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	328^40945+40945^328	103013	Norbert Schneider	12/2014
3002	65^56809-64^56809	102990	Robert Price	08/2013
3003	5^147338-6	102985	Lelio R Paula	11/2014
3004	2^342084-112739	102978	Enzo Doria	06/2014
3005	9*6^132330+7	102974	Lelio R Paula	11/2014
3006	2^342034-16737	102963	Enzo Doria	05/2013
3007	(9787*2^342011-1)/25	102959	Lelio R Paula	05/2015
3008	(3^215802-5)/124343756	102956	Lelio R Paula	12/2013
3009	2^341991-17421	102950	Enzo Doria	05/2013
3010	2^341969-112225	102943	Enzo Doria	06/2014
3011	(9787*2^341864-1)/3	102915	Lelio R Paula	05/2015
3012	2^341859+1869413	102910	Enzo Doria	05/2016
3013	10^102909+61	102910	Lelio R Paula	11/2016
3014	10^102909-67049	102909	Patrick De Geest	12/2016
3015	2^341659+1836773	102850	Enzo Doria	03/2016
3016	2^341608-110639	102835	Enzo Doria	05/2014
3017	10^102824+49	102825	Lelio R Paula	11/2016
3018	10^102824-168011	102824	Patrick De Geest	12/2016
3019	11^98708-8	102794	Lelio R Paula	10/2016
3020	2^341466+4429	102792	Lelio R Paula	09/2011
3021	2^341460-107	102790	Lelio R Paula	08/2011
3022	(2^341388+47)/21014943	102761	Lelio R Paula	12/2013
3023	2^341355+21	102759	Lelio R Paula	08/2011
3024	2^341246+40755	102726	Lelio R Paula	11/2016
3025	(2^341256-5)/991699	102723	Lelio R Paula	12/2013
3026	7^121547+78	102720	Lelio R Paula	10/2016
3027	2^341223-461197	102719	Enzo Doria	06/2015
3028	2^341190-20577	102709	Enzo Doria	06/2013
3029	(27*2^341212+1)/84674449	102709	Lelio R Paula	12/2013
3030	6^131976-65	102698	Lelio R Paula	10/2016
3031	2^341134+2533	102692	Henri Lifchitz	09/2005
3032	13^92184-54	102688	Lelio R Paula	10/2016
3033	2^341116-20873	102687	Enzo Doria	06/2013
3034	2^341094-19953	102680	Enzo Doria	06/2013
3035	2^341053+129	102668	Lelio R Paula	08/2011
3036	(31*2^341006-1)/3	102655	Lelio R Paula	03/2014
3037	7^121471+94	102655	Lelio R Paula	10/2016
3039	2^341004-173	102653	Lelio R Paula	08/2011
3038	20^78901+3	102653	Lelio R Paula	10/2016
3040	5^146853-52	102646	Lelio R Paula	10/2016
3041	2^340969-216931	102642	Enzo Doria	05/2014
3042	2^340952+1870021	102637	Enzo Doria	05/2016
3043	5*2^340940-3	102634	Lelio R Paula	08/2014
3044	(6^131891+1)/7	102631	Paul Bourdelais	01/2010
3045	(4*10^102612+83)/3	102613	Robert Price	02/2018
3046	75^54717+74	102598	Norbert Schneider	01/2015
3047	2^340806-20393	102593	Enzo Doria	06/2013
3048	(2^340790+5)/138267	102583	Lelio R Paula	12/2013
3049	6^131821+77	102577	Lelio R Paula	10/2016
3050	2^340688-29	102558	Henri Lifchitz	05/2005
3051	2^340685-109101	102557	Enzo Doria	04/2014
3052	65^56567-64	102552	Norbert Schneider	11/2014
3053	2^340547-108897	102515	Enzo Doria	03/2014
3054	7^121268+82	102484	Lelio R Paula	10/2016
3055	(6883*2^340443-1)/162401	102483	Lelio R Paula	05/2015
3056	2^340434-5955	102481	Lelio R Paula	11/2016
3057	(2^340381+47)/7	102465	Lelio R Paula	12/2013
3058	111^50095+110	102461	Norbert Schneider	04/2017
3059	2^340291-20301	102438	Enzo Doria	06/2013
3060	12^94915+89	102431	Lelio R Paula	10/2016
3061	2^340208-20373	102413	Enzo Doria	06/2013
3062	6^131598-17273	102404	Enzo Doria	02/2013
3063	2^340115-21181	102385	Enzo Doria	06/2013
3064	(55459*2^340090+1)/1591	102379	Lelio R Paula	07/2014
3065	89^52511-88^52511	102365	Robert Price	06/2015
3066	3^214539-112756	102362	Enzo Doria	07/2014
3067	2^340000-19877	102351	Enzo Doria	06/2013
