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
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| Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
| 3001 | 2^588912-113519 | 177281 | Enzo Doria | 08/2014 |
| 3002 | (682*10^177266-7)/9 | 177268 | Robert Price | 08/2021 |
| 3003 | 15^150706+2 | 177245 | Robert Price | 06/2015 |
| 3004 | 2^588403+335931 | 177127 | Enzo Doria | 09/2024 |
| 3005 | (31208^39601-1)/(31208^199-1) | 177084 | Ryan Propper | 11/2023 |
| 3006 | 2^588194-1861001 | 177065 | Enzo Doria | 11/2015 |
| 3007 | 5*10^177016-37 | 177017 | Robert Price | 11/2021 |
| 3008 | fibonacci(846926)-4 | 176997 | Jon Grantham | 08/2023 |
| 3009 | (23*10^176964-47)/3 | 176965 | Robert Price | 09/2019 |
| 3010 | 20530^41031+41031^20530 | 176942 | Norbert Schneider | 07/2022 |
| 3011 | (19*10^176932+521)/9 | 176933 | Robert Price | 05/2018 |
| 3012 | (8*10^176908+43)/3 | 176909 | Robert Price | 06/2018 |
| 3013 | (85*10^176900+203)/9 | 176901 | Robert Price | 09/2020 |
| 3014 | 2^587560-113699 | 176874 | Enzo Doria | 09/2014 |
| 3015 | 20596^40995+40995^20596 | 176844 | Norbert Schneider | 07/2022 |
| 3016 | (101*10^176815-17)/3 | 176817 | Robert Price | 02/2020 |
| 3017 | (25*10^176715-37)/3 | 176716 | Robert Price | 10/2019 |
| 3018 | 5^252763-12862 | 176674 | Enzo Doria | 05/2014 |
| 3019 | 38442^38531+38531^38442 | 176658 | Norbert Schneider | 09/2022 |
| 3020 | 2^586829+23961 | 176654 | Enzo Doria | 10/2023 |
| 3021 | 2^586804+81721 | 176646 | Enzo Doria | 08/2016 |
| 3022 | (10^176584+77)/3 | 176584 | Robert Price | 01/2018 |
| 3023 | 2^586570+1874419 | 176576 | Enzo Doria | 06/2016 |
| 3024 | (157*10^176482-1)/3 | 176484 | Robert Price | 01/2022 |
| 3025 | 5*2^586202+3 | 176466 | Jon Grantham | 07/2023 |
| 3026 | 27122^39799-39799^27122 | 176442 | Frank Doornink | 01/2024 |
| 3027 | 2^585994-3311 | 176402 | Yves Minet | 12/2014 |
| 3028 | 8*10^176383-81 | 176384 | Robert Price | 02/2021 |
| 3029 | (23*10^176357+61)/3 | 176358 | Robert Price | 01/2022 |
| 3030 | 2^585832-112799 | 176354 | Enzo Doria | 07/2014 |
| 3031 | fibonacci(843383)+4 | 176257 | Jon Grantham | 08/2023 |
| 3032 | (29*10^176240+49)/3 | 176241 | Robert Price | 09/2021 |
| 3033 | (2^585387-11)/3 | 176219 | Stefano Morozzi | 08/2022 |
| 3034 | 2^585336-461039 | 176204 | Enzo Doria | 06/2015 |
| 3035 | (25*10^176164+143)/3 | 176165 | Robert Price | 08/2020 |
| 3036 | 2^585095-1848127 | 176132 | Enzo Doria | 08/2015 |
| 3037 | (5*10^176101-311)/9 | 176101 | Robert Price | 12/2021 |
| 3038 | 6*10^176092+77 | 176093 | Robert Price | 06/2020 |
| 3039 | 2^584950-115451 | 176088 | Enzo Doria | 07/2015 |
| 3040 | (646*10^176044+11)/9 | 176046 | Robert Price | 10/2021 |
