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	(55459*2^340090+1)/1591	102379	Lelio R Paula	07/2014
3002	89^52511-88^52511	102365	Robert Price	06/2015
3003	3^214539-112756	102362	Enzo Doria	07/2014
3004	2^340000-19877	102351	Enzo Doria	06/2013
3005	2^339990-114845	102348	Enzo Doria	05/2015
3006	(3^214516-2)/51383	102346	Lelio R Paula	12/2013
3007	20^78661-99	102341	Lelio R Paula	09/2016
3008	2^339951-19585	102336	Enzo Doria	05/2013
3009	(13*2^339943+1)/45	102333	Lelio R Paula	12/2013
3010	2^339889+29327	102317	Yves Minet	06/2010
3011	2^339834-109493	102301	Enzo Doria	04/2014
3012	(11^98221-5^98221)/6	102286	Robert Price	01/2013
3013	3^214365+1820	102279	Lelio R Paula	10/2016
3014	(11*2^339705-1)/183	102261	Lelio R Paula	03/2014
3015	2^339694-16995	102259	Lelio R Paula	09/2016
3016	7^120985-38	102245	Lelio R Paula	10/2016
3017	10^102244+122961	102245	Patrick De Geest	12/2016
3018	10^102244-27	102244	Lelio R Paula	09/2016
3019	7^120982-62	102242	Lelio R Paula	10/2016
3020	4*6^131382-5	102236	Lelio R Paula	11/2014
3021	2^339586-1091	102226	Yves Minet	11/2012
3022	11^98161-3072000	102225	Enzo Doria	12/2012
3023	9*7^120961-4	102225	Lelio R Paula	11/2014
3024	5*3^214250+2	102224	Serge Batalov	10/2010
3025	12^94713-59	102213	Lelio R Paula	10/2016
3026	12^94705+89	102204	Lelio R Paula	10/2016
3027	2^339407-177	102172	Lelio R Paula	08/2011
3028	2^339355+65	102157	Lelio R Paula	07/2011
3029	(2^339323+47)/880715	102141	Lelio R Paula	12/2013
3030	2^339168+21	102100	Lelio R Paula	07/2011
3031	2^339167-108807	102100	Enzo Doria	03/2014
3032	2^339156+163	102097	Lelio R Paula	08/2011
3033	(2^338982-7)/1754517	102038	Lelio R Paula	12/2013
3034	2^338891-18885	102017	Enzo Doria	05/2013
3035	2^338829-113239	101998	Enzo Doria	07/2014
3036	2^338828-113297	101998	Enzo Doria	07/2014
3037	2^338796+93	101988	Donovan Johnson	06/2008
3038	lucasU(1373,1,32502)-lucasU(1373,1,32501)	101978	Mike Oakes	05/2009
3039	(71^55079-1)/70	101964	Paul Bourdelais	08/2017
3041	2^338682-19865	101954	Enzo Doria	06/2013
3040	(2^(112895*3+1)+243)/7	101954	Kevin Acres	12/2013
3042	2^338568+37	101920	Lelio R Paula	07/2011
3043	2^338559-1858777	101917	Enzo Doria	04/2016
3044	(9*2^338520+1)/365	101904	Lelio R Paula	12/2013
3045	2^338497-17041	101898	Enzo Doria	05/2013
3046	2^338475+54615	101892	Lelio R Paula	10/2016
3047	2^338426-19797	101877	Enzo Doria	06/2013
3048	2^338368-20369	101859	Enzo Doria	06/2013
3049	2^338366+74179	101859	Enzo Doria	04/2016
3050	2^338280-19745	101833	Enzo Doria	06/2013
3051	(3*2^338236-1)/347	101818	Lelio R Paula	03/2014
3052	6^130841+103	101815	Lelio R Paula	10/2016
3054	2^338122-20117	101785	Enzo Doria	06/2013
3053	(2^338139+5)/905333	101785	Lelio R Paula	12/2013
3055	35^65917-7092	101781	Enzo Doria	03/2013
3056	2^338010-19833	101752	Enzo Doria	06/2013
3057	3^213215-76	101730	Lelio R Paula	09/2016
3058	2^337930+63	101728	Lelio R Paula	07/2011
3059	2^337920+1869661	101725	Enzo Doria	05/2016
3060	2^337859-19645	101706	Enzo Doria	05/2013
3061	2^337754+1869169	101675	Enzo Doria	05/2016
3062	(31*2^337677-1)/593	101650	Lelio R Paula	03/2014
3063	11^97605-24	101646	Lelio R Paula	10/2016
3064	8^112539-112539	101633	Robert Price	01/2014
3065	2^337515-19869	101603	Enzo Doria	06/2013
3066	2^337473+719	101590	Lelio R Paula	08/2011
3067	(2^337485-509203)/656647157	101585	Lelio R Paula	12/2013
