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	4*10^106892-3	106893	Robert Price	10/2015
3002	(66^58741+1)/67	106881	Paul Bourdelais	08/2017
3003	2^354946-3	106850	M. Frind & P. Underwood	08/2002
3004	2^354873-18693	106828	Enzo Doria	05/2013
3005	2^354828+4257	106814	Lelio R Paula	01/2017
3006	436^40459+40459^436	106791	Norbert Schneider	03/2019
3007	(21^80761+1)/22	106783	Paul Bourdelais	03/2010
3008	2^354640-354640+1	106758	Robert Price	10/2014
3009	2^354585+95	106741	Lelio R Paula	10/2011
3010	2^354553+189	106732	Lelio R Paula	10/2011
3011	2^354514-109031	106720	Enzo Doria	04/2014
3012	2^354509-109465	106718	Enzo Doria	04/2014
3013	(15*2^354478-1)/26983	106706	Lelio R Paula	03/2014
3014	15^90710+28	106684	Lelio R Paula	04/2017
3015	7^126237+34	106683	Lelio R Paula	03/2017
3016	2^354385-115315	106681	Enzo Doria	06/2015
3017	2^354327-19305	106664	Enzo Doria	06/2013
3018	(35*10^106649+1)/9	106650	Serge Batalov	11/2010
3019	10^106636+97	106637	Lelio R Paula	02/2017
3020	10^106636-22923	106636	Patrick De Geest	03/2017
3021	2^354220-57	106631	Lelio R Paula	10/2011
3022	2^354157-17041	106612	Enzo Doria	05/2013
3023	12^98778+73	106600	Lelio R Paula	02/2017
3024	2^354064+1870651	106584	Enzo Doria	05/2016
3025	2^353992-57	106563	Lelio R Paula	10/2011
3026	NSW(139160)	106535	Robert Price	12/2018
3027	(7*10^106516+113)/3	106517	Robert Price	02/2018
3028	2^353832-1853849	106515	Enzo Doria	09/2015
3029	(7^126037-1)/6	106513	Paul Bourdelais	09/2008
3030	2^353794-18453	106503	Enzo Doria	05/2013
3031	2^353728+7695	106483	Lelio R Paula	01/2017
3032	2^353672-303	106466	Yves Minet	02/2012
3033	6^136811+101	106460	Lelio R Paula	02/2017
3034	2^353641+1871981	106457	Enzo Doria	05/2016
3035	(8*10^106454-29)/3	106455	Robert Price	07/2018
3036	2^353553+54615	106431	Lelio R Paula	01/2017
3037	2^353544-18897	106428	Enzo Doria	05/2013
3038	6^136729-133	106396	Lelio R Paula	02/2017
3039	2^353418+1605	106390	Lelio R Paula	01/2017
3040	2^353387+65	106381	Lelio R Paula	10/2011
3041	2^353372+74311	106376	Enzo Doria	04/2016
3042	2^353344-3693	106368	Yves Minet	03/2017
3044	2^353277-20089	106347	Enzo Doria	06/2013
3043	2^353275+72173	106347	Enzo Doria	04/2016
3045	2^353268-17705	106345	Enzo Doria	05/2013
3046	2^353267-19857	106344	Enzo Doria	06/2013
3047	(46*10^106343+143)/9	106344	Robert Price	01/2019
3048	222748^3+3^222748	106278	Anatoly F. Selevich	12/2010
3049	(9179*2^353019-1)/9	106273	Lelio R Paula	05/2015
3050	2^353025+72257	106272	Enzo Doria	04/2016
3051	2^352932-20345	106244	Enzo Doria	06/2013
3052	(2^353011-3)/745325861246794515484535	106244	Lelio R Paula	12/2013
3053	2^352883-187	106229	Lelio R Paula	10/2011
3054	20^81649-19^81649	106228	Jean-Louis Charton	03/2011
3055	(55*10^106222+377)/9	106223	Robert Price	02/2019
3056	2^352814-131	106208	Lelio R Paula	10/2011
3057	2^352752+73951	106189	Enzo Doria	04/2016
3058	6^136434+5	106167	Lelio R Paula	11/2014
3059	7*5^151872-8	106155	Lelio R Paula	11/2014
3060	105^52520-2	106153	Lelio R Paula	10/2017
3061	2^352601-1604809	106144	Enzo Doria	05/2015
3062	12^98353-43	106141	Lelio R Paula	02/2017
3063	2^352585-18901	106139	Enzo Doria	05/2013
3064	(2^352554-3)/193	106128	Lelio R Paula	12/2013
