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 | 32042^35123-35123^32042 | 158255 | Frank Doornink | 01/2024 |
| 3002 | 2^525690-9221 | 158249 | Lelio R Paula | 01/2013 |
| 3003 | 2*10^158242-7 | 158243 | Robert Price | 10/2015 |
| 3004 | 2^525667-525667^2 | 158242 | Henri Lifchitz | 12/2017 |
| 3005 | (56*10^158230+187)/9 | 158231 | Robert Price | 10/2021 |
| 3006 | 10^158209-7000000001 | 158209 | Robert Price | 12/2021 |
| 3007 | 31050^35207-35207^31050 | 158153 | Frank Doornink | 01/2024 |
| 3008 | 2^525186-1857431 | 158097 | Enzo Doria | 10/2015 |
| 3009 | 31527^35108-35108^31527 | 157940 | Frank Doornink | 01/2024 |
| 3010 | 2^524515-23245 | 157895 | Enzo Doria | 08/2013 |
| 3011 | 2^524499-109087 | 157890 | Enzo Doria | 04/2014 |
| 3012 | 2^524384-219533 | 157856 | Enzo Doria | 03/2024 |
| 3014 | 2^18067*(2^506221+1)-1 | 157827 | Makoto Morimoto | 05/2014 |
| 3015 | 2^524288+189093 | 157827 | Makoto Morimoto | 01/2016 |
| 3013 | 2^524288-164073 | 157827 | Matthias Baur | 03/2020 |
| 3016 | (2^(2^19)-9333)/(19*23*463*1213*31973) | 157814 | Makoto Morimoto | 09/2017 |
| 3017 | (10^157792+359)/9 | 157792 | Serge Batalov | 12/2014 |
| 3018 | 2^524154+25 | 157787 | Stefano Morozzi | 04/2021 |
| 3019 | 2^523924+1876591 | 157717 | Enzo Doria | 07/2016 |
| 3020 | (17*10^157705+67)/3 | 157706 | Robert Price | 01/2019 |
| 3021 | (46^94841+1)/47 | 157696 | Robert Price | 01/2014 |
| 3022 | 2^523774+77839 | 157672 | Enzo Doria | 05/2016 |
| 3023 | 2^523587+2799143 | 157616 | Enzo Doria | 04/2016 |
| 3024 | 2^523496+220141 | 157588 | Enzo Doria | 03/2024 |
| 3025 | 2^523371+1872113 | 157551 | Enzo Doria | 05/2016 |
| 3026 | 8*10^157477+27 | 157478 | Robert Price | 09/2021 |
| 3027 | 32268^34909-34909^32268 | 157397 | Frank Doornink | 02/2024 |
| 3028 | (8*10^157368+49)/3 | 157369 | Robert Price | 05/2020 |
| 3029 | (82*10^157319+449)/9 | 157320 | Robert Price | 11/2019 |
| 3030 | 2^522535-351457 | 157299 | Enzo Doria | 07/2015 |
| 3031 | 25401^35704-35704^25401 | 157271 | Frank Doornink | 01/2024 |
| 3032 | 2^522226+2799079 | 157206 | Enzo Doria | 04/2016 |
| 3033 | (134*10^157191-11)/3 | 157193 | Robert Price | 01/2022 |
| 3034 | 2^522134-1849451 | 157178 | Enzo Doria | 08/2015 |
| 3035 | 9*10^157152+71 | 157153 | Robert Price | 08/2020 |
| 3036 | 4*10^157150+93 | 157151 | Robert Price | 08/2018 |
| 3037 | 31227^34952-34952^31227 | 157093 | Frank Doornink | 01/2024 |
| 3038 | (32^104347+5^104347)/37 | 157057 | Anonymous | 12/2023 |
| 3039 | fibonacci(751442)-2 | 157042 | Jon Grantham | 08/2023 |
| 3040 | 2^521401-29593 | 156958 | Enzo Doria | 08/2015 |
| 3041 | 7*10^156956+87 | 156957 | Robert Price | 07/2019 |