3068	2^339990-114845	102348	Enzo Doria	05/2015
3069	(3^214516-2)/51383	102346	Lelio R Paula	12/2013
3070	20^78661-99	102341	Lelio R Paula	09/2016
3071	2^339951-19585	102336	Enzo Doria	05/2013
3072	(13*2^339943+1)/45	102333	Lelio R Paula	12/2013
3073	2^339889+29327	102317	Yves Minet	06/2010
3074	2^339834-109493	102301	Enzo Doria	04/2014
3075	(11^98221-5^98221)/6	102286	Robert Price	01/2013
3076	3^214365+1820	102279	Lelio R Paula	10/2016
3077	(11*2^339705-1)/183	102261	Lelio R Paula	03/2014
3078	2^339694-16995	102259	Lelio R Paula	09/2016
3079	7^120985-38	102245	Lelio R Paula	10/2016
3080	10^102244+122961	102245	Patrick De Geest	12/2016
3081	10^102244-27	102244	Lelio R Paula	09/2016
3082	7^120982-62	102242	Lelio R Paula	10/2016
3083	4*6^131382-5	102236	Lelio R Paula	11/2014
3084	2^339586-1091	102226	Yves Minet	11/2012
3085	11^98161-3072000	102225	Enzo Doria	12/2012
3086	9*7^120961-4	102225	Lelio R Paula	11/2014
3087	5*3^214250+2	102224	Serge Batalov	10/2010
3088	12^94713-59	102213	Lelio R Paula	10/2016
3089	12^94705+89	102204	Lelio R Paula	10/2016
3090	2^339407-177	102172	Lelio R Paula	08/2011
3091	2^339355+65	102157	Lelio R Paula	07/2011
3092	(2^339323+47)/880715	102141	Lelio R Paula	12/2013
3093	2^339168+21	102100	Lelio R Paula	07/2011
3094	2^339167-108807	102100	Enzo Doria	03/2014
3095	2^339156+163	102097	Lelio R Paula	08/2011
3096	(2^338982-7)/1754517	102038	Lelio R Paula	12/2013
3097	2^338891-18885	102017	Enzo Doria	05/2013
3098	2^338829-113239	101998	Enzo Doria	07/2014
3099	2^338828-113297	101998	Enzo Doria	07/2014
3100	2^338796+93	101988	Donovan Johnson	06/2008
3101	lucasU(1373,1,32502)-lucasU(1373,1,32501)	101978	Mike Oakes	05/2009
3102	(71^55079-1)/70	101964	Paul Bourdelais	08/2017
3103	2^338682-19865	101954	Enzo Doria	06/2013
3104	(2^(112895*3+1)+243)/7	101954	Kevin Acres	12/2013
3105	2^338568+37	101920	Lelio R Paula	07/2011
3106	2^338559-1858777	101917	Enzo Doria	04/2016
3107	(9*2^338520+1)/365	101904	Lelio R Paula	12/2013
3108	2^338497-17041	101898	Enzo Doria	05/2013
3109	2^338475+54615	101892	Lelio R Paula	10/2016
3110	2^338426-19797	101877	Enzo Doria	06/2013
3111	2^338368-20369	101859	Enzo Doria	06/2013
3112	2^338366+74179	101859	Enzo Doria	04/2016
3113	2^338280-19745	101833	Enzo Doria	06/2013
3114	(3*2^338236-1)/347	101818	Lelio R Paula	03/2014
3115	6^130841+103	101815	Lelio R Paula	10/2016
3116	2^338122-20117	101785	Enzo Doria	06/2013
3117	(2^338139+5)/905333	101785	Lelio R Paula	12/2013
3118	35^65917-7092	101781	Enzo Doria	03/2013
3119	2^338010-19833	101752	Enzo Doria	06/2013
3120	3^213215-76	101730	Lelio R Paula	09/2016
3121	2^337930+63	101728	Lelio R Paula	07/2011
3122	2^337920+1869661	101725	Enzo Doria	05/2016
3123	2^337859-19645	101706	Enzo Doria	05/2013
3124	2^337754+1869169	101675	Enzo Doria	05/2016
3125	(31*2^337677-1)/593	101650	Lelio R Paula	03/2014
3126	11^97605-24	101646	Lelio R Paula	10/2016
3127	8^112539-112539	101633	Robert Price	01/2014
3128	2^337515-19869	101603	Enzo Doria	06/2013
3129	2^337473+719	101590	Lelio R Paula	08/2011
3130	(2^337485-509203)/656647157	101585	Lelio R Paula	12/2013
3132	2^337452-108815	101584	Enzo Doria	03/2014
3131	2^337453+1185	101584	Lelio R Paula	09/2016
3133	2^337410-113561	101571	Enzo Doria	08/2014
3134	2^337387+855	101564	Lelio R Paula	09/2016
3135	2^337367-17295	101558	Lelio R Paula	09/2016
3136	2^337342-109035	101551	Enzo Doria	04/2014