| 3041 | (7^208283-5^208283)/2 | 176020 | Jon Grantham | 08/2023 |
| 3042 | 2^584671-3697 | 176004 | Yves Minet | 03/2017 |
| 3043 | (13*10^175965-37)/3 | 175966 | Robert Price | 01/2019 |
| 3044 | 31728^39089-39089^31728 | 175957 | Frank Doornink | 01/2024 |
| 3045 | 2*10^175860-87 | 175861 | Robert Price | 04/2018 |
| 3046 | 27009^39670-39670^27009 | 175798 | Frank Doornink | 01/2024 |
| 3047 | (86*10^175774-221)/9 | 175775 | Robert Price | 09/2019 |
| 3048 | 2^583614+216037 | 175686 | Enzo Doria | 11/2023 |
| 3049 | 9*10^175654+47 | 175655 | Robert Price | 01/2022 |
| 3050 | 25430^39869-39869^25430 | 175637 | Frank Doornink | 01/2024 |
| 3051 | 10^175608+2971 | 175609 | Mike Oakes | 05/2010 |
| 3052 | 10^175608-55829 | 175608 | Patrick De Geest | 09/2013 |
| 3053 | 2^583051+1879793 | 175516 | Enzo Doria | 09/2016 |
| 3054 | (76*10^175514+491)/9 | 175515 | Robert Price | 10/2021 |
| 3056 | 2^582860-23829 | 175459 | Enzo Doria | 08/2013 |
| 3055 | (200^76253-1)/199 | 175459 | Anonymous | 06/2024 |
| 3057 | (8*10^175428-53)/9 | 175428 | Serge Batalov | 11/2022 |
| 3058 | (28*10^175417-67)/3 | 175418 | Robert Price | 10/2020 |
| 3059 | 2^582670-23913 | 175402 | Enzo Doria | 08/2013 |
| 3060 | 2^582573-29563 | 175372 | Enzo Doria | 08/2015 |
| 3061 | 2^582435-1862767 | 175331 | Enzo Doria | 12/2015 |
| 3062 | 10^175295-40000001 | 175295 | Robert Price | 07/2022 |
| 3063 | 31093^39018-39018^31093 | 175295 | Frank Doornink | 01/2024 |
| 3064 | (11*10^175250-149)/3 | 175251 | Robert Price | 09/2018 |
| 3065 | (29*10^175236+31)/3 | 175237 | Robert Price | 04/2021 |
| 3066 | 2^582072-1848599 | 175222 | Enzo Doria | 08/2015 |
| 3067 | (404267#+465)/(3^4*5^2*31) | 175208 | Makoto Morimoto | 06/2019 |
| 3068 | Phi(262767,10)/259613797 | 175168 | Makoto Kamada | 12/2022 |
| 3069 | (2^581871-15)/7 | 175160 | Stefano Morozzi | 08/2022 |
| 3070 | (5*10^175117-311)/9 | 175117 | Robert Price | 12/2021 |
| 3071 | 31193^38966-38966^31193 | 175116 | Frank Doornink | 01/2024 |
| 3072 | 2^581695+225893 | 175108 | Enzo Doria | 08/2024 |
| 3073 | 10^175093-89 | 175093 | Riley Fisher | 10/2023 |
| 3074 | (220221^32768+1)/2 | 175075 | Serge Batalov | 03/2018 |
| 3075 | 2^581560+1874911 | 175068 | Enzo Doria | 06/2016 |
| 3076 | (25*10^174987-97)/9 | 174988 | Robert Price | 01/2022 |
| 3077 | (75^93307-1)/74 | 174955 | Paul Bourdelais | 09/2017 |
| 3078 | 26446^39555-39555^26446 | 174927 | Frank Doornink | 03/2024 |
| 3079 | 31522^38883-38883^31522 | 174920 | Frank Doornink | 01/2024 |
| 3080 | (27398^39601-1)/(27398^199-1) | 174855 | Ryan Propper | 11/2023 |
| 3081 | (861^59557-1)/860 | 174798 | Jinyuan Wang | 11/2023 |
