## PRP Records

### Probable Primes Top 10000

#### (295756 PRPs in the top)

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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See the Latest PRPs
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 1-250 251-500 501-750 751-1000 1001-1250 1251-1500 1501-1750 1751-2000 2001-2250 2251-2500 2501-2750 2751-3000 3001-3250 3251-3500 3501-3750 3751-4000 4001-4250 4251-4500 4501-4750 4751-5000 5001-5250 5251-5500 5501-5750 5751-6000 6001-6250 6251-6500 6501-6750 6751-7000 7001-7250 7251-7500 7501-7750 7751-8000 8001-8250 8251-8500 8501-8750 8751-9000 9001-9250 9251-9500 9501-9750 9751-10000

 Rank Probable prime Digits (> 50000) Who ? When ? 2001 9*10^198946-73 198947 Robert Price 01/2021 2002 45*10^198931-7 198933 Robert Price 07/2020 2003 2^660482-2891 198825 Yves Minet 05/2016 2004 2^659589-21 198557 Stefano Morozzi 07/2022 2005 2^659583+1879223 198555 Enzo Doria 08/2016 2006 (53*10^198529+1)/9 198530 Serge Batalov 07/2010 2007 (49*10^198403+311)/9 198404 Robert Price 06/2019 2008 96*10^198376-7 198378 Robert Price 03/2021 2009 (10^198375+7)/59/1201/87589 198366 Alfred Reich 08/2021 2010 2^658828-29819 198327 Enzo Doria 08/2015 2011 2^658776-2791229 198312 Enzo Doria 01/2016 2012 (35*10^198294-377)/9 198295 Robert Price 07/2018 2013 (4*10^198268+137)/3 198269 Robert Price 03/2018 2014 2^658544-1854029 198242 Enzo Doria 09/2015 2015 (62*10^198229-233)/9 198230 Robert Price 02/2022 2016 (26*10^198200-41)/3 198201 Robert Price 02/2022 2017 (157^90239-1)/156 198154 Alexander Zhirkov 06/2016 2018 2^657815+26213 198023 Enzo Doria 12/2023 2019 2*10^197959-37 197960 Robert Price 11/2021 2020 (29*10^197941-41)/3 197942 Tyler Busby 03/2024 2021 (232*10^197897+17)/3 197899 Robert Price 04/2021 2022 (4*10^197778+173)/3 197779 Robert Price 02/2018 2023 2^656763+211373 197706 Enzo Doria 08/2023 2024 78*10^197702-7 197704 Robert Price 10/2020 2025 (17*10^197640-23)/3 197641 Robert Price 03/2021 2026 (29*10^197629-77)/3 197630 Robert Price 02/2020 2027 2^656462+1874419 197615 Enzo Doria 06/2016 2028 (89^101363+1)/90 197595 Paul Bourdelais 11/2017 2029 2^655893-344563 197444 Enzo Doria 07/2015 2030 2^655875+71333 197439 Enzo Doria 04/2016 2031 2^655845-9 197430 Robert Price 01/2017 2032 (299*10^197426+1)/3 197428 Robert Price 04/2020 2033 2^655682-1849121 197380 Enzo Doria 08/2015 2034 4*10^197268-89 197269 Robert Price 11/2018 2035 (11*10^197198-89)/3 197199 Robert Price 05/2021 2036 2^655045-49603 197189 Enzo Doria 10/2015 2037 2^655000-2784089 197175 Enzo Doria 10/2015 2038 (18^157051-1)/17 197141 Paul Bourdelais 03/2010 2039 (4*10^197061+41)/9 197061 Serge Batalov 11/2022 2040 (154*10^197005+17)/9 197007 Robert Price 06/2022 2041 2^654400-39719 196995 Enzo Doria 09/2015 2042 (5^281807-2^281807)/3 196975 Jon Grantham 08/2023 2043 (14*10^196965-221)/9 196966 Robert Price 04/2018 2044 2^654216-459995 196939 Enzo Doria 06/2015 2045 (17*10^196921+31)/3 196922 Robert Price 01/2019 2046 (14*10^196885-89)/3 196886 Robert Price 05/2020 2047 3*10^196881-59 196882 Robert Price 09/2018 2048 2^653851+82295 196829 Enzo Doria 09/2016 2049 (38*10^196792+691)/9 196793 Robert Price 10/2018 2050 (65*10^196768+493)/9 196769 Robert Price 08/2021 2052 2^653636-29429 196765 Enzo Doria 08/2015 2051 2^653638-11 196765 Stefano Morozzi 07/2022 2053 2^653601-69673 196754 Enzo Doria 02/2016 2054 (44*10^196684+1)/9 