3068	2^337452-108815	101584	Enzo Doria	03/2014
3069	2^337453+1185	101584	Lelio R Paula	09/2016
3070	2^337410-113561	101571	Enzo Doria	08/2014
3071	2^337387+855	101564	Lelio R Paula	09/2016
3072	2^337367-17295	101558	Lelio R Paula	09/2016
3073	2^337342-109035	101551	Enzo Doria	04/2014
3074	2^337267-19	101528	Lelio R Paula	07/2011
3075	2^337183-19989	101503	Enzo Doria	06/2013
3076	2^337149+72425	101492	Enzo Doria	04/2016
3077	2^337101-20241	101478	Enzo Doria	06/2013
3078	2^337035-20001	101458	Enzo Doria	06/2013
3079	2^337017-16995	101453	Lelio R Paula	09/2016
3080	2^336979-115315	101441	Enzo Doria	06/2015
3081	2^336970-20885	101439	Enzo Doria	06/2013
3082	2^336958+79	101435	Lelio R Paula	10/2009
3083	2^336942+169	101430	Lelio R Paula	10/2009
3084	(15185*2^336894-1)/7939	101416	Lelio R Paula	05/2015
3085	2^336871+257463	101409	Tony Prest / Never Odd Or Even	04/2016
3086	2^336871+318105	101409	Tony Prest / Never Odd Or Even	04/2016
3087	2^336871+1010813	101409	Tony Prest / Never Odd Or Even	04/2016
3088	2^336871+2302245	101409	Tony Prest / Never Odd Or Even	04/2016
3089	2^336871+389273	101409	Tony Prest / Never Odd Or Even	04/2016
3090	2^336871+1685475	101409	Tony Prest / Never Odd Or Even	04/2016
3091	2^336871+1068119	101409	Tony Prest / Never Odd Or Even	04/2016
3092	2^336871+586905	101409	Tony Prest / Never Odd Or Even	04/2016
3093	2^336871+674571	101409	Tony Prest / Never Odd Or Even	04/2016
3094	2^336871+707009	101409	Tony Prest / Never Odd Or Even	04/2016
3095	2^336871+1210299	101409	Tony Prest / Never Odd Or Even	04/2016
3096	2^336871+1921185	101409	Tony Prest / Never Odd Or Even	04/2016
3097	2^336871+2003973	101409	Tony Prest / Never Odd Or Even	04/2016
3098	2^336871+2656475	101409	Tony Prest / Never Odd Or Even	04/2016
3099	2^336871+2703023	101409	Tony Prest / Never Odd Or Even	04/2016
3100	2^336871+2704545	101409	Tony Prest / Never Odd Or Even	04/2016
3101	2^336871+2766801	101409	Tony Prest / Never Odd Or Even	04/2016
3102	2^336871+2127735	101409	Tony Prest / Never Odd Or Even	04/2016
3103	(2^336871+821089)/3	101408	Tony Prest / Never Odd Or Even	05/2016
3104	(2^336871+119567)/5	101408	Tony Prest / Never Odd Or Even	05/2016
3105	(2^336871+398161)/3	101408	Tony Prest / Never Odd Or Even	05/2016
3106	(2^336871+625889)/7	101408	Tony Prest / Never Odd Or Even	05/2016
3107	2^336842+94065	101400	Lelio R Paula	09/2016
3108	(2^336871+904417)/3/3/3/5/19/9287177/9690011663/29993043103	101378	Tony Prest / Never Odd Or Even	04/2016
3109	(2^336871+631971)/13/251/1601/294277/614362921/30324278867	101377	Tony Prest / Never Odd Or Even	04/2016
3110	(2^336871+1443541)/3/89/1655197/11018131/47972707/468862691879	101374	Tony Prest / Never Odd Or Even	04/2016
3111	(2^336871+689863)/3/11/109/137/1867/7151/20800501/29243857/127778489	101373	Tony Prest / Never Odd Or Even	04/2016
3112	(2^336871+219839)/191/643/3011/9479/117127/175750007/4578271757	101373	Tony Prest / Never Odd Or Even	04/2016
3113	(2^336871+272895)/19/661/977572033/95853078653/520779768241	101373	Tony Prest / Never Odd Or Even	04/2016
3114	(2^336871+1023429)/2311/415873/991889/3630648341/207732189179	101373	Tony Prest / Never Odd Or Even	04/2016
3115	10^101369+203811	101370	Patrick De Geest	11/2016
3116	10^101369-99	101369	Lelio R Paula	09/2016
3117	(2^336871+1832627)/5/5/23/181/4397/91373/3746673331/115602484097/279351383917	101363	Tony Prest / Never Odd Or Even	04/2016
