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 (> 30000)	Who ?	When ?
3001	2^334294-113111	100633	Enzo Doria	07/2014
3002	6^129308-17723	100622	Enzo Doria	03/2013
3003	6^129305+95	100619	Lelio R Paula	10/2016
3004	2^334244-1167	100618	Lelio R Paula	09/2016
3005	(21*2^334050+1)/935	100558	Lelio R Paula	12/2013
3006	(78557*2^334018+1)/4326021	100548	Lelio R Paula	07/2014
3007	(35*10^100542+1)/9	100543	Serge Batalov	11/2010
3008	13^90251+24	100535	Lelio R Paula	10/2016
3009	2^333963+789	100533	Lelio R Paula	08/2011
3010	2^333919-1840087	100520	Enzo Doria	06/2015
3011	2^333911+72623	100518	Enzo Doria	04/2016
3012	18^80064-67	100503	Lelio R Paula	10/2016
3013	5^143742-48	100472	Lelio R Paula	10/2016
3014	2^333757-112123	100471	Enzo Doria	06/2014
3015	2^333603-108861	100425	Enzo Doria	03/2014
3016	9*7^118818-2	100414	Lelio R Paula	11/2014
3017	2^333546-17097	100408	Enzo Doria	05/2013
3018	17^81597+72	100401	Lelio R Paula	10/2016
3019	p(20559)#/2+8	100384	Robert Price	01/2017
3020	11^96390-24	100380	Lelio R Paula	10/2016
3021	4832563059*2^333333+30029	100353	Donovan Johnson	01/2008
3022	2^333354+763	100350	Lelio R Paula	08/2011
3023	2^333289-109483	100330	Enzo Doria	04/2014
3024	2^333240-2790209	100316	Enzo Doria	03/2016
3026	(2^333227-2^166614+1)/5	100311		11/2006
3025	2^333225+719	100311	Lelio R Paula	08/2011
3027	2^333221-2785333	100310	Enzo Doria	10/2015
3028	76^53332-75	100308	Norbert Schneider	02/2015
3029	6^128892-17573	100298	Enzo Doria	03/2013
3030	2^333105-113215	100275	Enzo Doria	07/2014
3031	(31*2^333102+1)/2375	100272	Lelio R Paula	11/2013
3032	17^81476-74	100253	Lelio R Paula	10/2016
3033	17^81417-16	100180	Theodore Burton	11/2005
3034	2^332739-113215	100165	Enzo Doria	07/2014
3035	2^332730-1865621	100162	Enzo Doria	03/2016
3036	91^51127-2	100160	Lelio R Paula	09/2013
3037	15^85159-32	100155	Lelio R Paula	10/2016
3038	6^128661+97	100118	Lelio R Paula	10/2016
3039	19^78285+40	100108	Lelio R Paula	07/2016
3040	6^128640+5	100102	Lelio R Paula	11/2014
3041	6^128565-127	100044	Lelio R Paula	08/2016
3042	2^332309-133	100035	Lelio R Paula	02/2011
3043	2^332307+731	100035	Lelio R Paula	07/2011
3044	2^332301+12927	100033	Lelio R Paula	04/2013
3045	12^92684-13	100023	Lelio R Paula	07/2016
3082	25206!+p(4114)	100001	Henri Lifchitz	09/2005
3083	25206!-p(5447)	100001	Henri Lifchitz	10/2005
3084	25206!-p(12402)	100001	Henri Lifchitz	04/2006
3085	25206!-p(16290)	100001	Henri Lifchitz	09/2006
3086	25206!-p(19647)	100001	Henri Lifchitz	02/2007
3087	2^332194+11473	100001	Henri Lifchitz	03/2007
3074	10^100000+342909	100001	Milton L. Brown	12/2007
3054	10^100000+346579	100001	Robert Price	04/2012
3055	10^100000+829767	100001	Robert Price	05/2012
3056	10^100000+871899	100001	Robert Price	05/2012
3057	10^100000+1475997	100001	Robert Price	07/2012
3075	10^100000+1751769	100001	Robert Price	08/2012
3076	10^100000+2155489	100001	Robert Price	10/2012
3077	10^100000+2483527	100001	Robert Price	12/2012
3078	10^100000+2503087	100001	Robert Price	12/2012
3079	10^100000+2686179	100001	Robert Price	12/2012
3080	10^100000+2688933	100001	Robert Price	12/2012
