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	2^344317-109933	103650	Enzo Doria	04/2014
3002	2^344309-1852033	103648	Enzo Doria	08/2015
3003	2^344213-21253	103619	Enzo Doria	06/2013
3004	2^344196-465	103614	Lelio R Paula	11/2016
3005	2^344187-20001	103611	Enzo Doria	06/2013
3006	(117191#+(355573#)/(117191#))/(200233679)	103602	Makoto Morimoto	10/2017
3007	20^79621-19^79621	103590	Jean-Louis Charton	03/2011
3008	Phi(155391,10)/1243129	103586	Maksym Voznyy	09/2015
3009	2^344085-20365	103580	Enzo Doria	06/2013
3010	5^148169+54	103566	Lelio R Paula	11/2016
3011	2^344017-108795	103560	Enzo Doria	03/2014
3012	2^343971-5077	103546	Lelio R Paula	09/2011
3013	(7*10^103531+71)/3	103532	Robert Price	05/2018
3014	2^343899+141	103524	Lelio R Paula	08/2011
3015	(2^343933+1)/(3*98294339989393)	103520	Gord Palameta	08/2018
3016	6^133029-67	103517	Lelio R Paula	11/2016
3017	(17*2^343877+1)/13625	103515	Lelio R Paula	12/2013
3018	(136*10^103474-1)/9	103476	Serge Batalov	12/2014
3019	5^148014-24	103458	Lelio R Paula	11/2016
3020	2^343604+9931	103436	Yves Minet	01/2011
3021	2^343601-21189	103435	Enzo Doria	06/2013
3022	2^343508-115229	103407	Enzo Doria	06/2015
3023	(509203*2^343491-1)/16147	103403	Lelio R Paula	05/2015
3024	3^216685-113056	103386	Enzo Doria	07/2014
3025	44^62903-43^62903	103379	Jean-Louis Charton	08/2012
3026	11^99262-20	103371	Lelio R Paula	12/2016
3027	(509203*2^343357-1)/5	103366	Lelio R Paula	05/2015
3029	2^343356-2791889	103361	Enzo Doria	03/2016
3028	(25*10^103360-241)/9	103361	Robert Price	05/2018
3030	Phi(104989,10)/2939693	103350	Maksym Voznyy	09/2015
3031	2^343182-171	103309	Lelio R Paula	08/2011
3032	(23619^23619+23620^23620)/7187	103294	David Broadhurst	09/2009
3033	2^343079-1835611	103278	Enzo Doria	05/2015
3034	2^343063-1147	103273	Yves Minet	06/2013
3035	9*6^132689+7	103254	Lelio R Paula	11/2014
3036	2^342979-18085	103247	Enzo Doria	05/2013
3037	2^342966-16995	103244	Lelio R Paula	11/2016
3038	5^147650+16	103203	Lelio R Paula	11/2016
3039	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
3040	2^342817+2707067	103199	Enzo Doria	03/2016
3041	43^63177-42	103198	Theodore Burton	02/2007
3042	2^342805-21025	103195	Enzo Doria	06/2013
3043	2^342714+12285	103168	Lelio R Paula	11/2016
3044	18^82178-4481	103156	Enzo Doria	03/2013
3045	2^342665-17349	103153	Enzo Doria	05/2013
3046	2^342612+175	103137	Lelio R Paula	08/2011
3047	5*2^342585-3	103130	Lelio R Paula	09/2014
3048	2^342503-19209	103104	Enzo Doria	05/2013
3049	2^342476+51	103096	Lelio R Paula	08/2011
3050	2^342460-18885	103091	Enzo Doria	05/2013
3051	7^121968+82	103075	Lelio R Paula	10/2016
3052	2^342392-108863	103071	Enzo Doria	03/2014
3053	3^216014+28	103065	Lelio R Paula	11/2016
3054	2^342353-108879	103059	Enzo Doria	03/2014
3055	10^103055+276081	103056	Patrick De Geest	12/2016
3056	10^103055-53	103055	Lelio R Paula	11/2016
3057	7^121933+4	103046	Lelio R Paula	11/2014
3058	19^80560-68	103017	Lelio R Paula	10/2016
3059	2^342209+76607	103016	Enzo Doria	05/2016
3061	328^40945+40945^328	103013	Norbert Schneider	12/2014
3060	12^95454-91	103013	Lelio R Paula	10/2016
3062	65^56809-64^56809	102990	Robert Price	08/2013
3063	5^147338-6	102985	Lelio R Paula	11/2014
3064	2^342084-112739	102978	Enzo Doria	06/2014
3065	9*6^132330+7	102974	Lelio R Paula	11/2014
3066	2^342034-16737	102963	Enzo Doria	05/2013
