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
See the Top discoverers
See the Latest PRPs
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| Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
| 3001 | 2*10^173809-87 | 173810 | Robert Price | 04/2018 |
| 3002 | (2^577372-23)/7 | 173806 | Stefano Morozzi | 08/2022 |
| 3003 | (L!41532)/2 | 173772 | Serge Batalov | 07/2017 |
| 3004 | 2^577146-49877 | 173739 | Enzo Doria | 10/2015 |
| 3005 | 2^576889+49727 | 173661 | Enzo Doria | 09/2016 |
| 3006 | (167*10^173571-17)/3 | 173573 | Robert Price | 03/2020 |
| 3007 | 37803^37916+37916^37803 | 173562 | Norbert Schneider | 06/2022 |
| 3008 | 5*10^173534+29 | 173535 | Robert Price | 12/2020 |
| 3009 | (2^576551-1)/4612409/64758208321/242584327930759 | 173528 | Dario Alpern | 06/2014 |
| 3010 | 4*10^173509+99 | 173510 | Robert Price | 12/2020 |
| 3011 | (13*10^173467-37)/3 | 173468 | Robert Price | 01/2019 |
| 3012 | 2^576016-113919 | 173399 | Enzo Doria | 11/2014 |
| 3013 | 2^575911-1849387 | 173367 | Enzo Doria | 08/2015 |
| 3014 | 2^575879+215843 | 173357 | Enzo Doria | 11/2023 |
| 3015 | 2^575871+28733 | 173355 | Enzo Doria | 01/2024 |
| 3016 | 515^63898+63898^515 | 173280 | Norbert Schneider | 12/2022 |
| 3017 | 2^575614+9 | 173278 | Stefano Morozzi | 04/2021 |
| 3018 | 2^575606-219533 | 173275 | Enzo Doria | 03/2024 |
| 3019 | (16*10^173251+107)/3 | 173252 | Robert Price | 03/2019 |
| 3020 | 26618^39149-39149^26618 | 173242 | Frank Doornink | 03/2024 |
| 3021 | 2^575196-114053 | 173152 | Enzo Doria | 11/2014 |
| 3022 | 7*10^173135-53 | 173136 | Robert Price | 06/2020 |
| 3023 | (301*10^173047+23)/9 | 173049 | Robert Price | 06/2021 |
| 3024 | 2^574591-115387 | 172970 | Enzo Doria | 07/2015 |
| 3025 | 25210^39297-39297^25210 | 172969 | Frank Doornink | 12/2023 |
| 3026 | (202*10^172940-13)/9 | 172942 | Robert Price | 01/2020 |
| 3027 | 45^104608+104608^45 | 172940 | Norbert Schneider | 06/2021 |
| 3028 | 2^574328+81121 | 172890 | Enzo Doria | 07/2016 |
| 3029 | (115*10^172862-1)/3 | 172864 | Serge Batalov | 12/2014 |
| 3030 | 3*10^172812+13 | 172813 | Robert Price | 07/2018 |
| 3031 | 4*5^247217-9 | 172798 | Lelio R Paula | 10/2015 |
| 3032 | 6*10^172772-31 | 172773 | Robert Price | 07/2020 |
| 3033 | 69061#+(467617#)/(69061#) | 172766 | Makoto Morimoto | 10/2017 |
| 3034 | (34*10^172693-547)/9 | 172694 | Robert Price | 03/2021 |
| 3035 | 5*10^172692+57 | 172693 | Robert Price | 12/2018 |
| 3036 | 2^573668-2782319 | 172692 | Enzo Doria | 09/2015 |
| 3037 | 2^573444-1855109 | 172624 | Enzo Doria | 09/2015 |
| 3038 | 25500^39173-39173^25500 | 172618 | Frank Doornink | 02/2024 |
| 3039 | 27180^38917-38917^27180 | 172568 | Frank Doornink | 01/2024 |
