Henri & Renaud Lifchitz's PRP Top records

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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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	2^451787-21805	136002	Enzo Doria	07/2013
3002	2^451734-112817	135986	Enzo Doria	06/2014
3003	(11*2^451714+1)/75	135979	Lelio R Paula	07/2015
3004	2^451705-21879	135977	Enzo Doria	07/2013
3005	2^451560-112349	135934	Enzo Doria	06/2014
3006	2^451530+45	135925	Lelio R Paula	08/2017
3007	31622^19875+19875^31622	135922	Hans Havermann	11/2020
3008	(25*10^135906-73)/3	135907	Robert Price	09/2019
3009	2^451450-21743	135900	Enzo Doria	07/2013
3010	35218^7199+7199^35218	135846	Hans Havermann	11/2020
3011	35661^6446+6446^35661	135844	Hans Havermann	11/2020
3012	31869^18248+18248^31869	135801	Hans Havermann	12/2020
3013	(77*10^135789+157)/9	135790	Robert Price	05/2022
3014	2^450805+65	135706	Lelio R Paula	08/2017
3015	30761^25728+25728^30761	135669	Hans Havermann	12/2020
3016	2*10^135663+69	135664	Robert Price	06/2020
3017	33962^9867+9867^33962	135651	Hans Havermann	11/2020
3018	34474^8605+8605^34474	135647	Hans Havermann	11/2020
3019	34501^8508+8508^34501	135583	Hans Havermann	12/2020
3020	35487^6614+6614^35487	135577	Hans Havermann	12/2020
3021	(13725^32768+1)/131074	135573	Lelio R Paula	03/2012
3022	(313007#+121876)/(230469424867)	135559	Makoto Morimoto	08/2020
3023	(5^193939+1)/6	135557	Paul Bourdelais	12/2008
3024	(844*10^135527-7)/9	135529	Robert Price	05/2021
3025	40387^2260+2260^40387	135463	Hans Havermann	12/2020
3026	2^449944-113247	135447	Enzo Doria	07/2014
3027	2^449770-113247	135395	Enzo Doria	07/2014
3028	2^449637-21471	135355	Enzo Doria	07/2013
3029	2^449571-75	135335	Lelio R Paula	08/2017
3030	(14*10^135301-53)/3	135302	Robert Price	12/2018
3031	(3*2^449494+1)/61340334013	135301	Lelio R Paula	07/2015
3032	(13*10^135279+437)/9	135280	Robert Price	04/2018
3033	2^449330-35	135262	Lelio R Paula	08/2017
3034	(19*2^449325+1)/9	135261	Lelio R Paula	07/2015
3035	(13*10^135184-43)/3	135185	Robert Price	11/2018
3036	2^449049-115309	135178	Enzo Doria	07/2015
3037	(10^135174+191)/3	135174	Robert Price	02/2018
3038	2^449030-15	135172	Lelio R Paula	08/2017
3039	(157*10^135151-1)/3	135153	Robert Price	01/2022
3040	(2^448966+100280245065)	135153	Paul Bourdelais	05/2022
3041	(27*2^448936-1)/11	135144	Lelio R Paula	07/2015
3042	(37*10^135099+251)/9	135100	Robert Price	09/2021
3043	32221^15586+15586^32221	135095	Hans Havermann	12/2020
3044	2^448762-351401	135091	Enzo Doria	07/2015
3045	2*10^135083-43	135084	Robert Price	04/2018
3046	31357^20278+20278^31357	135056	Hans Havermann	12/2020
3047	32242^15445+15445^32242	135055	Hans Havermann	12/2020
3048	k(198476)	135054	Robert Price	07/2020
3049	32461^14470+14470^32461	135053	Hans Havermann	12/2020
3050	31353^20288+20288^31353	135045	Hans Havermann	12/2020
3051	5*10^135019+77	135020	Robert Price	12/2018
3052	(10^135011+719)/9	135011	Serge Batalov	12/2014
3053	(197*10^134978+7)/3	134980	Robert Price	12/2020
3054	2^448386-2786261	134978	Enzo Doria	03/2016
3055	(73*10^134939+143)/9	134940	Robert Price	07/2019
3056	33957^9392+9392^33957	134903	Hans Havermann	12/2020
3057	2^448113-113949	134896	Enzo Doria	11/2014
3058	30958^22755+22755^30958	134887	Hans Havermann	12/2020
3059	2^447888-2786639	134828	Enzo Doria	03/2016
3060	2^447870-396765	134823	Enzo Doria	07/2013
3061	2^447766-21791	134791	Enzo Doria	07/2013
