## PRP Records

### Probable Primes Top 10000

#### (293510 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 (8*10^180725-629)/9 180725 Robert Price 01/2022 2002 (79*10^180710-1)/3 180712 Robert Price 02/2020 2003 2^600300-1852559 180709 Enzo Doria 08/2015 2004 (2*10^180706-77)/3 180706 Robert Price 02/2021 2005 (10^180689+71)/9 180689 Serge Batalov 07/2015 2006 2^600209+76487 180681 Enzo Doria 05/2016 2007 2^599999+378461 180617 Norman Luhn 09/2023 2008 (8*10^180536-269)/9 180536 Robert Price 09/2021 2009 2^599702-369885 180529 Enzo Doria 11/2013 2010 Tau(643^11688) 180524 Nik Lygeros / Olivier Rozier 05/2015 2011 (2951*29^123418-3)/4 180490 Curtis Bright 05/2015 2012 (29*10^180432-17)/3 180433 Robert Price 09/2019 2013 4*10^180360+93 180361 Robert Price 08/2018 2014 2^598942+80779 180300 Enzo Doria 07/2016 2015 (38*10^180296+403)/9 180297 Robert Price 10/2018 2016 (85*10^180241+77)/9 180242 Robert Price 07/2022 2017 2^598591-1844797 180194 Enzo Doria 06/2015 2018 (100^90089+1)/101 180176 Paul Bourdelais 08/2017 2019 (29*10^180072+691)/9 180073 Robert Price 08/2021 2020 (59*10^180038+157)/9 180039 Robert Price 12/2021 2021 95*10^180019-9 180021 Robert Price 01/2022 2022 6*10^179970+91 179971 Robert Price 05/2019 2023 (4*10^179963-79)/3 179964 Robert Price 02/2018 2024 (403*10^179944-43)/9 179946 Robert Price 06/2021 2025 Gamma-Prime(179849) 179849 Eric W. Weisstein 06/2011 2026 2^597424-1859729 179843 Enzo Doria 11/2015 2027 Phi(180683,10) 179760 Maksym Voznyy 09/2015 2028 (10^180683-1)*9/(10^643-1)/(10^281-1) 179760 Robert Price 07/2016 2029 (3^376657-2^376657)/22301107657 179701 Mike Oakes 04/2017 2030 (29*10^179697+223)/9 179698 Robert Price 09/2018 2031 2^596884+73 179680 Stefano Morozzi 04/2021 2032 (11*10^179679+13)/3 179680 Robert Price 03/2022 2033 (68*10^179656+7)/3 179658 Robert Price 01/2020 2034 (10^179643+173)/3 179643 Robert Price 05/2021 2035 2^596690-461261 179622 Enzo Doria 07/2015 2036 2^596684-113939 179620 Enzo Doria 10/2014 2037 2^596642+39 179608 Jon Grantham 08/2023 2038 2*10^179602+63 179603 Robert Price 05/2018 2039 (25*10^179488-403)/9 179489 Robert Price 01/2021 2040 7*10^179460+99 179461 Robert Price 05/2021 2041 2^596127+74333 179453 Enzo Doria 07/2023 2042 3^375887-112696 179344 Enzo Doria 07/2014 2043 4*10^179265-71 179266 Robert Price 12/2018 2044 2*10^179193+83 179194 Robert Price 12/2021 2045 2^595144-1850429 179157 Enzo Doria 08/2015 2046 2^595122-5 179150 Stefano Morozzi 07/2022 2047 3*10^179138+89 179139 Robert Price 10/2018 2048 (52*10^179062-133)/9 179063 Robert Price 09/2021 2049 2^594531+82253 178972 Enzo Doria 09/2016 2050 (664*10^178939-61)/9 178941 Robert Price 09/2021 2051 2^594260-2787899 178891 Enzo Doria 11/2015 2052 (14*10^178822+67)/9 178823 Robert Price 05/2022 2053 (29*10^178732-119)/9 178733 Robert Price 12/2021 2054 2^593631+101381 178701 Jorge Menendez 04/2018 2055 10^178695+136719 178696 Patrick De Geest 05/2016 2056 10^178695-71 178695 Serge Batalov 12/2014 2057 (2*10^178649-161)/3 178649 Robert Price 12/2020 2058 (691^62903-1)/690 178609 Michael Stocker 05/2020 2059 (2^148330+1)^4-2 178608 Cletus Emmanuel 12/2003 2060 2^593222-14145 178578 Jorge Menendez 10/2017 2061 7*10^178566+33 178567 Robert Price 06/2020 2062 2^593178+1867219 178565 Enzo