| 3040 | (14*10^172532-29)/3 | 172533 | Robert Price | 09/2021 |
| 3041 | 3^361608+2 | 172531 | Robert Price | 08/2014 |
| 3042 | (54^99563+1)/55 | 172481 | Paul Bourdelais | 11/2017 |
| 3043 | 2^572592-114893 | 172368 | Enzo Doria | 05/2015 |
| 3044 | 4*10^172354-39 | 172355 | Robert Price | 09/2020 |
| 3045 | 37535^37674+37674^37535 | 172338 | Norbert Schneider | 05/2022 |
| 3046 | (11*10^172322-119)/9 | 172323 | Robert Price | 11/2021 |
| 3047 | 5^246497-4^246497 | 172295 | Jean-Louis Charton | 11/2008 |
| 3048 | (38^109037-1)/37 | 172254 | Paul Bourdelais | 10/2017 |
| 3049 | (4*10^172241+89)/3 | 172242 | Robert Price | 08/2021 |
| 3050 | 3*10^172219+73 | 172220 | Robert Price | 08/2018 |
| 3051 | 2^571810+28549 | 172132 | Enzo Doria | 01/2024 |
| 3052 | A352736(15) | 172032 | Kellen Shenton | 05/2022 |
| 3053 | 32298^38149-38149^32298 | 172021 | Frank Doornink | 02/2024 |
| 3054 | 2^571300+25861 | 171979 | Enzo Doria | 11/2023 |
| 3055 | (36^110503+1)/37 | 171975 | Lelio R Paula | 04/2017 |
| 3056 | 8*10^171934+71 | 171935 | Robert Price | 05/2022 |
| 3057 | (11*10^171933+601)/9 | 171934 | Robert Price | 02/2022 |
| 3058 | (22*10^171929-73)/3 | 171930 | Robert Price | 04/2019 |
| 3059 | (49*10^171892-319)/9 | 171893 | Robert Price | 10/2021 |
| 3060 | 4*10^171891-63 | 171892 | Robert Price | 10/2018 |
| 3061 | 67*10^171882-9 | 171884 | Robert Price | 03/2021 |
| 3062 | 2^570980-2782289 | 171883 | Enzo Doria | 09/2015 |
| 3063 | (25*10^171849-37)/3 | 171850 | Robert Price | 10/2019 |
| 3064 | 10^171832+387909 | 171833 | Patrick De Geest | 08/2021 |
| 3065 | 10^171832-10001 | 171832 | Robert Price | 02/2021 |
| 3067 | (2^(12*47563+13)-9)/7 | 171818 | Kevin Acres | 11/2013 |
| 3066 | (2^570769-9)/7 | 171818 | Stefano Morozzi | 08/2022 |
| 3068 | 2^570545+11025 | 171752 | Henri Lifchitz | 01/2025 |
| 3069 | 24^124375-124375^24 | 171664 | Henri Lifchitz | 08/2024 |
| 3070 | (74*10^171651-29)/9 | 171652 | Robert Price | 06/2022 |
| 3071 | (536*10^171601-23)/9 | 171603 | Robert Price | 02/2020 |
| 3072 | 7*10^171535-99 | 171536 | Robert Price | 06/2019 |
| 3073 | (28*10^171534+101)/3 | 171535 | Robert Price | 09/2020 |
| 3074 | 2^569563-1854607 | 171456 | Enzo Doria | 09/2015 |
| 3075 | 32133^38042-38042^32133 | 171454 | Frank Doornink | 02/2024 |
| 3076 | 3*10^171391+59 | 171392 | Robert Price | 08/2018 |
| 3077 | (13*10^171306-37)/3 | 171307 | Robert Price | 01/2019 |
| 3078 | 8*10^171296+87 | 171297 | Robert Price | 10/2019 |
| 3079 | (55^98419-1)/54 | 171284 | Paul Bourdelais | 12/2017 |
| 3080 | (29*10^171275+67)/3 | 171276 | Robert Price | 12/2019 |
| 3081 | (457*10^171248-7)/9 | 171250 | Robert Price | 09/2022 |