3062	(19*10^134786-49)/3	134787	Robert Price	05/2019
3063	Phi(202173,10)/10064306514895399941409	134758	Makoto Kamada	05/2019
3064	(23*2^447647+1)/155	134755	Lelio R Paula	07/2015
3065	2^447552-1019	134727	Yves Minet	02/2014
3066	(2*10^134720-41)/3	134720	Robert Price	02/2018
3067	(25*10^134695-97)/9	134696	Robert Price	01/2022
3068	2^447437-113569	134692	Enzo Doria	08/2014
3069	2^447426-65	134689	Lelio R Paula	08/2017
3070	2^447357-2797573	134668	Enzo Doria	04/2016
3071	2^447278+93	134645	Lelio R Paula	08/2017
3072	33193^11370+11370^33193	134623	Hans Havermann	12/2020
3073	30736^23979+23979^30736	134619	Hans Havermann	11/2020
3074	2^447094-113193	134589	Enzo Doria	07/2014
3075	3^282041-9934	134568	Enzo Doria	05/2014
3076	2^447019-109039	134567	Enzo Doria	04/2014
3077	31376^19437+19437^31376	134561	Hans Havermann	12/2020
3078	2^446990-22041	134558	Enzo Doria	07/2013
3079	123^64370+122	134528	Karsten Bonath	04/2018
3080	30100^29461+29461^30100	134525	Hans Havermann	11/2020
3081	31251^20158+20158^31251	134519	Hans Havermann	11/2020
3082	2^446782-39701	134495	Enzo Doria	09/2015
3083	31817^16858+16858^31817	134485	Hans Havermann	12/2020
3084	32448^13937+13937^32448	134471	Hans Havermann	12/2020
3085	2^446494-16485	134409	Enzo Doria	04/2013
3086	30042^29785+29785^30042	134408	Hans Havermann	12/2020
3087	29504^30069-30069^29504	134405	Norbert Schneider	12/2014
3088	2^446441+65	134393	Lelio R Paula	08/2017
3089	(10^134385+719)/9	134385	Serge Batalov	12/2014
3090	30043^29688+29688^30043	134370	Hans Havermann	12/2020
3091	(2*10^134364+529)/9	134364	Robert Price	01/2018
3092	34657^7512+7512^34657	134323	Hans Havermann	11/2020
3093	(13*2^446187-1)/661	134314	Lelio R Paula	07/2015
3094	5^192103+3^192103+2^192103+1	134275	Matthias Baur	12/2019
3095	42035^1564+1564^42035	134270	Hans Havermann	12/2020
3097	(2^446022-7)/339	134264	Lelio R Paula	07/2015
3096	30621^24248+24248^30621	134264	Hans Havermann	12/2020
3098	30341^26562+26562^30341	134237	Hans Havermann	11/2020
3099	10^134209+99867	134210	Patrick De Geest	05/2021
3100	10^134209-80000001	134209	Robert Price	04/2021
3101	10^134209-323283	134209	Patrick De Geest	05/2021
3102	29976^29953+29953^29976	134186	Hans Havermann	12/2020
3103	35038^6755+6755^35038	134183	Hans Havermann	12/2020
3104	63^74568+2	134174	Lelio R Paula	06/2017
3105	2^445671-22071	134161	Enzo Doria	07/2013
3106	532^49205+49205^532	134129	Norbert Schneider	02/2019
3107	36453^4780+4780^36453	134127	Hans Havermann	04/2021
3108	(28*10^134122-1)/9	134123	Serge Batalov	10/2014
3109	2^445515-113859	134114	Enzo Doria	10/2014
3111	(22*10^134111-37)/3	134112	Robert Price	04/2019
3110	31083^20636+20636^31083	134112	Hans Havermann	04/2021
3112	31622^17379+17379^31622	134079	Hans Havermann	04/2021
3113	(277*10^134059-7)/9	134061	Robert Price	02/2022
3114	2^445328-216917	134058	Enzo Doria	05/2014
3115	2^445202+1874899	134020	Enzo Doria	06/2016
3116	(35*10^134003-89)/9	134004	Robert Price	02/2022
3117	(13*2^445102+1)/17	133989	Lelio R Paula	07/2015
3118	(35*10^133979-593)/9	133980	Robert Price	07/2018
3119	2*10^133955+51	133956	Robert Price	05/2018
3120	(49*10^133952+437)/9	133953	Robert Price	09/2021
3121	2^444964-113639	133948	Enzo Doria	08/2014
3122	31811^16240+16240^31811	133943	Hans Havermann	04/2021
3123	10^133902+167841	133903	Patrick De Geest	05/2021
3125	28118^30097-30097^28118	133902	Norbert Schneider	01/2015
