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	20^81649-19^81649	106228	Jean-Louis Charton	03/2011
3002	(55*10^106222+377)/9	106223	Robert Price	02/2019
3003	2^352814-131	106208	Lelio R Paula	10/2011
3004	2^352752+73951	106189	Enzo Doria	04/2016
3005	6^136434+5	106167	Lelio R Paula	11/2014
3006	7*5^151872-8	106155	Lelio R Paula	11/2014
3007	105^52520-2	106153	Lelio R Paula	10/2017
3008	2^352601-1604809	106144	Enzo Doria	05/2015
3009	12^98353-43	106141	Lelio R Paula	02/2017
3010	2^352585-18901	106139	Enzo Doria	05/2013
3011	(2^352554-3)/193	106128	Lelio R Paula	12/2013
3012	2^352540+15015	106126	Lelio R Paula	01/2017
3013	2^352524-3149	106121	Yves Minet	10/2014
3014	2^352486-1858781	106109	Enzo Doria	04/2016
3015	2^352444+12705	106097	Lelio R Paula	01/2017
3016	2^352228-18953	106032	Enzo Doria	05/2013
3017	2^352107+1872533	105995	Enzo Doria	05/2016
3018	2^352066-2591	105983	Yves Minet	07/2014
3019	2^352030+715	105972	Lelio R Paula	10/2011
3020	9*6^136176-5	105967	Lelio R Paula	11/2014
3021	17099*2^351991+58329	105965	Paul Vanderveen	12/2017
3022	155^48377+2	105962	Lelio R Paula	08/2013
3023	2^351865+1869707	105922	Enzo Doria	05/2016
3024	2^351831+23	105912	Lelio R Paula	10/2011
3025	9*2^351784-5	105899	Lelio R Paula	09/2014
3026	2^351671-112387	105864	Enzo Doria	06/2014
3027	2^351669-109501	105863	Enzo Doria	04/2014
3028	2^351644+74731	105856	Enzo Doria	04/2016
3029	13^95025-42	105853	Lelio R Paula	12/2016
3030	2^351599+15015	105842	Lelio R Paula	01/2017
3031	19^82763+90	105834	Lelio R Paula	01/2017
3032	(9179*2^351540-1)/221	105826	Lelio R Paula	05/2015
3033	20^81329-51	105812	Lelio R Paula	01/2017
3034	(5*10^105811+211)/9	105811	Robert Price	02/2018
3035	2^351483+28425	105807	Lelio R Paula	01/2017
3036	15^89960+86	105802	Lelio R Paula	02/2017
3037	2^351460-17289	105801	Enzo Doria	05/2013
3038	19^82735+22	105798	Lelio R Paula	01/2017
3039	2^351435-109077	105793	Enzo Doria	04/2014
3040	2^351393+1089	105780	Lelio R Paula	01/2017
3041	2^351364+72631	105772	Enzo Doria	04/2016
3042	2^351305+1872467	105754	Enzo Doria	05/2016
3043	3^221649+16	105754	Lelio R Paula	11/2016
3044	8*3^221637-5	105749	Lelio R Paula	09/2014
3045	2^351279-2780449	105746	Enzo Doria	03/2016
3046	15^89903-26	105735	Lelio R Paula	02/2017
3047	2^351213-73	105726	Lelio R Paula	10/2011
3048	2^351192-4589	105720	Yves Minet	07/2011
3049	20^81250-33	105709	Lelio R Paula	12/2016
3050	2^351076-113159	105685	Enzo Doria	07/2014
3051	93^53688-2	105684	Lelio R Paula	09/2013
3052	2^351060-4559	105680	Yves Minet	07/2011
3053	11^101473-750	105674	Enzo Doria	11/2012
3054	3*5^151181-8	105672	Lelio R Paula	11/2014
3055	15^89831-34	105650	Lelio R Paula	02/2017
3057	11^101448-360	105648	Enzo Doria	08/2012
3056	3*7^125011+4	105648	Lelio R Paula	11/2014
3058	2^350943-113269	105645	Enzo Doria	07/2014
3059	2^350868-19725	105622	Enzo Doria	06/2013
3060	2^350858-59291	105619	Enzo Doria	10/2015
3061	2^350851+135	105617	Lelio R Paula	10/2011
3062	2^350841-741	105614	Lelio R Paula	01/2017
3063	3*10^105582+77	105583	Robert Price	09/2018
3064	8*10^105571+3	105572	Robert Price	08/2015