Doria 03/2016 2063 (38*10^178456+151)/9 178457 Robert Price 03/2022 2064 (302*10^178369+13)/9 178371 Robert Price 02/2020 2065 (26*10^178296-113)/3 178297 Robert Price 06/2020 2066 (18^142031-1)/17 178287 Paul Bourdelais 03/2010 2067 (13*10^178233+137)/3 178234 Robert Price 06/2021 2068 (5*10^178206+91)/3 178207 Robert Price 04/2018 2069 2^591872-291929 178172 Enzo Doria 07/2015 2070 2^591682-286871 178115 Enzo Doria 07/2015 2071 (7^210761-5^210761)/2 178114 Jon Grantham 08/2023 2072 4*10^178091+9 178092 Robert Price 05/2015 2073 410747#+478483 178007 Makoto Morimoto 02/2016 2074 3*10^177872+73 177873 Robert Price 08/2018 2075 2^590762-396765 177838 Enzo Doria 08/2013 2076 (136*10^177754-1)/9 177756 Serge Batalov 12/2014 2078 ReverseConsecutiveIntegerPrime(37765) 177719 Eric W. Weisstein 04/2010 2077 Smr(37765) 177719 Eric W. Weisstein 12/2021 2079 (266*10^177577-11)/3 177579 Robert Price 04/2020 2080 (11*10^177466-113)/3 177467 Robert Price 10/2018 2081 3*10^177373-97 177374 Robert Price 07/2018 2082 2^589204+1881151 177369 Enzo Doria 11/2016 2083 2^589132-69479 177347 Enzo Doria 01/2016 2084 (101*10^177302-17)/3 177304 Robert Price 02/2020 2085 2^588912-113519 177281 Enzo Doria 08/2014 2086 (682*10^177266-7)/9 177268 Robert Price 08/2021 2087 15^150706+2 177245 Robert Price 06/2015 2088 2^588194-1861001 177065 Enzo Doria 11/2015 2089 5*10^177016-37 177017 Robert Price 11/2021 2090 fibonacci(846926)-4 176997 Jon Grantham 08/2023 2091 (23*10^176964-47)/3 176965 Robert Price 09/2019 2092 20530^41031+41031^20530 176942 Norbert Schneider 07/2022 2093 (19*10^176932+521)/9 176933 Robert Price 05/2018 2094 (8*10^176908+43)/3 176909 Robert Price 06/2018 2095 (85*10^176900+203)/9 176901 Robert Price 09/2020 2096 2^587560-113699 176874 Enzo Doria 09/2014 2097 20596^40995+40995^20596 176844 Norbert Schneider 07/2022 2098 (101*10^176815-17)/3 176817 Robert Price 02/2020 2099 (25*10^176715-37)/3 176716 Robert Price 10/2019 2100 5^252763-12862 176674 Enzo Doria 05/2014 2101 38442^38531+38531^38442 176658 Norbert Schneider 09/2022 2102 2^586804+81721 176646 Enzo Doria 08/2016 2103 (10^176584+77)/3 176584 Robert Price 01/2018 2104 2^586570+1874419 176576 Enzo Doria 06/2016 2105 (157*10^176482-1)/3 176484 Robert Price 01/2022 2106 5*2^586202+3 176466 Jon Grantham 07/2023 2107 2^585994-3311 176402 Yves Minet 12/2014 2108 8*10^176383-81 176384 Robert Price 02/2021 2109 (23*10^176357+61)/3 176358 Robert Price 01/2022 2110 2^585832-112799 176354 Enzo Doria 07/2014 2111 fibonacci(843383)+4 176257 Jon Grantham 08/2023 2112 (29*10^176240+49)/3 176241 Robert Price 09/2021 2113 (2^585387-11)/3 176219 Stefano Morozzi 08/2022 2114 2^585336-461039 176204 Enzo Doria 06/2015 2115 (25*10^176164+143)/3 176165 Robert Price 08/2020 2116 2^585095-1848127 176132 Enzo Doria 08/2015 2117 (5*10^176101-311)/9 176101 Robert Price 12/2021 2118 6*10^176092+77 176093 Robert Price 06/2020 2119 2^584950-115451 176088 Enzo Doria 07/2015 2120 (646*10^176044+11)/9 176046 Robert Price 10/2021 2121 (7^208283-5^208283)/2 176020 Jon Grantham 08/2023 2122 2^584671-3697 176004 Yves Minet 03/2017 2123 (13*10^175965-37)/3 175966 Robert Price 01/2019 2124 2*10^175860-87 175861 Robert Price 04/2018 2125 (86*10^175774-221)/9 175775 Robert Price 09/2019 2126 