3124	10^133902-100001	133902	Robert Price	07/2020
3126	2^444784-113859	133894	Enzo Doria	10/2014
3127	32303^13914+13914^32303	133846	Hans Havermann	04/2021
3128	30739^22458+22458^30739	133757	Hans Havermann	04/2021
3129	34942^6721+6721^34942	133739	Hans Havermann	04/2021
3130	(2^444046+100280245065)	133672	Paul Bourdelais	05/2022
3131	34792^6935+6935^34792	133638	Hans Havermann	04/2021
3132	(266*10^133603+1)/3	133605	Robert Price	04/2020
3133	32261^13842+13842^32261	133600	Hans Havermann	04/2021
3134	(89*10^133580+1)/9	133581	Serge Batalov	05/2010
3135	(134*10^133573-11)/3	133575	Robert Price	01/2022
3136	62^74521-61^74521	133571	Robert Price	05/2013
3137	(182*10^133543+1)/3	133545	Robert Price	02/2020
3138	(103*10^133535+11)/3	133537	Robert Price	01/2021
3139	32589^12520+12520^32589	133537	Hans Havermann	03/2021
3140	34516^7373+7373^34516	133496	Hans Havermann	04/2021
3141	8*10^133487-37	133488	Robert Price	03/2022
3142	30135^26882+26882^30135	133482	Hans Havermann	04/2021
3143	2^443198-1867301	133416	Enzo Doria	03/2016
3144	(19*10^133390+101)/3	133391	Robert Price	09/2019
3145	(71^72043-1)/70	133369	Paul Bourdelais	09/2017
3146	36117^4910+4910^36117	133311	Hans Havermann	04/2021
3147	2^442799+1874633	133296	Enzo Doria	06/2016
3148	L(637751)	133283	Henri Lifchitz	09/2008
3149	109^65410-2	133269	Lelio R Paula	10/2017
3150	2^442688-113489	133263	Enzo Doria	08/2014
3151	(7*2^442640-1)/783	133246	Lelio R Paula	07/2015
3152	(9*2^442463+1)/17441	133192	Lelio R Paula	07/2015
3153	2^442437-1849993	133187	Enzo Doria	08/2015
3154	2^442430-2791721	133185	Enzo Doria	03/2016
3155	(13*2^442428-1)/309	133183	Lelio R Paula	07/2015
3156	29959^27870+27870^29959	133172	Hans Havermann	03/2021
3157	(25*2^442379-1)/71	133169	Lelio R Paula	07/2015
3158	34240^7737+7737^34240	133145	Hans Havermann	03/2021
3159	452^50145+50145^452	133142	Norbert Schneider	09/2020
3160	30659^21796+21796^30659	133011	Hans Havermann	04/2021
3161	33276^9935+9935^33276	133010	Hans Havermann	04/2021
3162	30111^26122+26122^30111	133001	Hans Havermann	04/2021
3163	30790^20869+20869^30790	132998	Hans Havermann	04/2021
3165	(2^441799+78557)/5	132995	Lelio R Paula	07/2015
3164	8*10^132994-27	132995	Robert Price	10/2021
3166	(109*10^132992+11)/3	132994	Robert Price	06/2022
3167	2^441781-2787883	132990	Enzo Doria	03/2016
3168	(3*2^441685+1)/749	132959	Lelio R Paula	07/2015
3169	2^441618+37	132941	Lelio R Paula	08/2017
3170	34857^6514+6514^34857	132940	Hans Havermann	04/2021
3171	34065^7988+7988^34065	132937	Hans Havermann	04/2021
3172	35571^5452+5452^35571	132914	Hans Havermann	04/2021
3173	2^441521-113575	132912	Enzo Doria	08/2014
3174	7*10^132884-99	132885	Robert Price	06/2019
3175	(103*10^132879+17)/3	132881	Robert Price	08/2020
3176	2^441396-65	132874	Lelio R Paula	08/2017
3177	33350^9633+9633^33350	132859	Hans Havermann	04/2021
3178	2^441330+1871959	132854	Enzo Doria	05/2016
3179	2^441063+383	132774	Lelio R Paula	06/2012
3180	(10^132753+7)/17/19	132751	Alfred Reich	06/2021
3181	(22*10^132746+53)/3	132747	Robert Price	07/2019
3182	(77*10^132744-149)/9	132745	Robert Price	03/2022
3183	(22*10^132732+119)/3	132733	Robert Price	04/2021
3184	2^440846+1870909	132708	Enzo Doria	05/2016
3185	2^440656-113489	132651	Enzo Doria	08/2014
3186	numbpart(14180123587)	132646	Serge Batalov	04/2017
3187	32950^10591+10591^32950	132622	Hans Havermann	04/2021
3188	33302^9597+9597^33302	132614	Hans Havermann	04/2021