3065	2^352540+15015	106126	Lelio R Paula	01/2017
3066	2^352524-3149	106121	Yves Minet	10/2014
3067	2^352486-1858781	106109	Enzo Doria	04/2016
3068	2^352444+12705	106097	Lelio R Paula	01/2017
3069	2^352228-18953	106032	Enzo Doria	05/2013
3070	2^352107+1872533	105995	Enzo Doria	05/2016
3071	2^352066-2591	105983	Yves Minet	07/2014
3072	2^352030+715	105972	Lelio R Paula	10/2011
3073	9*6^136176-5	105967	Lelio R Paula	11/2014
3074	17099*2^351991+58329	105965	Paul Vanderveen	12/2017
3075	155^48377+2	105962	Lelio R Paula	08/2013
3076	2^351865+1869707	105922	Enzo Doria	05/2016
3077	2^351831+23	105912	Lelio R Paula	10/2011
3078	9*2^351784-5	105899	Lelio R Paula	09/2014
3079	2^351671-112387	105864	Enzo Doria	06/2014
3080	2^351669-109501	105863	Enzo Doria	04/2014
3081	2^351644+74731	105856	Enzo Doria	04/2016
3082	13^95025-42	105853	Lelio R Paula	12/2016
3083	2^351599+15015	105842	Lelio R Paula	01/2017
3084	19^82763+90	105834	Lelio R Paula	01/2017
3085	(9179*2^351540-1)/221	105826	Lelio R Paula	05/2015
3086	20^81329-51	105812	Lelio R Paula	01/2017
3087	(5*10^105811+211)/9	105811	Robert Price	02/2018
3088	2^351483+28425	105807	Lelio R Paula	01/2017
3089	15^89960+86	105802	Lelio R Paula	02/2017
3090	2^351460-17289	105801	Enzo Doria	05/2013
3091	19^82735+22	105798	Lelio R Paula	01/2017
3092	2^351435-109077	105793	Enzo Doria	04/2014
3093	2^351393+1089	105780	Lelio R Paula	01/2017
3094	2^351364+72631	105772	Enzo Doria	04/2016
3095	2^351305+1872467	105754	Enzo Doria	05/2016
3096	3^221649+16	105754	Lelio R Paula	11/2016
3097	8*3^221637-5	105749	Lelio R Paula	09/2014
3098	2^351279-2780449	105746	Enzo Doria	03/2016
3099	15^89903-26	105735	Lelio R Paula	02/2017
3100	2^351213-73	105726	Lelio R Paula	10/2011
3101	2^351192-4589	105720	Yves Minet	07/2011
3102	20^81250-33	105709	Lelio R Paula	12/2016
3103	2^351076-113159	105685	Enzo Doria	07/2014
3104	93^53688-2	105684	Lelio R Paula	09/2013
3105	2^351060-4559	105680	Yves Minet	07/2011
3106	11^101473-750	105674	Enzo Doria	11/2012
3107	3*5^151181-8	105672	Lelio R Paula	11/2014
3108	15^89831-34	105650	Lelio R Paula	02/2017
3110	11^101448-360	105648	Enzo Doria	08/2012
3109	3*7^125011+4	105648	Lelio R Paula	11/2014
3111	2^350943-113269	105645	Enzo Doria	07/2014
3112	2^350868-19725	105622	Enzo Doria	06/2013
3113	2^350858-59291	105619	Enzo Doria	10/2015
3114	2^350851+135	105617	Lelio R Paula	10/2011
3115	2^350841-741	105614	Lelio R Paula	01/2017
3116	3*10^105582+77	105583	Robert Price	09/2018
3117	8*10^105571+3	105572	Robert Price	08/2015
3118	2^350674-78557	105564	Jorge Menendez	03/2018
3119	2*5^151026-3	105563	Lelio R Paula	11/2014
3120	(2^350702+5)/34264674063	105562	Lelio R Paula	12/2013
3121	6^135647-5^135647	105554	Jean-Louis Charton	02/2009
3122	3^221211+236	105545	Lelio R Paula	11/2016
3123	(32*10^105530-77)/9	105531	Robert Price	06/2018
3124	10^105515+33	105516	Lelio R Paula	11/2016
3125	10^105515-41033	105515	Patrick De Geest	12/2016
3126	(29*2^350473-1)/267927	105499	Lelio R Paula	03/2014
3127	17^85732-72	105489	Lelio R Paula	01/2017
3128	2^350307-110329	105453	Enzo Doria	05/2014
3129	2^350253-20365	105437	Enzo Doria	06/2013
3130	(3*29^72089-1075)/4	105423	Curtis Bright	05/2015