| 3042 | 2^521348-23397 | 156942 | Enzo Doria | 08/2013 |
| 3043 | 10^156902+34509 | 156903 | Patrick De Geest | 08/2021 |
| 3045 | 10^156902-80000001 | 156902 | Robert Price | 04/2021 |
| 3044 | 10^156902-69789 | 156902 | Patrick De Geest | 08/2021 |
| 3046 | (98^78797+1)/99 | 156901 | Paul Bourdelais | 12/2017 |
| 3047 | 65^86522+64 | 156857 | Lelio R Paula | 04/2016 |
| 3048 | 8^173687-7^173687 | 156855 | Jean-Louis Charton | 09/2004 |
| 3049 | 2^520977-1858183 | 156830 | Enzo Doria | 10/2015 |
| 3050 | (8*10^156718-101)/3 | 156719 | Robert Price | 08/2018 |
| 3051 | (10^156640+7)/53 | 156639 | Alfred Reich | 07/2021 |
| 3052 | 2^520314-1849481 | 156631 | Enzo Doria | 08/2015 |
| 3053 | (16*10^156563-637)/9 | 156564 | Robert Price | 09/2022 |
| 3054 | (13*10^156522+89)/3 | 156523 | Robert Price | 09/2018 |
| 3056 | (2^(6*86654+1)-5)/3 | 156513 | Kevin Acres | 12/2013 |
| 3055 | (2^519925-5)/3 | 156513 | Stefano Morozzi | 08/2022 |
| 3057 | (4*10^156501+119)/3 | 156502 | Robert Price | 12/2021 |
| 3058 | (83*10^156476-101)/9 | 156477 | Robert Price | 08/2021 |
| 3059 | 3*10^156435-97 | 156436 | Robert Price | 07/2018 |
| 3060 | (8*10^156371-77)/3 | 156372 | Robert Price | 07/2018 |
| 3061 | 53^90679-52^90679 | 156356 | Robert Price | 01/2013 |
| 3062 | 31267^34782-34782^31267 | 156349 | Frank Doornink | 01/2024 |
| 3063 | (418*10^156309-31)/9 | 156311 | Robert Price | 05/2022 |
| 3064 | 2^519106-59141 | 156267 | Enzo Doria | 10/2015 |
| 3065 | 25929^35404-35404^25929 | 156266 | Frank Doornink | 03/2024 |
| 3066 | 2^519053+6077 | 156251 | Enzo Doria | 02/2016 |
| 3067 | 31199^34764-34764^31199 | 156235 | Frank Doornink | 01/2024 |
| 3068 | 2^518968-1860989 | 156225 | Enzo Doria | 11/2015 |
| 3069 | (25*10^156221-7)/9 | 156222 | Robert Price | 05/2018 |
| 3070 | 2^518931-2782297 | 156214 | Enzo Doria | 09/2015 |
| 3071 | 2^518608-2939 | 156117 | Yves Minet | 09/2014 |
| 3072 | 10*27^109005+697 | 156027 | Curtis Bright | 05/2015 |
| 3073 | (49*10^155933-319)/9 | 155934 | Robert Price | 10/2021 |
| 3074 | 2^517967-113485 | 155924 | Enzo Doria | 08/2014 |
| 3075 | (103*10^155904+17)/3 | 155906 | Robert Price | 08/2020 |
| 3076 | (8*10^155887-719)/9 | 155887 | Robert Price | 03/2021 |
| 3077 | 2^517789+29231 | 155871 | Enzo Doria | 02/2024 |
| 3078 | 4*10^155853-39 | 155854 | Robert Price | 09/2020 |
| 3079 | 2^517698+4429 | 155843 | Lelio R Paula | 01/2013 |
| 3080 | 32015^34584-34584^32015 | 155814 | Frank Doornink | 01/2024 |
| 3081 | 2^517543-113257 | 155796 | Enzo Doria | 07/2014 |
| 3082 | (14*10^155740-143)/3 | 155741 | Robert Price | 11/2018 |
| 3083 | 31959^34564-34564^31959 | 155697 | Frank Doornink | 01/2024 |