3189	(19*10^132550+191)/3	132551	Robert Price	05/2019
3190	(2^440399-1)/(1621082028116197820931518475633880799)	132538	Dario Alpern	01/2015
3191	(38^83891+1)/39	132529	Robert Price	09/2013
3192	2*10^132493-43	132494	Robert Price	04/2018
3193	31352^16809+16809^31352	132480	Hans Havermann	04/2021
3194	(418*10^132441+23)/9	132443	Robert Price	02/2020
3195	2^439931-21	132433	Lelio R Paula	08/2017
3196	47^79201-46^79201	132432	Robert Price	10/2012
3197	2^439897-113653	132423	Enzo Doria	08/2014
3198	35505^5362+5362^35505	132410	Hans Havermann	03/2021
3199	30079^25222+25222^30079	132402	Hans Havermann	04/2021
3200	(5*2^439822+1)/9	132400	Lelio R Paula	06/2015
3201	(695*10^132356+7)/9	132358	Robert Price	12/2021
3202	(112*10^132337-1)/3	132339	Serge Batalov	12/2014
3203	2^439576-113247	132326	Enzo Doria	07/2014
3204	30059^25230+25230^30059	132318	Hans Havermann	04/2021
3205	2^439497-29143	132302	Enzo Doria	07/2015
3206	2^439409-114193	132276	Enzo Doria	12/2014
3207	(44*10^132233-233)/9	132234	Robert Price	01/2019
3208	9*10^132148-7	132149	Robert Price	09/2015
3209	(47*10^132125-119)/9	132126	Robert Price	05/2019
3210	2^438845+1870217	132106	Enzo Doria	05/2016
3211	2^438789+87855	132089	Lelio R Paula	01/2016
3212	2^438774-2786411	132085	Enzo Doria	03/2016
3213	2^438755-1848205	132079	Enzo Doria	07/2015
3214	30502^21381+21381^30502	132075	Hans Havermann	04/2021
3215	2^438739-112087	132074	Enzo Doria	06/2014
3216	(2^438438+100280245065)	131983	Paul Bourdelais	05/2022
3217	35872^4777+4777^35872	131979	Hans Havermann	04/2021
3218	31198^16945+16945^31198	131938	Hans Havermann	03/2021
3219	13907#+(318259#)/(13907#)	131923	Makoto Morimoto	10/2017
3220	L(631181)	131910	Henri Lifchitz	09/2008
3221	(47*10^131886-119)/9	131887	Robert Price	05/2019
3222	(3*2^438121+1)/4308193883	131879	Lelio R Paula	06/2015
3223	2^438079-1863877	131875	Enzo Doria	03/2016
3224	(16*10^131872-37)/3	131873	Robert Price	05/2021
3225	(2^438067+5)/329	131869	Lelio R Paula	06/2015
3226	2^437908-113855	131824	Enzo Doria	09/2014
3227	2^437884-286349	131817	Enzo Doria	07/2015
3228	5^188558+4	131797	Tyler NeSmith	05/2021
3229	(11*10^131784-17)/3	131785	Robert Price	06/2018
3231	4*10^131719-93	131720	Robert Price	07/2020
3230	31629^14606+14606^31629	131720	Hans Havermann	04/2021
3232	3^276062-112292	131716	Enzo Doria	07/2014
3233	(7*10^131682+89)/3	131683	Robert Price	08/2020
3234	29512^28969+28969^29512	131681	Hans Havermann	03/2021
3235	2^437343+75953	131654	Enzo Doria	04/2016
3236	35^85243-34^85243	131621	Robert Price	05/2012
3237	(28*10^131586+59)/3	131587	Robert Price	05/2021
3238	(59*10^131575+391)/9	131576	Robert Price	03/2021
3239	39984^1945+1945^39984	131505	Hans Havermann	03/2021
3240	(203*10^131457+1)/3	131459	Robert Price	03/2020
3241	7*10^131421-41	131422	Robert Price	08/2021
3242	87309^32+32^87309	131414	Hans Havermann	03/2021
3243	(68^71713+1)/69	131413	Paul Bourdelais	09/2017
3244	2^436451+1884713	131385	Enzo Doria	03/2017
3245	2^436365+35	131359	Robert Price	11/2015
3246	2^436300+1866871	131340	Enzo Doria	03/2016
3247	(7*10^131339+179)/3	131340	Robert Price	09/2018
3248	14^114592-3	131338	Paul Bourdelais	12/2020
3249	36197^4236+4236^36197	131285	Hans Havermann	04/2021
3250	(37*10^131270+341)/9	131271	Robert Price	08/2018

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Probable Primes Top 10000

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