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	(10^104212-71)/1	104212	Serge Batalov	12/2014
3002	2^346078+7695	104180	Lelio R Paula	12/2016
3004	2^346055-19537	104173	Enzo Doria	05/2013
3003	(3*2^346057+1)/77	104173	Lelio R Paula	12/2013
3005	2^346037-20125	104168	Enzo Doria	06/2013
3006	(34*10^104168-7)/9/13/551179	104162	Makoto Morimoto	05/2016
3007	6^133854-17993	104159	Enzo Doria	03/2013
3008	2^345990+1874239	104154	Enzo Doria	06/2016
3009	2^345988-20373	104153	Enzo Doria	06/2013
3010	(26*10^104132-503)/9	104133	Robert Price	07/2018
3011	3*5^148968+8	104125	Lelio R Paula	11/2014
3012	(7*10^104113+53)/3	104114	Robert Price	05/2018
3013	p(21253)#/2+8	104113	Robert Price	01/2017
3014	322^41507+41507^322	104094	Norbert Schneider	12/2014
3015	6^133768-17423	104092	Enzo Doria	03/2013
3016	2^345786-19557	104092	Enzo Doria	05/2013
3017	171^46606-2	104072	Lelio R Paula	10/2017
3018	2^345704-149	104068	Lelio R Paula	09/2011
3019	6^133704-17273	104042	Enzo Doria	02/2013
3020	(3*2^345590-1)/23	104033	Lelio R Paula	03/2014
3021	(19*2^345590+1)/33859	104030	Lelio R Paula	12/2013
3022	2^345547+11	104021	Lelio R Paula	09/2011
3023	2^345504+723	104008	Lelio R Paula	09/2011
3024	2^345498-20037	104006	Enzo Doria	06/2013
3025	18^82854-37	104005	Lelio R Paula	01/2017
3026	2^345486-109065	104002	Enzo Doria	04/2014
3027	2^345487-1851507	104002	Enzo Doria	08/2015
3028	2^345476+777	103999	Lelio R Paula	09/2011
3029	4*10^103981-83	103982	Robert Price	10/2018
3030	(5*2^345321-1)/3	103953	Lelio R Paula	03/2014
3031	(2^345267-9)/539049127	103927	Lelio R Paula	12/2013
3032	(78557*2^345163+1)/78589	103905	Lelio R Paula	07/2014
3033	2^345106-112181	103888	Enzo Doria	06/2014
3034	2^345079+99	103880	Lelio R Paula	09/2011
3035	11^99736-1500	103865	Enzo Doria	12/2012
3036	2^344842-20157	103808	Enzo Doria	06/2013
3037	(47*2^344822+1)/1071	103801	Lelio R Paula	05/2015
3038	2^344802-20765	103796	Enzo Doria	06/2013
3039	2^344794-3821	103794	Yves Minet	05/2011
3040	2^344782-109103	103790	Enzo Doria	04/2014
3041	3^217521-112292	103784	Enzo Doria	06/2014
3042	2^344759-3505	103783	Lelio R Paula	11/2016
3043	2^344735-147	103776	Lelio R Paula	09/2011
3044	L(496533)-p(496533)	103770	Robert Price	02/2018
3045	2*10^103749-69	103750	Robert Price	03/2018
3046	(55459*2^344617+1)/3	103745	Lelio R Paula	07/2014
3047	2^344607-108891	103738	Enzo Doria	03/2014
3048	2^344541-19561	103718	Enzo Doria	05/2013
3049	(1017*2^344529-1)/569	103714	Lelio R Paula	05/2015
3050	(4*10^103703-1)/3	103704	Serge Batalov	08/2009
3051	2^344444-455	103688	Yves Minet	03/2012
3052	(1353^238539617^9)/10^307661	103673	Hans Havermann	06/2017
3053	2^344317-109933	103650	Enzo Doria	04/2014
3054	2^344309-1852033	103648	Enzo Doria	08/2015
3055	2^344213-21253	103619	Enzo Doria	06/2013
3056	2^344196-465	103614	Lelio R Paula	11/2016
3057	2^344187-20001	103611	Enzo Doria	06/2013
3058	(117191#+(355573#)/(117191#))/(200233679)	103602	Makoto Morimoto	10/2017
3059	20^79621-19^79621	103590	Jean-Louis Charton	03/2011
3060	Phi(155391,10)/1243129	103586	Maksym Voznyy	09/2015
3061	2^344085-20365	103580	Enzo Doria	06/2013
3062	5^148169+54	103566	Lelio R Paula	11/2016
