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 (> 50000)	Who ?	When ?
3001	2^357885+12857	107735	Yves Minet	07/2010
3002	(248587#+9289)/(71327111512899)	107733	Makoto Morimoto	06/2019
3003	7^127473+40	107728	Lelio R Paula	03/2017
3004	5*2^357850+9	107725	Lelio R Paula	09/2014
3005	2^357786-291191	107705	Enzo Doria	06/2015
3006	18^85798-23	107700	Lelio R Paula	04/2017
3007	(14*10^107694-83)/3	107695	Robert Price	12/2018
3008	2^357688-1854269	107675	Enzo Doria	09/2015
3009	2^357671-112225	107670	Enzo Doria	06/2014
3010	2^357618-21005	107654	Enzo Doria	06/2013
3011	2^357615-17505	107653	Enzo Doria	05/2013
3012	(30^72871-1)/29	107638	Robert Price	12/2011
3013	2^357521+1870217	107625	Enzo Doria	05/2016
3014	2^357477-1203	107612	Lelio R Paula	03/2017
3015	5^153894-18	107568	Lelio R Paula	02/2017
3016	2^357324-69059	107566	Enzo Doria	11/2015
3017	467^40296+40296^467	107563	Norbert Schneider	03/2019
3018	2^357283-869688105	107553	Lelio R Paula	01/2017
3019	2^357280-16805	107552	Enzo Doria	05/2013
3020	10^107547+481719	107548	Patrick De Geest	03/2017
3021	10^107547-47	107547	Lelio R Paula	02/2017
3022	17^87396-32	107537	Lelio R Paula	04/2017
3023	2^357081+107	107493	Lelio R Paula	12/2011
3024	2^357058-3911	107486	Yves Minet	04/2017
3025	3^225274+64	107484	Lelio R Paula	03/2017
3026	18^85619-95	107476	Lelio R Paula	04/2017
3027	3^225248-130	107471	Lelio R Paula	03/2017
3028	(5*2^356961+1)/143	107455	Lelio R Paula	03/2014
3029	2^356935-18085	107449	Enzo Doria	05/2013
3030	10^107409+37	107410	Lelio R Paula	02/2017
3031	10^107409-329633	107409	Patrick De Geest	03/2017
3032	2^356787-109027	107404	Enzo Doria	04/2014
3033	(2^356767+78557)/5	107397	Lelio R Paula	12/2013
3034	3*10^107389+77	107390	Robert Price	09/2018
3035	5^153622-42	107378	Lelio R Paula	02/2017
3036	2^356699-97305	107378	Lelio R Paula	03/2017
3037	2^356654+85	107364	Lelio R Paula	11/2011
3038	2^356641-19921	107360	Enzo Doria	06/2013
3039	5*10^107355+11	107356	Robert Price	08/2019
3040	2^356623-465	107355	Lelio R Paula	03/2017
3041	19^83945-92	107345	Lelio R Paula	02/2017
3042	10^107334+28149	107335	Patrick De Geest	03/2017
3043	10^107334-83	107334	Lelio R Paula	02/2017
3044	2^356518+885	107323	Lelio R Paula	03/2017
3045	(3*2^356506-1)/467	107317	Lelio R Paula	03/2014
3046	2^356442-114713	107300	Enzo Doria	04/2015
3047	2^356425+72257	107295	Enzo Doria	04/2016
3048	2^356351-112237	107273	Enzo Doria	06/2014
3049	(6^137845-11)/5	107264	Paul Bourdelais	11/2011
3050	2^356322+74539	107264	Enzo Doria	04/2016
3051	2^356274+1874479	107250	Enzo Doria	06/2016
3052	20^82422-93	107234	Lelio R Paula	02/2017
3053	2^356157-20365	107214	Enzo Doria	06/2013
3054	2^356129-18949	107206	Enzo Doria	05/2013
3055	2^356100-109587	107197	Enzo Doria	04/2014
3056	(31*2^355970+1)/5	107159	Lelio R Paula	03/2014
3057	2^355968-64875	107158	Lelio R Paula	01/2017
3058	2^355952+1870321	107153	Enzo Doria	05/2016
3059	2^355915-117	107142	Lelio R Paula	11/2011
3060	(16*10^107140+77)/3	107141	Robert Price	03/2019
3061	(19*2^355838-1)/15	107119	Lelio R Paula	03/2014
3062	3^224495-8	107112	Lelio R Paula	12/2013