| 3082 | 31492^38859-38859^31492 | 174796 | Frank Doornink | 01/2024 |
| 3083 | (47*10^174790+493)/9 | 174791 | Robert Price | 03/2019 |
| 3084 | 2^580528-114035 | 174757 | Enzo Doria | 11/2014 |
| 3085 | (19*10^174754+737)/9 | 174755 | Robert Price | 07/2018 |
| 3086 | V(1045270)/4181081/12543241/81333115129561 | 174730 | Serge Batalov | 07/2024 |
| 3087 | (35*10^174704-377)/9 | 174705 | Robert Price | 07/2018 |
| 3089 | (49*10^174681+293)/9 | 174682 | Robert Price | 03/2021 |
| 3088 | 6*10^174681+11 | 174682 | Robert Price | 07/2022 |
| 3090 | 3*10^174665-97 | 174666 | Robert Price | 07/2018 |
| 3091 | 2^580046-459161 | 174612 | Enzo Doria | 05/2015 |
| 3092 | 2^579992-39779 | 174595 | Enzo Doria | 09/2015 |
| 3093 | 25613^39582-39582^25613 | 174496 | Frank Doornink | 02/2024 |
| 3094 | (29*10^174481-149)/3 | 174482 | Robert Price | 08/2022 |
| 3095 | (4*10^174423+101)/3 | 174424 | Robert Price | 11/2021 |
| 3096 | (2^579371-17)/3 | 174408 | Stefano Morozzi | 08/2022 |
| 3097 | (2*10^174301-71)/3 | 174301 | Robert Price | 12/2017 |
| 3098 | 14^152048+3 | 174267 | Paul Bourdelais | 12/2020 |
| 3099 | (2^578696+1)/257 | 174203 | Lelio R Paula | 09/2015 |
| 3100 | 2^578656-1851809 | 174193 | Enzo Doria | 08/2015 |
| 3101 | 2^578583-113917 | 174171 | Enzo Doria | 10/2014 |
| 3102 | 2^578434-83 | 174126 | Yves Minet | 07/2017 |
| 3103 | 15^148048-2 | 174118 | Robert Price | 06/2015 |
| 3104 | 5*10^174101+81 | 174102 | Robert Price | 03/2019 |
| 3105 | 2^578346+2794249 | 174100 | Enzo Doria | 03/2016 |
| 3106 | 10^173947+1372429 | 173948 | Patrick De Geest | 08/2021 |
| 3108 | 10^173947-500000001 | 173947 | Robert Price | 12/2020 |
| 3107 | 10^173947-286391 | 173947 | Patrick De Geest | 08/2021 |
| 3109 | 5*10^173904-13 | 173905 | Robert Price | 01/2019 |
| 3110 | (8*10^173862-59)/3 | 173863 | Robert Price | 08/2021 |
| 3111 | (71*10^173854-287)/9 | 173855 | Robert Price | 09/2019 |
| 3112 | (43*10^173826+101)/9 | 173827 | Robert Price | 11/2018 |
| 3114 | 2*10^173809-87 | 173810 | Robert Price | 04/2018 |
| 3113 | (17^141263-1)/27122512 | 173810 | Paul Vanderveen | 05/2025 |
| 3115 | (2^577372-23)/7 | 173806 | Stefano Morozzi | 08/2022 |
| 3116 | (L!41532)/2 | 173772 | Serge Batalov | 07/2017 |
| 3117 | 2^577146-49877 | 173739 | Enzo Doria | 10/2015 |
| 3118 | 2^576889+49727 | 173661 | Enzo Doria | 09/2016 |
| 3119 | (19^173604)%(10^173604) | 173604 | Henri Lifchitz | 05/2025 |
| 3120 | (167*10^173571-17)/3 | 173573 | Robert Price | 03/2020 |
| 3121 | 37803^37916+37916^37803 | 173562 | Norbert Schneider | 06/2022 |
| 3122 | 5*10^173534+29 | 173535 | Robert Price | 12/2020 |
| 3123 | (2^576551-1)/4612409/64758208321/242584327930759 | 173528 | Dario Alpern | 06/2014 |
