## PRP Records

### Probable Primes Top 10000

#### (295461 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) !!!

See the Top discoverers
See the Latest PRPs
Search by form

 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 2^653601-69673 196754 Enzo Doria 02/2016 2002 (44*10^196684+1)/9 196685 Serge Batalov 07/2010 2003 2^652786-1852571 196509 Enzo Doria 08/2015 2004 2^652752-1325 196498 Yves Minet 07/2015 2005 2^652470-1859141 196414 Enzo Doria 10/2015 2006 2^652346+29329 196376 Enzo Doria 02/2024 2007 2^652307+1877483 196364 Enzo Doria 08/2016 2008 2^652293-115273 196360 Enzo Doria 06/2015 2009 (47*10^196281+403)/9 196282 Robert Price 03/2019 2010 2^652025+218027 196280 Enzo Doria 01/2024 2011 2^652004+23961 196273 Enzo Doria 10/2023 2012 (7*10^196125-31)/3 196126 Robert Price 12/2021 2013 33^129128+129128^33 196083 Norbert Schneider 06/2022 2014 6*10^196070+73 196071 Robert Price 04/2019 2015 2^651218-1868201 196037 Enzo Doria 04/2016 2016 2^651047-49687 195985 Enzo Doria 10/2015 2017 10^195968-700001 195968 Robert Price 08/2021 2018 fibonacci(937485)+3 195923 Jon Grantham 08/2023 2019 (29*10^195875-197)/3 195876 Robert Price 08/2021 2020 (25*10^195808-97)/9 195809 Robert Price 01/2022 2021 2^650285-2785333 195756 Enzo Doria 10/2015 2022 (10^195732+7)/18089/49605893 195721 Alfred Reich 08/2021 2023 (29*10^195648-41)/3 195649 Tyler Busby 03/2024 2024 (69^106397-1)/68 195647 Paul Bourdelais 10/2017 2025 2^649811+1877573 195613 Enzo Doria 08/2016 2026 2^649662-170531 195568 Hans Havermann 10/2018 2027 2^649586+182839 195545 Enzo Doria 11/2016 2028 2^649537-1867363 195531 Enzo Doria 04/2016 2029 2^649536-1861499 195530 Enzo Doria 12/2015 2030 2^649493+25907 195517 Enzo Doria 11/2023 2031 (103*10^195478-1)/3 195480 Serge Batalov 12/2014 2032 2^649102-59351 195400 Enzo Doria 10/2015 2033 (2*10^195399+529)/9 195399 Robert Price 01/2018 2034 (202*10^195383-13)/9 195385 Robert Price 01/2020 2035 2^648988+1178971 195365 Enzo Doria 06/2016 2036 2^648975-114319 195361 Enzo Doria 02/2015 2037 (11*10^195350-137)/9 195351 Robert Price 01/2018 2038 2^648619-24835 195254 Enzo Doria 09/2013 2039 5*10^195250-21 195251 Robert Price 12/2021 2040 (14*10^195234-83)/3 195235 Robert Price 12/2018 2041 5*10^195221+81 195222 Robert Price 03/2019 2042 10^195143-5001 195143 Robert Price 12/2021 2043 2^648190-24737 195125 Enzo Doria 09/2013 2044 (57^111119+1)/58 195110 Paul Bourdelais 10/2017 2045 (29*10^195098-197)/3 195099 Robert Price 08/2021 2046 10^195060+89701 195061 Patrick De Geest 02/2021 2048 10^195060-40000000001 195060 Robert Price 09/2020 2047 10^195060-110337 195060 Patrick De Geest 02/2021 2049 56*10^195032-3 195034 Robert Price 03/2020 2050 11^187185-90 194934 Enzo Doria 09/2012 2051 2^647468+220141 194908 Enzo Doria 03/2024 2052 (86*10^194818-437)/9 194819 Robert Price 03/2021 2053 2^647068+77281 194787 Enzo Doria 05/2016 2054 2*10^194716-93 194717 Robert Price 12/2021 2055 15^165559-14^165559 194713 Jean-Louis Charton 03/2011 2056 F(931517) 194676 Henri Lifchitz 09/2008 2057 4*10^194668+49 194669 Robert Price 01/2019 2058 2^646589+1179407 194643 Enzo Doria 06/2016 2059 2^646289-114621 194553 Enzo Doria 05/2015 2060 2^646236-39659 194537 Enzo Doria 09/2015 2061 (16*10^194536+53)/3 194537 Robert Price 