3063	7^126691-44	107067	Lelio R Paula	03/2017
3064	4^177830-8243	107065	Mike Oakes	02/2011
3065	2^355524-21237	107024	Enzo Doria	06/2013
3066	(10223*2^355515+1)/4855	107022	Lelio R Paula	07/2014
3067	2^355494-19901	107015	Enzo Doria	06/2013
3068	2^355454-869688105	107003	Lelio R Paula	01/2017
3069	2^355366+54615	106976	Lelio R Paula	01/2017
3070	(31*2^355346-1)/1563	106969	Lelio R Paula	03/2014
3071	2^355275-19861	106949	Enzo Doria	06/2013
3072	(9179*2^355234-1)/1915	106937	Lelio R Paula	05/2015
3073	4*10^106892-3	106893	Robert Price	10/2015
3074	(66^58741+1)/67	106881	Paul Bourdelais	08/2017
3075	2^354946-3	106850	M. Frind & P. Underwood	08/2002
3076	2^354873-18693	106828	Enzo Doria	05/2013
3077	2^354828+4257	106814	Lelio R Paula	01/2017
3078	436^40459+40459^436	106791	Norbert Schneider	03/2019
3079	(21^80761+1)/22	106783	Paul Bourdelais	03/2010
3080	2^354640-354640+1	106758	Robert Price	10/2014
3081	2^354585+95	106741	Lelio R Paula	10/2011
3082	2^354553+189	106732	Lelio R Paula	10/2011
3083	2^354514-109031	106720	Enzo Doria	04/2014
3084	2^354509-109465	106718	Enzo Doria	04/2014
3085	(15*2^354478-1)/26983	106706	Lelio R Paula	03/2014
3086	Phi(217618,10)/899798636917	106693	Makoto Kamada	06/2019
3087	15^90710+28	106684	Lelio R Paula	04/2017
3088	7^126237+34	106683	Lelio R Paula	03/2017
3089	2^354385-115315	106681	Enzo Doria	06/2015
3090	2^354327-19305	106664	Enzo Doria	06/2013
3091	(35*10^106649+1)/9	106650	Serge Batalov	11/2010
3092	10^106636+97	106637	Lelio R Paula	02/2017
3093	10^106636-22923	106636	Patrick De Geest	03/2017
3094	2^354220-57	106631	Lelio R Paula	10/2011
3095	2^354157-17041	106612	Enzo Doria	05/2013
3096	12^98778+73	106600	Lelio R Paula	02/2017
3097	2^354064+1870651	106584	Enzo Doria	05/2016
3098	2^353992-57	106563	Lelio R Paula	10/2011
3099	NSW(139160)	106535	Robert Price	12/2018
3100	(7*10^106516+113)/3	106517	Robert Price	02/2018
3101	2^353832-1853849	106515	Enzo Doria	09/2015
3102	(7^126037-1)/6	106513	Paul Bourdelais	09/2008
3103	2^353794-18453	106503	Enzo Doria	05/2013
3104	2^353728+7695	106483	Lelio R Paula	01/2017
3105	2^353672-303	106466	Yves Minet	02/2012
3106	6^136811+101	106460	Lelio R Paula	02/2017
3107	2^353641+1871981	106457	Enzo Doria	05/2016
3108	(8*10^106454-29)/3	106455	Robert Price	07/2018
3109	2^353553+54615	106431	Lelio R Paula	01/2017
3110	2^353544-18897	106428	Enzo Doria	05/2013
3111	6^136729-133	106396	Lelio R Paula	02/2017
3112	2^353418+1605	106390	Lelio R Paula	01/2017
3113	2^353387+65	106381	Lelio R Paula	10/2011
3114	2^353372+74311	106376	Enzo Doria	04/2016
3115	2^353344-3693	106368	Yves Minet	03/2017
3116	2^353277-20089	106347	Enzo Doria	06/2013
3117	2^353275+72173	106347	Enzo Doria	04/2016
3118	2^353268-17705	106345	Enzo Doria	05/2013
3119	2^353267-19857	106344	Enzo Doria	06/2013
3120	(46*10^106343+143)/9	106344	Robert Price	01/2019
3121	222748^3+3^222748	106278	Anatoly F. Selevich	12/2010
3122	(9179*2^353019-1)/9	106273	Lelio R Paula	05/2015
3123	2^353025+72257	106272	Enzo Doria	04/2016
3124	2^352932-20345	106244	Enzo Doria	06/2013
3125	(2^353011-3)/745325861246794515484535	106244	Lelio R Paula	12/2013