3137	2^337267-19	101528	Lelio R Paula	07/2011
3138	2^337183-19989	101503	Enzo Doria	06/2013
3139	2^337149+72425	101492	Enzo Doria	04/2016
3140	2^337101-20241	101478	Enzo Doria	06/2013
3141	2^337035-20001	101458	Enzo Doria	06/2013
3142	2^337017-16995	101453	Lelio R Paula	09/2016
3143	2^336979-115315	101441	Enzo Doria	06/2015
3144	2^336970-20885	101439	Enzo Doria	06/2013
3145	2^336958+79	101435	Lelio R Paula	10/2009
3146	2^336942+169	101430	Lelio R Paula	10/2009
3147	(15185*2^336894-1)/7939	101416	Lelio R Paula	05/2015
3148	2^336871+257463	101409	Tony Prest / Never Odd Or Even	04/2016
3149	2^336871+318105	101409	Tony Prest / Never Odd Or Even	04/2016
3150	2^336871+1010813	101409	Tony Prest / Never Odd Or Even	04/2016
3151	2^336871+2302245	101409	Tony Prest / Never Odd Or Even	04/2016
3152	2^336871+389273	101409	Tony Prest / Never Odd Or Even	04/2016
3153	2^336871+1685475	101409	Tony Prest / Never Odd Or Even	04/2016
3154	2^336871+1068119	101409	Tony Prest / Never Odd Or Even	04/2016
3155	2^336871+586905	101409	Tony Prest / Never Odd Or Even	04/2016
3156	2^336871+674571	101409	Tony Prest / Never Odd Or Even	04/2016
3157	2^336871+707009	101409	Tony Prest / Never Odd Or Even	04/2016
3158	2^336871+1210299	101409	Tony Prest / Never Odd Or Even	04/2016
3159	2^336871+1921185	101409	Tony Prest / Never Odd Or Even	04/2016
3160	2^336871+2003973	101409	Tony Prest / Never Odd Or Even	04/2016
3161	2^336871+2656475	101409	Tony Prest / Never Odd Or Even	04/2016
3162	2^336871+2703023	101409	Tony Prest / Never Odd Or Even	04/2016
3163	2^336871+2704545	101409	Tony Prest / Never Odd Or Even	04/2016
3164	2^336871+2766801	101409	Tony Prest / Never Odd Or Even	04/2016
3165	2^336871+2127735	101409	Tony Prest / Never Odd Or Even	04/2016
3166	(2^336871+821089)/3	101408	Tony Prest / Never Odd Or Even	05/2016
3167	(2^336871+119567)/5	101408	Tony Prest / Never Odd Or Even	05/2016
3168	(2^336871+398161)/3	101408	Tony Prest / Never Odd Or Even	05/2016
3169	(2^336871+625889)/7	101408	Tony Prest / Never Odd Or Even	05/2016
3170	2^336842+94065	101400	Lelio R Paula	09/2016
3171	(2^336871+904417)/3/3/3/5/19/9287177/9690011663/29993043103	101378	Tony Prest / Never Odd Or Even	04/2016
3172	(2^336871+631971)/13/251/1601/294277/614362921/30324278867	101377	Tony Prest / Never Odd Or Even	04/2016
3173	(2^336871+1443541)/3/89/1655197/11018131/47972707/468862691879	101374	Tony Prest / Never Odd Or Even	04/2016
3174	(2^336871+689863)/3/11/109/137/1867/7151/20800501/29243857/127778489	101373	Tony Prest / Never Odd Or Even	04/2016
3175	(2^336871+219839)/191/643/3011/9479/117127/175750007/4578271757	101373	Tony Prest / Never Odd Or Even	04/2016
3176	(2^336871+272895)/19/661/977572033/95853078653/520779768241	101373	Tony Prest / Never Odd Or Even	04/2016
3177	(2^336871+1023429)/2311/415873/991889/3630648341/207732189179	101373	Tony Prest / Never Odd Or Even	04/2016
3178	10^101369+203811	101370	Patrick De Geest	11/2016
3179	10^101369-99	101369	Lelio R Paula	09/2016
3180	(2^336871+1832627)/5/5/23/181/4397/91373/3746673331/115602484097/279351383917	101363	Tony Prest / Never Odd Or Even	04/2016
3181	2^336701-113563	101358	Enzo Doria	08/2014
3182	2^336644-109023	101340	Enzo Doria	04/2014
3183	2^336601-21081	101327	Enzo Doria	06/2013
3184	20^77869+63	101310	Lelio R Paula	09/2016
3185	(13*2^336523-1)/19	101304	Lelio R Paula	03/2014