3063	2^344017-108795	103560	Enzo Doria	03/2014
3064	2^343971-5077	103546	Lelio R Paula	09/2011
3065	(7*10^103531+71)/3	103532	Robert Price	05/2018
3066	2^343899+141	103524	Lelio R Paula	08/2011
3067	(2^343933+1)/(3*98294339989393)	103520	Gord Palameta	08/2018
3068	6^133029-67	103517	Lelio R Paula	11/2016
3069	(17*2^343877+1)/13625	103515	Lelio R Paula	12/2013
3070	(136*10^103474-1)/9	103476	Serge Batalov	12/2014
3071	5^148014-24	103458	Lelio R Paula	11/2016
3072	2^343604+9931	103436	Yves Minet	01/2011
3073	2^343601-21189	103435	Enzo Doria	06/2013
3074	2^343508-115229	103407	Enzo Doria	06/2015
3075	(509203*2^343491-1)/16147	103403	Lelio R Paula	05/2015
3076	3^216685-113056	103386	Enzo Doria	07/2014
3077	44^62903-43^62903	103379	Jean-Louis Charton	08/2012
3078	11^99262-20	103371	Lelio R Paula	12/2016
3079	(509203*2^343357-1)/5	103366	Lelio R Paula	05/2015
3081	2^343356-2791889	103361	Enzo Doria	03/2016
3080	(25*10^103360-241)/9	103361	Robert Price	05/2018
3082	Phi(104989,10)/2939693	103350	Maksym Voznyy	09/2015
3083	2^343182-171	103309	Lelio R Paula	08/2011
3084	(23619^23619+23620^23620)/7187	103294	David Broadhurst	09/2009
3085	2^343079-1835611	103278	Enzo Doria	05/2015
3086	2^343063-1147	103273	Yves Minet	06/2013
3087	9*6^132689+7	103254	Lelio R Paula	11/2014
3088	2^342979-18085	103247	Enzo Doria	05/2013
3089	2^342966-16995	103244	Lelio R Paula	11/2016
3090	5^147650+16	103203	Lelio R Paula	11/2016
3091	gcd(Phi(852060,10),(10^42603+1)^3(10^42603+1-10^21302)+(10^85206+10^42603)(10^21302+1)+10^127809)	103201	Serge Batalov	04/2015
3092	2^342817+2707067	103199	Enzo Doria	03/2016
3093	43^63177-42	103198	Theodore Burton	02/2007
3094	2^342805-21025	103195	Enzo Doria	06/2013
3095	2^342714+12285	103168	Lelio R Paula	11/2016
3096	18^82178-4481	103156	Enzo Doria	03/2013
3097	2^342665-17349	103153	Enzo Doria	05/2013
3098	2^342612+175	103137	Lelio R Paula	08/2011
3099	5*2^342585-3	103130	Lelio R Paula	09/2014
3100	2^342503-19209	103104	Enzo Doria	05/2013
3101	2^342476+51	103096	Lelio R Paula	08/2011
3102	2^342460-18885	103091	Enzo Doria	05/2013
3103	7^121968+82	103075	Lelio R Paula	10/2016
3104	2^342392-108863	103071	Enzo Doria	03/2014
3105	3^216014+28	103065	Lelio R Paula	11/2016
3106	2^342353-108879	103059	Enzo Doria	03/2014
3107	10^103055+276081	103056	Patrick De Geest	12/2016
3108	10^103055-53	103055	Lelio R Paula	11/2016
3109	7^121933+4	103046	Lelio R Paula	11/2014
3110	19^80560-68	103017	Lelio R Paula	10/2016
3111	2^342209+76607	103016	Enzo Doria	05/2016
3113	328^40945+40945^328	103013	Norbert Schneider	12/2014
3112	12^95454-91	103013	Lelio R Paula	10/2016
3114	65^56809-64^56809	102990	Robert Price	08/2013
3115	5^147338-6	102985	Lelio R Paula	11/2014
3116	2^342084-112739	102978	Enzo Doria	06/2014
3117	9*6^132330+7	102974	Lelio R Paula	11/2014
3118	2^342034-16737	102963	Enzo Doria	05/2013
3119	(9787*2^342011-1)/25	102959	Lelio R Paula	05/2015
3120	(3^215802-5)/124343756	102956	Lelio R Paula	12/2013
3121	2^341991-17421	102950	Enzo Doria	05/2013
3122	2^341969-112225	102943	Enzo Doria	06/2014
3123	(9787*2^341864-1)/3	102915	Lelio R Paula	05/2015
3124	2^341859+1869413	102910	Enzo Doria	05/2016