| 3082 | (194*10^171193+1)/3 | 171195 | Robert Price | 01/2022 |
| 3083 | 2^568642+1876129 | 171179 | Enzo Doria | 07/2016 |
| 3084 | 4*10^171146-47 | 171147 | Robert Price | 10/2021 |
| 3085 | (19*10^170970+131)/3 | 170971 | Robert Price | 06/2020 |
| 3086 | (46*10^170932+143)/9 | 170933 | Robert Price | 01/2019 |
| 3087 | (79*10^170901-1)/3 | 170903 | Robert Price | 02/2020 |
| 3088 | (58*10^170842+221)/9 | 170843 | Robert Price | 02/2017 |
| 3089 | (29*10^170830+583)/9 | 170831 | Robert Price | 06/2021 |
| 3090 | 3*10^170800+73 | 170801 | Robert Price | 08/2018 |
| 3091 | (29*10^170799-119)/9 | 170800 | Robert Price | 12/2021 |
| 3092 | 11^164009-270 | 170798 | Enzo Doria | 10/2012 |
| 3093 | 2*10^170767+41 | 170768 | Robert Price | 05/2018 |
| 3094 | 3^357706-112358 | 170670 | Enzo Doria | 07/2014 |
| 3095 | TheodorusPrime(170657) | 170657 | Eric W. Weisstein | 08/2013 |
| 3096 | 2^566871+1876163 | 170646 | Enzo Doria | 07/2016 |
| 3097 | (10657#+(404267#)/(10657#))/(1675379) | 170624 | Makoto Morimoto | 10/2017 |
| 3098 | 2^566496+7 | 170533 | Donovan Johnson | 07/2006 |
| 3099 | (7^201653+1)/8 | 170416 | Paul Bourdelais | 02/2010 |
| 3100 | 32150^37807-37807^32150 | 170403 | Frank Doornink | 02/2024 |
| 3101 | 7*10^170348+33 | 170349 | Robert Price | 06/2020 |
| 3102 | 2^565799+216011 | 170323 | Enzo Doria | 12/2023 |
| 3103 | 2^565183-352021 | 170138 | Enzo Doria | 07/2015 |
| 3104 | 2^565143-114457 | 170125 | Enzo Doria | 02/2015 |
| 3105 | 3*2^565024-5 | 170090 | Jon Grantham | 07/2023 |
| 3106 | 2^564976-49869 | 170075 | Enzo Doria | 10/2015 |
| 3107 | 2^564561+225 | 169950 | Henri Lifchitz | 11/2024 |
| 3108 | (7*10^169944+23)/3 | 169945 | Robert Price | 06/2020 |
| 3109 | (37*10^169943+251)/9 | 169944 | Robert Price | 09/2021 |
| 3110 | 2^564526-351401 | 169940 | Enzo Doria | 07/2015 |
| 3111 | 3^355902+4 | 169809 | Aurel Gibier | 10/2024 |
| 3112 | 4*10^169759+19 | 169760 | Robert Price | 10/2018 |
| 3113 | (2^563903-13)/5 | 169752 | Stefano Morozzi | 08/2022 |
| 3114 | 21^128327-20^128327 | 169677 | Jean-Louis Charton | 11/2014 |
| 3115 | 2^563583+89 | 169656 | Stefano Morozzi | 04/2021 |
| 3116 | 2^563311+215813 | 169574 | Enzo Doria | 11/2023 |
| 3117 | (4*10^169559+83)/3 | 169560 | Robert Price | 02/2018 |
| 3118 | (194*10^169461-17)/3 | 169463 | Robert Price | 09/2020 |
| 3119 | 2^562749+2793047 | 169405 | Enzo Doria | 02/2016 |
| 3120 | (154*10^169337-1)/9 | 169339 | Serge Batalov | 12/2014 |
| 3121 | (109*10^169337+11)/3 | 169339 | Robert Price | 06/2022 |
| 3122 | (56*10^169311+691)/9 | 169312 | Robert Price | 05/2019 |
| 3123 | 2^562369-29503 | 169290 | Enzo Doria | 08/2015 |
| 3124 | (17*10^169283+19)/9 | 169284 | Robert Price | 03/2021 |