| 3124 | 4*10^173509+99 | 173510 | Robert Price | 12/2020 |
| 3125 | (13*10^173467-37)/3 | 173468 | Robert Price | 01/2019 |
| 3126 | 2^576016-113919 | 173399 | Enzo Doria | 11/2014 |
| 3127 | 2^575911-1849387 | 173367 | Enzo Doria | 08/2015 |
| 3128 | 21554^40005-40005^21554 | 173363 | Norbert Schneider | 04/2025 |
| 3129 | 2^575879+215843 | 173357 | Enzo Doria | 11/2023 |
| 3130 | 2^575871+28733 | 173355 | Enzo Doria | 01/2024 |
| 3131 | 515^63898+63898^515 | 173280 | Norbert Schneider | 12/2022 |
| 3132 | 2^575614+9 | 173278 | Stefano Morozzi | 04/2021 |
| 3133 | 2^575606-219533 | 173275 | Enzo Doria | 03/2024 |
| 3134 | (16*10^173251+107)/3 | 173252 | Robert Price | 03/2019 |
| 3135 | 26618^39149-39149^26618 | 173242 | Frank Doornink | 03/2024 |
| 3136 | 2^575196-114053 | 173152 | Enzo Doria | 11/2014 |
| 3137 | 7*10^173135-53 | 173136 | Robert Price | 06/2020 |
| 3138 | (301*10^173047+23)/9 | 173049 | Robert Price | 06/2021 |
| 3139 | 2^574591-115387 | 172970 | Enzo Doria | 07/2015 |
| 3140 | 25210^39297-39297^25210 | 172969 | Frank Doornink | 12/2023 |
| 3141 | (202*10^172940-13)/9 | 172942 | Robert Price | 01/2020 |
| 3142 | 45^104608+104608^45 | 172940 | Norbert Schneider | 06/2021 |
| 3143 | 2^574328+81121 | 172890 | Enzo Doria | 07/2016 |
| 3144 | (115*10^172862-1)/3 | 172864 | Serge Batalov | 12/2014 |
| 3145 | 3*10^172812+13 | 172813 | Robert Price | 07/2018 |
| 3146 | 4*5^247217-9 | 172798 | Lelio R Paula | 10/2015 |
| 3147 | 6*10^172772-31 | 172773 | Robert Price | 07/2020 |
| 3148 | 69061#+(467617#)/(69061#) | 172766 | Makoto Morimoto | 10/2017 |
| 3149 | (34*10^172693-547)/9 | 172694 | Robert Price | 03/2021 |
| 3150 | 5*10^172692+57 | 172693 | Robert Price | 12/2018 |
| 3151 | 2^573668-2782319 | 172692 | Enzo Doria | 09/2015 |
| 3152 | 2^573444-1855109 | 172624 | Enzo Doria | 09/2015 |
| 3153 | 25500^39173-39173^25500 | 172618 | Frank Doornink | 02/2024 |
| 3154 | 27180^38917-38917^27180 | 172568 | Frank Doornink | 01/2024 |
| 3155 | (14*10^172532-29)/3 | 172533 | Robert Price | 09/2021 |
| 3156 | 3^361608+2 | 172531 | Robert Price | 08/2014 |
| 3157 | (54^99563+1)/55 | 172481 | Paul Bourdelais | 11/2017 |
| 3158 | 2^572592-114893 | 172368 | Enzo Doria | 05/2015 |
| 3159 | 4*10^172354-39 | 172355 | Robert Price | 09/2020 |
| 3160 | 37535^37674+37674^37535 | 172338 | Norbert Schneider | 05/2022 |
| 3161 | (11*10^172322-119)/9 | 172323 | Robert Price | 11/2021 |
| 3162 | 5^246497-4^246497 | 172295 | Jean-Louis Charton | 11/2008 |
| 3163 | (38^109037-1)/37 | 172254 | Paul Bourdelais | 10/2017 |
| 3164 | (4*10^172241+89)/3 | 172242 | Robert Price | 08/2021 |
| 3165 | 3*10^172219+73 | 172220 | Robert Price | 08/2018 |
