## PRP Records

### Probable Primes Top 10000

#### (295149 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 ? 3001 (861^54181-1)/860 159019 Jinyuan Wang 11/2023 3002 2^528000-23307 158944 Enzo Doria 08/2013 3003 (29*10^158909+61)/9 158910 Robert Price 08/2018 3004 2^527817+1876817 158889 Enzo Doria 07/2016 3005 2^527774-49451 158876 Enzo Doria 10/2015 3006 2^527745-291553 158868 Enzo Doria 07/2015 3007 (91*10^158862+11)/3 158864 Robert Price 02/2020 3008 2^527644-1856999 158837 Enzo Doria 10/2015 3009 (37200^37199-37198^37199)/(2^37199) 158822 Henri Lifchitz 06/2013 3010 (17*10^158819+7)/3 158820 Robert Price 06/2023 3011 2^527573-1863253 158816 Enzo Doria 12/2015 3012 2^527553-23401 158810 Enzo Doria 08/2013 3013 (49*10^158783+437)/9 158784 Robert Price 09/2021 3014 10^158755+310207 158756 Patrick De Geest 08/2021 3015 10^158755-50001 158755 Robert Price 08/2020 3016 (61*10^158748-619)/9 158749 Robert Price 03/2022 3017 11^152420-210 158730 Enzo Doria 09/2012 3018 (13*10^158694+401)/9 158695 Robert Price 01/2018 3019 2^527052-69059 158659 Enzo Doria 11/2015 3020 2^526849-113233 158598 Enzo Doria 07/2014 3021 24286^36161+36161^24286 158579 Norbert Schneider 08/2023 3022 (2^526763-lucasV(1,2,526763)+1)/2 158572 Mike Oakes 11/2016 3023 (299*10^158544-17)/3 158546 Robert Price 04/2020 3024 2^526658-3551 158540 Yves Minet 03/2017 3025 7*10^158465-11 158466 Robert Price 06/2019 3026 (7^187507-3^187507)/4 158462 Jon Grantham 08/2023 3027 2^526375-23115 158455 Enzo Doria 08/2013 3028 (77*10^158407-293)/9 158408 Robert Price 09/2019 3029 31209^35242-35242^31209 158388 Frank Doornink 01/2024 3030 32071^35144-35144^32071 158363 Frank Doornink 01/2024 3031 2^526028-112793 158351 Enzo Doria 07/2014 3032 (229*10^158339-1)/3 158341 Robert Price 07/2020 3033 32042^35123-35123^32042 158255 Frank Doornink 01/2024 3034 2^525690-9221 158249 Lelio R Paula 01/2013 3035 2*10^158242-7 158243 Robert Price 10/2015 3036 2^525667-525667^2 158242 Henri Lifchitz 12/2017 3037 (56*10^158230+187)/9 158231 Robert Price 10/2021 3038 10^158209-7000000001 158209 Robert Price 12/2021 3039 31050^35207-35207^31050 158153 Frank Doornink 01/2024 3040 2^525186-1857431 158097 Enzo Doria 10/2015 3041 31527^35108-35108^31527 157940 Frank Doornink 01/2024 3042 2^524515-23245 157895 Enzo Doria 08/2013 3043 2^524499-109087 157890 Enzo Doria 04/2014 3044 2^524384-219533 157856 Enzo Doria 03/2024 3046 2^18067*(2^506221+1)-1 157827 Makoto Morimoto 05/2014 3047 2^524288+189093 157827 Makoto Morimoto 01/2016 3045 2^524288-164073 157827 Matthias Baur 03/2020 3048 (2^(2^19)-9333)/(19*23*463*1213*31973) 157814 Makoto Morimoto 09/2017 3049 (10^157792+359)/9 157792 Serge Batalov 12/2014 3050 2^524154+25 157787 Stefano Morozzi 04/2021 3051 2^523924+1876591 157717 Enzo Doria 07/2016 3052 (17*10^157705+67)/3 157706 Robert Price 01/2019 3053 (46^94841+1)/47 157696 Robert Price 01/2014 3054 2^523774+77839 157672 Enzo Doria 05/2016 3055 2^523587+2799143 157616 Enzo Doria 04/2016 3056 2^523496+220141 157588 Enzo Doria 03/2024 3057 2^523371+1872113 157551 Enzo Doria 05/2016 3058 8*10^157477+27 157478 Robert Price 09/2021 3059 32268^34909-34909^32268 157397 Frank Doornink 02/2024 3060 (8*10^157368+49)/3 157369 Robert Price 05/2020 3061 (82*10^157319+449)/9 157320 Robert Price 11/2019 3062 2^522535-351457 