3118	2^336701-113563	101358	Enzo Doria	08/2014
3119	2^336644-109023	101340	Enzo Doria	04/2014
3120	2^336601-21081	101327	Enzo Doria	06/2013
3121	20^77869+63	101310	Lelio R Paula	09/2016
3122	(13*2^336523-1)/19	101304	Lelio R Paula	03/2014
3123	6^130179-137	101299	Lelio R Paula	10/2016
3124	(2^336506+lucasV(1,2,336506)+1)/2	101299	Mike Oakes	11/2016
3125	(24737*2^336485+1)/7285	101293	Lelio R Paula	07/2014
3126	(2^336448+9)/497405	101276	Lelio R Paula	12/2013
3127	2^336369-19753	101258	Enzo Doria	05/2013
3128	2^336350-344291	101252	Enzo Doria	07/2015
3129	2^336243-108777	101220	Enzo Doria	03/2014
3130	(31*2^336189-1)/19	101204	Lelio R Paula	03/2014
3131	(78557*2^336178+1)/1268757	101199	Lelio R Paula	07/2014
3132	2^336150-20393	101192	Enzo Doria	06/2013
3133	2^336112-1865249	101180	Enzo Doria	03/2016
3134	2^336103-109015	101178	Enzo Doria	04/2014
3135	13^90809-96	101157	Lelio R Paula	10/2016
3136	19^79098-30	101147	Lelio R Paula	10/2016
3137	19^79095+88	101144	Lelio R Paula	10/2016
3138	15^85976+32	101116	Lelio R Paula	10/2016
3139	(3^211950+7)/28854513015920697088	101107	Lelio R Paula	11/2013
3140	(4^167933+17)/3	101106	Robert Price	02/2017
3141	2^335858+153	101104	Lelio R Paula	10/2009
3142	6^129918-35	101096	Lelio R Paula	10/2016
3143	3^211885-70	101095	Lelio R Paula	09/2016
3144	(29*2^335835-1)/550599	101093	Lelio R Paula	03/2014
3145	2^335818-20033	101092	Enzo Doria	06/2013
3146	2^335813-110083	101090	Enzo Doria	04/2014
3147	2^335804+2155	101088	Lelio R Paula	09/2016
3148	2^335784-16145	101082	Enzo Doria	04/2013
3149	11^97051+62	101069	Lelio R Paula	10/2016
3150	(2^335691-3)/26515	101049	Lelio R Paula	12/2013
3151	2^335658-94395	101044	Lelio R Paula	09/2016
3152	2^335586+169	101022	Lelio R Paula	10/2009
3153	(56^57787-1)/55	101021	Paul Bourdelais	08/2017
3154	47599!2+1024	100991	Robert Price	02/2015
3155	2^335468-18629	100986	Enzo Doria	05/2013
3156	2^335454-20961	100982	Enzo Doria	06/2013
3157	10^100978+61	100979	Lelio R Paula	09/2016
3158	10^100978-156437	100978	Patrick De Geest	11/2016
3159	(15*2^335417+1)/481	100970	Lelio R Paula	12/2013
3160	2^335403-1859167	100967	Enzo Doria	03/2016
3161	9*2^335364-5	100956	Lelio R Paula	08/2014
3162	2^335349+72287	100951	Enzo Doria	04/2016
3163	2^335329+16095	100945	Lelio R Paula	09/2016
3164	232823#+233663	100937	Makoto Morimoto	10/2017
3165	2^335237-20893	100917	Enzo Doria	06/2013
3166	2^335222-19337	100912	Enzo Doria	05/2013
3167	2^335222-109985	100912	Enzo Doria	04/2014
3168	2^335182-17237	100900	Enzo Doria	05/2013
3169	2^335043-16737	100858	Enzo Doria	05/2013
3170	(21181*2^335049+1)/1343811	100858	Lelio R Paula	07/2014
3171	2^335038-20633	100857	Enzo Doria	06/2013
3172	2^335031+1873373	100855	Enzo Doria	06/2016
3173	3^211354-8816	100842	Enzo Doria	05/2014
3174	2^334984-112757	100841	Enzo Doria	06/2014
3176	2^334857+48527	100803	Lelio R Paula	08/2011
3175	12^93406+29	100803	Lelio R Paula	10/2016
3177	(5*2^334825+1)/47	100792	Lelio R Paula	12/2013
3178	2^334809-13	100788	Lelio R Paula	04/2011
3179	(82*10^100780-1)/9	100781	Robert Price	12/2014
3180	(2^334779+47)/5	100778	Lelio R Paula	12/2013
3181	2^334751+2049	100771	Lelio R Paula	09/2016
3182	13^90443-98	100749	Lelio R Paula	10/2016
3183	(24737*2^334628+1)/3	100737	Lelio R Paula	07/2014
3184	15^85639-28	100720	Lelio R Paula	10/2016
3185	2^334562+577294575	100711	Lelio R Paula	09/2016