| 3084 | 31^104309-30^104309 | 155563 | Henri Lifchitz | 08/2013 |
| 3085 | 2^516742-39851 | 155555 | Enzo Doria | 09/2015 |
| 3086 | (22*10^155543+47)/3 | 155544 | Robert Price | 06/2021 |
| 3087 | (19*10^155504+131)/3 | 155505 | Robert Price | 06/2020 |
| 3088 | 7*10^155496+61 | 155497 | Robert Price | 08/2019 |
| 3089 | 2^516440+1878421 | 155464 | Enzo Doria | 08/2016 |
| 3090 | 26012^35173-35173^26012 | 155295 | Frank Doornink | 03/2024 |
| 3091 | 2^515863-1867237 | 155291 | Enzo Doria | 03/2016 |
| 3092 | 2^515786-461861 | 155268 | Enzo Doria | 07/2015 |
| 3093 | 2^515644-113247 | 155225 | Enzo Doria | 07/2014 |
| 3094 | (7*10^155203+107)/3 | 155204 | Robert Price | 02/2018 |
| 3095 | 10^155163+206871 | 155164 | Patrick De Geest | 05/2021 |
| 3096 | 10^155163-40001 | 155163 | Robert Price | 01/2021 |
| 3097 | (17*10^155133-89)/9 | 155134 | Robert Price | 07/2018 |
| 3098 | 26024^35131-35131^26024 | 155117 | Frank Doornink | 03/2024 |
| 3099 | 2^515249+214457 | 155106 | Enzo Doria | 10/2023 |
| 3100 | 2^515227-114997 | 155099 | Enzo Doria | 06/2015 |
| 3101 | 26510^35061-35061^26510 | 155090 | Frank Doornink | 03/2024 |
| 3103 | EPrime(155025) | 155025 | Eric W. Weisstein | 10/2010 |
| 3102 | (14*10^155024-221)/9 | 155025 | Robert Price | 04/2018 |
| 3104 | (4*10^155022+173)/3 | 155023 | Robert Price | 02/2018 |
| 3105 | (266*10^154897+1)/3 | 154899 | Robert Price | 04/2020 |
| 3106 | (115*10^154869-1)/3 | 154871 | Serge Batalov | 12/2014 |
| 3107 | (86*10^154853-221)/9 | 154854 | Robert Price | 09/2019 |
| 3108 | 2^514361+78167 | 154839 | Enzo Doria | 05/2016 |
| 3109 | 2^514281-115033 | 154815 | Enzo Doria | 06/2015 |
| 3110 | 25701^35104-35104^25701 | 154807 | Frank Doornink | 02/2024 |
| 3111 | 2^514194-3311 | 154788 | Yves Minet | 12/2014 |
| 3112 | 25930^35067-35067^25930 | 154779 | Frank Doornink | 03/2024 |
| 3113 | (14*10^154773+37)/3 | 154774 | Robert Price | 12/2018 |
| 3114 | (16*10^154748+131)/3 | 154749 | Robert Price | 03/2022 |
| 3115 | 6*10^154742-31 | 154743 | Robert Price | 07/2020 |
| 3116 | (14*10^154645+139)/9 | 154646 | Robert Price | 11/2021 |
| 3117 | 2^513690+216949 | 154637 | Enzo Doria | 12/2023 |
| 3118 | 5*10^154618-79 | 154619 | Robert Price | 03/2021 |
| 3119 | (167*10^154595+1)/3 | 154597 | Robert Price | 04/2021 |
| 3120 | 2^513437+1879337 | 154560 | Enzo Doria | 09/2016 |
| 3121 | 2^513306-113201 | 154521 | Enzo Doria | 07/2014 |
| 3122 | 26415^34942-34942^26415 | 154509 | Frank Doornink | 03/2024 |
| 3123 | (10^154494-13)/3 | 154494 | Robert Price | 12/2017 |
| 3124 | 23462^35343+35343^23462 | 154462 | Norbert Schneider | 04/2023 |