157299 Enzo Doria 07/2015 3063 25401^35704-35704^25401 157271 Frank Doornink 01/2024 3064 2^522226+2799079 157206 Enzo Doria 04/2016 3065 (134*10^157191-11)/3 157193 Robert Price 01/2022 3066 2^522134-1849451 157178 Enzo Doria 08/2015 3067 9*10^157152+71 157153 Robert Price 08/2020 3068 4*10^157150+93 157151 Robert Price 08/2018 3069 31227^34952-34952^31227 157093 Frank Doornink 01/2024 3070 (32^104347+5^104347)/37 157057 Anonymous 12/2023 3071 fibonacci(751442)-2 157042 Jon Grantham 08/2023 3072 2^521401-29593 156958 Enzo Doria 08/2015 3073 7*10^156956+87 156957 Robert Price 07/2019 3074 2^521348-23397 156942 Enzo Doria 08/2013 3075 10^156902+34509 156903 Patrick De Geest 08/2021 3077 10^156902-80000001 156902 Robert Price 04/2021 3076 10^156902-69789 156902 Patrick De Geest 08/2021 3078 (98^78797+1)/99 156901 Paul Bourdelais 12/2017 3079 65^86522+64 156857 Lelio R Paula 04/2016 3080 8^173687-7^173687 156855 Jean-Louis Charton 09/2004 3081 2^520977-1858183 156830 Enzo Doria 10/2015 3082 (8*10^156718-101)/3 156719 Robert Price 08/2018 3083 (10^156640+7)/53 156639 Alfred Reich 07/2021 3084 2^520314-1849481 156631 Enzo Doria 08/2015 3085 (16*10^156563-637)/9 156564 Robert Price 09/2022 3086 (13*10^156522+89)/3 156523 Robert Price 09/2018 3088 (2^(6*86654+1)-5)/3 156513 Kevin Acres 12/2013 3087 (2^519925-5)/3 156513 Stefano Morozzi 08/2022 3089 (4*10^156501+119)/3 156502 Robert Price 12/2021 3090 (83*10^156476-101)/9 156477 Robert Price 08/2021 3091 3*10^156435-97 156436 Robert Price 07/2018 3092 (8*10^156371-77)/3 156372 Robert Price 07/2018 3093 53^90679-52^90679 156356 Robert Price 01/2013 3094 31267^34782-34782^31267 156349 Frank Doornink 01/2024 3095 (418*10^156309-31)/9 156311 Robert Price 05/2022 3096 2^519106-59141 156267 Enzo Doria 10/2015 3097 25929^35404-35404^25929 156266 Frank Doornink 03/2024 3098 2^519053+6077 156251 Enzo Doria 02/2016 3099 31199^34764-34764^31199 156235 Frank Doornink 01/2024 3100 2^518968-1860989 156225 Enzo Doria 11/2015 3101 (25*10^156221-7)/9 156222 Robert Price 05/2018 3102 2^518931-2782297 156214 Enzo Doria 09/2015 3103 2^518608-2939 156117 Yves Minet 09/2014 3104 10*27^109005+697 156027 Curtis Bright 05/2015 3105 (49*10^155933-319)/9 155934 Robert Price 10/2021 3106 2^517967-113485 155924 Enzo Doria 08/2014 3107 (103*10^155904+17)/3 155906 Robert Price 08/2020 3108 (8*10^155887-719)/9 155887 Robert Price 03/2021 3109 2^517789+29231 155871 Enzo Doria 02/2024 3110 4*10^155853-39 155854 Robert Price 09/2020 3111 2^517698+4429 155843 Lelio R Paula 01/2013 3112 32015^34584-34584^32015 155814 Frank Doornink 01/2024 3113 2^517543-113257 155796 Enzo Doria 07/2014 3114 (14*10^155740-143)/3 155741 Robert Price 11/2018 3115 31959^34564-34564^31959 155697 Frank Doornink 01/2024 3116 31^104309-30^104309 155563 Henri Lifchitz 08/2013 3117 2^516742-39851 155555 Enzo Doria 09/2015 3118 (22*10^155543+47)/3 155544 Robert Price 06/2021 3119 (19*10^155504+131)/3 155505 Robert Price 06/2020 3120 7*10^155496+61 155497 Robert Price 08/2019 3121 2^516440+1878421 155464 Enzo Doria 08/2016 3122 26012^35173-35173^26012 155295 Frank Doornink 03/2024 3123 2^515863-1867237 155291 Enzo Doria 03/2016 3124 2^515786-461861 155268 Enzo Doria 07/2015 3125 2^515644-113247 155225 Enzo Doria 07/2014 3126 (7*10^155203+107)/3 155204 