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
Search by form
| Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
| 3001 | 2^536569-22881 | 161524 | Enzo Doria | 07/2013 |
| 3002 | (46*10^161505+593)/9 | 161506 | Robert Price | 04/2022 |
| 3003 | 10^161253+573493 | 161254 | Patrick De Geest | 07/2018 |
| 3004 | 10^161253-8001 | 161253 | Robert Price | 03/2018 |
| 3005 | 97*10^161247-3 | 161249 | Robert Price | 05/2020 |
| 3006 | 7*10^161192-9 | 161193 | Robert Price | 10/2015 |
| 3007 | 2^535415-19 | 161176 | Stefano Morozzi | 07/2022 |
| 3008 | 2^535269-113803 | 161133 | Enzo Doria | 09/2014 |
| 3009 | 2^535205-23295 | 161113 | Enzo Doria | 08/2013 |
| 3010 | (49*10^161105+437)/9 | 161106 | Robert Price | 09/2021 |
| 3011 | (89^82609+1)/90 | 161036 | Paul Bourdelais | 10/2017 |
| 3012 | 2^534429-19 | 160880 | Stefano Morozzi | 07/2022 |
| 3013 | 2^534359-23229 | 160859 | Enzo Doria | 08/2013 |
| 3014 | 10^160836-1001 | 160836 | Robert Price | 10/2022 |
| 3015 | 457^60454+60454^457 | 160803 | Norbert Schneider | 07/2021 |
| 3016 | 8*10^160782+53 | 160783 | Robert Price | 08/2020 |
| 3017 | 67^88037-66^88037 | 160763 | Robert Price | 10/2013 |
| 3018 | (88*10^160761-637)/9 | 160762 | Robert Price | 11/2020 |
| 3019 | 2^533948-1852559 | 160735 | Enzo Doria | 08/2015 |
| 3020 | 2^533665-23335 | 160650 | Enzo Doria | 08/2013 |
| 3021 | 2^533600+217981 | 160630 | Enzo Doria | 01/2024 |
| 3022 | (19*10^160619+77)/3 | 160620 | Robert Price | 05/2019 |
| 3023 | 2^533350-5 | 160555 | Stefano Morozzi | 07/2022 |
| 3024 | (38*10^160508+151)/9 | 160509 | Robert Price | 03/2022 |
| 3025 | 3^336353-2^336353 | 160482 | Mike Oakes | 10/2007 |
| 3026 | 26134^36315-36315^26134 | 160411 | Frank Doornink | 03/2024 |
| 3027 | 25821^36358-36358^25821 | 160411 | Frank Doornink | 03/2024 |
| 3028 | 2*10^160339-63 | 160340 | Robert Price | 01/2022 |
| 3029 | 24419^36532+36532^24419 | 160293 | Norbert Schneider | 10/2023 |
| 3030 | (91*10^160249+11)/3 | 160251 | Robert Price | 02/2020 |
| 3031 | (772*10^160239-7)/9 | 160241 | Robert Price | 06/2022 |
| 3032 | (2*10^160226+187)/9 | 160226 | Robert Price | 06/2022 |
| 3033 | 2^532253+1868417 | 160225 | Enzo Doria | 04/2016 |
| 3034 | 2^532108-291989 | 160181 | Enzo Doria | 07/2015 |
| 3035 | (28*10^160171-79)/3 | 160172 | Robert Price | 02/2021 |
| 3036 | (26*10^160166-131)/3 | 160167 | Robert Price | 10/2019 |
| 3037 | 55*10^160145+9 | 160147 | Robert Price | 03/2022 |
| 3038 | (17*10^160143+67)/3 | 160144 | Robert Price | 01/2019 |
| 3039 | (394^61637-1)/393 | 159977 | Jinyuan Wang | 04/2023 |
| 3040 | (19*10^159921-49)/3 | 159922 | Robert Price | 05/2019 |
| 3041 | 2^531110-1853771 | 159881 | Enzo Doria | 09/2015 |