196685 Serge Batalov 07/2010 2055 2^652786-1852571 196509 Enzo Doria 08/2015 2056 2^652752-1325 196498 Yves Minet 07/2015 2057 2^652470-1859141 196414 Enzo Doria 10/2015 2058 2^652346+29329 196376 Enzo Doria 02/2024 2059 2^652307+1877483 196364 Enzo Doria 08/2016 2060 2^652293-115273 196360 Enzo Doria 06/2015 2061 (47*10^196281+403)/9 196282 Robert Price 03/2019 2062 2^652025+218027 196280 Enzo Doria 01/2024 2063 2^652004+23961 196273 Enzo Doria 10/2023 2064 (7*10^196125-31)/3 196126 Robert Price 12/2021 2065 33^129128+129128^33 196083 Norbert Schneider 06/2022 2066 6*10^196070+73 196071 Robert Price 04/2019 2067 2^651218-1868201 196037 Enzo Doria 04/2016 2068 2^651047-49687 195985 Enzo Doria 10/2015 2069 10^195968-700001 195968 Robert Price 08/2021 2070 fibonacci(937485)+3 195923 Jon Grantham 08/2023 2071 (29*10^195875-197)/3 195876 Robert Price 08/2021 2072 (25*10^195808-97)/9 195809 Robert Price 01/2022 2073 2^650285-2785333 195756 Enzo Doria 10/2015 2074 (10^195732+7)/18089/49605893 195721 Alfred Reich 08/2021 2075 (29*10^195648-41)/3 195649 Tyler Busby 03/2024 2076 (69^106397-1)/68 195647 Paul Bourdelais 10/2017 2077 2^649811+1877573 195613 Enzo Doria 08/2016 2078 2^649662-170531 195568 Hans Havermann 10/2018 2079 2^649586+182839 195545 Enzo Doria 11/2016 2080 2^649537-1867363 195531 Enzo Doria 04/2016 2081 2^649536-1861499 195530 Enzo Doria 12/2015 2082 2^649493+25907 195517 Enzo Doria 11/2023 2083 (103*10^195478-1)/3 195480 Serge Batalov 12/2014 2084 2^649102-59351 195400 Enzo Doria 10/2015 2085 (2*10^195399+529)/9 195399 Robert Price 01/2018 2086 (202*10^195383-13)/9 195385 Robert Price 01/2020 2087 2^648988+1178971 195365 Enzo Doria 06/2016 2088 2^648975-114319 195361 Enzo Doria 02/2015 2089 (11*10^195350-137)/9 195351 Robert Price 01/2018 2090 2^648619-24835 195254 Enzo Doria 09/2013 2091 5*10^195250-21 195251 Robert Price 12/2021 2092 (14*10^195234-83)/3 195235 Robert Price 12/2018 2093 5*10^195221+81 195222 Robert Price 03/2019 2094 10^195143-5001 195143 Robert Price 12/2021 2095 2^648190-24737 195125 Enzo Doria 09/2013 2096 (57^111119+1)/58 195110 Paul Bourdelais 10/2017 2097 (29*10^195098-197)/3 195099 Robert Price 08/2021 2098 10^195060+89701 195061 Patrick De Geest 02/2021 2100 10^195060-40000000001 195060 Robert Price 09/2020 2099 10^195060-110337 195060 Patrick De Geest 02/2021 2101 56*10^195032-3 195034 Robert Price 03/2020 2102 11^187185-90 194934 Enzo Doria 09/2012 2103 2^647468+220141 194908 Enzo Doria 03/2024 2104 (86*10^194818-437)/9 194819 Robert Price 03/2021 2105 7^230492-230492^7 194789 Henri Lifchitz 07/2024 2106 2^647068+77281 194787 Enzo Doria 05/2016 2107 2*10^194716-93 194717 Robert Price 12/2021 2108 15^165559-14^165559 194713 Jean-Louis Charton 03/2011 2109 F(931517) 194676 Henri Lifchitz 09/2008 2110 4*10^194668+49 194669 Robert Price 01/2019 2111 2^646589+1179407 194643 Enzo Doria 06/2016 2112 2^646289-114621 194553 Enzo Doria 05/2015 2113 2^646236-39659 194537 Enzo Doria 09/2015 2114 (16*10^194536+53)/3 194537 Robert Price 03/2019 2115 2^646161-59833 194514 Enzo Doria 11/2015 2116 (17*10^194502+31)/3 194503 Robert Price 01/2019 2117 (19*10^194428+287)/9 194429 Robert Price 10/2021 2118 2*10^194413+3 194414 Robert Price 07/2015 2119 2^645360-1848599 194273 Enzo Doria 08/2015 2120 22470^44641+44641^22470 194260 Norbert Schneider 08/2023 2121 (112*10^194150-1)/3 194152 Serge