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	2^360641-113185	108564	Enzo Doria	07/2014
3002	2^360618+75019	108557	Enzo Doria	04/2016
3003	(14*10^108545-221)/9	108546	Robert Price	04/2018
3004	(44*10^108544-233)/9	108545	Robert Price	01/2019
3005	3*5^155286+2	108541	Lelio R Paula	11/2014
3006	7^128422+4	108530	Lelio R Paula	11/2014
3007	7^128421-80	108529	Lelio R Paula	03/2017
3008	2^360497+53807	108521	Yves Minet	07/2010
3009	2^360468-4559	108512	Yves Minet	03/2019
3010	2^360366+1459	108481	Lelio R Paula	09/2011
3011	2^360364-1499	108481	Yves Minet	05/2013
3012	14^94642-23	108472	Lelio R Paula	05/2017
3013	4*10^108412+9	108413	Robert Price	05/2015
3014	133^51042-132	108406	Norbert Schneider	02/2019
3015	2^360093-351103	108399	Enzo Doria	06/2015
3016	2^360042+723	108384	Lelio R Paula	01/2012
3017	85^56164-2	108364	Lelio R Paula	10/2013
3018	2^359937-29323	108352	Enzo Doria	07/2015
3019	2^359898-19997	108341	Enzo Doria	06/2013
3020	2*5^154948-7	108305	Lelio R Paula	11/2014
3021	10^108303+13	108304	Lelio R Paula	02/2017
3022	10^108303-207959	108303	Patrick De Geest	03/2017
3023	7*10^108300+69	108301	Robert Price	07/2019
3024	2^359730+753	108290	Lelio R Paula	12/2011
3025	(8*10^108273+13)/3	108274	Robert Price	06/2018
3026	2^359650-19797	108266	Enzo Doria	06/2013
3027	91^55259-90^55259	108255	Robert Price	07/2015
3028	4*10^108238-71	108239	Robert Price	12/2018
3029	3^226845+68	108233	Lelio R Paula	03/2017
3030	5^154822-12866	108216	Enzo Doria	05/2014
3031	(9*2^359480+1)/5	108215	Lelio R Paula	03/2014
3032	2^359454-177	108207	Lelio R Paula	12/2011
3033	(19*10^108184+191)/3	108185	Robert Price	05/2019
3034	6^139022-59	108181	Lelio R Paula	02/2017
3035	(19*10^108176-43)/3	108177	Robert Price	05/2019
3036	2^359352-179	108176	Lelio R Paula	12/2011
3037	2^359338-1858781	108172	Enzo Doria	04/2016
3038	12^100230-97	108167	Lelio R Paula	03/2017
3039	(25*2^359297-1)/137	108159	Lelio R Paula	03/2014
3040	(2^359262-509203)/9	108148	Lelio R Paula	12/2013
3041	(3^226648-8)/352715633	108131	Lelio R Paula	12/2013
3042	6^138956-59	108129	Lelio R Paula	02/2017
3043	2^359184+30285	108126	Lelio R Paula	04/2017
3044	13^97059+10	108119	Lelio R Paula	03/2017
3045	2^359137-81	108112	Lelio R Paula	12/2011
3047	(15185*2^359105-1)/567	108103	Lelio R Paula	05/2015
3046	2^359110-11655	108103	Lelio R Paula	04/2017
3048	8*6^138875+5	108067	Lelio R Paula	11/2014
3049	2^358987-216919	108066	Enzo Doria	05/2014
3050	39^67918-67918^39	108062	Norbert Schneider	02/2017
3051	2^358785-16933	108006	Enzo Doria	05/2013
3052	(2^358783+5)/33383	108000	Lelio R Paula	12/2013
3053	6^138770-77	107985	Lelio R Paula	02/2017
3054	(2^358727-1017)/94178479	107980	Lelio R Paula	12/2013
3055	10^107976+19	107977	Lelio R Paula	02/2017
3056	10^107976-202103	107976	Patrick De Geest	03/2017
3057	2^358684+75781	107975	Enzo Doria	04/2016
3058	99^54094+2	107952	Lelio R Paula	06/2013
3059	(2^358583-9)/391	107942	Lelio R Paula	12/2013
3060	2^358538+55	107931	Lelio R Paula	12/2011
3061	2^358517-109009	107925	Enzo Doria	03/2014
3062	3^226159+104	107906	Lelio R Paula	03/2017