03/2019 2062 2^646161-59833 194514 Enzo Doria 11/2015 2063 (17*10^194502+31)/3 194503 Robert Price 01/2019 2064 (19*10^194428+287)/9 194429 Robert Price 10/2021 2065 2*10^194413+3 194414 Robert Price 07/2015 2066 2^645360-1848599 194273 Enzo Doria 08/2015 2067 22470^44641+44641^22470 194260 Norbert Schneider 08/2023 2068 (112*10^194150-1)/3 194152 Serge Batalov 12/2014 2069 Phi(293127,10) 194041 Makoto Kamada 12/2023 2070 2*10^193981-43 193982 Robert Price 04/2018 2071 2^644382+75169 193979 Enzo Doria 04/2016 2072 2^644304-1861409 193955 Enzo Doria 11/2015 2073 (29*10^193950-23)/3 193951 Robert Price 03/2022 2074 5*10^193907-9 193908 Robert Price 05/2015 2075 2^644043+1876703 193877 Enzo Doria 07/2016 2076 2*10^193841-63 193842 Robert Price 01/2022 2077 2^643735+1879733 193784 Enzo Doria 09/2016 2078 (5^277183+1)/6 193742 Paul Bourdelais 07/2010 2079 9*10^193712+71 193713 Robert Price 08/2020 2080 2^643216-286565 193628 Enzo Doria 07/2015 2081 2^643204+215011 193624 Enzo Doria 11/2023 2082 10^193566+1126339 193567 Patrick De Geest 09/2022 2084 10^193566-10000000001 193566 Robert Price 04/2021 2083 10^193566-454041 193566 Patrick De Geest 08/2021 2086 2^642888-24965 193529 Enzo Doria 09/2013 2085 2^642889+25367 193529 Enzo Doria 11/2023 2087 2^642448-114825 193397 Enzo Doria 05/2015 2088 2^642437-1856623 193393 Enzo Doria 10/2015 2089 2^642039-59797 193273 Enzo Doria 11/2015 2090 2^641987+39 193258 Jon Grantham 08/2023 2091 10^193230+513861 193231 Patrick De Geest 07/2018 2092 10^193230-8001 193230 Robert Price 03/2018 2093 (62*10^193225-233)/9 193226 Robert Price 02/2022 2094 2^641692-286349 193169 Enzo Doria 07/2015 2095 2^641690-24737 193168 Enzo Doria 09/2013 2096 22268^44421+44421^22268 193129 Norbert Schneider 06/2023 2097 2^641514+1876549 193115 Enzo Doria 07/2016 2098 2^640888-2785619 192927 Enzo Doria 10/2015 2099 2^640874-2783741 192923 Enzo Doria 09/2015 2100 10^192922+192207 192923 Patrick De Geest 08/2021 2101 10^192922-7001 192922 Robert Price 04/2021 2102 2^640854+25 192917 Stefano Morozzi 05/2021 2103 34*10^192868-9 192870 Robert Price 06/2020 2104 (46*10^192841+683)/9 192842 Robert Price 03/2019 2105 2^640181+467 192714 Lelio R Paula 08/2013 2106 2^640072+27541 192681 Enzo Doria 01/2024 2107 2^639536-1850249 192520 Enzo Doria 08/2015 2108 40714<>40712<>...<>1086421357911<>...<>40711<>40713 192464 Hans Havermann 12/2019 2109 5*10^192422-43 192423 Robert Price 01/2019 2110 2^639110-2792441 192392 Enzo Doria 02/2016 2111 (241^80761-1)/240 192372 Anonymous 04/2024 2112 2^638955-29827 192345 Enzo Doria 08/2015 2113 15^163539+14 192337 Alfred Reich 10/2023 2114 2^638713-2784223 192272 Enzo Doria 10/2015 2115 (10^192216+7)/149 192214 Alfred Reich 07/2021 2116 2^638490-113507 192205 Enzo Doria 08/2014 2117 2^638189-39943 192115 Enzo Doria 09/2015 2118 2^638110+1877119 192091 Enzo Doria 07/2016 2119 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 2120 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 2121 2^638066-2785211 192078 Enzo Doria 10/2015 2122 (35*10^191973-341)/9 191974 Robert Price 08/2021 2123 (112*10^191900+17)/3 191902 Robert Price 03/2020 2124 2^637475-115309 191900 Enzo Doria 07/2015 2125 (68*10^191754-113)/9 191755 Robert Price 03/2021 2126 2^636930-11 191736 Stefano