| 3125 | 2^513042-113787 | 154442 | Enzo Doria | 09/2014 |
| 3126 | (151*10^154434-7)/9 | 154436 | Robert Price | 01/2020 |
| 3127 | (118*10^154428+11)/3 | 154430 | Robert Price | 03/2022 |
| 3128 | 2^512987+29153 | 154425 | Enzo Doria | 02/2024 |
| 3129 | (14*10^154413+139)/9 | 154414 | Robert Price | 11/2021 |
| 3130 | (77*10^154389-149)/9 | 154390 | Robert Price | 03/2022 |
| 3131 | 32184^34247-34247^32184 | 154374 | Frank Doornink | 02/2024 |
| 3132 | 10^154359+49 | 154360 | Robert Price | 02/2023 |
| 3133 | 2^512628-114053 | 154317 | Enzo Doria | 11/2014 |
| 3134 | 2^512529-49783 | 154287 | Enzo Doria | 10/2015 |
| 3135 | (355573#+6991)/(6991*2031599) | 154285 | Makoto Morimoto | 06/2019 |
| 3136 | 2^512315-115297 | 154223 | Enzo Doria | 06/2015 |
| 3137 | (47*10^154221+241)/9 | 154222 | Robert Price | 06/2022 |
| 3138 | (7*10^154211+173)/9 | 154211 | Robert Price | 01/2022 |
| 3139 | 2^512243+22703 | 154201 | Enzo Doria | 09/2023 |
| 3140 | 2^512168+79561 | 154178 | Enzo Doria | 06/2016 |
| 3141 | (77*10^154175+67)/9 | 154176 | Robert Price | 12/2021 |
| 3142 | (59*19^120562-5)/18 | 154170 | Anonymous | 12/2023 |
| 3143 | (5*10^154158-311)/9 | 154158 | Robert Price | 12/2021 |
| 3144 | 27169^34758-34758^27169 | 154120 | Frank Doornink | 01/2024 |
| 3145 | (89*10^154103-737)/9 | 154104 | Robert Price | 01/2022 |
| 3146 | 2^511857+23327 | 154085 | Enzo Doria | 10/2023 |
| 3147 | 4*10^154078-57 | 154079 | Robert Price | 10/2018 |
| 3148 | 26242^34863-34863^26242 | 154060 | Frank Doornink | 03/2024 |
| 3149 | (355049#+1859)/(11*13*10148891*62587751) | 154051 | Makoto Morimoto | 06/2019 |
| 3150 | 7*10^154038-57 | 154039 | Robert Price | 06/2020 |
| 3151 | 2^511658-114371 | 154025 | Enzo Doria | 02/2015 |
| 3152 | (57^87719+1)/58 | 154022 | Paul Bourdelais | 11/2017 |
| 3153 | 2^511580-1846679 | 154001 | Enzo Doria | 07/2015 |
| 3154 | (259*10^153998-1)/3 | 154000 | Robert Price | 12/2020 |
| 3155 | 2^511541-113713 | 153990 | Enzo Doria | 09/2014 |
| 3156 | 49958^32768+49957^32768 | 153965 | Kellen Shenton | 11/2020 |
| 3157 | 10^153935+970801 | 153936 | Patrick De Geest | 05/2021 |
| 3158 | 10^153935-1000001 | 153935 | Robert Price | 08/2020 |
| 3159 | (16*10^153868-73)/3 | 153869 | Robert Price | 07/2020 |
| 3160 | 9*10^153851-67 | 153852 | Robert Price | 11/2020 |
| 3161 | 2^511077-112723 | 153850 | Enzo Doria | 06/2014 |
| 3162 | 69^83653-68^83653 | 153826 | Robert Price | 12/2013 |
| 3163 | 2^510963-113707 | 153816 | Enzo Doria | 09/2014 |
| 3164 | (154*10^153810-1)/9 | 153812 | Serge Batalov | 12/2014 |
| 3165 | (181*25^109991-75077)/8 | 153763 | Curtis Bright | 05/2015 |