| 3042 | (275^65536+53^65536)/2 | 159864 | Kellen Shenton | 11/2020 |
| 3043 | 2^530992-1845299 | 159845 | Enzo Doria | 07/2015 |
| 3044 | 2^530810+25 | 159790 | Stefano Morozzi | 04/2021 |
| 3045 | 25590^36241-36241^25590 | 159753 | Frank Doornink | 02/2024 |
| 3046 | (136*10^159736-1)/9 | 159738 | Serge Batalov | 12/2014 |
| 3047 | 2^530417-113833 | 159672 | Enzo Doria | 09/2014 |
| 3048 | 2^530406-69701 | 159669 | Enzo Doria | 02/2016 |
| 3049 | 5*10^159656+41 | 159657 | Robert Price | 03/2019 |
| 3050 | 8*10^159614+29 | 159615 | Robert Price | 11/2021 |
| 3051 | 7^188858-188858^7 | 159604 | Norbert Schneider | 05/2018 |
| 3052 | 28^110278+27 | 159590 | Alfred Reich | 02/2024 |
| 3053 | 7*10^159553-27 | 159554 | Robert Price | 11/2022 |
| 3054 | 3^334409-5*2^334409 | 159554 | Jon Grantham | 08/2023 |
| 3055 | (24^115597-1)/23 | 159547 | Paul Bourdelais | 09/2017 |
| 3056 | 25472^36209-36209^25472 | 159540 | Frank Doornink | 01/2024 |
| 3057 | (17*10^159438-377)/9 | 159439 | Robert Price | 03/2018 |
| 3058 | (203*10^159381+1)/3 | 159383 | Robert Price | 03/2020 |
| 3059 | 32282^35343-35343^32282 | 159361 | Frank Doornink | 02/2024 |
| 3060 | 2^529215+219383 | 159310 | Enzo Doria | 02/2024 |
| 3061 | 89*10^159258-9 | 159260 | Robert Price | 05/2020 |
| 3062 | 2^528944-461315 | 159229 | Enzo Doria | 07/2015 |
| 3063 | (13*10^159147+161)/3 | 159148 | Robert Price | 11/2018 |
| 3064 | 2^528620-113879 | 159131 | Enzo Doria | 10/2014 |
| 3065 | 32125^35306-35306^32125 | 159119 | Frank Doornink | 02/2024 |
| 3066 | (47*10^159083+259)/9 | 159084 | Robert Price | 03/2022 |
| 3067 | (861^54181-1)/860 | 159019 | Jinyuan Wang | 11/2023 |
| 3068 | 2^528000-23307 | 158944 | Enzo Doria | 08/2013 |
| 3069 | (29*10^158909+61)/9 | 158910 | Robert Price | 08/2018 |
| 3070 | 2^527817+1876817 | 158889 | Enzo Doria | 07/2016 |
| 3071 | 2^527774-49451 | 158876 | Enzo Doria | 10/2015 |
| 3072 | 2^527745-291553 | 158868 | Enzo Doria | 07/2015 |
| 3073 | (91*10^158862+11)/3 | 158864 | Robert Price | 02/2020 |
| 3074 | 2^527644-1856999 | 158837 | Enzo Doria | 10/2015 |
| 3075 | (37200^37199-37198^37199)/(2^37199) | 158822 | Henri Lifchitz | 06/2013 |
| 3076 | (17*10^158819+7)/3 | 158820 | Robert Price | 06/2023 |
| 3077 | 2^527573-1863253 | 158816 | Enzo Doria | 12/2015 |
| 3078 | 2^527553-23401 | 158810 | Enzo Doria | 08/2013 |
| 3079 | (49*10^158783+437)/9 | 158784 | Robert Price | 09/2021 |
| 3080 | 10^158755+310207 | 158756 | Patrick De Geest | 08/2021 |
| 3081 | 10^158755-50001 | 158755 | Robert Price | 08/2020 |
| 3082 | (61*10^158748-619)/9 | 158749 | Robert Price | 03/2022 |
| 3083 | 11^152420-210 | 158730 | Enzo Doria | 09/2012 |