3081	10^100000+3667159	100001	Robert Price	08/2013
3058	10^100000+3938473	100001	Robert Price	05/2015
3059	10^100000+3979761	100001	Robert Price	05/2015
3060	10^100000+4293973	100001	Robert Price	09/2015
3088	10^100000+4858267	100001	Robert Price	12/2015
3089	10^100000+5113299	100001	Robert Price	02/2016
3090	10^100000+5169411	100001	Robert Price	02/2016
3046	10^100000+5354043	100001	Robert Price	05/2016
3047	10^100000+5717979	100001	Robert Price	05/2016
3048	10^100000+6080631	100001	Robert Price	07/2016
3049	10^100000+6308469	100001	Robert Price	07/2016
3050	10^100000+6512023	100001	Robert Price	08/2016
3051	10^100000+6596557	100001	Robert Price	08/2016
3052	10^100000+7115409	100001	Robert Price	10/2016
3053	10^100000+7235803	100001	Robert Price	10/2016
3061	10^100000+7867333	100001	Robert Price	12/2016
3062	10^100000+8743093	100001	Robert Price	02/2017
3063	10^100000+8955391	100001	Robert Price	03/2017
3064	10^100000+9180019	100001	Robert Price	03/2017
3065	10^100000+9225987	100001	Robert Price	04/2017
3066	10^100000+9265587	100001	Robert Price	04/2017
3067	10^100000+9287049	100001	Robert Price	04/2017
3068	10^100000+9425053	100001	Robert Price	05/2017
3069	10^100000+9450769	100001	Robert Price	05/2017
3070	10^100000+9528747	100001	Robert Smith	05/2017
3071	10^100000+9548071	100001	Robert Price	06/2017
3072	10^100000+10064287	100001	Robert Price	08/2017
3073	10^100000+10229569	100001	Robert Price	10/2017
3092	10^99999+309403	100000	Daniel Heuer	01/2004
3091	10^100000-260199	100000	Patrick De Geest	01/2010
3093	10^99999-59511	99999	Patrick De Geest	07/2009
3094	2^332141-113073	99985	Enzo Doria	07/2014
3095	(3^209561+2)/728101255	99978	Lelio R Paula	09/2013
3096	2^332085+1865897	99968	Enzo Doria	03/2016
3097	(9787*2^332070-1)/936402369	99959	Lelio R Paula	05/2015
3098	2^332023+191	99949	Lelio R Paula	02/2011
3099	2^331938+71149	99924	Enzo Doria	04/2016
3100	2^331932-78795	99922	Lelio R Paula	09/2016
3101	2^331921+771	99919	Lelio R Paula	01/2013
3102	(3^209419-2)/5132755	99912	Lelio R Paula	09/2013
3103	2^331860-114989	99900	Enzo Doria	05/2015
3104	2^331746-11655	99866	Lelio R Paula	09/2016
3105	11^95891-28	99861	Lelio R Paula	08/2016
3106	(2^331694-5)/11	99849	Lelio R Paula	10/2013
3107	(3^209246+7)/64	99834	Lelio R Paula	09/2013
3108	15^84866-52	99811	Lelio R Paula	08/2016
3109	13^89600+30	99810	Lelio R Paula	08/2016
3110	5^142772-38	99794	Lelio R Paula	08/2016
3111	(23*2^331459+1)/475	99778	Lelio R Paula	11/2013
3112	2^331416-331416+1	99767	Robert Price	10/2014
3113	2^331256-57	99718	Lelio R Paula	12/2012
3114	2^331185+737	99697	Lelio R Paula	01/2013
3115	(4*10^99693+149)/9	99693	Robert Price	03/2017
3116	2^331154+1880527	99688	Enzo Doria	10/2016
3117	(19^77951+1)/20	99679	Paul Bourdelais	03/2010
3118	2^331110+1870459	99675	Enzo Doria	05/2016
3119	5*2^331075+7	99665	Lelio R Paula	08/2014
3120	(16*10^99656-31)/3	99657	Robert Price	03/2016
3121	2^330968+345	99632	Lelio R Paula	09/2016
3123	2*5^142528-7	99624	Lelio R Paula	11/2014
3122	2^330942+77329	99624	Enzo Doria	05/2016
3124	14^86914-99	99615	Lelio R Paula	08/2016