Morozzi 07/2022 2127 (47*10^191732+259)/9 191733 Robert Price 03/2022 2128 2^636661+1876577 191655 Enzo Doria 07/2016 2129 (9^200807-2^200807)/7 191618 Jon Grantham 07/2023 2130 (34^125101-1)/33 191589 Paul Bourdelais 11/2017 2131 fibonacci(916540)-2 191546 Jon Grantham 08/2023 2132 2^636177-1855123 191509 Enzo Doria 09/2015 2133 2^636158-113627 191503 Enzo Doria 08/2014 2134 (37*25^136966+63)/4 191472 Curtis Bright 05/2015 2135 2^636035+79823 191466 Enzo Doria 06/2016 2136 2^636011-1860847 191459 Enzo Doria 11/2015 2137 2^635926-1860611 191433 Enzo Doria 11/2015 2138 3*2^635755+5 191382 Jon Grantham 07/2023 2139 3*10^191152-7 191153 Robert Price 08/2015 2140 2^634883-1865677 191119 Enzo Doria 02/2016 2141 2^634801+1871957 191095 Enzo Doria 05/2016 2142 (77*10^191080+157)/9 191081 Robert Price 05/2022 2143 (35*10^191073+1)/9 191074 Serge Batalov 07/2010 2144 9*10^191018-41 191019 Robert Price 08/2020 2145 2^634470-59861 190995 Enzo Doria 11/2015 2146 2^634368-29519 190964 Enzo Doria 08/2015 2147 (19*10^190935+11)/3 190936 Robert Price 07/2023 2148 2^634188-350609 190910 Enzo Doria 06/2015 2149 (65*10^190899+493)/9 190900 Robert Price 08/2021 2150 (62*10^190795-413)/9 190796 Robert Price 09/2021 2151 (26*10^190789-131)/3 190790 Robert Price 10/2019 2152 (13*10^190732-61)/3 190733 Robert Price 11/2018 2153 3*2^633524+5 190711 Jon Grantham 07/2023 2154 (7*10^190683+143)/3 190684 Robert Price 03/2018 2155 2^633088-113879 190579 Enzo Doria 10/2014 2156 2^633064+1874911 190572 Enzo Doria 06/2016 2157 5*3^399402+2^399402 190564 Jon Grantham 08/2023 2158 (43*10^190547+83)/9 190548 Robert Price 11/2018 2159 99*10^190543+7 190545 Robert Price 05/2021 2160 (299*10^190533+1)/3 190535 Robert Price 04/2020 2161 (1744*10^190519-1747)/3 190522 Robert Price 12/2020 2162 2^632815-15 190497 Stefano Morozzi 07/2022 2163 2^632795-351205 190491 Enzo Doria 06/2015 2164 41171^41272+41272^41171 190454 Norbert Schneider 05/2023 2165 (16*10^190420-19)/3 190421 Robert Price 02/2019 2166 (43*10^190351+101)/9 190352 Robert Price 11/2018 2167 2^632156+78391 190298 Enzo Doria 06/2016 2168 97*10^190295-3 190297 Robert Price 05/2020 2169 2^632082-1851971 190276 Enzo Doria 08/2015 2170 2^632020+1880311 190257 Enzo Doria 09/2016 2171 (5*10^190242-77)/9 190242 Robert Price 04/2021 2172 7*10^190210+13 190211 Robert Price 03/2021 2173 2^631637-462373 190142 Enzo Doria 08/2015 2174 2*10^190126-21 190127 Robert Price 09/2020 2175 (28*10^190105+191)/3 190106 Robert Price 02/2020 2176 2*10^190093+33 190094 Robert Price 11/2021 2177 (68*10^190053-113)/9 190054 Robert Price 03/2021 2178 2^631183+213413 190006 Enzo Doria 09/2023 2179 2^631122-39251 189987 Enzo Doria 08/2015 2180 (26*10^189928-89)/9 189929 Robert Price 06/2018 2181 2^630839-97 189902 Yves Minet 07/2017 2182 99*10^189876-7 189878 Robert Price 07/2020 2183 2^630359+1788953 189757 Enzo Doria 05/2016 2184 2^630228+1871971 189718 Enzo Doria 05/2016 2185 2^630108+781 189682 Lelio R Paula 08/2013 2186 2^629870-1867811 189610 Enzo Doria 04/2016 2187 (359^74189-1)/358 189558 Alexander Zhirkov 11/2017 2188 2^629326+2792929 189447 Enzo Doria 02/2016 2189 4*10^189401+13 189402 Robert Price 02/2021 2190 (10^189385-61)/3 189385 Serge Batalov 12/2014 2191 2^629036+1874011 189359 Enzo Doria 