| 3166 | 2*10^153746-3 | 153747 | Robert Price | 07/2015 |
| 3167 | 2^510626+1179379 | 153714 | Enzo Doria | 05/2016 |
| 3168 | (7*10^153664+113)/3 | 153665 | Robert Price | 02/2018 |
| 3169 | 2^510448+24991 | 153661 | Enzo Doria | 11/2023 |
| 3170 | 2^510420+81121 | 153652 | Enzo Doria | 07/2016 |
| 3171 | (197*7^181761-1)/2 | 153608 | Karsten Bonath | 05/2017 |
| 3172 | 2^509894-459161 | 153494 | Enzo Doria | 05/2015 |
| 3173 | (74*10^153489+673)/9 | 153490 | Robert Price | 02/2022 |
| 3174 | (49*10^153484-211)/9 | 153485 | Robert Price | 06/2022 |
| 3175 | 2^509841+71657 | 153478 | Enzo Doria | 04/2016 |
| 3176 | 9*10^153446+41 | 153447 | Robert Price | 08/2020 |
| 3177 | 2^509533-1846723 | 153385 | Enzo Doria | 07/2015 |
| 3178 | 2^509468-39989 | 153366 | Enzo Doria | 09/2015 |
| 3179 | 70^83117-69^83117 | 153360 | Robert Price | 01/2014 |
| 3180 | (209246*34^99997-81)/11 | 153148 | Eric Chen | 08/2023 |
| 3181 | (7*10^153116-1)/3 | 153117 | Robert Price | 08/2022 |
| 3182 | (112*10^153025-1)/3 | 153027 | Serge Batalov | 12/2014 |
| 3183 | 31912^33975-33975^31912 | 153022 | Frank Doornink | 01/2024 |
| 3184 | (19*10^153010+131)/3 | 153011 | Robert Price | 06/2020 |
| 3185 | 2^508174-1855151 | 152976 | Enzo Doria | 09/2015 |
| 3186 | 181^67757-2 | 152974 | Lelio R Paula | 12/2017 |
| 3187 | 2^508160-1864829 | 152972 | Enzo Doria | 01/2016 |
| 3188 | 10^152960+412563 | 152961 | Patrick De Geest | 05/2021 |
| 3189 | 10^152960-50000000001 | 152960 | Robert Price | 12/2020 |
| 3190 | 10^152960-423749 | 152960 | Patrick De Geest | 05/2021 |
| 3191 | (71*10^152933-143)/9 | 152934 | Robert Price | 10/2021 |
| 3192 | 32109^33932-33932^32109 | 152919 | Frank Doornink | 02/2024 |
| 3193 | 2^507857-1848199 | 152881 | Enzo Doria | 07/2015 |
| 3194 | 2^507638-115361 | 152815 | Enzo Doria | 07/2015 |
| 3195 | 2^507551-114025 | 152789 | Enzo Doria | 11/2014 |
| 3196 | (6^196337+1)/7 | 152780 | Paul Bourdelais | 02/2010 |
| 3197 | (22*10^152670-13)/9 | 152671 | Robert Price | 06/2018 |
| 3198 | 2^507085+28517 | 152648 | Enzo Doria | 01/2024 |
| 3199 | 2^506917+28847 | 152598 | Enzo Doria | 02/2024 |
| 3200 | 2^506451-22339 | 152457 | Enzo Doria | 07/2013 |
| 3201 | 26463^34460-34460^26463 | 152405 | Frank Doornink | 03/2024 |
| 3202 | 31898^33837-33837^31898 | 152394 | Frank Doornink | 01/2024 |
| 3203 | 2^505995-113185 | 152320 | Enzo Doria | 07/2014 |
| 3204 | (8*10^152260-17)/9 | 152260 | Serge Batalov | 11/2022 |
| 3205 | (4*10^152253+149)/9 | 152253 | Robert Price | 04/2018 |
| 3206 | 578^55117-577^55117 | 152230 | Jean-Louis Charton | 08/2012 |
| 3207 | 2^505431-505431 | 152150 | Henri Lifchitz | 04/2005 |