3125	(19*2^330902+1)/77	99611	Lelio R Paula	11/2013
3126	2^330845+71687	99595	Enzo Doria	04/2016
3127	(23*2^330770+1)/3	99573	Lelio R Paula	11/2013
3128	2^330735+8415	99562	Lelio R Paula	09/2016
3129	2^330720+74071	99557	Enzo Doria	04/2016
3130	31^66738-2	99531	Lelio R Paula	09/2013
3131	7*3^208567+4	99513	Lelio R Paula	08/2014
3132	(13*10^99508+47)/3	99509	Robert Price	01/2017
3133	2^330553+779	99507	Lelio R Paula	01/2013
3134	15^84606-94	99505	Lelio R Paula	08/2016
3135	6^127858+47	99493	Lelio R Paula	08/2016
3136	5^142337+48	99490	Lelio R Paula	08/2016
3137	7^117724-20	99489	Lelio R Paula	08/2016
3138	(29*10^99474-17)/3	99475	Erik Branger	09/2014
3139	(9*2^330407-1)/7	99463	Lelio R Paula	03/2014
3140	(68*10^99441+7)/3	99443	Robert Price	03/2016
3141	46^59791-45^59791	99418	Jean-Louis Charton	01/2013
3142	(2*10^99408+529)/9	99408	Robert Price	01/2017
3143	53^57646-2	99398	Lelio R Paula	09/2013
3144	2^330165+1870025	99390	Enzo Doria	05/2016
3145	2^330142-155	99383	Lelio R Paula	12/2012
3146	2^330088-115259	99367	Enzo Doria	06/2015
3147	(746*10^99303+1)/9	99305	Robert Price	02/2017
3148	3^208107+40	99293	Lelio R Paula	08/2016
3149	(5*2^329833-1)/369	99288	Lelio R Paula	02/2014
3150	8*3^208093+5	99287	Lelio R Paula	08/2014
3151	5^142043+56	99284	Lelio R Paula	08/2016
3152	22*10^99275+7	99277	Robert Price	04/2016
3153	2^329778+1876189	99274	Enzo Doria	07/2016
3154	(10^99239-13)/3	99239	Robert Price	02/2017
3155	3^207987+62	99236	Lelio R Paula	08/2016
3156	2^329638+49	99231	Lelio R Paula	12/2012
3157	7^117413-18	99226	Lelio R Paula	08/2016
3158	2^329586-458903	99216	Enzo Doria	04/2015
3159	2^329553+101	99206	Lelio R Paula	12/2012
3160	2^329551-112897	99205	Enzo Doria	06/2014
3161	(3^207925+7)/50	99204	Lelio R Paula	09/2013
3162	6^127458-17993	99182	Enzo Doria	03/2013
3163	27197^4428+4428^27197	99166	Hans Havermann	10/2017
3164	(46*10^99143-1)/9	99144	Robert Price	12/2014
3165	18^78968-3065	99127	Enzo Doria	03/2013
3166	25927^6654+6654^25927	99122	Hans Havermann	10/2017
3167	2^329259+189	99117	Lelio R Paula	12/2012
3168	8*10^99113+39	99114	Robert Price	01/2017
3169	6^127364+77	99109	Lelio R Paula	08/2016
3170	6^127285+13	99047	Lelio R Paula	08/2016
3171	2^329007+73283	99041	Enzo Doria	04/2016
3172	5*3^207543-8	99024	Lelio R Paula	08/2014
3173	2^328885+149	99005	Lelio R Paula	12/2012
3174	23392^17075+17075^23392	99004	Hans Havermann	09/2017
3175	(2^328879-9)/119	99001	Lelio R Paula	10/2013
3176	5^141618+54	98987	Lelio R Paula	08/2016
3177	8*10^98982+51	98983	Robert Price	05/2017
3178	(21*2^328809-1)/7709	98979	Lelio R Paula	03/2014
3179	2^328794-2797601	98977	Enzo Doria	04/2016
3180	6^127176+5	98963	Lelio R Paula	11/2014
3181	24262^11989+11989^24262	98960	Hans Havermann	09/2017
3182	2^328700-109709	98949	Enzo Doria	04/2014
3183	46711!2-2^46711	98916	Robert Price	09/2015
3184	9*7^117037+4	98909	Lelio R Paula	11/2014
3185	(10^98890+149)/3	98890	Serge Batalov	12/2014
3186	22775^21978+21978^22775	98889	Hans Havermann	08/2017
3187	2^328497-216933	98888	Enzo Doria	05/2014
3188	2^328487+32769	98885	Lelio R Paula	08/2016