Robert Price 02/2018 3127 10^155163+206871 155164 Patrick De Geest 05/2021 3128 10^155163-40001 155163 Robert Price 01/2021 3129 (17*10^155133-89)/9 155134 Robert Price 07/2018 3130 26024^35131-35131^26024 155117 Frank Doornink 03/2024 3131 2^515249+214457 155106 Enzo Doria 10/2023 3132 2^515227-114997 155099 Enzo Doria 06/2015 3133 26510^35061-35061^26510 155090 Frank Doornink 03/2024 3135 EPrime(155025) 155025 Eric W. Weisstein 10/2010 3134 (14*10^155024-221)/9 155025 Robert Price 04/2018 3136 (4*10^155022+173)/3 155023 Robert Price 02/2018 3137 (266*10^154897+1)/3 154899 Robert Price 04/2020 3138 (115*10^154869-1)/3 154871 Serge Batalov 12/2014 3139 (86*10^154853-221)/9 154854 Robert Price 09/2019 3140 2^514361+78167 154839 Enzo Doria 05/2016 3141 2^514281-115033 154815 Enzo Doria 06/2015 3142 25701^35104-35104^25701 154807 Frank Doornink 02/2024 3143 2^514194-3311 154788 Yves Minet 12/2014 3144 25930^35067-35067^25930 154779 Frank Doornink 03/2024 3145 (14*10^154773+37)/3 154774 Robert Price 12/2018 3146 (16*10^154748+131)/3 154749 Robert Price 03/2022 3147 6*10^154742-31 154743 Robert Price 07/2020 3148 (14*10^154645+139)/9 154646 Robert Price 11/2021 3149 2^513690+216949 154637 Enzo Doria 12/2023 3150 5*10^154618-79 154619 Robert Price 03/2021 3151 (167*10^154595+1)/3 154597 Robert Price 04/2021 3152 2^513437+1879337 154560 Enzo Doria 09/2016 3153 2^513306-113201 154521 Enzo Doria 07/2014 3154 26415^34942-34942^26415 154509 Frank Doornink 03/2024 3155 18^120818+19^120818-2 154497 Harsh Aggarwal 05/2024 3156 (10^154494-13)/3 154494 Robert Price 12/2017 3157 23462^35343+35343^23462 154462 Norbert Schneider 04/2023 3158 2^513042-113787 154442 Enzo Doria 09/2014 3159 (151*10^154434-7)/9 154436 Robert Price 01/2020 3160 (118*10^154428+11)/3 154430 Robert Price 03/2022 3161 2^512987+29153 154425 Enzo Doria 02/2024 3162 (14*10^154413+139)/9 154414 Robert Price 11/2021 3163 (77*10^154389-149)/9 154390 Robert Price 03/2022 3164 32184^34247-34247^32184 154374 Frank Doornink 02/2024 3165 10^154359+49 154360 Robert Price 02/2023 3166 2^512628-114053 154317 Enzo Doria 11/2014 3167 2^512529-49783 154287 Enzo Doria 10/2015 3168 (355573#+6991)/(6991*2031599) 154285 Makoto Morimoto 06/2019 3169 2^512315-115297 154223 Enzo Doria 06/2015 3170 (47*10^154221+241)/9 154222 Robert Price 06/2022 3171 (7*10^154211+173)/9 154211 Robert Price 01/2022 3172 2^512243+22703 154201 Enzo Doria 09/2023 3173 2^512168+79561 154178 Enzo Doria 06/2016 3174 (77*10^154175+67)/9 154176 Robert Price 12/2021 3175 (59*19^120562-5)/18 154170 Anonymous 12/2023 3176 (5*10^154158-311)/9 154158 Robert Price 12/2021 3177 27169^34758-34758^27169 154120 Frank Doornink 01/2024 3178 (89*10^154103-737)/9 154104 Robert Price 01/2022 3179 2^511857+23327 154085 Enzo Doria 10/2023 3180 4*10^154078-57 154079 Robert Price 10/2018 3181 26242^34863-34863^26242 154060 Frank Doornink 03/2024 3182 (355049#+1859)/(11*13*10148891*62587751) 154051 Makoto Morimoto 06/2019 3183 7*10^154038-57 154039 Robert Price 06/2020 3184 2^511658-114371 154025 Enzo Doria 02/2015 3185 (57^87719+1)/58 154022 Paul Bourdelais 11/2017 3186 2^511580-1846679 154001 Enzo Doria 07/2015 3187 (259*10^153998-1)/3 154000 Robert Price 12/2020 3188 2^511541-113713 153990 Enzo Doria 09/2014 3189 49958^32768+49957^32768 153965 Kellen