| 3166 | 2^571810+28549 | 172132 | Enzo Doria | 01/2024 |
| 3167 | A352736(15) | 172032 | Kellen Shenton | 05/2022 |
| 3168 | 32298^38149-38149^32298 | 172021 | Frank Doornink | 02/2024 |
| 3169 | 2^571300+25861 | 171979 | Enzo Doria | 11/2023 |
| 3170 | (36^110503+1)/37 | 171975 | Lelio R Paula | 04/2017 |
| 3171 | 8*10^171934+71 | 171935 | Robert Price | 05/2022 |
| 3172 | (11*10^171933+601)/9 | 171934 | Robert Price | 02/2022 |
| 3173 | (22*10^171929-73)/3 | 171930 | Robert Price | 04/2019 |
| 3174 | (49*10^171892-319)/9 | 171893 | Robert Price | 10/2021 |
| 3175 | 4*10^171891-63 | 171892 | Robert Price | 10/2018 |
| 3176 | 67*10^171882-9 | 171884 | Robert Price | 03/2021 |
| 3177 | 2^570980-2782289 | 171883 | Enzo Doria | 09/2015 |
| 3178 | (25*10^171849-37)/3 | 171850 | Robert Price | 10/2019 |
| 3179 | 10^171832+387909 | 171833 | Patrick De Geest | 08/2021 |
| 3180 | 10^171832-10001 | 171832 | Robert Price | 02/2021 |
| 3182 | (2^(12*47563+13)-9)/7 | 171818 | Kevin Acres | 11/2013 |
| 3181 | (2^570769-9)/7 | 171818 | Stefano Morozzi | 08/2022 |
| 3183 | 2^570545+11025 | 171752 | Henri Lifchitz | 01/2025 |
| 3184 | 24^124375-124375^24 | 171664 | Henri Lifchitz | 08/2024 |
| 3185 | (74*10^171651-29)/9 | 171652 | Robert Price | 06/2022 |
| 3186 | (536*10^171601-23)/9 | 171603 | Robert Price | 02/2020 |
| 3187 | 7*10^171535-99 | 171536 | Robert Price | 06/2019 |
| 3188 | (28*10^171534+101)/3 | 171535 | Robert Price | 09/2020 |
| 3189 | 2^569563-1854607 | 171456 | Enzo Doria | 09/2015 |
| 3190 | 32133^38042-38042^32133 | 171454 | Frank Doornink | 02/2024 |
| 3191 | 3*10^171391+59 | 171392 | Robert Price | 08/2018 |
| 3192 | (13*10^171306-37)/3 | 171307 | Robert Price | 01/2019 |
| 3193 | 8*10^171296+87 | 171297 | Robert Price | 10/2019 |
| 3194 | (55^98419-1)/54 | 171284 | Paul Bourdelais | 12/2017 |
| 3195 | (29*10^171275+67)/3 | 171276 | Robert Price | 12/2019 |
| 3196 | (457*10^171248-7)/9 | 171250 | Robert Price | 09/2022 |
| 3197 | (194*10^171193+1)/3 | 171195 | Robert Price | 01/2022 |
| 3198 | 2^568642+1876129 | 171179 | Enzo Doria | 07/2016 |
| 3199 | 4*10^171146-47 | 171147 | Robert Price | 10/2021 |
| 3200 | (19*10^170970+131)/3 | 170971 | Robert Price | 06/2020 |
| 3201 | (46*10^170932+143)/9 | 170933 | Robert Price | 01/2019 |
| 3202 | (79*10^170901-1)/3 | 170903 | Robert Price | 02/2020 |
| 3203 | (58*10^170842+221)/9 | 170843 | Robert Price | 02/2017 |
| 3204 | (29*10^170830+583)/9 | 170831 | Robert Price | 06/2021 |
| 3205 | 3*10^170800+73 | 170801 | Robert Price | 08/2018 |
| 3206 | (29*10^170799-119)/9 | 170800 | Robert Price | 12/2021 |
| 3207 | 11^164009-270 | 170798 | Enzo Doria | 10/2012 |
| 3208 | 2*10^170767+41 | 170768 | Robert Price | 05/2018 |