| 3125 | 390151#-2322911 | 169082 | Hayden Chesnut | 07/2024 |
| 3126 | 10^169074-5000000001 | 169074 | Robert Price | 09/2022 |
| 3127 | 8*10^169071+59 | 169072 | Robert Price | 11/2021 |
| 3128 | (10^169044+173)/3 | 169044 | Robert Price | 05/2021 |
| 3129 | (22*10^169019+383)/9 | 169020 | Robert Price | 05/2018 |
| 3130 | (64*10^168935+143)/9 | 168936 | Robert Price | 05/2021 |
| 3131 | (22*10^168906+47)/3 | 168907 | Robert Price | 06/2021 |
| 3132 | 5*10^168807+87 | 168808 | Robert Price | 02/2019 |
| 3133 | (77*10^168803-149)/9 | 168804 | Robert Price | 03/2022 |
| 3134 | 4*10^168788-47 | 168789 | Robert Price | 10/2021 |
| 3135 | (154*10^168781+17)/9 | 168783 | Robert Price | 06/2022 |
| 3136 | (418*10^168751-31)/9 | 168753 | Robert Price | 05/2022 |
| 3137 | (29*10^168711+691)/9 | 168712 | Robert Price | 08/2021 |
| 3138 | 2^560405-39943 | 168699 | Enzo Doria | 09/2015 |
| 3139 | (397*10^168634+17)/9 | 168636 | Robert Price | 03/2022 |
| 3140 | 2^560189+36587 | 168634 | Enzo Doria | 09/2024 |
| 3141 | 89*10^168614-7 | 168616 | Robert Price | 04/2020 |
| 3142 | (23*10^168608-83)/3 | 168609 | Robert Price | 08/2019 |
| 3143 | (94*10^168541+11)/3 | 168543 | Robert Price | 04/2020 |
| 3144 | 2^559686-350471 | 168483 | Enzo Doria | 06/2015 |
| 3145 | 2^559672-1855889 | 168479 | Enzo Doria | 09/2015 |
| 3146 | (5*10^168379-473)/9 | 168379 | Robert Price | 01/2018 |
| 3147 | 2024^50920+3 | 168353 | Martin Hopf | 01/2024 |
| 3148 | 2^559000-59939 | 168276 | Enzo Doria | 11/2015 |
| 3149 | 2^558830+25009 | 168225 | Enzo Doria | 11/2023 |
| 3150 | (16*10^168181+41)/3 | 168182 | Robert Price | 03/2019 |
| 3151 | (19*10^168173+77)/3 | 168174 | Robert Price | 05/2019 |
| 3152 | (74*10^168170+529)/9 | 168171 | Robert Price | 02/2022 |
| 3153 | 2^558640-114149 | 168168 | Enzo Doria | 12/2014 |
| 3154 | 2^558498-1849277 | 168125 | Enzo Doria | 08/2015 |
| 3155 | 2^558476-1850249 | 168119 | Enzo Doria | 08/2015 |
| 3156 | (7*10^168067+71)/3 | 168068 | Robert Price | 05/2018 |
| 3157 | 2^558150-1852211 | 168020 | Enzo Doria | 08/2015 |
| 3158 | 2^558125-113661 | 168013 | Enzo Doria | 09/2014 |
| 3159 | 393^64747-392^64747 | 167980 | Jean-Louis Charton | 08/2012 |
| 3160 | (8*10^167965-11)/3 | 167966 | Robert Price | 07/2023 |
| 3161 | 2^557916+216151 | 167950 | Enzo Doria | 12/2023 |
| 3162 | (13*10^167911+179)/3 | 167912 | Robert Price | 11/2018 |
| 3163 | (26*10^167861-167)/3 | 167862 | Robert Price | 10/2019 |
| 3164 | 36^107827-107827 | 167812 | Kellen Shenton | 06/2023 |
| 3165 | 32027^37242-37242^32027 | 167795 | Frank Doornink | 01/2024 |
| 3166 | 39^105456+2 | 167788 | Robert Price | 04/2015 |
| 3167 | 2^557322+217519 | 167771 | Enzo Doria | 01/2024 |