3186	6^130179-137	101299	Lelio R Paula	10/2016
3187	(2^336506+lucasV(1,2,336506)+1)/2	101299	Mike Oakes	11/2016
3188	(24737*2^336485+1)/7285	101293	Lelio R Paula	07/2014
3189	(2^336448+9)/497405	101276	Lelio R Paula	12/2013
3190	2^336369-19753	101258	Enzo Doria	05/2013
3191	2^336350-344291	101252	Enzo Doria	07/2015
3192	2^336243-108777	101220	Enzo Doria	03/2014
3193	(31*2^336189-1)/19	101204	Lelio R Paula	03/2014
3194	(78557*2^336178+1)/1268757	101199	Lelio R Paula	07/2014
3195	2^336150-20393	101192	Enzo Doria	06/2013
3196	2^336112-1865249	101180	Enzo Doria	03/2016
3197	2^336103-109015	101178	Enzo Doria	04/2014
3198	13^90809-96	101157	Lelio R Paula	10/2016
3199	19^79098-30	101147	Lelio R Paula	10/2016
3200	19^79095+88	101144	Lelio R Paula	10/2016
3201	15^85976+32	101116	Lelio R Paula	10/2016
3202	(3^211950+7)/28854513015920697088	101107	Lelio R Paula	11/2013
3203	(4^167933+17)/3	101106	Robert Price	02/2017
3204	2^335858+153	101104	Lelio R Paula	10/2009
3205	6^129918-35	101096	Lelio R Paula	10/2016
3206	3^211885-70	101095	Lelio R Paula	09/2016
3207	(29*2^335835-1)/550599	101093	Lelio R Paula	03/2014
3208	2^335818-20033	101092	Enzo Doria	06/2013
3209	2^335813-110083	101090	Enzo Doria	04/2014
3210	2^335804+2155	101088	Lelio R Paula	09/2016
3211	2^335784-16145	101082	Enzo Doria	04/2013
3212	11^97051+62	101069	Lelio R Paula	10/2016
3213	(2^335691-3)/26515	101049	Lelio R Paula	12/2013
3214	2^335658-94395	101044	Lelio R Paula	09/2016
3215	2^335586+169	101022	Lelio R Paula	10/2009
3216	(56^57787-1)/55	101021	Paul Bourdelais	08/2017
3217	47599!2+1024	100991	Robert Price	02/2015
3218	2^335468-18629	100986	Enzo Doria	05/2013
3219	2^335454-20961	100982	Enzo Doria	06/2013
3220	10^100978+61	100979	Lelio R Paula	09/2016
3221	10^100978-156437	100978	Patrick De Geest	11/2016
3222	(15*2^335417+1)/481	100970	Lelio R Paula	12/2013
3223	2^335403-1859167	100967	Enzo Doria	03/2016
3224	9*2^335364-5	100956	Lelio R Paula	08/2014
3225	2^335349+72287	100951	Enzo Doria	04/2016
3226	2^335329+16095	100945	Lelio R Paula	09/2016
3227	232823#+233663	100937	Makoto Morimoto	10/2017
3228	2^335237-20893	100917	Enzo Doria	06/2013
3229	2^335222-19337	100912	Enzo Doria	05/2013
3230	2^335222-109985	100912	Enzo Doria	04/2014
3231	2^335182-17237	100900	Enzo Doria	05/2013
3232	2^335043-16737	100858	Enzo Doria	05/2013
3233	(21181*2^335049+1)/1343811	100858	Lelio R Paula	07/2014
3234	2^335038-20633	100857	Enzo Doria	06/2013
3235	2^335031+1873373	100855	Enzo Doria	06/2016
3236	3^211354-8816	100842	Enzo Doria	05/2014
3237	2^334984-112757	100841	Enzo Doria	06/2014
3238	2^334857+48527	100803	Lelio R Paula	08/2011
3239	12^93406+29	100803	Lelio R Paula	10/2016
3240	(5*2^334825+1)/47	100792	Lelio R Paula	12/2013
3241	2^334809-13	100788	Lelio R Paula	04/2011
3242	(82*10^100780-1)/9	100781	Robert Price	12/2014
3243	(2^334779+47)/5	100778	Lelio R Paula	12/2013
3244	2^334751+2049	100771	Lelio R Paula	09/2016
3245	13^90443-98	100749	Lelio R Paula	10/2016
3246	(7*10^100737+71)/3	100738	Robert Price	05/2018
3247	(24737*2^334628+1)/3	100737	Lelio R Paula	07/2014
3248	15^85639-28	100720	Lelio R Paula	10/2016
3249	2^334562+577294575	100711	Lelio R Paula	09/2016
3250	4*3^211077-5	100710	Lelio R Paula	08/2014

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Probable Primes Top 10000

(212140 PRPs in the top)