| 3084 | (13*10^158694+401)/9 | 158695 | Robert Price | 01/2018 |
| 3085 | 2^527052-69059 | 158659 | Enzo Doria | 11/2015 |
| 3086 | 2^526849-113233 | 158598 | Enzo Doria | 07/2014 |
| 3087 | 24286^36161+36161^24286 | 158579 | Norbert Schneider | 08/2023 |
| 3088 | (2^526763-lucasV(1,2,526763)+1)/2 | 158572 | Mike Oakes | 11/2016 |
| 3089 | (299*10^158544-17)/3 | 158546 | Robert Price | 04/2020 |
| 3090 | 2^526658-3551 | 158540 | Yves Minet | 03/2017 |
| 3091 | 7*10^158465-11 | 158466 | Robert Price | 06/2019 |
| 3092 | (7^187507-3^187507)/4 | 158462 | Jon Grantham | 08/2023 |
| 3093 | 2^526375-23115 | 158455 | Enzo Doria | 08/2013 |
| 3094 | (77*10^158407-293)/9 | 158408 | Robert Price | 09/2019 |
| 3095 | 31209^35242-35242^31209 | 158388 | Frank Doornink | 01/2024 |
| 3096 | 32071^35144-35144^32071 | 158363 | Frank Doornink | 01/2024 |
| 3097 | 2^526028-112793 | 158351 | Enzo Doria | 07/2014 |
| 3098 | (229*10^158339-1)/3 | 158341 | Robert Price | 07/2020 |
| 3099 | 32042^35123-35123^32042 | 158255 | Frank Doornink | 01/2024 |
| 3100 | 2^525690-9221 | 158249 | Lelio R Paula | 01/2013 |
| 3101 | 2*10^158242-7 | 158243 | Robert Price | 10/2015 |
| 3102 | 2^525667-525667^2 | 158242 | Henri Lifchitz | 12/2017 |
| 3103 | (56*10^158230+187)/9 | 158231 | Robert Price | 10/2021 |
| 3104 | 10^158209-7000000001 | 158209 | Robert Price | 12/2021 |
| 3105 | 31050^35207-35207^31050 | 158153 | Frank Doornink | 01/2024 |
| 3106 | 2^525186-1857431 | 158097 | Enzo Doria | 10/2015 |
| 3107 | 31527^35108-35108^31527 | 157940 | Frank Doornink | 01/2024 |
| 3108 | 2^524515-23245 | 157895 | Enzo Doria | 08/2013 |
| 3109 | 2^524499-109087 | 157890 | Enzo Doria | 04/2014 |
| 3110 | 2^524384-219533 | 157856 | Enzo Doria | 03/2024 |
| 3112 | 2^18067*(2^506221+1)-1 | 157827 | Makoto Morimoto | 05/2014 |
| 3113 | 2^524288+189093 | 157827 | Makoto Morimoto | 01/2016 |
| 3111 | 2^524288-164073 | 157827 | Matthias Baur | 03/2020 |
| 3114 | (2^(2^19)-9333)/(19*23*463*1213*31973) | 157814 | Makoto Morimoto | 09/2017 |
| 3115 | (10^157792+359)/9 | 157792 | Serge Batalov | 12/2014 |
| 3116 | 2^524154+25 | 157787 | Stefano Morozzi | 04/2021 |
| 3117 | 2^523924+1876591 | 157717 | Enzo Doria | 07/2016 |
| 3118 | (17*10^157705+67)/3 | 157706 | Robert Price | 01/2019 |
| 3119 | (46^94841+1)/47 | 157696 | Robert Price | 01/2014 |
| 3120 | 2^523774+77839 | 157672 | Enzo Doria | 05/2016 |
| 3121 | 2^523587+2799143 | 157616 | Enzo Doria | 04/2016 |
| 3122 | 2^523496+220141 | 157588 | Enzo Doria | 03/2024 |
| 3123 | 2^523371+1872113 | 157551 | Enzo Doria | 05/2016 |
| 3124 | 8*10^157477+27 | 157478 | Robert Price | 09/2021 |