9*10^175654+47 175655 Robert Price 01/2022 2127 10^175608+2971 175609 Mike Oakes 05/2010 2128 10^175608-55829 175608 Patrick De Geest 09/2013 2129 2^583051+1879793 175516 Enzo Doria 09/2016 2130 (76*10^175514+491)/9 175515 Robert Price 10/2021 2131 2^582860-23829 175459 Enzo Doria 08/2013 2132 (8*10^175428-53)/9 175428 Serge Batalov 11/2022 2133 (28*10^175417-67)/3 175418 Robert Price 10/2020 2134 2^582670-23913 175402 Enzo Doria 08/2013 2135 2^582573-29563 175372 Enzo Doria 08/2015 2136 2^582435-1862767 175331 Enzo Doria 12/2015 2137 10^175295-40000001 175295 Robert Price 07/2022 2138 (11*10^175250-149)/3 175251 Robert Price 09/2018 2139 (29*10^175236+31)/3 175237 Robert Price 04/2021 2140 2^582072-1848599 175222 Enzo Doria 08/2015 2141 (404267#+465)/(3^4*5^2*31) 175208 Makoto Morimoto 06/2019 2142 Phi(262767,10)/259613797 175168 Makoto Kamada 12/2022 2143 (2^581871-15)/7 175160 Stefano Morozzi 08/2022 2144 (5*10^175117-311)/9 175117 Robert Price 12/2021 2145 (220221^32768+1)/2 175075 Serge Batalov 03/2018 2146 2^581560+1874911 175068 Enzo Doria 06/2016 2147 (25*10^174987-97)/9 174988 Robert Price 01/2022 2148 (75^93307-1)/74 174955 Paul Bourdelais 09/2017 2149 (47*10^174790+493)/9 174791 Robert Price 03/2019 2150 2^580528-114035 174757 Enzo Doria 11/2014 2151 (19*10^174754+737)/9 174755 Robert Price 07/2018 2152 (35*10^174704-377)/9 174705 Robert Price 07/2018 2153 (49*10^174681+293)/9 174682 Robert Price 03/2021 2154 6*10^174681+11 174682 Robert Price 07/2022 2155 3*10^174665-97 174666 Robert Price 07/2018 2156 2^580046-459161 174612 Enzo Doria 05/2015 2157 2^579992-39779 174595 Enzo Doria 09/2015 2158 (29*10^174481-149)/3 174482 Robert Price 08/2022 2159 (4*10^174423+101)/3 174424 Robert Price 11/2021 2160 (2^579371-17)/3 174408 Stefano Morozzi 08/2022 2161 (2*10^174301-71)/3 174301 Robert Price 12/2017 2162 14^152048+3 174267 Paul Bourdelais 12/2020 2163 (2^578696+1)/257 174203 Lelio R Paula 09/2015 2164 2^578656-1851809 174193 Enzo Doria 08/2015 2165 2^578583-113917 174171 Enzo Doria 10/2014 2166 2^578434-83 174126 Yves Minet 07/2017 2167 15^148048-2 174118 Robert Price 06/2015 2168 5*10^174101+81 174102 Robert Price 03/2019 2169 2^578346+2794249 174100 Enzo Doria 03/2016 2170 10^173947+1372429 173948 Patrick De Geest 08/2021 2172 10^173947-500000001 173947 Robert Price 12/2020 2171 10^173947-286391 173947 Patrick De Geest 08/2021 2173 5*10^173904-13 173905 Robert Price 01/2019 2174 (8*10^173862-59)/3 173863 Robert Price 08/2021 2175 (71*10^173854-287)/9 173855 Robert Price 09/2019 2176 (43*10^173826+101)/9 173827 Robert Price 11/2018 2177 2*10^173809-87 173810 Robert Price 04/2018 2178 (2^577372-23)/7 173806 Stefano Morozzi 08/2022 2179 (L!41532)/2 173772 Serge Batalov 07/2017 2180 2^577146-49877 173739 Enzo Doria 10/2015 2181 2^576889+49727 173661 Enzo Doria 09/2016 2182 (167*10^173571-17)/3 173573 Robert Price 03/2020 2183 37803^37916+37916^37803 173562 Norbert Schneider 06/2022 2184 5*10^173534+29 173535 Robert Price 12/2020 2185 (2^576551-1)/4612409/64758208321/242584327930759 173528 Dario Alpern 06/2014 2186 4*10^173509+99 173510 Robert Price 12/2020 2187 (13*10^173467-37)/3 173468 Robert Price 01/2019 2188 2^576016-113919 173399 Enzo Doria 11/2014 2189 2^575911-1849387 173367 Enzo Doria 08/2015 