3189	3^207250-112358	98884	Enzo Doria	06/2014
3190	13^88754-90	98867	Lelio R Paula	08/2016
3191	2^328406+709	98861	Lelio R Paula	02/2013
3192	(17*2^328413-1)/16173	98860	Lelio R Paula	03/2014
3193	7^116976+76	98857	Lelio R Paula	08/2016
3194	2^328335+1155	98839	Lelio R Paula	08/2016
3196	(3*2^328311+1)/5	98832	Lelio R Paula	11/2013
3195	287^40210+40210^287	98832	Norbert Schneider	11/2014
3197	(2^328284+9)/1325	98821	Lelio R Paula	10/2013
3198	(21*2^328258+1)/2125	98814	Lelio R Paula	11/2013
3199	65^54491+48	98788	Lelio R Paula	04/2016
3200	3^207042+98	98785	Lelio R Paula	08/2016
3201	3^206977-112756	98754	Enzo Doria	07/2014
3202	7^116846-50	98747	Lelio R Paula	08/2016
3203	2^327967-28635	98728	Lelio R Paula	08/2016
3204	6^126850-47	98709	Lelio R Paula	08/2016
3205	8*6^126830-7	98694	Lelio R Paula	11/2014
3206	11^94770-270	98693	Enzo Doria	08/2012
3207	2^327832+43	98688	Lelio R Paula	12/2012
3208	2^327795+761	98677	Lelio R Paula	02/2013
3209	10^98669+147411	98670	Patrick De Geest	11/2016
3211	10^98669-9^(98669-1)	98669	Robert Price	05/2016
3210	10^98669-105249	98669	Patrick De Geest	11/2016
3212	2^327671-109801	98639	Enzo Doria	04/2014
3213	5^141090-14	98618	Lelio R Paula	08/2016
3214	20^75799+47	98617	Lelio R Paula	08/2016
3215	2^327515-1017	98592	Lelio R Paula	08/2016
3216	6^126692+97681	98586	Mike Oakes	04/2011
3217	2^327467-741	98578	Lelio R Paula	08/2016
3218	(2^327329+9)/19	98535	Lelio R Paula	10/2013
3219	7^116577-66	98519	Lelio R Paula	08/2016
3220	(3*2^327250+1)/7	98512	Lelio R Paula	11/2013
3221	(19*2^327192+1)/275	98494	Lelio R Paula	11/2013
3222	2^327162-66945	98486	Lelio R Paula	08/2016
3223	4*10^98472-3	98473	Erik Branger	11/2013
3224	(6883*2^327047-1)/77	98453	Lelio R Paula	05/2015
3225	(71*10^98446+1)/9	98447	Serge Batalov	11/2010
3226	13^88363+94	98432	Lelio R Paula	08/2016
3227	48^58543-47^58543	98425	Jean-Louis Charton	11/2005
3228	6^126481+41	98422	Lelio R Paula	08/2016
3229	78*10^98413-7	98415	Robert Price	05/2017
3230	7^116416+46	98383	Lelio R Paula	08/2016
3231	7^116407-24	98376	Lelio R Paula	07/2016
3233	2^326782-1860671	98372	Enzo Doria	03/2016
3232	17^79948+58	98372	Lelio R Paula	08/2016
3234	3^206143-98	98356	Lelio R Paula	08/2016
3235	8*5^140705+7	98350	Lelio R Paula	11/2014
3236	2^326585+11	98312	Lelio R Paula	12/2012
3237	2^326582-459161	98311	Enzo Doria	05/2015
3238	(2^326548+9)/5	98301	Lelio R Paula	10/2013
3239	2^326538+71659	98298	Enzo Doria	04/2016
3240	15^83575-58	98292	Lelio R Paula	08/2016
3241	10^98288+3	98289	Robert Price	03/2011
3242	10^98288-117017	98288	Patrick De Geest	11/2011
3243	2^326421-2797573	98263	Enzo Doria	04/2016
3244	2^326401+16095	98257	Lelio R Paula	07/2016
3245	7^116240-116240^7	98235	Norbert Schneider	05/2017
3246	17^79826-78	98222	Lelio R Paula	08/2016
3247	2^326268-809	98217	Yves Minet	04/2011
3248	(418*10^98199+23)/9	98201	Robert Price	08/2017
3249	15^83496-76	98199	Lelio R Paula	08/2016
3250	(10223*2^326179+1)/6125	98190	Lelio R Paula	07/2014

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PRP Records

Probable Primes Top 10000

(183432 PRPs in the top)