3125	10^102909+61	102910	Lelio R Paula	11/2016
3126	10^102909-67049	102909	Patrick De Geest	12/2016
3127	2^341659+1836773	102850	Enzo Doria	03/2016
3128	2^341608-110639	102835	Enzo Doria	05/2014
3129	10^102824+49	102825	Lelio R Paula	11/2016
3130	10^102824-168011	102824	Patrick De Geest	12/2016
3131	11^98708-8	102794	Lelio R Paula	10/2016
3132	2^341466+4429	102792	Lelio R Paula	09/2011
3133	2^341460-107	102790	Lelio R Paula	08/2011
3134	(2^341388+47)/21014943	102761	Lelio R Paula	12/2013
3135	2^341355+21	102759	Lelio R Paula	08/2011
3136	2^341246+40755	102726	Lelio R Paula	11/2016
3137	(2^341256-5)/991699	102723	Lelio R Paula	12/2013
3138	7^121547+78	102720	Lelio R Paula	10/2016
3139	2^341223-461197	102719	Enzo Doria	06/2015
3141	2^341190-20577	102709	Enzo Doria	06/2013
3140	(27*2^341212+1)/84674449	102709	Lelio R Paula	12/2013
3142	6^131976-65	102698	Lelio R Paula	10/2016
3143	2^341134+2533	102692	Henri Lifchitz	09/2005
3144	13^92184-54	102688	Lelio R Paula	10/2016
3145	2^341116-20873	102687	Enzo Doria	06/2013
3146	2^341094-19953	102680	Enzo Doria	06/2013
3147	2^341053+129	102668	Lelio R Paula	08/2011
3148	(31*2^341006-1)/3	102655	Lelio R Paula	03/2014
3149	7^121471+94	102655	Lelio R Paula	10/2016
3151	2^341004-173	102653	Lelio R Paula	08/2011
3150	20^78901+3	102653	Lelio R Paula	10/2016
3152	5^146853-52	102646	Lelio R Paula	10/2016
3153	2^340969-216931	102642	Enzo Doria	05/2014
3154	2^340952+1870021	102637	Enzo Doria	05/2016
3155	5*2^340940-3	102634	Lelio R Paula	08/2014
3156	(6^131891+1)/7	102631	Paul Bourdelais	01/2010
3157	(4*10^102612+83)/3	102613	Robert Price	02/2018
3158	75^54717+74	102598	Norbert Schneider	01/2015
3159	2^340806-20393	102593	Enzo Doria	06/2013
3160	(2^340790+5)/138267	102583	Lelio R Paula	12/2013
3161	6^131821+77	102577	Lelio R Paula	10/2016
3162	2^340688-29	102558	Henri Lifchitz	05/2005
3163	2^340685-109101	102557	Enzo Doria	04/2014
3164	65^56567-64	102552	Norbert Schneider	11/2014
3165	2^340547-108897	102515	Enzo Doria	03/2014
3166	7^121268+82	102484	Lelio R Paula	10/2016
3167	(6883*2^340443-1)/162401	102483	Lelio R Paula	05/2015
3168	2^340434-5955	102481	Lelio R Paula	11/2016
3169	(2^340381+47)/7	102465	Lelio R Paula	12/2013
3170	111^50095+110	102461	Norbert Schneider	04/2017
3171	2^340291-20301	102438	Enzo Doria	06/2013
3172	12^94915+89	102431	Lelio R Paula	10/2016
3173	2^340208-20373	102413	Enzo Doria	06/2013
3174	6^131598-17273	102404	Enzo Doria	02/2013
3175	2^340115-21181	102385	Enzo Doria	06/2013
3176	(55459*2^340090+1)/1591	102379	Lelio R Paula	07/2014
3177	89^52511-88^52511	102365	Robert Price	06/2015
3178	3^214539-112756	102362	Enzo Doria	07/2014
3179	2^340000-19877	102351	Enzo Doria	06/2013
3180	2^339990-114845	102348	Enzo Doria	05/2015
3181	(3^214516-2)/51383	102346	Lelio R Paula	12/2013
3182	20^78661-99	102341	Lelio R Paula	09/2016
3183	2^339951-19585	102336	Enzo Doria	05/2013
3184	(13*2^339943+1)/45	102333	Lelio R Paula	12/2013
3185	2^339889+29327	102317	Yves Minet	06/2010
3186	2^339834-109493	102301	Enzo Doria	04/2014
3187	(11^98221-5^98221)/6	102286	Robert Price	01/2013
3188	3^214365+1820	102279	Lelio R Paula	10/2016