3067	(9787*2^342011-1)/25	102959	Lelio R Paula	05/2015
3068	(3^215802-5)/124343756	102956	Lelio R Paula	12/2013
3069	2^341991-17421	102950	Enzo Doria	05/2013
3070	2^341969-112225	102943	Enzo Doria	06/2014
3071	(9787*2^341864-1)/3	102915	Lelio R Paula	05/2015
3072	2^341859+1869413	102910	Enzo Doria	05/2016
3073	10^102909+61	102910	Lelio R Paula	11/2016
3074	10^102909-67049	102909	Patrick De Geest	12/2016
3075	2^341659+1836773	102850	Enzo Doria	03/2016
3076	2^341608-110639	102835	Enzo Doria	05/2014
3077	10^102824+49	102825	Lelio R Paula	11/2016
3078	10^102824-168011	102824	Patrick De Geest	12/2016
3079	11^98708-8	102794	Lelio R Paula	10/2016
3080	2^341466+4429	102792	Lelio R Paula	09/2011
3081	2^341460-107	102790	Lelio R Paula	08/2011
3082	(2^341388+47)/21014943	102761	Lelio R Paula	12/2013
3083	2^341355+21	102759	Lelio R Paula	08/2011
3084	2^341246+40755	102726	Lelio R Paula	11/2016
3085	(2^341256-5)/991699	102723	Lelio R Paula	12/2013
3086	7^121547+78	102720	Lelio R Paula	10/2016
3087	2^341223-461197	102719	Enzo Doria	06/2015
3089	2^341190-20577	102709	Enzo Doria	06/2013
3088	(27*2^341212+1)/84674449	102709	Lelio R Paula	12/2013
3090	6^131976-65	102698	Lelio R Paula	10/2016
3091	2^341134+2533	102692	Henri Lifchitz	09/2005
3092	13^92184-54	102688	Lelio R Paula	10/2016
3093	2^341116-20873	102687	Enzo Doria	06/2013
3094	2^341094-19953	102680	Enzo Doria	06/2013
3095	2^341053+129	102668	Lelio R Paula	08/2011
3096	(31*2^341006-1)/3	102655	Lelio R Paula	03/2014
3097	7^121471+94	102655	Lelio R Paula	10/2016
3099	2^341004-173	102653	Lelio R Paula	08/2011
3098	20^78901+3	102653	Lelio R Paula	10/2016
3100	5^146853-52	102646	Lelio R Paula	10/2016
3101	2^340969-216931	102642	Enzo Doria	05/2014
3102	2^340952+1870021	102637	Enzo Doria	05/2016
3103	5*2^340940-3	102634	Lelio R Paula	08/2014
3104	(6^131891+1)/7	102631	Paul Bourdelais	01/2010
3105	(4*10^102612+83)/3	102613	Robert Price	02/2018
3106	75^54717+74	102598	Norbert Schneider	01/2015
3107	2^340806-20393	102593	Enzo Doria	06/2013
3108	(2^340790+5)/138267	102583	Lelio R Paula	12/2013
3109	6^131821+77	102577	Lelio R Paula	10/2016
3110	2^340688-29	102558	Henri Lifchitz	05/2005
3111	2^340685-109101	102557	Enzo Doria	04/2014
3112	65^56567-64	102552	Norbert Schneider	11/2014
3113	2^340547-108897	102515	Enzo Doria	03/2014
3114	7^121268+82	102484	Lelio R Paula	10/2016
3115	(6883*2^340443-1)/162401	102483	Lelio R Paula	05/2015
3116	2^340434-5955	102481	Lelio R Paula	11/2016
3117	(2^340381+47)/7	102465	Lelio R Paula	12/2013
3118	111^50095+110	102461	Norbert Schneider	04/2017
3119	2^340291-20301	102438	Enzo Doria	06/2013
3120	12^94915+89	102431	Lelio R Paula	10/2016
3121	2^340208-20373	102413	Enzo Doria	06/2013
3122	6^131598-17273	102404	Enzo Doria	02/2013
3123	2^340115-21181	102385	Enzo Doria	06/2013
3124	(55459*2^340090+1)/1591	102379	Lelio R Paula	07/2014
3125	89^52511-88^52511	102365	Robert Price	06/2015
3126	3^214539-112756	102362	Enzo Doria	07/2014
3127	2^340000-19877	102351	Enzo Doria	06/2013
3128	2^339990-114845	102348	Enzo Doria	05/2015
3129	(3^214516-2)/51383	102346	Lelio R Paula	12/2013
3130	20^78661-99	102341	Lelio R Paula	09/2016
3131	2^339951-19585	102336	Enzo Doria	05/2013
3132	(13*2^339943+1)/45	102333	Lelio R Paula	12/2013
3133	2^339889+29327	102317	Yves Minet	06/2010
3134	2^339834-109493	102301	Enzo Doria	04/2014
3135	(11^98221-5^98221)/6	102286	Robert Price	01/2013