| 3125 | 32268^34909-34909^32268 | 157397 | Frank Doornink | 02/2024 |
| 3126 | (8*10^157368+49)/3 | 157369 | Robert Price | 05/2020 |
| 3127 | (82*10^157319+449)/9 | 157320 | Robert Price | 11/2019 |
| 3128 | 2^522535-351457 | 157299 | Enzo Doria | 07/2015 |
| 3129 | 25401^35704-35704^25401 | 157271 | Frank Doornink | 01/2024 |
| 3130 | 2^522226+2799079 | 157206 | Enzo Doria | 04/2016 |
| 3131 | (134*10^157191-11)/3 | 157193 | Robert Price | 01/2022 |
| 3132 | 2^522134-1849451 | 157178 | Enzo Doria | 08/2015 |
| 3133 | 9*10^157152+71 | 157153 | Robert Price | 08/2020 |
| 3134 | 4*10^157150+93 | 157151 | Robert Price | 08/2018 |
| 3135 | 31227^34952-34952^31227 | 157093 | Frank Doornink | 01/2024 |
| 3136 | (32^104347+5^104347)/37 | 157057 | Anonymous | 12/2023 |
| 3137 | fibonacci(751442)-2 | 157042 | Jon Grantham | 08/2023 |
| 3138 | 2^521401-29593 | 156958 | Enzo Doria | 08/2015 |
| 3139 | 7*10^156956+87 | 156957 | Robert Price | 07/2019 |
| 3140 | 2^521348-23397 | 156942 | Enzo Doria | 08/2013 |
| 3141 | 10^156902+34509 | 156903 | Patrick De Geest | 08/2021 |
| 3143 | 10^156902-80000001 | 156902 | Robert Price | 04/2021 |
| 3142 | 10^156902-69789 | 156902 | Patrick De Geest | 08/2021 |
| 3144 | (98^78797+1)/99 | 156901 | Paul Bourdelais | 12/2017 |
| 3145 | 65^86522+64 | 156857 | Lelio R Paula | 04/2016 |
| 3146 | 8^173687-7^173687 | 156855 | Jean-Louis Charton | 09/2004 |
| 3147 | 2^520977-1858183 | 156830 | Enzo Doria | 10/2015 |
| 3148 | (8*10^156718-101)/3 | 156719 | Robert Price | 08/2018 |
| 3149 | (10^156640+7)/53 | 156639 | Alfred Reich | 07/2021 |
| 3150 | 2^520314-1849481 | 156631 | Enzo Doria | 08/2015 |
| 3151 | (16*10^156563-637)/9 | 156564 | Robert Price | 09/2022 |
| 3152 | (13*10^156522+89)/3 | 156523 | Robert Price | 09/2018 |
| 3154 | (2^(6*86654+1)-5)/3 | 156513 | Kevin Acres | 12/2013 |
| 3153 | (2^519925-5)/3 | 156513 | Stefano Morozzi | 08/2022 |
| 3155 | (4*10^156501+119)/3 | 156502 | Robert Price | 12/2021 |
| 3156 | (83*10^156476-101)/9 | 156477 | Robert Price | 08/2021 |
| 3157 | 3*10^156435-97 | 156436 | Robert Price | 07/2018 |
| 3158 | (8*10^156371-77)/3 | 156372 | Robert Price | 07/2018 |
| 3159 | 53^90679-52^90679 | 156356 | Robert Price | 01/2013 |
| 3160 | 31267^34782-34782^31267 | 156349 | Frank Doornink | 01/2024 |
| 3161 | (418*10^156309-31)/9 | 156311 | Robert Price | 05/2022 |
| 3162 | 2^519106-59141 | 156267 | Enzo Doria | 10/2015 |
| 3163 | 25929^35404-35404^25929 | 156266 | Frank Doornink | 03/2024 |
| 3164 | 2^519053+6077 | 156251 | Enzo Doria | 02/2016 |
| 3165 | 31199^34764-34764^31199 | 156235 | Frank Doornink | 01/2024 |
| 3166 | 2^518968-1860989 | 156225 | Enzo Doria | 11/2015 |