3063	2^358310-11655	107863	Lelio R Paula	03/2017
3064	2^358275-112987	107852	Enzo Doria	07/2014
3065	2^358233-20005	107839	Enzo Doria	06/2013
3066	2^358194+175	107828	Lelio R Paula	12/2011
3067	107^53125-106	107812	Norbert Schneider	12/2016
3068	(25*10^107804+161)/3	107805	Robert Price	09/2019
3069	3^225922-2	107793	Lelio R Paula	10/2013
3070	12^99874-95	107783	Lelio R Paula	03/2017
3071	2^358030-171	107778	Lelio R Paula	12/2011
3072	11^103488-4170	107772	Enzo Doria	12/2012
3073	2^357930-4547	107748	Yves Minet	03/2019
3074	2^357911-20089	107742	Enzo Doria	06/2013
3075	2^357885+12857	107735	Yves Minet	07/2010
3076	(248587#+9289)/(71327111512899)	107733	Makoto Morimoto	06/2019
3077	7^127473+40	107728	Lelio R Paula	03/2017
3078	5*2^357850+9	107725	Lelio R Paula	09/2014
3079	2^357786-291191	107705	Enzo Doria	06/2015
3080	18^85798-23	107700	Lelio R Paula	04/2017
3081	(14*10^107694-83)/3	107695	Robert Price	12/2018
3082	2^357688-1854269	107675	Enzo Doria	09/2015
3083	2^357671-112225	107670	Enzo Doria	06/2014
3084	2^357618-21005	107654	Enzo Doria	06/2013
3085	2^357615-17505	107653	Enzo Doria	05/2013
3086	(30^72871-1)/29	107638	Robert Price	12/2011
3087	2^357521+1870217	107625	Enzo Doria	05/2016
3088	2^357477-1203	107612	Lelio R Paula	03/2017
3089	5^153894-18	107568	Lelio R Paula	02/2017
3090	2^357324-69059	107566	Enzo Doria	11/2015
3091	467^40296+40296^467	107563	Norbert Schneider	03/2019
3092	2^357283-869688105	107553	Lelio R Paula	01/2017
3093	2^357280-16805	107552	Enzo Doria	05/2013
3094	10^107547+481719	107548	Patrick De Geest	03/2017
3095	10^107547-47	107547	Lelio R Paula	02/2017
3096	17^87396-32	107537	Lelio R Paula	04/2017
3097	2^357081+107	107493	Lelio R Paula	12/2011
3098	2^357058-3911	107486	Yves Minet	04/2017
3099	3^225274+64	107484	Lelio R Paula	03/2017
3100	18^85619-95	107476	Lelio R Paula	04/2017
3101	3^225248-130	107471	Lelio R Paula	03/2017
3102	(5*2^356961+1)/143	107455	Lelio R Paula	03/2014
3103	2^356935-18085	107449	Enzo Doria	05/2013
3104	10^107409+37	107410	Lelio R Paula	02/2017
3105	10^107409-329633	107409	Patrick De Geest	03/2017
3106	2^356787-109027	107404	Enzo Doria	04/2014
3107	(2^356767+78557)/5	107397	Lelio R Paula	12/2013
3108	3*10^107389+77	107390	Robert Price	09/2018
3109	5^153622-42	107378	Lelio R Paula	02/2017
3110	2^356699-97305	107378	Lelio R Paula	03/2017
3111	2^356654+85	107364	Lelio R Paula	11/2011
3112	2^356641-19921	107360	Enzo Doria	06/2013
3113	5*10^107355+11	107356	Robert Price	08/2019
3114	2^356623-465	107355	Lelio R Paula	03/2017
3115	19^83945-92	107345	Lelio R Paula	02/2017
3116	10^107334+28149	107335	Patrick De Geest	03/2017
3117	10^107334-83	107334	Lelio R Paula	02/2017
3118	2^356518+885	107323	Lelio R Paula	03/2017
3119	(3*2^356506-1)/467	107317	Lelio R Paula	03/2014
3120	2^356442-114713	107300	Enzo Doria	04/2015
3121	2^356425+72257	107295	Enzo Doria	04/2016
3122	2^356351-112237	107273	Enzo Doria	06/2014
3124	(6^137845-11)/5	107264	Paul Bourdelais	11/2011
3123	2^356322+74539	107264	Enzo Doria	04/2016
3125	2^356274+1874479	107250	Enzo Doria	06/2016
3126	20^82422-93	107234	Lelio R Paula	02/2017