3136	3^214365+1820	102279	Lelio R Paula	10/2016
3137	(11*2^339705-1)/183	102261	Lelio R Paula	03/2014
3138	2^339694-16995	102259	Lelio R Paula	09/2016
3139	7^120985-38	102245	Lelio R Paula	10/2016
3140	10^102244+122961	102245	Patrick De Geest	12/2016
3141	10^102244-27	102244	Lelio R Paula	09/2016
3142	7^120982-62	102242	Lelio R Paula	10/2016
3143	4*6^131382-5	102236	Lelio R Paula	11/2014
3144	2^339586-1091	102226	Yves Minet	11/2012
3145	11^98161-3072000	102225	Enzo Doria	12/2012
3146	9*7^120961-4	102225	Lelio R Paula	11/2014
3147	5*3^214250+2	102224	Serge Batalov	10/2010
3148	12^94713-59	102213	Lelio R Paula	10/2016
3149	12^94705+89	102204	Lelio R Paula	10/2016
3150	2^339407-177	102172	Lelio R Paula	08/2011
3151	2^339355+65	102157	Lelio R Paula	07/2011
3152	(2^339323+47)/880715	102141	Lelio R Paula	12/2013
3153	2^339168+21	102100	Lelio R Paula	07/2011
3154	2^339167-108807	102100	Enzo Doria	03/2014
3155	2^339156+163	102097	Lelio R Paula	08/2011
3156	(2^338982-7)/1754517	102038	Lelio R Paula	12/2013
3157	2^338891-18885	102017	Enzo Doria	05/2013
3158	2^338829-113239	101998	Enzo Doria	07/2014
3159	2^338828-113297	101998	Enzo Doria	07/2014
3160	2^338796+93	101988	Donovan Johnson	06/2008
3161	lucasU(1373,1,32502)-lucasU(1373,1,32501)	101978	Mike Oakes	05/2009
3162	(71^55079-1)/70	101964	Paul Bourdelais	08/2017
3164	2^338682-19865	101954	Enzo Doria	06/2013
3163	(2^(112895*3+1)+243)/7	101954	Kevin Acres	12/2013
3165	2^338568+37	101920	Lelio R Paula	07/2011
3166	2^338559-1858777	101917	Enzo Doria	04/2016
3167	(9*2^338520+1)/365	101904	Lelio R Paula	12/2013
3168	2^338497-17041	101898	Enzo Doria	05/2013
3169	2^338475+54615	101892	Lelio R Paula	10/2016
3170	2^338426-19797	101877	Enzo Doria	06/2013
3171	2^338368-20369	101859	Enzo Doria	06/2013
3172	2^338366+74179	101859	Enzo Doria	04/2016
3173	2^338280-19745	101833	Enzo Doria	06/2013
3174	(3*2^338236-1)/347	101818	Lelio R Paula	03/2014
3175	6^130841+103	101815	Lelio R Paula	10/2016
3176	2^338122-20117	101785	Enzo Doria	06/2013
3177	(2^338139+5)/905333	101785	Lelio R Paula	12/2013
3178	35^65917-7092	101781	Enzo Doria	03/2013
3179	2^338010-19833	101752	Enzo Doria	06/2013
3180	3^213215-76	101730	Lelio R Paula	09/2016
3181	2^337930+63	101728	Lelio R Paula	07/2011
3182	2^337920+1869661	101725	Enzo Doria	05/2016
3183	2^337859-19645	101706	Enzo Doria	05/2013
3184	2^337754+1869169	101675	Enzo Doria	05/2016
3185	3*10^101657-37	101658	Robert Price	07/2018
3186	(31*2^337677-1)/593	101650	Lelio R Paula	03/2014
3187	11^97605-24	101646	Lelio R Paula	10/2016
3188	8^112539-112539	101633	Robert Price	01/2014
3189	2^337515-19869	101603	Enzo Doria	06/2013
3190	2^337473+719	101590	Lelio R Paula	08/2011
3191	(2^337485-509203)/656647157	101585	Lelio R Paula	12/2013
3192	2^337452-108815	101584	Enzo Doria	03/2014
3193	2^337453+1185	101584	Lelio R Paula	09/2016
3194	2^337410-113561	101571	Enzo Doria	08/2014
3195	2^337387+855	101564	Lelio R Paula	09/2016
3196	2^337367-17295	101558	Lelio R Paula	09/2016
3197	2^337342-109035	101551	Enzo Doria	04/2014
3198	2^337267-19	101528	Lelio R Paula	07/2011
3199	2^337183-19989	101503	Enzo Doria	06/2013
3200	2^337149+72425	101492	Enzo Doria	04/2016
3201	2^337101-20241	101478	Enzo Doria	06/2013
3202	2^337035-20001	101458	Enzo Doria	06/2013
3203	2^337017-16995	101453	Lelio R Paula	09/2016
3204	2^336979-115315	101441	Enzo Doria	06/2015