3065	2^350674-78557	105564	Jorge Menendez	03/2018
3066	2*5^151026-3	105563	Lelio R Paula	11/2014
3067	(2^350702+5)/34264674063	105562	Lelio R Paula	12/2013
3068	6^135647-5^135647	105554	Jean-Louis Charton	02/2009
3069	3^221211+236	105545	Lelio R Paula	11/2016
3070	(32*10^105530-77)/9	105531	Robert Price	06/2018
3071	10^105515+33	105516	Lelio R Paula	11/2016
3072	10^105515-41033	105515	Patrick De Geest	12/2016
3073	(29*2^350473-1)/267927	105499	Lelio R Paula	03/2014
3074	17^85732-72	105489	Lelio R Paula	01/2017
3075	2^350307-110329	105453	Enzo Doria	05/2014
3076	2^350253-20365	105437	Enzo Doria	06/2013
3077	(3*29^72089-1075)/4	105423	Curtis Bright	05/2015
3078	2^350139-109009	105403	Enzo Doria	04/2014
3079	3*5^150763+4	105380	Lelio R Paula	11/2014
3080	12^97643+91	105375	Lelio R Paula	02/2017
3081	6*5^150744-7	105367	Lelio R Paula	11/2014
3082	2^349996-112169	105360	Enzo Doria	06/2014
3083	11^101142-1080	105329	Enzo Doria	12/2012
3084	(68*10^105320-41)/9	105321	Robert Price	10/2013
3085	3^220712-9934	105307	Enzo Doria	05/2014
3086	7*10^105296+9	105297	Robert Price	09/2015
3087	2^349739+1873373	105282	Enzo Doria	06/2016
3088	7^124574+24	105278	Lelio R Paula	11/2016
3089	2^349708-20957	105273	Enzo Doria	06/2013
3090	2^349649-20469	105255	Enzo Doria	06/2013
3091	2^349607-20109	105243	Enzo Doria	06/2013
3092	2^349594-19085	105239	Enzo Doria	05/2013
3093	2^349530+1874479	105220	Enzo Doria	06/2016
3094	(3^220528+8)/8081	105215	Lelio R Paula	12/2013
3095	3^220464-112852	105189	Enzo Doria	07/2014
3096	2^349419-17349	105186	Enzo Doria	05/2013
3097	2^349400-2579	105180	Yves Minet	07/2014
3098	8*5^150471+3	105176	Lelio R Paula	11/2014
3099	655^37342+37342^655	105165	Norbert Schneider	08/2018
3100	13^94403+94	105160	Lelio R Paula	12/2016
3101	2^349301-112309	105151	Enzo Doria	06/2014
3102	9*2^349220+5	105127	Lelio R Paula	09/2014
3103	7*3^220317+8	105119	Lelio R Paula	09/2014
3104	7^124386+88	105119	Lelio R Paula	11/2016
3105	2^349171-19657	105111	Enzo Doria	06/2013
3106	(2^(6*58185+1)-5)/3	105093	Kevin Acres	11/2013
3107	(2^349111-5)/3	105093	Lelio R Paula	12/2013
3108	675^37142+37142^675	105087	Norbert Schneider	08/2018
3109	2^348981-2797573	105054	Enzo Doria	04/2016
3110	2^348869-6555	105021	Lelio R Paula	01/2017
3111	5^150217+78	104998	Lelio R Paula	11/2016
3112	2^348703-113005	104971	Enzo Doria	06/2014
3114	2^348612-809	104943	Yves Minet	05/2013
3113	(73*10^104942-1)/9	104943	Robert Price	01/2015
3115	2^348583-350407	104934	Enzo Doria	06/2015
3116	2^348531-949	104919	Yves Minet	05/2012
3117	20^80636-59	104910	Lelio R Paula	12/2016
3118	2^348437+35	104890	Lelio R Paula	09/2011
3119	2^348348+135	104864	Lelio R Paula	09/2011
3121	(2^348284+9)/25	104843	Lelio R Paula	12/2013
3120	75^55914-74	104843	Norbert Schneider	01/2015
3122	2^348268+255255	104840	Lelio R Paula	01/2017
3123	5^149985-52	104836	Lelio R Paula	11/2016
3124	2^348224-20249	104826	Enzo Doria	06/2013
3125	2^348212-20105	104823	Enzo Doria	06/2013
3126	20^80562+19	104814	Lelio R Paula	12/2016
3127	2*10^104811-87	104812	Robert Price	04/2018
3128	2^348149-20053	104804	Enzo Doria	06/2013