| 3167 | (25*10^156221-7)/9 | 156222 | Robert Price | 05/2018 |
| 3168 | 2^518931-2782297 | 156214 | Enzo Doria | 09/2015 |
| 3169 | 2^518608-2939 | 156117 | Yves Minet | 09/2014 |
| 3170 | 10*27^109005+697 | 156027 | Curtis Bright | 05/2015 |
| 3171 | (49*10^155933-319)/9 | 155934 | Robert Price | 10/2021 |
| 3172 | 2^517967-113485 | 155924 | Enzo Doria | 08/2014 |
| 3173 | (103*10^155904+17)/3 | 155906 | Robert Price | 08/2020 |
| 3174 | (8*10^155887-719)/9 | 155887 | Robert Price | 03/2021 |
| 3175 | 2^517789+29231 | 155871 | Enzo Doria | 02/2024 |
| 3176 | 4*10^155853-39 | 155854 | Robert Price | 09/2020 |
| 3177 | 2^517698+4429 | 155843 | Lelio R Paula | 01/2013 |
| 3178 | 32015^34584-34584^32015 | 155814 | Frank Doornink | 01/2024 |
| 3179 | 2^517543-113257 | 155796 | Enzo Doria | 07/2014 |
| 3180 | (14*10^155740-143)/3 | 155741 | Robert Price | 11/2018 |
| 3181 | 31959^34564-34564^31959 | 155697 | Frank Doornink | 01/2024 |
| 3182 | 31^104309-30^104309 | 155563 | Henri Lifchitz | 08/2013 |
| 3183 | 2^516742-39851 | 155555 | Enzo Doria | 09/2015 |
| 3184 | (22*10^155543+47)/3 | 155544 | Robert Price | 06/2021 |
| 3185 | (19*10^155504+131)/3 | 155505 | Robert Price | 06/2020 |
| 3186 | 7*10^155496+61 | 155497 | Robert Price | 08/2019 |
| 3187 | 2^516440+1878421 | 155464 | Enzo Doria | 08/2016 |
| 3188 | 26012^35173-35173^26012 | 155295 | Frank Doornink | 03/2024 |
| 3189 | 2^515863-1867237 | 155291 | Enzo Doria | 03/2016 |
| 3190 | 2^515786-461861 | 155268 | Enzo Doria | 07/2015 |
| 3191 | 2^515644-113247 | 155225 | Enzo Doria | 07/2014 |
| 3192 | (7*10^155203+107)/3 | 155204 | Robert Price | 02/2018 |
| 3193 | 10^155163+206871 | 155164 | Patrick De Geest | 05/2021 |
| 3194 | 10^155163-40001 | 155163 | Robert Price | 01/2021 |
| 3195 | (17*10^155133-89)/9 | 155134 | Robert Price | 07/2018 |
| 3196 | 26024^35131-35131^26024 | 155117 | Frank Doornink | 03/2024 |
| 3197 | 2^515249+214457 | 155106 | Enzo Doria | 10/2023 |
| 3198 | 2^515227-114997 | 155099 | Enzo Doria | 06/2015 |
| 3199 | 26510^35061-35061^26510 | 155090 | Frank Doornink | 03/2024 |
| 3201 | EPrime(155025) | 155025 | Eric W. Weisstein | 10/2010 |
| 3200 | (14*10^155024-221)/9 | 155025 | Robert Price | 04/2018 |
| 3202 | (4*10^155022+173)/3 | 155023 | Robert Price | 02/2018 |
| 3203 | (266*10^154897+1)/3 | 154899 | Robert Price | 04/2020 |
| 3204 | (115*10^154869-1)/3 | 154871 | Serge Batalov | 12/2014 |
| 3205 | (86*10^154853-221)/9 | 154854 | Robert Price | 09/2019 |
| 3206 | 2^514361+78167 | 154839 | Enzo Doria | 05/2016 |
| 3207 | 2^514281-115033 | 154815 | Enzo Doria | 06/2015 |
| 3208 | 25701^35104-35104^25701 | 154807 | Frank Doornink | 02/2024 |