3205	2^336970-20885	101439	Enzo Doria	06/2013
3206	2^336958+79	101435	Lelio R Paula	10/2009
3207	2^336942+169	101430	Lelio R Paula	10/2009
3208	(15185*2^336894-1)/7939	101416	Lelio R Paula	05/2015
3209	2^336871+257463	101409	Tony Prest / Never Odd Or Even	04/2016
3210	2^336871+318105	101409	Tony Prest / Never Odd Or Even	04/2016
3211	2^336871+1010813	101409	Tony Prest / Never Odd Or Even	04/2016
3212	2^336871+2302245	101409	Tony Prest / Never Odd Or Even	04/2016
3213	2^336871+389273	101409	Tony Prest / Never Odd Or Even	04/2016
3214	2^336871+1685475	101409	Tony Prest / Never Odd Or Even	04/2016
3215	2^336871+1068119	101409	Tony Prest / Never Odd Or Even	04/2016
3216	2^336871+586905	101409	Tony Prest / Never Odd Or Even	04/2016
3217	2^336871+674571	101409	Tony Prest / Never Odd Or Even	04/2016
3218	2^336871+707009	101409	Tony Prest / Never Odd Or Even	04/2016
3219	2^336871+1210299	101409	Tony Prest / Never Odd Or Even	04/2016
3220	2^336871+1921185	101409	Tony Prest / Never Odd Or Even	04/2016
3221	2^336871+2003973	101409	Tony Prest / Never Odd Or Even	04/2016
3222	2^336871+2656475	101409	Tony Prest / Never Odd Or Even	04/2016
3223	2^336871+2703023	101409	Tony Prest / Never Odd Or Even	04/2016
3224	2^336871+2704545	101409	Tony Prest / Never Odd Or Even	04/2016
3225	2^336871+2766801	101409	Tony Prest / Never Odd Or Even	04/2016
3226	2^336871+2127735	101409	Tony Prest / Never Odd Or Even	04/2016
3227	(2^336871+821089)/3	101408	Tony Prest / Never Odd Or Even	05/2016
3228	(2^336871+119567)/5	101408	Tony Prest / Never Odd Or Even	05/2016
3229	(2^336871+398161)/3	101408	Tony Prest / Never Odd Or Even	05/2016
3230	(2^336871+625889)/7	101408	Tony Prest / Never Odd Or Even	05/2016
3231	2^336842+94065	101400	Lelio R Paula	09/2016
3232	(2^336871+904417)/3/3/3/5/19/9287177/9690011663/29993043103	101378	Tony Prest / Never Odd Or Even	04/2016
3233	(2^336871+631971)/13/251/1601/294277/614362921/30324278867	101377	Tony Prest / Never Odd Or Even	04/2016
3234	(2^336871+1443541)/3/89/1655197/11018131/47972707/468862691879	101374	Tony Prest / Never Odd Or Even	04/2016
3235	(2^336871+689863)/3/11/109/137/1867/7151/20800501/29243857/127778489	101373	Tony Prest / Never Odd Or Even	04/2016
3236	(2^336871+219839)/191/643/3011/9479/117127/175750007/4578271757	101373	Tony Prest / Never Odd Or Even	04/2016
3237	(2^336871+272895)/19/661/977572033/95853078653/520779768241	101373	Tony Prest / Never Odd Or Even	04/2016
3238	(2^336871+1023429)/2311/415873/991889/3630648341/207732189179	101373	Tony Prest / Never Odd Or Even	04/2016
3239	10^101369+203811	101370	Patrick De Geest	11/2016
3240	10^101369-99	101369	Lelio R Paula	09/2016
3241	(2^336871+1832627)/5/5/23/181/4397/91373/3746673331/115602484097/279351383917	101363	Tony Prest / Never Odd Or Even	04/2016
3242	2^336701-113563	101358	Enzo Doria	08/2014
3243	2^336644-109023	101340	Enzo Doria	04/2014
3244	2^336601-21081	101327	Enzo Doria	06/2013
3245	20^77869+63	101310	Lelio R Paula	09/2016
3246	(13*2^336523-1)/19	101304	Lelio R Paula	03/2014
3247	6^130179-137	101299	Lelio R Paula	10/2016
3248	(2^336506+lucasV(1,2,336506)+1)/2	101299	Mike Oakes	11/2016
3249	(24737*2^336485+1)/7285	101293	Lelio R Paula	07/2014
3250	(2^336448+9)/497405	101276	Lelio R Paula	12/2013

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Probable Primes Top 10000

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