06/2016 2192 2^628930+80779 189327 Enzo Doria 07/2016 2193 (134*10^189309-11)/3 189311 Robert Price 01/2022 2194 9*10^189306-11 189307 Mischa Rodermond 04/2023 2195 3^396740-396740^3 189294 Henri Lifchitz 07/2024 2196 2^628582+1179439 189223 Enzo Doria 06/2016 2197 (44*10^188999-503)/9 189000 Robert Price 12/2018 2198 (16*10^188823+167)/3 188824 Robert Price 06/2019 2199 (10^188796+7)/4967/71933 188788 Alfred Reich 08/2021 2200 2^627037-2785843 188757 Enzo Doria 10/2015 2201 (10^188566+7)/311640753181661 188552 Alfred Reich 04/2022 2202 (16*10^188457+161)/3 188458 Robert Price 02/2019 2203 L(901657) 188436 Renaud Lifchitz 11/2008 2204 (19*10^188375+137)/3 188376 Robert Price 03/2022 2205 2^625651+74213 188340 Enzo Doria 04/2016 2206 2^625584-460919 188320 Enzo Doria 06/2015 2207 (8*10^188308-71)/9 188308 Serge Batalov 11/2022 2208 5^269399-3^269399-1 188302 Jon Grantham 08/2023 2209 (14*10^188218+139)/9 188219 Robert Price 11/2021 2210 (10^188164+359)/9 188164 Serge Batalov 12/2014 2211 2^624481-113611 187988 Enzo Doria 08/2014 2212 (2^624389+125582)/2 187960 Stefano Morozzi 09/2019 2213 (2^624389+166982)/2 187960 Stefano Morozzi 09/2019 2214 (2^624389+179886)/2 187960 Stefano Morozzi 09/2019 2215 (2^624387+64466)/2 187959 Stefano Morozzi 09/2019 2216 (2^624378+112990)/2 187957 Stefano Morozzi 09/2019 2217 (2^624380+161986)/2 187957 Stefano Morozzi 09/2019 2219 (2^624376+55762)/2 187956 Stefano Morozzi 09/2019 2218 (2^624377+169506)/2 187956 Stefano Morozzi 09/2019 2220 (2^624355+80178)/2 187950 Stefano Morozzi 09/2019 2221 (2^624351+61350)/2 187949 Stefano Morozzi 09/2019 2222 (2^624341+63462)/2 187946 Stefano Morozzi 09/2019 2223 (2^624344+135990)/2 187946 Stefano Morozzi 09/2019 2224 (2^624344+183898)/2 187946 Stefano Morozzi 09/2019 2226 (2^624340+126982)/2 187945 Stefano Morozzi 09/2019 2225 (2^624338+196110)/2 187945 Stefano Morozzi 09/2019 2227 (2^624337+105162)/2 187944 Stefano Morozzi 09/2019 2228 (2^624333+44594)/2 187943 Stefano Morozzi 09/2019 2229 (2^624321+88742)/2 187940 Stefano Morozzi 09/2019 2230 (2^624324+135178)/2 187940 Stefano Morozzi 09/2019 2231 (2^624317+14186)/2 187938 Stefano Morozzi 09/2019 2232 (2^624313+24450)/2 187937 Stefano Morozzi 09/2019 2233 (2^624309+184590)/2 187936 Stefano Morozzi 09/2019 2235 (2^624307+152658)/2 187935 Stefano Morozzi 09/2019 2234 (2^624307+185978)/2 187935 Stefano Morozzi 09/2019 2236 (2^624303+40814)/2 187934 Stefano Morozzi 09/2019 2237 (2^624304+99238)/2 187934 Stefano Morozzi 09/2019 2238 2^624077-112723 187866 Enzo Doria 07/2014 2239 2^624008+1874941 187846 Enzo Doria 06/2016 2240 2^623870+78679 187804 Enzo Doria 05/2016 2241 2^623714-114035 187757 Enzo Doria 11/2014 2242 2^623651-1834251 187738 Enzo Doria 07/2015 2243 (7*10^187645+53)/3 187646 Robert Price 05/2018 2244 21650^43269+43269^21650 187591 Norbert Schneider 02/2023 2245 2^623146+1879609 187586 Enzo Doria 09/2016 2246 (401*10^187512+13)/9 187514 Robert Price 09/2021 2247 (5*10^187471+91)/3 187472 Robert Price 04/2018 2248 2^622500+81931 187392 Enzo Doria 08/2016 2249 (13*10^187382-157)/9 187383 Robert Price 05/2021 2250 2^622300-1861739 187331 Enzo Doria 12/2015

Find by discoverer :

Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: July, 19 2024 15:29 (Time in France)

Go back