3127	2^356157-20365	107214	Enzo Doria	06/2013
3128	2^356129-18949	107206	Enzo Doria	05/2013
3129	2^356100-109587	107197	Enzo Doria	04/2014
3130	(31*2^355970+1)/5	107159	Lelio R Paula	03/2014
3131	2^355968-64875	107158	Lelio R Paula	01/2017
3132	2^355952+1870321	107153	Enzo Doria	05/2016
3133	2^355915-117	107142	Lelio R Paula	11/2011
3134	(16*10^107140+77)/3	107141	Robert Price	03/2019
3135	(19*2^355838-1)/15	107119	Lelio R Paula	03/2014
3136	3^224495-8	107112	Lelio R Paula	12/2013
3137	7^126691-44	107067	Lelio R Paula	03/2017
3138	4^177830-8243	107065	Mike Oakes	02/2011
3139	2^355524-21237	107024	Enzo Doria	06/2013
3140	(10223*2^355515+1)/4855	107022	Lelio R Paula	07/2014
3141	2^355494-19901	107015	Enzo Doria	06/2013
3142	2^355454-869688105	107003	Lelio R Paula	01/2017
3143	2^355366+54615	106976	Lelio R Paula	01/2017
3144	(31*2^355346-1)/1563	106969	Lelio R Paula	03/2014
3145	2^355275-19861	106949	Enzo Doria	06/2013
3146	(9179*2^355234-1)/1915	106937	Lelio R Paula	05/2015
3147	4*10^106892-3	106893	Robert Price	10/2015
3148	(66^58741+1)/67	106881	Paul Bourdelais	08/2017
3149	2^354946-3	106850	M. Frind & P. Underwood	08/2002
3150	2^354873-18693	106828	Enzo Doria	05/2013
3151	2^354828+4257	106814	Lelio R Paula	01/2017
3152	436^40459+40459^436	106791	Norbert Schneider	03/2019
3153	(21^80761+1)/22	106783	Paul Bourdelais	03/2010
3154	2^354640-354640+1	106758	Robert Price	10/2014
3155	2^354585+95	106741	Lelio R Paula	10/2011
3156	2^354553+189	106732	Lelio R Paula	10/2011
3157	2^354514-109031	106720	Enzo Doria	04/2014
3158	2^354509-109465	106718	Enzo Doria	04/2014
3159	(15*2^354478-1)/26983	106706	Lelio R Paula	03/2014
3160	Phi(217618,10)/899798636917	106693	Makoto Kamada	06/2019
3161	15^90710+28	106684	Lelio R Paula	04/2017
3162	7^126237+34	106683	Lelio R Paula	03/2017
3163	2^354385-115315	106681	Enzo Doria	06/2015
3164	2^354327-19305	106664	Enzo Doria	06/2013
3165	(35*10^106649+1)/9	106650	Serge Batalov	11/2010
3166	10^106636+97	106637	Lelio R Paula	02/2017
3167	10^106636-22923	106636	Patrick De Geest	03/2017
3168	2^354220-57	106631	Lelio R Paula	10/2011
3169	2^354157-17041	106612	Enzo Doria	05/2013
3170	12^98778+73	106600	Lelio R Paula	02/2017
3171	2^354064+1870651	106584	Enzo Doria	05/2016
3172	2^353992-57	106563	Lelio R Paula	10/2011
3173	NSW(139160)	106535	Robert Price	12/2018
3174	(7*10^106516+113)/3	106517	Robert Price	02/2018
3175	2^353832-1853849	106515	Enzo Doria	09/2015
3176	(7^126037-1)/6	106513	Paul Bourdelais	09/2008
3177	2^353794-18453	106503	Enzo Doria	05/2013
3178	2^353728+7695	106483	Lelio R Paula	01/2017
3179	2^353672-303	106466	Yves Minet	02/2012
3180	6^136811+101	106460	Lelio R Paula	02/2017
3181	2^353641+1871981	106457	Enzo Doria	05/2016
3182	(8*10^106454-29)/3	106455	Robert Price	07/2018
3183	2^353553+54615	106431	Lelio R Paula	01/2017
3184	2^353544-18897	106428	Enzo Doria	05/2013
3185	6^136729-133	106396	Lelio R Paula	02/2017
3186	2^353418+1605	106390	Lelio R Paula	01/2017
3187	2^353387+65	106381	Lelio R Paula	10/2011
3188	2^353372+74311	106376	Enzo Doria	04/2016
3189	2^353344-3693	106368	Yves Minet	03/2017