Batalov 12/2014 2122 Phi(293127,10) 194041 Makoto Kamada 12/2023 2123 2*10^193981-43 193982 Robert Price 04/2018 2124 2^644382+75169 193979 Enzo Doria 04/2016 2125 2^644304-1861409 193955 Enzo Doria 11/2015 2126 (29*10^193950-23)/3 193951 Robert Price 03/2022 2127 5*10^193907-9 193908 Robert Price 05/2015 2128 2^644043+1876703 193877 Enzo Doria 07/2016 2129 2*10^193841-63 193842 Robert Price 01/2022 2130 2^643735+1879733 193784 Enzo Doria 09/2016 2131 (5^277183+1)/6 193742 Paul Bourdelais 07/2010 2132 9*10^193712+71 193713 Robert Price 08/2020 2133 2^643216-286565 193628 Enzo Doria 07/2015 2134 2^643204+215011 193624 Enzo Doria 11/2023 2135 10^193566+1126339 193567 Patrick De Geest 09/2022 2137 10^193566-10000000001 193566 Robert Price 04/2021 2136 10^193566-454041 193566 Patrick De Geest 08/2021 2139 2^642888-24965 193529 Enzo Doria 09/2013 2138 2^642889+25367 193529 Enzo Doria 11/2023 2140 2^642448-114825 193397 Enzo Doria 05/2015 2141 2^642437-1856623 193393 Enzo Doria 10/2015 2142 2^642039-59797 193273 Enzo Doria 11/2015 2143 2^641987+39 193258 Jon Grantham 08/2023 2144 10^193230+513861 193231 Patrick De Geest 07/2018 2145 10^193230-8001 193230 Robert Price 03/2018 2146 (62*10^193225-233)/9 193226 Robert Price 02/2022 2147 2^641692-286349 193169 Enzo Doria 07/2015 2148 2^641690-24737 193168 Enzo Doria 09/2013 2149 22268^44421+44421^22268 193129 Norbert Schneider 06/2023 2150 2^641514+1876549 193115 Enzo Doria 07/2016 2151 2^640888-2785619 192927 Enzo Doria 10/2015 2152 2^640874-2783741 192923 Enzo Doria 09/2015 2153 10^192922+192207 192923 Patrick De Geest 08/2021 2154 10^192922-7001 192922 Robert Price 04/2021 2155 2^640854+25 192917 Stefano Morozzi 05/2021 2156 34*10^192868-9 192870 Robert Price 06/2020 2157 (46*10^192841+683)/9 192842 Robert Price 03/2019 2158 2^640181+467 192714 Lelio R Paula 08/2013 2159 2^640072+27541 192681 Enzo Doria 01/2024 2160 2^639536-1850249 192520 Enzo Doria 08/2015 2161 40714<>40712<>...<>1086421357911<>...<>40711<>40713 192464 Hans Havermann 12/2019 2162 5*10^192422-43 192423 Robert Price 01/2019 2163 2^639110-2792441 192392 Enzo Doria 02/2016 2164 (241^80761-1)/240 192372 Anonymous 04/2024 2165 2^638955-29827 192345 Enzo Doria 08/2015 2166 15^163539+14 192337 Alfred Reich 10/2023 2167 2^638713-2784223 192272 Enzo Doria 10/2015 2168 (10^192216+7)/149 192214 Alfred Reich 07/2021 2169 2^638490-113507 192205 Enzo Doria 08/2014 2170 2^638189-39943 192115 Enzo Doria 09/2015 2171 2^638110+1877119 192091 Enzo Doria 07/2016 2172 MillsLike(2,1,4,12,4,22,12,114,4,138,142,2956,6388,5248,17532,96930,83782,1464,897448,300832)+82440 192083 Sergey Batalov 05/2024 2173 MillsLike(2,1,4,12,4,22,12,114,4,138,142,2956,6388,5248,17532,96930,83782,1464,897448,300832) 192083 Sergey Batalov 05/2024 2174 2^638066-2785211 192078 Enzo Doria 10/2015 2175 (35*10^191973-341)/9 191974 Robert Price 08/2021 2176 (112*10^191900+17)/3 191902 Robert Price 03/2020 2177 2^637475-115309 191900 Enzo Doria 07/2015 2178 (68*10^191754-113)/9 191755 Robert Price 03/2021 2179 2^636930-11 191736 Stefano Morozzi 07/2022 2180 (47*10^191732+259)/9 191733 Robert Price 03/2022 2181 2^636661+1876577 191655 Enzo Doria 07/2016 2182 (9^200807-2^200807)/7 191618 Jon Grantham 07/2023 2183 (34^125101-1)/33 191589 Paul Bourdelais 11/2017 2184 fibonacci(916540)-2 191546 Jon Grantham 08/2023 2185 2^636177-1855123 191509 Enzo Doria 09/2015 