| 3209 | 2^514194-3311 | 154788 | Yves Minet | 12/2014 |
| 3210 | 25930^35067-35067^25930 | 154779 | Frank Doornink | 03/2024 |
| 3211 | (14*10^154773+37)/3 | 154774 | Robert Price | 12/2018 |
| 3212 | (16*10^154748+131)/3 | 154749 | Robert Price | 03/2022 |
| 3213 | 6*10^154742-31 | 154743 | Robert Price | 07/2020 |
| 3214 | (14*10^154645+139)/9 | 154646 | Robert Price | 11/2021 |
| 3215 | 2^513690+216949 | 154637 | Enzo Doria | 12/2023 |
| 3216 | 5*10^154618-79 | 154619 | Robert Price | 03/2021 |
| 3217 | (167*10^154595+1)/3 | 154597 | Robert Price | 04/2021 |
| 3218 | 2^513437+1879337 | 154560 | Enzo Doria | 09/2016 |
| 3219 | 2^513306-113201 | 154521 | Enzo Doria | 07/2014 |
| 3220 | 26415^34942-34942^26415 | 154509 | Frank Doornink | 03/2024 |
| 3221 | 18^120818+19^120818-2 | 154497 | Harsh Aggarwal | 05/2024 |
| 3222 | (10^154494-13)/3 | 154494 | Robert Price | 12/2017 |
| 3223 | 23462^35343+35343^23462 | 154462 | Norbert Schneider | 04/2023 |
| 3224 | 2^513042-113787 | 154442 | Enzo Doria | 09/2014 |
| 3225 | (151*10^154434-7)/9 | 154436 | Robert Price | 01/2020 |
| 3226 | (118*10^154428+11)/3 | 154430 | Robert Price | 03/2022 |
| 3227 | 2^512987+29153 | 154425 | Enzo Doria | 02/2024 |
| 3228 | (14*10^154413+139)/9 | 154414 | Robert Price | 11/2021 |
| 3229 | (77*10^154389-149)/9 | 154390 | Robert Price | 03/2022 |
| 3230 | 32184^34247-34247^32184 | 154374 | Frank Doornink | 02/2024 |
| 3231 | 10^154359+49 | 154360 | Robert Price | 02/2023 |
| 3232 | 2^512628-114053 | 154317 | Enzo Doria | 11/2014 |
| 3233 | 2^512529-49783 | 154287 | Enzo Doria | 10/2015 |
| 3234 | (355573#+6991)/(6991*2031599) | 154285 | Makoto Morimoto | 06/2019 |
| 3235 | 2^512315-115297 | 154223 | Enzo Doria | 06/2015 |
| 3236 | (47*10^154221+241)/9 | 154222 | Robert Price | 06/2022 |
| 3237 | (7*10^154211+173)/9 | 154211 | Robert Price | 01/2022 |
| 3238 | 2^512243+22703 | 154201 | Enzo Doria | 09/2023 |
| 3239 | 2^512168+79561 | 154178 | Enzo Doria | 06/2016 |
| 3240 | (77*10^154175+67)/9 | 154176 | Robert Price | 12/2021 |
| 3241 | (59*19^120562-5)/18 | 154170 | Anonymous | 12/2023 |
| 3242 | (5*10^154158-311)/9 | 154158 | Robert Price | 12/2021 |
| 3243 | 27169^34758-34758^27169 | 154120 | Frank Doornink | 01/2024 |
| 3244 | (89*10^154103-737)/9 | 154104 | Robert Price | 01/2022 |
| 3245 | 2^511857+23327 | 154085 | Enzo Doria | 10/2023 |
| 3246 | 4*10^154078-57 | 154079 | Robert Price | 10/2018 |
| 3247 | 26242^34863-34863^26242 | 154060 | Frank Doornink | 03/2024 |
| 3248 | (355049#+1859)/(11*13*10148891*62587751) | 154051 | Makoto Morimoto | 06/2019 |
| 3249 | 7*10^154038-57 | 154039 | Robert Price | 06/2020 |
| 3250 | 2^511658-114371 | 154025 | Enzo Doria | 02/2015 |