3126	2^352883-187	106229	Lelio R Paula	10/2011
3127	20^81649-19^81649	106228	Jean-Louis Charton	03/2011
3128	(55*10^106222+377)/9	106223	Robert Price	02/2019
3129	2^352814-131	106208	Lelio R Paula	10/2011
3130	2^352752+73951	106189	Enzo Doria	04/2016
3131	6^136434+5	106167	Lelio R Paula	11/2014
3132	8*10^106157-13	106158	Robert Price	08/2019
3133	7*5^151872-8	106155	Lelio R Paula	11/2014
3134	105^52520-2	106153	Lelio R Paula	10/2017
3135	2^352601-1604809	106144	Enzo Doria	05/2015
3136	12^98353-43	106141	Lelio R Paula	02/2017
3137	2^352585-18901	106139	Enzo Doria	05/2013
3138	(2^352554-3)/193	106128	Lelio R Paula	12/2013
3139	2^352540+15015	106126	Lelio R Paula	01/2017
3140	2^352524-3149	106121	Yves Minet	10/2014
3141	2^352486-1858781	106109	Enzo Doria	04/2016
3142	2^352444+12705	106097	Lelio R Paula	01/2017
3143	2^352228-18953	106032	Enzo Doria	05/2013
3144	2^352107+1872533	105995	Enzo Doria	05/2016
3145	2^352066-2591	105983	Yves Minet	07/2014
3146	2^352030+715	105972	Lelio R Paula	10/2011
3147	9*6^136176-5	105967	Lelio R Paula	11/2014
3148	17099*2^351991+58329	105965	Paul Vanderveen	12/2017
3149	155^48377+2	105962	Lelio R Paula	08/2013
3150	2^351865+1869707	105922	Enzo Doria	05/2016
3151	2^351831+23	105912	Lelio R Paula	10/2011
3152	9*2^351784-5	105899	Lelio R Paula	09/2014
3153	2^351671-112387	105864	Enzo Doria	06/2014
3154	2^351669-109501	105863	Enzo Doria	04/2014
3155	2^351644+74731	105856	Enzo Doria	04/2016
3156	13^95025-42	105853	Lelio R Paula	12/2016
3157	2^351599+15015	105842	Lelio R Paula	01/2017
3158	19^82763+90	105834	Lelio R Paula	01/2017
3159	(9179*2^351540-1)/221	105826	Lelio R Paula	05/2015
3160	20^81329-51	105812	Lelio R Paula	01/2017
3161	(5*10^105811+211)/9	105811	Robert Price	02/2018
3162	2^351483+28425	105807	Lelio R Paula	01/2017
3163	15^89960+86	105802	Lelio R Paula	02/2017
3164	2^351460-17289	105801	Enzo Doria	05/2013
3165	19^82735+22	105798	Lelio R Paula	01/2017
3166	2^351435-109077	105793	Enzo Doria	04/2014
3167	2^351393+1089	105780	Lelio R Paula	01/2017
3168	2^351364+72631	105772	Enzo Doria	04/2016
3169	2^351305+1872467	105754	Enzo Doria	05/2016
3170	3^221649+16	105754	Lelio R Paula	11/2016
3171	8*3^221637-5	105749	Lelio R Paula	09/2014
3172	2^351279-2780449	105746	Enzo Doria	03/2016
3173	15^89903-26	105735	Lelio R Paula	02/2017
3174	2^351213-73	105726	Lelio R Paula	10/2011
3175	2^351192-4589	105720	Yves Minet	07/2011
3176	20^81250-33	105709	Lelio R Paula	12/2016
3177	2^351076-113159	105685	Enzo Doria	07/2014
3178	93^53688-2	105684	Lelio R Paula	09/2013
3179	2^351060-4559	105680	Yves Minet	07/2011
3180	((10^52836-1)10000/9+5927)10^52836+(10^52836-1)/9	105676	Hans Havermann	08/2019
3181	11^101473-750	105674	Enzo Doria	11/2012
3182	3*5^151181-8	105672	Lelio R Paula	11/2014
3183	15^89831-34	105650	Lelio R Paula	02/2017
3185	11^101448-360	105648	Enzo Doria	08/2012
3184	3*7^125011+4	105648	Lelio R Paula	11/2014
3186	2^350943-113269	105645	Enzo Doria	07/2014
3187	2^350868-19725	105622	Enzo Doria	06/2013
3188	2^350858-59291	105619	Enzo Doria	10/2015
3189	2^350851+135	105617	Lelio R Paula	10/2011