3186	4*3^211077-5	100710	Lelio R Paula	08/2014
3187	2^334524+145	100702	Lelio R Paula	07/2009
3188	(1017*2^334391-1)/3535	100662	Lelio R Paula	05/2015
3189	2^334294-113111	100633	Enzo Doria	07/2014
3190	6^129308-17723	100622	Enzo Doria	03/2013
3191	6^129305+95	100619	Lelio R Paula	10/2016
3192	2^334244-1167	100618	Lelio R Paula	09/2016
3193	(21*2^334050+1)/935	100558	Lelio R Paula	12/2013
3194	(78557*2^334018+1)/4326021	100548	Lelio R Paula	07/2014
3195	(35*10^100542+1)/9	100543	Serge Batalov	11/2010
3196	13^90251+24	100535	Lelio R Paula	10/2016
3197	2^333963+789	100533	Lelio R Paula	08/2011
3198	2^333919-1840087	100520	Enzo Doria	06/2015
3199	2^333911+72623	100518	Enzo Doria	04/2016
3200	18^80064-67	100503	Lelio R Paula	10/2016
3201	5^143742-48	100472	Lelio R Paula	10/2016
3202	2^333757-112123	100471	Enzo Doria	06/2014
3203	2^333603-108861	100425	Enzo Doria	03/2014
3204	9*7^118818-2	100414	Lelio R Paula	11/2014
3205	2^333546-17097	100408	Enzo Doria	05/2013
3206	17^81597+72	100401	Lelio R Paula	10/2016
3207	p(20559)#/2+8	100384	Robert Price	01/2017
3208	11^96390-24	100380	Lelio R Paula	10/2016
3209	4832563059*2^333333+30029	100353	Donovan Johnson	01/2008
3210	2^333354+763	100350	Lelio R Paula	08/2011
3211	2^333289-109483	100330	Enzo Doria	04/2014
3212	2^333240-2790209	100316	Enzo Doria	03/2016
3214	(2^333227-2^166614+1)/5	100311		11/2006
3213	2^333225+719	100311	Lelio R Paula	08/2011
3215	2^333221-2785333	100310	Enzo Doria	10/2015
3216	76^53332-75	100308	Norbert Schneider	02/2015
3217	6^128892-17573	100298	Enzo Doria	03/2013
3218	2^333105-113215	100275	Enzo Doria	07/2014
3219	(31*2^333102+1)/2375	100272	Lelio R Paula	11/2013
3220	17^81476-74	100253	Lelio R Paula	10/2016
3221	17^81417-16	100180	Theodore Burton	11/2005
3222	2^332739-113215	100165	Enzo Doria	07/2014
3223	2^332730-1865621	100162	Enzo Doria	03/2016
3224	91^51127-2	100160	Lelio R Paula	09/2013
3225	15^85159-32	100155	Lelio R Paula	10/2016
3226	6^128661+97	100118	Lelio R Paula	10/2016
3227	19^78285+40	100108	Lelio R Paula	07/2016
3228	6^128640+5	100102	Lelio R Paula	11/2014
3229	6^128565-127	100044	Lelio R Paula	08/2016
3230	2^332309-133	100035	Lelio R Paula	02/2011
3231	2^332307+731	100035	Lelio R Paula	07/2011
3232	2^332301+12927	100033	Lelio R Paula	04/2013
3233	23406^18781+18781^23406	100031	Hans Havermann	04/2018
3234	12^92684-13	100023	Lelio R Paula	07/2016
3235	(10^100002-1)/9-10^33441	100002	Akihiko Yoshida	03/2018
3236	(10^100002-1)/9-10^44692	100002	Akihiko Yoshida	03/2018
3242	25206!+p(4114)	100001	Henri Lifchitz	09/2005
3243	25206!-p(5447)	100001	Henri Lifchitz	10/2005
3244	25206!-p(12402)	100001	Henri Lifchitz	04/2006
3245	25206!-p(16290)	100001	Henri Lifchitz	09/2006
3246	25206!-p(19647)	100001	Henri Lifchitz	02/2007
3247	2^332194+11473	100001	Henri Lifchitz	03/2007
3239	10^100000+3938473	100001	Robert Price	05/2015
3240	10^100000+3979761	100001	Robert Price	05/2015
3241	10^100000+4293973	100001	Robert Price	09/2015
3248	10^100000+4858267	100001	Robert Price	12/2015
3249	10^100000+5113299	100001	Robert Price	02/2016
3250	10^100000+5169411	100001	Robert Price	02/2016
3237	10^100000+11187931	100001	Robert Price	03/2018
3238	10^100000+11264721	100001	Robert Price	04/2018

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PRP Records

Probable Primes Top 10000

(205869 PRPs in the top)