| 3168 | (28^115877-1)/27 | 167691 | Paul Bourdelais | 12/2017 |
| 3169 | 6*10^167662-13 | 167663 | Robert Price | 07/2022 |
| 3170 | 10^167639+121911 | 167640 | Patrick De Geest | 07/2018 |
| 3171 | 10^167639-8001 | 167639 | Robert Price | 03/2018 |
| 3172 | 2^556504-462059 | 167525 | Enzo Doria | 07/2015 |
| 3173 | (88*10^167522-637)/9 | 167523 | Robert Price | 11/2020 |
| 3174 | 5*10^167510+9 | 167511 | Robert Price | 08/2015 |
| 3175 | 7*10^167437-93 | 167438 | Robert Price | 08/2020 |
| 3176 | 25455^37978-37978^25455 | 167323 | Frank Doornink | 01/2024 |
| 3177 | 11^160663+6 | 167314 | Paul Bourdelais | 02/2021 |
| 3178 | (7*10^167308-493)/9 | 167308 | Robert Price | 04/2021 |
| 3179 | 2^555759+74333 | 167301 | Enzo Doria | 07/2023 |
| 3180 | 26084^37871-37871^26084 | 167253 | Frank Doornink | 03/2024 |
| 3181 | 2^555343+1874333 | 167175 | Enzo Doria | 06/2016 |
| 3182 | 2^555210-461261 | 167135 | Enzo Doria | 07/2015 |
| 3183 | 9*10^166996+59 | 166997 | Robert Price | 01/2020 |
| 3184 | (68*10^166976-329)/9 | 166977 | Robert Price | 03/2021 |
| 3185 | (64*10^166901+683)/9 | 166902 | Robert Price | 06/2022 |
| 3186 | 2^554372+1880527 | 166883 | Enzo Doria | 11/2016 |
| 3187 | 2^554299+72173 | 166861 | Enzo Doria | 04/2016 |
| 3188 | (185*10^166837+7)/3 | 166839 | Robert Price | 03/2020 |
| 3189 | (14*10^166813+139)/9 | 166814 | Robert Price | 11/2021 |
| 3190 | 26084^37767-37767^26084 | 166794 | Frank Doornink | 03/2024 |
| 3191 | 2^554037-2797063 | 166782 | Enzo Doria | 03/2016 |
| 3192 | 31861^37028-37028^31861 | 166747 | Frank Doornink | 01/2024 |
| 3193 | (49*10^166721-139)/9 | 166722 | Robert Price | 03/2019 |
| 3194 | 2*10^166646+69 | 166647 | Robert Price | 06/2020 |
| 3195 | 2^553484-29819 | 166616 | Enzo Doria | 08/2015 |
| 3196 | (188*10^166611+7)/3 | 166613 | Robert Price | 03/2020 |
| 3197 | 2^553383-2784217 | 166585 | Enzo Doria | 10/2015 |
| 3198 | 2^553069+76427 | 166491 | Enzo Doria | 05/2016 |
| 3199 | 25218^37819-37819^25218 | 166469 | Frank Doornink | 12/2023 |
| 3200 | 2*10^166458+51 | 166459 | Robert Price | 05/2018 |
| 3201 | 589^60089-588^60089 | 166454 | Jean-Louis Charton | 09/2012 |
| 3202 | 25214^37799-37799^25214 | 166378 | Frank Doornink | 11/2023 |
| 3203 | 11^159756-2424 | 166369 | Mike Oakes | 06/2010 |
| 3204 | 2^552649-361275 | 166364 | Enzo Doria | 05/2014 |
| 3205 | 2^552628-113669 | 166358 | Enzo Doria | 09/2014 |
| 3206 | (19*10^166325+137)/3 | 166326 | Robert Price | 03/2022 |
| 3207 | 10^166324+550603 | 166325 | Patrick De Geest | 07/2018 |
| 3208 | 10^166324-801 | 166324 | Robert Price | 02/2018 |
| 3209 | (85*10^166297-1)/3 | 166299 | Robert Price | 02/2020 |
| 3210 | (19*10^166280-7)/3 | 166281 | Robert Price | 12/2023 |
