzo Doria | 04/2016 |
2225 | 2^404813-114703 | 121861 | Enzo Doria | 04/2015 |
2226 | 2^404764+77791 | 121847 | Enzo Doria | 05/2016 |
2227 | 317^48694+48694^317 | 121787 | Norbert Schneider | 08/2015 |
2228 | 2^404536-115259 | 121778 | Enzo Doria | 06/2015 |
2229 | 2^404501-631 | 121767 | Yves Minet | 07/2012 |
2230 | 63^67620+2 | 121672 | Lelio R Paula | 08/2015 |
2231 | (17*10^121621+1)/9 | 121622 | Serge Batalov | 05/2010 |
2232 | (15*2^403912+1)/271 | 121589 | Lelio R Paula | 05/2014 |
2233 | (10^121543-79)/3 | 121543 | Robert Price | 01/2018 |
2234 | 2^403676+76831 | 121519 | Enzo Doria | 05/2016 |
2235 | (7*10^121487+143)/3 | 121488 | Robert Price | 03/2018 |
2236 | 2^403363-113635 | 121425 | Enzo Doria | 08/2014 |
2237 | 2^403336-1861469 | 121417 | Enzo Doria | 03/2016 |
2238 | p(24442)#/2-64 | 121381 | Robert Price | 04/2017 |
2239 | 11^116555-720 | 121380 | Enzo Doria | 11/2012 |
2240 | 2^403100-461267 | 121346 | Enzo Doria | 07/2015 |
2241 | 2^403093-112213 | 121344 | Enzo Doria | 06/2014 |
2242 | (316^48539+1)/317 | 121330 | Eric Chen | 10/2017 |
2243 | 2^403004+1866361 | 121317 | Enzo Doria | 03/2016 |
2244 | 2^402953+89 | 121301 | Lelio R Paula | 10/2013 |
2245 | 2^402944-2788319 | 121299 | Enzo Doria | 03/2016 |
2246 | (44*10^121297-719)/9 | 121298 | Robert Price | 12/2018 |
2247 | (27*2^402865+1)/5 | 121276 | Lelio R Paula | 04/2014 |
2248 | 2^402828-113183 | 121264 | Enzo Doria | 07/2014 |
2249 | (17*10^121242+1)/9 | 121243 | Serge Batalov | 05/2010 |
2250 | (15*2^402757+1)/101 | 121242 | Lelio R Paula | 05/2014 |