2186 2^636158-113627 191503 Enzo Doria 08/2014 2187 (37*25^136966+63)/4 191472 Curtis Bright 05/2015 2188 2^636035+79823 191466 Enzo Doria 06/2016 2189 2^636011-1860847 191459 Enzo Doria 11/2015 2190 2^635926-1860611 191433 Enzo Doria 11/2015 2191 3*2^635755+5 191382 Jon Grantham 07/2023 2192 3*10^191152-7 191153 Robert Price 08/2015 2193 2^634883-1865677 191119 Enzo Doria 02/2016 2194 2^634801+1871957 191095 Enzo Doria 05/2016 2195 (77*10^191080+157)/9 191081 Robert Price 05/2022 2196 (35*10^191073+1)/9 191074 Serge Batalov 07/2010 2197 9*10^191018-41 191019 Robert Price 08/2020 2198 2^634470-59861 190995 Enzo Doria 11/2015 2199 2^634368-29519 190964 Enzo Doria 08/2015 2200 (19*10^190935+11)/3 190936 Robert Price 07/2023 2201 2^634188-350609 190910 Enzo Doria 06/2015 2202 (65*10^190899+493)/9 190900 Robert Price 08/2021 2203 (62*10^190795-413)/9 190796 Robert Price 09/2021 2204 (26*10^190789-131)/3 190790 Robert Price 10/2019 2205 (13*10^190732-61)/3 190733 Robert Price 11/2018 2206 3*2^633524+5 190711 Jon Grantham 07/2023 2207 (7*10^190683+143)/3 190684 Robert Price 03/2018 2208 2^633088-113879 190579 Enzo Doria 10/2014 2209 2^633064+1874911 190572 Enzo Doria 06/2016 2210 5*3^399402+2^399402 190564 Jon Grantham 08/2023 2211 (43*10^190547+83)/9 190548 Robert Price 11/2018 2212 99*10^190543+7 190545 Robert Price 05/2021 2213 (299*10^190533+1)/3 190535 Robert Price 04/2020 2214 (1744*10^190519-1747)/3 190522 Robert Price 12/2020 2215 2^632815-15 190497 Stefano Morozzi 07/2022 2216 2^632795-351205 190491 Enzo Doria 06/2015 2217 41171^41272+41272^41171 190454 Norbert Schneider 05/2023 2218 (16*10^190420-19)/3 190421 Robert Price 02/2019 2219 (43*10^190351+101)/9 190352 Robert Price 11/2018 2220 2^632156+78391 190298 Enzo Doria 06/2016 2221 97*10^190295-3 190297 Robert Price 05/2020 2222 2^632082-1851971 190276 Enzo Doria 08/2015 2223 2^632020+1880311 190257 Enzo Doria 09/2016 2224 (5*10^190242-77)/9 190242 Robert Price 04/2021 2225 7*10^190210+13 190211 Robert Price 03/2021 2226 2^631637-462373 190142 Enzo Doria 08/2015 2227 2*10^190126-21 190127 Robert Price 09/2020 2228 (28*10^190105+191)/3 190106 Robert Price 02/2020 2229 2*10^190093+33 190094 Robert Price 11/2021 2230 (68*10^190053-113)/9 190054 Robert Price 03/2021 2231 2^631183+213413 190006 Enzo Doria 09/2023 2232 2^631122-39251 189987 Enzo Doria 08/2015 2233 (26*10^189928-89)/9 189929 Robert Price 06/2018 2234 2^630839-97 189902 Yves Minet 07/2017 2235 99*10^189876-7 189878 Robert Price 07/2020 2236 41147^41147+30^30 189867 Henri Lifchitz 09/2024 2237 2^630359+1788953 189757 Enzo Doria 05/2016 2238 2^630228+1871971 189718 Enzo Doria 05/2016 2239 2^630108+781 189682 Lelio R Paula 08/2013 2240 2^629870-1867811 189610 Enzo Doria 04/2016 2241 (359^74189-1)/358 189558 Alexander Zhirkov 11/2017 2242 2^629326+2792929 189447 Enzo Doria 02/2016 2243 4*10^189401+13 189402 Robert Price 02/2021 2244 (10^189385-61)/3 189385 Serge Batalov 12/2014 2245 2^629036+1874011 189359 Enzo Doria 06/2016 2246 2^628930+80779 189327 Enzo Doria 07/2016 2247 (134*10^189309-11)/3 189311 Robert Price 01/2022 2248 9*10^189306-11 189307 Mischa Rodermond 04/2023 2249 3^396740-396740^3 189294 Henri Lifchitz 07/2024 2250 2^628582+1179439 189223 Enzo Doria 06/2016

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 12 2024 08:27 (Time in France)

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