| 3208 | (203*10^152143+1)/3 | 152145 | Robert Price | 03/2020 |
| 3209 | 31730^33787-33787^31730 | 152092 | Frank Doornink | 01/2024 |
| 3210 | 2^505089+217787 | 152047 | Enzo Doria | 01/2024 |
| 3211 | 2^505053+73097 | 152037 | Enzo Doria | 04/2016 |
| 3212 | 22*10^151998+3 | 152000 | Robert Price | 01/2020 |
| 3213 | (238*10^151979-1)/3 | 151981 | Robert Price | 04/2020 |
| 3214 | (2^504793-7)/46765 | 151954 | Lelio R Paula | 12/2017 |
| 3215 | 350377#+797581 | 151937 | Nicolas PALAU | 08/2017 |
| 3216 | (79*10^151906-529)/9 | 151907 | Robert Price | 01/2022 |
| 3217 | 2^504618-343991 | 151906 | Enzo Doria | 07/2015 |
| 3218 | 2^504259+211193 | 151798 | Enzo Doria | 08/2023 |
| 3219 | 2^504212-461939 | 151783 | Enzo Doria | 07/2015 |
| 3220 | 7*10^151772-41 | 151773 | Robert Price | 08/2021 |
| 3221 | 2^504054-2231 | 151736 | Yves Minet | 10/2011 |
| 3222 | 25237^34458-34458^25237 | 151686 | Frank Doornink | 11/2023 |
| 3223 | (28*10^151682+191)/3 | 151683 | Robert Price | 02/2020 |
| 3224 | 2^503817+23961 | 151665 | Enzo Doria | 10/2023 |
| 3225 | 2^503475-933075 | 151562 | Paul Bourdelais | 06/2021 |
| 3226 | 2^503371+26289 | 151530 | Enzo Doria | 12/2023 |
| 3227 | 2^503361-39883 | 151527 | Enzo Doria | 09/2015 |
| 3228 | 2^503225+382667 | 151486 | Enzo Doria | 10/2016 |
| 3229 | (206*10^151483-11)/3 | 151485 | Robert Price | 02/2022 |
| 3230 | (844*10^151396-7)/9 | 151398 | Robert Price | 05/2021 |
| 3231 | (26*10^151391-503)/9 | 151392 | Robert Price | 07/2018 |
| 3232 | 2^502769+1877567 | 151349 | Enzo Doria | 08/2016 |
| 3233 | 2^502576-4019 | 151291 | Yves Minet | 10/2011 |
| 3234 | 5*10^151257+41 | 151258 | Robert Price | 03/2019 |
| 3235 | 2^502290-2792501 | 151205 | Enzo Doria | 02/2016 |
| 3236 | 2^502181+1868417 | 151172 | Enzo Doria | 04/2016 |
| 3237 | 2^502055+22583 | 151134 | Enzo Doria | 09/2023 |
| 3238 | (3*23^110967+41)/22 | 151106 | Anonymous | 12/2023 |
| 3239 | 6*10^151063-77 | 151064 | Robert Price | 09/2021 |
| 3240 | 2^501781-1850503 | 151052 | Enzo Doria | 08/2015 |
| 3241 | (5*10^151007+37)/3 | 151008 | Robert Price | 03/2018 |
| 3242 | 3^316494+5*2^316494 | 151007 | Jon Grantham | 08/2023 |
| 3243 | 2^501627-991 | 151005 | Yves Minet | 02/2014 |
| 3244 | 2^501577-115333 | 150990 | Enzo Doria | 07/2015 |
| 3245 | 25239^34298-34298^25239 | 150983 | Frank Doornink | 12/2023 |
| 3246 | (19*10^150977-7)/3 | 150978 | Robert Price | 12/2023 |
| 3247 | 8*10^150975+3 | 150976 | Robert Price | 08/2015 |
| 3248 | 2^501512-113669 | 150971 | Enzo Doria | 09/2014 |
| 3249 | (83*10^150908+493)/9 | 150909 | Robert Price | 12/2021 |
| 3250 | 2*10^150818+83 | 150819 | Robert Price | 12/2021 |