2190 515^63898+63898^515 173280 Norbert Schneider 12/2022 2191 2^575614+9 173278 Stefano Morozzi 04/2021 2192 (16*10^173251+107)/3 173252 Robert Price 03/2019 2193 2^575196-114053 173152 Enzo Doria 11/2014 2194 7*10^173135-53 173136 Robert Price 06/2020 2195 (301*10^173047+23)/9 173049 Robert Price 06/2021 2196 2^574591-115387 172970 Enzo Doria 07/2015 2197 (202*10^172940-13)/9 172942 Robert Price 01/2020 2198 45^104608+104608^45 172940 Norbert Schneider 06/2021 2199 2^574328+81121 172890 Enzo Doria 07/2016 2200 (115*10^172862-1)/3 172864 Serge Batalov 12/2014 2201 3*10^172812+13 172813 Robert Price 07/2018 2202 4*5^247217-9 172798 Lelio R Paula 10/2015 2203 6*10^172772-31 172773 Robert Price 07/2020 2204 69061#+(467617#)/(69061#) 172766 Makoto Morimoto 10/2017 2205 (34*10^172693-547)/9 172694 Robert Price 03/2021 2206 5*10^172692+57 172693 Robert Price 12/2018 2207 2^573668-2782319 172692 Enzo Doria 09/2015 2208 2^573444-1855109 172624 Enzo Doria 09/2015 2209 (14*10^172532-29)/3 172533 Robert Price 09/2021 2210 3^361608+2 172531 Robert Price 08/2014 2211 (54^99563+1)/55 172481 Paul Bourdelais 11/2017 2212 2^572592-114893 172368 Enzo Doria 05/2015 2213 4*10^172354-39 172355 Robert Price 09/2020 2214 37535^37674+37674^37535 172338 Norbert Schneider 05/2022 2215 (11*10^172322-119)/9 172323 Robert Price 11/2021 2216 5^246497-4^246497 172295 Jean-Louis Charton 11/2008 2217 (38^109037-1)/37 172254 Paul Bourdelais 10/2017 2218 (4*10^172241+89)/3 172242 Robert Price 08/2021 2219 3*10^172219+73 172220 Robert Price 08/2018 2220 A352736(15) 172032 Kellen Shenton 05/2022 2221 (36^110503+1)/37 171975 Lelio R Paula 04/2017 2222 8*10^171934+71 171935 Robert Price 05/2022 2223 (11*10^171933+601)/9 171934 Robert Price 02/2022 2224 (22*10^171929-73)/3 171930 Robert Price 04/2019 2225 (49*10^171892-319)/9 171893 Robert Price 10/2021 2226 4*10^171891-63 171892 Robert Price 10/2018 2227 67*10^171882-9 171884 Robert Price 03/2021 2228 2^570980-2782289 171883 Enzo Doria 09/2015 2229 (25*10^171849-37)/3 171850 Robert Price 10/2019 2230 10^171832+387909 171833 Patrick De Geest 08/2021 2231 10^171832-10001 171832 Robert Price 02/2021 2233 (2^(12*47563+13)-9)/7 171818 Kevin Acres 11/2013 2232 (2^570769-9)/7 171818 Stefano Morozzi 08/2022 2234 (74*10^171651-29)/9 171652 Robert Price 06/2022 2235 (536*10^171601-23)/9 171603 Robert Price 02/2020 2236 7*10^171535-99 171536 Robert Price 06/2019 2237 (28*10^171534+101)/3 171535 Robert Price 09/2020 2238 2^569563-1854607 171456 Enzo Doria 09/2015 2239 3*10^171391+59 171392 Robert Price 08/2018 2240 (13*10^171306-37)/3 171307 Robert Price 01/2019 2241 8*10^171296+87 171297 Robert Price 10/2019 2242 (55^98419-1)/54 171284 Paul Bourdelais 12/2017 2243 (29*10^171275+67)/3 171276 Robert Price 12/2019 2244 (457*10^171248-7)/9 171250 Robert Price 09/2022 2245 (194*10^171193+1)/3 171195 Robert Price 01/2022 2246 2^568642+1876129 171179 Enzo Doria 07/2016 2247 4*10^171146-47 171147 Robert Price 10/2021 2248 (19*10^170970+131)/3 170971 Robert Price 06/2020 2249 (46*10^170932+143)/9 170933 Robert Price 01/2019 2250 (79*10^170901-1)/3 170903 Robert Price 02/2020

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 29 2023 15:19 (Time in France)

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