3189	(11*2^339705-1)/183	102261	Lelio R Paula	03/2014
3190	2^339694-16995	102259	Lelio R Paula	09/2016
3191	7^120985-38	102245	Lelio R Paula	10/2016
3192	10^102244+122961	102245	Patrick De Geest	12/2016
3193	10^102244-27	102244	Lelio R Paula	09/2016
3194	7^120982-62	102242	Lelio R Paula	10/2016
3195	4*6^131382-5	102236	Lelio R Paula	11/2014
3196	2^339586-1091	102226	Yves Minet	11/2012
3197	11^98161-3072000	102225	Enzo Doria	12/2012
3198	9*7^120961-4	102225	Lelio R Paula	11/2014
3199	5*3^214250+2	102224	Serge Batalov	10/2010
3200	12^94713-59	102213	Lelio R Paula	10/2016
3201	12^94705+89	102204	Lelio R Paula	10/2016
3202	2^339407-177	102172	Lelio R Paula	08/2011
3203	4*10^102163-57	102164	Robert Price	10/2018
3204	2^339355+65	102157	Lelio R Paula	07/2011
3205	(2^339323+47)/880715	102141	Lelio R Paula	12/2013
3206	2^339168+21	102100	Lelio R Paula	07/2011
3207	2^339167-108807	102100	Enzo Doria	03/2014
3208	2^339156+163	102097	Lelio R Paula	08/2011
3209	(2^338982-7)/1754517	102038	Lelio R Paula	12/2013
3210	2^338891-18885	102017	Enzo Doria	05/2013
3211	2^338829-113239	101998	Enzo Doria	07/2014
3212	2^338828-113297	101998	Enzo Doria	07/2014
3213	2^338796+93	101988	Donovan Johnson	06/2008
3214	lucasU(1373,1,32502)-lucasU(1373,1,32501)	101978	Mike Oakes	05/2009
3215	(71^55079-1)/70	101964	Paul Bourdelais	08/2017
3216	2^338682-19865	101954	Enzo Doria	06/2013
3217	(2^(112895*3+1)+243)/7	101954	Kevin Acres	12/2013
3218	2^338568+37	101920	Lelio R Paula	07/2011
3219	2^338559-1858777	101917	Enzo Doria	04/2016
3220	(9*2^338520+1)/365	101904	Lelio R Paula	12/2013
3221	2^338497-17041	101898	Enzo Doria	05/2013
3222	2^338475+54615	101892	Lelio R Paula	10/2016
3223	2^338426-19797	101877	Enzo Doria	06/2013
3224	2^338368-20369	101859	Enzo Doria	06/2013
3225	2^338366+74179	101859	Enzo Doria	04/2016
3226	2^338280-19745	101833	Enzo Doria	06/2013
3227	(3*2^338236-1)/347	101818	Lelio R Paula	03/2014
3228	6^130841+103	101815	Lelio R Paula	10/2016
3229	2^338122-20117	101785	Enzo Doria	06/2013
3230	(2^338139+5)/905333	101785	Lelio R Paula	12/2013
3231	35^65917-7092	101781	Enzo Doria	03/2013
3232	2^338010-19833	101752	Enzo Doria	06/2013
3233	3^213215-76	101730	Lelio R Paula	09/2016
3234	2^337930+63	101728	Lelio R Paula	07/2011
3235	2^337920+1869661	101725	Enzo Doria	05/2016
3236	2^337859-19645	101706	Enzo Doria	05/2013
3237	2^337754+1869169	101675	Enzo Doria	05/2016
3238	3*10^101657-37	101658	Robert Price	07/2018
3239	(31*2^337677-1)/593	101650	Lelio R Paula	03/2014
3240	11^97605-24	101646	Lelio R Paula	10/2016
3241	8^112539-112539	101633	Robert Price	01/2014
3242	2^337515-19869	101603	Enzo Doria	06/2013
3243	2^337473+719	101590	Lelio R Paula	08/2011
3244	(2^337485-509203)/656647157	101585	Lelio R Paula	12/2013
3245	2^337452-108815	101584	Enzo Doria	03/2014
3246	2^337453+1185	101584	Lelio R Paula	09/2016
3247	2^337410-113561	101571	Enzo Doria	08/2014
3248	2^337387+855	101564	Lelio R Paula	09/2016
3249	2^337367-17295	101558	Lelio R Paula	09/2016
3250	2^337342-109035	101551	Enzo Doria	04/2014

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Probable Primes Top 10000

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