3129	2^348095-171	104788	Lelio R Paula	09/2011
3130	2^348003-20377	104760	Enzo Doria	06/2013
3131	2^347994-741	104757	Lelio R Paula	12/2016
3132	(13*2^347972-1)/282309	104746	Lelio R Paula	03/2014
3133	2^347910-109937	104732	Enzo Doria	04/2014
3134	5^149794+28	104702	Lelio R Paula	11/2016
3135	105^51800-2	104698	Lelio R Paula	10/2017
3136	(16^86939+3^86939)/19	104684	Robert Price	06/2013
3137	(15^89009-1)/14	104682	Paul Bourdelais	03/2010
3138	2^347731-18609	104678	Enzo Doria	05/2013
3139	4*6^134519+7	104677	Lelio R Paula	11/2014
3140	2^347612-18545	104642	Enzo Doria	05/2013
3141	6^134465+95	104635	Lelio R Paula	11/2016
3142	2^347517-17301	104614	Enzo Doria	05/2013
3143	3^219222-310	104596	Lelio R Paula	11/2016
3144	(15*2^347399-1)/13	104578	Lelio R Paula	03/2014
3145	2^347372-17853	104570	Enzo Doria	05/2013
3146	2^347314+99	104552	Lelio R Paula	09/2011
3147	2^347300-22233	104548	Enzo Doria	06/2013
3148	2^347287-19845	104544	Enzo Doria	06/2013
3149	(31*2^347254-1)/891	104533	Lelio R Paula	03/2014
3150	5F(250091)(F(250091)-1)+1	104532	Serge Batalov	04/2015
3151	7*2^347239-3	104531	Lelio R Paula	09/2014
3152	(3^219098-8)/514147439969	104525	Lelio R Paula	12/2013
3153	5*3^219047+8	104513	Lelio R Paula	09/2014
3154	2^347148-109073	104502	Enzo Doria	04/2014
3155	2^347129-20145	104497	Enzo Doria	06/2013
3156	4*10^104461-57	104462	Robert Price	10/2018
3157	2^346923-19585	104435	Enzo Doria	05/2013
3158	(11*2^346864-1)/175	104416	Lelio R Paula	03/2014
3159	2^346854+346854^2+1	104414	Robert Price	06/2014
3160	2^346834+11715	104408	Lelio R Paula	04/2015
3161	79^55009+78	104387	Norbert Schneider	02/2015
3162	3^218744+58	104368	Lelio R Paula	11/2016
3163	2^346649+65	104352	Lelio R Paula	09/2011
3164	2^346638-17265	104349	Enzo Doria	05/2013
3165	5*10^104326+77	104327	Robert Price	12/2018
3167	2^346527-111817	104316	Enzo Doria	05/2014
3166	6^134055+101	104316	Lelio R Paula	11/2016
3168	6^134013+163	104283	Lelio R Paula	11/2016
3169	18^83049-89	104250	Lelio R Paula	01/2017
3170	2^346213+484049	104221	Enzo Doria	04/2017
3171	18^83021-91	104214	Lelio R Paula	01/2017
3172	10^104212+128779	104213	Patrick De Geest	05/2016
3173	10^104212+237447	104213	Patrick De Geest	05/2016
3174	10^104212+242139	104213	Patrick De Geest	05/2016
3175	10^104212+269199	104213	Patrick De Geest	05/2016
3176	(10^104212-71)/1	104212	Serge Batalov	12/2014
3177	2^346078+7695	104180	Lelio R Paula	12/2016
3179	2^346055-19537	104173	Enzo Doria	05/2013
3178	(3*2^346057+1)/77	104173	Lelio R Paula	12/2013
3180	2^346037-20125	104168	Enzo Doria	06/2013
3181	(34*10^104168-7)/9/13/551179	104162	Makoto Morimoto	05/2016
3182	6^133854-17993	104159	Enzo Doria	03/2013
3183	2^345990+1874239	104154	Enzo Doria	06/2016
3184	2^345988-20373	104153	Enzo Doria	06/2013
3185	(26*10^104132-503)/9	104133	Robert Price	07/2018
3186	3*5^148968+8	104125	Lelio R Paula	11/2014
3187	(7*10^104113+53)/3	104114	Robert Price	05/2018
3188	p(21253)#/2+8	104113	Robert Price	01/2017
3189	322^41507+41507^322	104094	Norbert Schneider	12/2014
3190	6^133768-17423	104092	Enzo Doria	03/2013
3191	2^345786-19557	104092	Enzo Doria	05/2013