| 3211 | 25533^37726-37726^25533 | 166263 | Frank Doornink | 02/2024 |
| 3212 | 8*10^166227+87 | 166228 | Robert Price | 10/2019 |
| 3213 | 2^552137+1879397 | 166210 | Enzo Doria | 09/2016 |
| 3214 | 262273205671539190984629()252475512364409752762433 | 166141 | Anonymous | 01/2025 |
| 3215 | 490079063773165613318095()218182139934160868002603 | 166141 | Anonymous | 01/2025 |
| 3216 | 140717254840416411192803()712689271538459396766869 | 166140 | Anonymous | 01/2025 |
| 3217 | 122398296040696255481419()271117913237372866926417 | 166140 | Anonymous | 01/2025 |
| 3218 | (103*10^166126+11)/3 | 166128 | Robert Price | 01/2021 |
| 3219 | (22*10^166077+179)/3 | 166078 | Robert Price | 02/2022 |
| 3220 | (23^121949-1)/22 | 166061 | Paul Bourdelais | 10/2017 |
| 3221 | 2^551542+19249 | 166031 | Payam Samidoost | 08/2002 |
| 3222 | 2^551535-23821 | 166029 | Enzo Doria | 08/2013 |
| 3223 | 2^551507-23557 | 166021 | Enzo Doria | 08/2013 |
| 3224 | 32030^36841-36841^32030 | 165990 | Frank Doornink | 01/2024 |
| 3225 | 10^165947-7000000001 | 165947 | Robert Price | 12/2021 |
| 3226 | 4*10^165938-47 | 165939 | Robert Price | 10/2021 |
| 3227 | 7*10^165916-3 | 165917 | Robert Price | 08/2015 |
| 3228 | (29*10^165796+67)/3 | 165797 | Robert Price | 12/2019 |
| 3229 | 81^86837-80^86837 | 165728 | Robert Price | 01/2015 |
| 3230 | (71*10^165716-17)/9 | 165717 | Serge Batalov | 01/2023 |
| 3231 | fibonacci(792909)+3 | 165708 | Jon Grantham | 08/2023 |
| 3232 | (71*10^165663-539)/9 | 165664 | Robert Price | 07/2019 |
| 3233 | 25682^37567-37567^25682 | 165657 | Frank Doornink | 02/2024 |
| 3234 | 2^550270-69551 | 165648 | Enzo Doria | 12/2015 |
| 3235 | 2^550250+29329 | 165642 | Enzo Doria | 03/2024 |
| 3236 | (202*10^165569-13)/9 | 165571 | Robert Price | 01/2020 |
| 3237 | 2^550000-23625 | 165567 | Enzo Doria | 08/2013 |
| 3238 | 31688^36783-36783^31688 | 165557 | Frank Doornink | 01/2024 |
| 3239 | 2^549675-1852057 | 165469 | Enzo Doria | 08/2015 |
| 3240 | 2^549663+212543 | 165466 | Enzo Doria | 08/2023 |
| 3241 | (529*10^165394-7)/9 | 165396 | Robert Price | 08/2021 |
| 3242 | 26253^37424-37424^26253 | 165384 | Frank Doornink | 03/2024 |
| 3243 | -tau(103^14938) | 165374 | Nik Lygeros / Olivier Rozier | 10/2013 |
| 3244 | (28*10^165358-1)/9 | 165359 | Serge Batalov | 10/2014 |
| 3245 | 2^549278+1879669 | 165350 | Enzo Doria | 09/2016 |
| 3246 | (7*10^165350-439)/9 | 165350 | Robert Price | 02/2018 |
| 3247 | 2^549252-351269 | 165342 | Enzo Doria | 06/2015 |
| 3248 | 2^549221+335931 | 165332 | Enzo Doria | 09/2024 |
| 3249 | 67*10^165327-9 | 165329 | Robert Price | 03/2021 |
| 3250 | (14*10^165282+73)/3 | 165283 | Robert Price | 12/2018 |