3190	2^350841-741	105614	Lelio R Paula	01/2017
3191	3*10^105582+77	105583	Robert Price	09/2018
3192	8*10^105571+3	105572	Robert Price	08/2015
3193	2^350674-78557	105564	Jorge Menendez	03/2018
3194	2*5^151026-3	105563	Lelio R Paula	11/2014
3195	(2^350702+5)/34264674063	105562	Lelio R Paula	12/2013
3196	6^135647-5^135647	105554	Jean-Louis Charton	02/2009
3197	3^221211+236	105545	Lelio R Paula	11/2016
3198	(32*10^105530-77)/9	105531	Robert Price	06/2018
3199	10^105515+33	105516	Lelio R Paula	11/2016
3200	10^105515-41033	105515	Patrick De Geest	12/2016
3201	(29*2^350473-1)/267927	105499	Lelio R Paula	03/2014
3202	17^85732-72	105489	Lelio R Paula	01/2017
3203	2^350307-110329	105453	Enzo Doria	05/2014
3204	2^350253-20365	105437	Enzo Doria	06/2013
3205	(3*29^72089-1075)/4	105423	Curtis Bright	05/2015
3206	2^350139-109009	105403	Enzo Doria	04/2014
3207	3*5^150763+4	105380	Lelio R Paula	11/2014
3208	12^97643+91	105375	Lelio R Paula	02/2017
3209	6*5^150744-7	105367	Lelio R Paula	11/2014
3210	2^349996-112169	105360	Enzo Doria	06/2014
3211	11^101142-1080	105329	Enzo Doria	12/2012
3212	(68*10^105320-41)/9	105321	Robert Price	10/2013
3213	3^220712-9934	105307	Enzo Doria	05/2014
3214	7*10^105296+9	105297	Robert Price	09/2015
3215	2^349739+1873373	105282	Enzo Doria	06/2016
3216	7^124574+24	105278	Lelio R Paula	11/2016
3217	2^349708-20957	105273	Enzo Doria	06/2013
3218	2^349649-20469	105255	Enzo Doria	06/2013
3219	2^349607-20109	105243	Enzo Doria	06/2013
3220	2^349594-19085	105239	Enzo Doria	05/2013
3221	2^349530+1874479	105220	Enzo Doria	06/2016
3222	(3^220528+8)/8081	105215	Lelio R Paula	12/2013
3223	3^220464-112852	105189	Enzo Doria	07/2014
3224	2^349419-17349	105186	Enzo Doria	05/2013
3225	2^349400-2579	105180	Yves Minet	07/2014
3226	8*5^150471+3	105176	Lelio R Paula	11/2014
3227	655^37342+37342^655	105165	Norbert Schneider	08/2018
3228	13^94403+94	105160	Lelio R Paula	12/2016
3229	2^349301-112309	105151	Enzo Doria	06/2014
3230	9*2^349220+5	105127	Lelio R Paula	09/2014
3231	7*3^220317+8	105119	Lelio R Paula	09/2014
3232	7^124386+88	105119	Lelio R Paula	11/2016
3233	2^349171-19657	105111	Enzo Doria	06/2013
3234	(2^(6*58185+1)-5)/3	105093	Kevin Acres	11/2013
3235	(2^349111-5)/3	105093	Lelio R Paula	12/2013
3236	675^37142+37142^675	105087	Norbert Schneider	08/2018
3237	2^348981-2797573	105054	Enzo Doria	04/2016
3238	2^348869-6555	105021	Lelio R Paula	01/2017
3239	5^150217+78	104998	Lelio R Paula	11/2016
3240	2^348703-113005	104971	Enzo Doria	06/2014
3242	2^348612-809	104943	Yves Minet	05/2013
3241	(73*10^104942-1)/9	104943	Robert Price	01/2015
3243	2^348583-350407	104934	Enzo Doria	06/2015
3244	2^348531-949	104919	Yves Minet	05/2012
3245	20^80636-59	104910	Lelio R Paula	12/2016
3246	8*10^104893-13	104894	Robert Price	08/2019
3247	2^348437+35	104890	Lelio R Paula	09/2011
3248	2^348348+135	104864	Lelio R Paula	09/2011
3250	(2^348284+9)/25	104843	Lelio R Paula	12/2013
3249	75^55914-74	104843	Norbert Schneider	01/2015

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PRP Records

Probable Primes Top 10000

(253476 PRPs in the top)