3191	2^353277-20089	106347	Enzo Doria	06/2013
3190	2^353275+72173	106347	Enzo Doria	04/2016
3192	2^353268-17705	106345	Enzo Doria	05/2013
3193	2^353267-19857	106344	Enzo Doria	06/2013
3194	(46*10^106343+143)/9	106344	Robert Price	01/2019
3195	222748^3+3^222748	106278	Anatoly F. Selevich	12/2010
3196	(9179*2^353019-1)/9	106273	Lelio R Paula	05/2015
3197	2^353025+72257	106272	Enzo Doria	04/2016
3199	2^352932-20345	106244	Enzo Doria	06/2013
3198	(2^353011-3)/745325861246794515484535	106244	Lelio R Paula	12/2013
3200	2^352883-187	106229	Lelio R Paula	10/2011
3201	20^81649-19^81649	106228	Jean-Louis Charton	03/2011
3202	(55*10^106222+377)/9	106223	Robert Price	02/2019
3203	2^352814-131	106208	Lelio R Paula	10/2011
3204	2^352752+73951	106189	Enzo Doria	04/2016
3205	6^136434+5	106167	Lelio R Paula	11/2014
3206	8*10^106157-13	106158	Robert Price	08/2019
3207	7*5^151872-8	106155	Lelio R Paula	11/2014
3208	105^52520-2	106153	Lelio R Paula	10/2017
3209	2^352601-1604809	106144	Enzo Doria	05/2015
3210	12^98353-43	106141	Lelio R Paula	02/2017
3211	2^352585-18901	106139	Enzo Doria	05/2013
3212	(2^352554-3)/193	106128	Lelio R Paula	12/2013
3213	2^352540+15015	106126	Lelio R Paula	01/2017
3214	2^352524-3149	106121	Yves Minet	10/2014
3215	2^352486-1858781	106109	Enzo Doria	04/2016
3216	2^352444+12705	106097	Lelio R Paula	01/2017
3217	2^352228-18953	106032	Enzo Doria	05/2013
3218	2^352107+1872533	105995	Enzo Doria	05/2016
3219	2^352066-2591	105983	Yves Minet	07/2014
3220	2^352030+715	105972	Lelio R Paula	10/2011
3221	9*6^136176-5	105967	Lelio R Paula	11/2014
3222	17099*2^351991+58329	105965	Paul Vanderveen	12/2017
3223	155^48377+2	105962	Lelio R Paula	08/2013
3224	2^351865+1869707	105922	Enzo Doria	05/2016
3225	2^351831+23	105912	Lelio R Paula	10/2011
3226	9*2^351784-5	105899	Lelio R Paula	09/2014
3227	2^351671-112387	105864	Enzo Doria	06/2014
3228	2^351669-109501	105863	Enzo Doria	04/2014
3229	2^351644+74731	105856	Enzo Doria	04/2016
3230	13^95025-42	105853	Lelio R Paula	12/2016
3231	2^351599+15015	105842	Lelio R Paula	01/2017
3232	19^82763+90	105834	Lelio R Paula	01/2017
3233	(9179*2^351540-1)/221	105826	Lelio R Paula	05/2015
3234	20^81329-51	105812	Lelio R Paula	01/2017
3235	(5*10^105811+211)/9	105811	Robert Price	02/2018
3236	2^351483+28425	105807	Lelio R Paula	01/2017
3237	15^89960+86	105802	Lelio R Paula	02/2017
3238	2^351460-17289	105801	Enzo Doria	05/2013
3239	19^82735+22	105798	Lelio R Paula	01/2017
3240	2^351435-109077	105793	Enzo Doria	04/2014
3241	2^351393+1089	105780	Lelio R Paula	01/2017
3242	2^351364+72631	105772	Enzo Doria	04/2016
3244	2^351305+1872467	105754	Enzo Doria	05/2016
3243	3^221649+16	105754	Lelio R Paula	11/2016
3245	8*3^221637-5	105749	Lelio R Paula	09/2014
3246	2^351279-2780449	105746	Enzo Doria	03/2016
3247	15^89903-26	105735	Lelio R Paula	02/2017
3248	2^351213-73	105726	Lelio R Paula	10/2011
3249	2^351192-4589	105720	Yves Minet	07/2011
3250	20^81250-33	105709	Lelio R Paula	12/2016

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Probable Primes Top 10000

(255244 PRPs in the top)