Shenton 11/2020 3190 10^153935+970801 153936 Patrick De Geest 05/2021 3191 10^153935-1000001 153935 Robert Price 08/2020 3192 (16*10^153868-73)/3 153869 Robert Price 07/2020 3193 9*10^153851-67 153852 Robert Price 11/2020 3194 2^511077-112723 153850 Enzo Doria 06/2014 3195 69^83653-68^83653 153826 Robert Price 12/2013 3196 2^510963-113707 153816 Enzo Doria 09/2014 3197 (154*10^153810-1)/9 153812 Serge Batalov 12/2014 3198 (181*25^109991-75077)/8 153763 Curtis Bright 05/2015 3199 2*10^153746-3 153747 Robert Price 07/2015 3200 2^510626+1179379 153714 Enzo Doria 05/2016 3201 (7*10^153664+113)/3 153665 Robert Price 02/2018 3202 2^510448+24991 153661 Enzo Doria 11/2023 3203 2^510420+81121 153652 Enzo Doria 07/2016 3204 (197*7^181761-1)/2 153608 Karsten Bonath 05/2017 3205 2^509894-459161 153494 Enzo Doria 05/2015 3206 (74*10^153489+673)/9 153490 Robert Price 02/2022 3207 (49*10^153484-211)/9 153485 Robert Price 06/2022 3208 2^509841+71657 153478 Enzo Doria 04/2016 3209 9*10^153446+41 153447 Robert Price 08/2020 3210 2^509533-1846723 153385 Enzo Doria 07/2015 3211 2^509468-39989 153366 Enzo Doria 09/2015 3212 70^83117-69^83117 153360 Robert Price 01/2014 3213 (209246*34^99997-81)/11 153148 Eric Chen 08/2023 3214 (7*10^153116-1)/3 153117 Robert Price 08/2022 3215 (112*10^153025-1)/3 153027 Serge Batalov 12/2014 3216 31912^33975-33975^31912 153022 Frank Doornink 01/2024 3217 (19*10^153010+131)/3 153011 Robert Price 06/2020 3218 2^508174-1855151 152976 Enzo Doria 09/2015 3219 181^67757-2 152974 Lelio R Paula 12/2017 3220 2^508160-1864829 152972 Enzo Doria 01/2016 3221 10^152960+412563 152961 Patrick De Geest 05/2021 3222 10^152960-50000000001 152960 Robert Price 12/2020 3223 10^152960-423749 152960 Patrick De Geest 05/2021 3224 (71*10^152933-143)/9 152934 Robert Price 10/2021 3225 32109^33932-33932^32109 152919 Frank Doornink 02/2024 3226 2^507857-1848199 152881 Enzo Doria 07/2015 3227 2^507638-115361 152815 Enzo Doria 07/2015 3228 2^507551-114025 152789 Enzo Doria 11/2014 3229 (6^196337+1)/7 152780 Paul Bourdelais 02/2010 3230 (22*10^152670-13)/9 152671 Robert Price 06/2018 3231 2^507085+28517 152648 Enzo Doria 01/2024 3232 2^506917+28847 152598 Enzo Doria 02/2024 3233 2^506451-22339 152457 Enzo Doria 07/2013 3234 26463^34460-34460^26463 152405 Frank Doornink 03/2024 3235 31898^33837-33837^31898 152394 Frank Doornink 01/2024 3236 2^505995-113185 152320 Enzo Doria 07/2014 3237 (8*10^152260-17)/9 152260 Serge Batalov 11/2022 3238 (4*10^152253+149)/9 152253 Robert Price 04/2018 3239 33530^33643-33643^33530 152250 Norbert Schneider 04/2024 3240 578^55117-577^55117 152230 Jean-Louis Charton 08/2012 3241 2^505431-505431 152150 Henri Lifchitz 04/2005 3242 (203*10^152143+1)/3 152145 Robert Price 03/2020 3243 31730^33787-33787^31730 152092 Frank Doornink 01/2024 3244 2^505089+217787 152047 Enzo Doria 01/2024 3245 33565^33594-33594^33565 152043 Norbert Schneider 04/2024 3246 2^505053+73097 152037 Enzo Doria 04/2016 3247 22*10^151998+3 152000 Robert Price 01/2020 3248 (238*10^151979-1)/3 151981 Robert Price 04/2020 3249 (2^504793-7)/46765 151954 Lelio R Paula 12/2017 3250 350377#+797581 151937 Nicolas PALAU 08/2017

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 22 2024 21:19 (Time in France)

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