| 3209 | 3^357706-112358 | 170670 | Enzo Doria | 07/2014 |
| 3210 | TheodorusPrime(170657) | 170657 | Eric W. Weisstein | 08/2013 |
| 3211 | 2^566871+1876163 | 170646 | Enzo Doria | 07/2016 |
| 3212 | (10657#+(404267#)/(10657#))/(1675379) | 170624 | Makoto Morimoto | 10/2017 |
| 3213 | 2^566496+7 | 170533 | Donovan Johnson | 07/2006 |
| 3214 | (7^201653+1)/8 | 170416 | Paul Bourdelais | 02/2010 |
| 3215 | 32150^37807-37807^32150 | 170403 | Frank Doornink | 02/2024 |
| 3216 | 7*10^170348+33 | 170349 | Robert Price | 06/2020 |
| 3217 | 2^565799+216011 | 170323 | Enzo Doria | 12/2023 |
| 3218 | 2^565183-352021 | 170138 | Enzo Doria | 07/2015 |
| 3219 | 2^565143-114457 | 170125 | Enzo Doria | 02/2015 |
| 3220 | 3*2^565024-5 | 170090 | Jon Grantham | 07/2023 |
| 3221 | 2^564976-49869 | 170075 | Enzo Doria | 10/2015 |
| 3222 | 2^564561+225 | 169950 | Henri Lifchitz | 11/2024 |
| 3223 | (7*10^169944+23)/3 | 169945 | Robert Price | 06/2020 |
| 3224 | (37*10^169943+251)/9 | 169944 | Robert Price | 09/2021 |
| 3225 | 2^564526-351401 | 169940 | Enzo Doria | 07/2015 |
| 3226 | 3^355902+4 | 169809 | Aurel Gibier | 10/2024 |
| 3227 | 4*10^169759+19 | 169760 | Robert Price | 10/2018 |
| 3228 | (2^563903-13)/5 | 169752 | Stefano Morozzi | 08/2022 |
| 3229 | 21^128327-20^128327 | 169677 | Jean-Louis Charton | 11/2014 |
| 3230 | 2^563583+89 | 169656 | Stefano Morozzi | 04/2021 |
| 3231 | 2^563311+215813 | 169574 | Enzo Doria | 11/2023 |
| 3232 | (4*10^169559+83)/3 | 169560 | Robert Price | 02/2018 |
| 3233 | (194*10^169461-17)/3 | 169463 | Robert Price | 09/2020 |
| 3234 | 2^562749+2793047 | 169405 | Enzo Doria | 02/2016 |
| 3235 | (154*10^169337-1)/9 | 169339 | Serge Batalov | 12/2014 |
| 3236 | (109*10^169337+11)/3 | 169339 | Robert Price | 06/2022 |
| 3237 | (56*10^169311+691)/9 | 169312 | Robert Price | 05/2019 |
| 3238 | 2^562369-29503 | 169290 | Enzo Doria | 08/2015 |
| 3239 | (17*10^169283+19)/9 | 169284 | Robert Price | 03/2021 |
| 3240 | 390151#-2322911 | 169082 | Hayden Chesnut | 07/2024 |
| 3241 | 10^169074-5000000001 | 169074 | Robert Price | 09/2022 |
| 3242 | 8*10^169071+59 | 169072 | Robert Price | 11/2021 |
| 3243 | (10^169044+173)/3 | 169044 | Robert Price | 05/2021 |
| 3244 | (22*10^169019+383)/9 | 169020 | Robert Price | 05/2018 |
| 3245 | (64*10^168935+143)/9 | 168936 | Robert Price | 05/2021 |
| 3246 | (22*10^168906+47)/3 | 168907 | Robert Price | 06/2021 |
| 3247 | 5*10^168807+87 | 168808 | Robert Price | 02/2019 |
| 3248 | (77*10^168803-149)/9 | 168804 | Robert Price | 03/2022 |
| 3249 | 4*10^168788-47 | 168789 | Robert Price | 10/2021 |
| 3250 | (154*10^168781+17)/9 | 168783 | Robert Price | 06/2022 |