3192	171^46606-2	104072	Lelio R Paula	10/2017
3193	2^345704-149	104068	Lelio R Paula	09/2011
3194	6^133704-17273	104042	Enzo Doria	02/2013
3195	(3*2^345590-1)/23	104033	Lelio R Paula	03/2014
3196	(19*2^345590+1)/33859	104030	Lelio R Paula	12/2013
3197	2^345547+11	104021	Lelio R Paula	09/2011
3198	2^345504+723	104008	Lelio R Paula	09/2011
3199	2^345498-20037	104006	Enzo Doria	06/2013
3200	18^82854-37	104005	Lelio R Paula	01/2017
3201	2^345486-109065	104002	Enzo Doria	04/2014
3202	2^345487-1851507	104002	Enzo Doria	08/2015
3203	2^345476+777	103999	Lelio R Paula	09/2011
3204	4*10^103981-83	103982	Robert Price	10/2018
3205	(5*2^345321-1)/3	103953	Lelio R Paula	03/2014
3206	(2^345267-9)/539049127	103927	Lelio R Paula	12/2013
3207	(78557*2^345163+1)/78589	103905	Lelio R Paula	07/2014
3208	2^345106-112181	103888	Enzo Doria	06/2014
3209	2^345079+99	103880	Lelio R Paula	09/2011
3210	11^99736-1500	103865	Enzo Doria	12/2012
3211	2^344842-20157	103808	Enzo Doria	06/2013
3212	(47*2^344822+1)/1071	103801	Lelio R Paula	05/2015
3213	2^344802-20765	103796	Enzo Doria	06/2013
3214	2^344794-3821	103794	Yves Minet	05/2011
3215	2^344782-109103	103790	Enzo Doria	04/2014
3216	3^217521-112292	103784	Enzo Doria	06/2014
3217	2^344759-3505	103783	Lelio R Paula	11/2016
3218	2^344735-147	103776	Lelio R Paula	09/2011
3219	L(496533)-p(496533)	103770	Robert Price	02/2018
3220	2*10^103749-69	103750	Robert Price	03/2018
3221	(55459*2^344617+1)/3	103745	Lelio R Paula	07/2014
3222	2^344607-108891	103738	Enzo Doria	03/2014
3223	2^344541-19561	103718	Enzo Doria	05/2013
3224	(1017*2^344529-1)/569	103714	Lelio R Paula	05/2015
3225	(4*10^103703-1)/3	103704	Serge Batalov	08/2009
3226	2^344444-455	103688	Yves Minet	03/2012
3227	(1353^238539617^9)/10^307661	103673	Hans Havermann	06/2017
3228	2^344317-109933	103650	Enzo Doria	04/2014
3229	2^344309-1852033	103648	Enzo Doria	08/2015
3230	2^344213-21253	103619	Enzo Doria	06/2013
3231	2^344196-465	103614	Lelio R Paula	11/2016
3232	2^344187-20001	103611	Enzo Doria	06/2013
3233	(117191#+(355573#)/(117191#))/(200233679)	103602	Makoto Morimoto	10/2017
3234	20^79621-19^79621	103590	Jean-Louis Charton	03/2011
3235	Phi(155391,10)/1243129	103586	Maksym Voznyy	09/2015
3236	2^344085-20365	103580	Enzo Doria	06/2013
3237	5^148169+54	103566	Lelio R Paula	11/2016
3238	2^344017-108795	103560	Enzo Doria	03/2014
3239	2^343971-5077	103546	Lelio R Paula	09/2011
3240	(7*10^103531+71)/3	103532	Robert Price	05/2018
3241	2^343899+141	103524	Lelio R Paula	08/2011
3242	(2^343933+1)/(3*98294339989393)	103520	Gord Palameta	08/2018
3243	6^133029-67	103517	Lelio R Paula	11/2016
3244	(17*2^343877+1)/13625	103515	Lelio R Paula	12/2013
3245	(136*10^103474-1)/9	103476	Serge Batalov	12/2014
3246	5^148014-24	103458	Lelio R Paula	11/2016
3247	2^343604+9931	103436	Yves Minet	01/2011
3248	2^343601-21189	103435	Enzo Doria	06/2013
3249	2^343508-115229	103407	Enzo Doria	06/2015
3250	(509203*2^343491-1)/16147	103403	Lelio R Paula	05/2015

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PRP Records

Probable Primes Top 10000

(252675 PRPs in the top)