3131	2^350139-109009	105403	Enzo Doria	04/2014
3132	3*5^150763+4	105380	Lelio R Paula	11/2014
3133	12^97643+91	105375	Lelio R Paula	02/2017
3134	6*5^150744-7	105367	Lelio R Paula	11/2014
3135	2^349996-112169	105360	Enzo Doria	06/2014
3136	11^101142-1080	105329	Enzo Doria	12/2012
3137	(68*10^105320-41)/9	105321	Robert Price	10/2013
3138	3^220712-9934	105307	Enzo Doria	05/2014
3139	7*10^105296+9	105297	Robert Price	09/2015
3140	2^349739+1873373	105282	Enzo Doria	06/2016
3141	7^124574+24	105278	Lelio R Paula	11/2016
3142	2^349708-20957	105273	Enzo Doria	06/2013
3143	2^349649-20469	105255	Enzo Doria	06/2013
3144	2^349607-20109	105243	Enzo Doria	06/2013
3145	2^349594-19085	105239	Enzo Doria	05/2013
3146	2^349530+1874479	105220	Enzo Doria	06/2016
3147	(3^220528+8)/8081	105215	Lelio R Paula	12/2013
3148	3^220464-112852	105189	Enzo Doria	07/2014
3149	2^349419-17349	105186	Enzo Doria	05/2013
3150	2^349400-2579	105180	Yves Minet	07/2014
3151	8*5^150471+3	105176	Lelio R Paula	11/2014
3152	655^37342+37342^655	105165	Norbert Schneider	08/2018
3153	13^94403+94	105160	Lelio R Paula	12/2016
3154	2^349301-112309	105151	Enzo Doria	06/2014
3155	9*2^349220+5	105127	Lelio R Paula	09/2014
3156	7*3^220317+8	105119	Lelio R Paula	09/2014
3157	7^124386+88	105119	Lelio R Paula	11/2016
3158	2^349171-19657	105111	Enzo Doria	06/2013
3159	(2^(6*58185+1)-5)/3	105093	Kevin Acres	11/2013
3160	(2^349111-5)/3	105093	Lelio R Paula	12/2013
3161	675^37142+37142^675	105087	Norbert Schneider	08/2018
3162	2^348981-2797573	105054	Enzo Doria	04/2016
3163	2^348869-6555	105021	Lelio R Paula	01/2017
3164	5^150217+78	104998	Lelio R Paula	11/2016
3165	2^348703-113005	104971	Enzo Doria	06/2014
3167	2^348612-809	104943	Yves Minet	05/2013
3166	(73*10^104942-1)/9	104943	Robert Price	01/2015
3168	2^348583-350407	104934	Enzo Doria	06/2015
3169	2^348531-949	104919	Yves Minet	05/2012
3170	20^80636-59	104910	Lelio R Paula	12/2016
3171	2^348437+35	104890	Lelio R Paula	09/2011
3172	2^348348+135	104864	Lelio R Paula	09/2011
3174	(2^348284+9)/25	104843	Lelio R Paula	12/2013
3173	75^55914-74	104843	Norbert Schneider	01/2015
3175	2^348268+255255	104840	Lelio R Paula	01/2017
3176	5^149985-52	104836	Lelio R Paula	11/2016
3177	2^348224-20249	104826	Enzo Doria	06/2013
3178	2^348212-20105	104823	Enzo Doria	06/2013
3179	20^80562+19	104814	Lelio R Paula	12/2016
3180	2*10^104811-87	104812	Robert Price	04/2018
3181	2^348149-20053	104804	Enzo Doria	06/2013
3182	2^348095-171	104788	Lelio R Paula	09/2011
3183	2^348003-20377	104760	Enzo Doria	06/2013
3184	2^347994-741	104757	Lelio R Paula	12/2016
3185	(13*2^347972-1)/282309	104746	Lelio R Paula	03/2014
3186	2^347910-109937	104732	Enzo Doria	04/2014
3187	5^149794+28	104702	Lelio R Paula	11/2016
3188	105^51800-2	104698	Lelio R Paula	10/2017
3189	(16^86939+3^86939)/19	104684	Robert Price	06/2013
3190	(15^89009-1)/14	104682	Paul Bourdelais	03/2010
3191	2^347731-18609	104678	Enzo Doria	05/2013
3192	4*6^134519+7	104677	Lelio R Paula	11/2014
3193	2^347612-18545	104642	Enzo Doria	05/2013
3194	6^134465+95	104635	Lelio R Paula	11/2016
3195	2^347517-17301	104614	Enzo Doria	05/2013
3196	3^219222-310	104596	Lelio R Paula	11/2016
3197	(15*2^347399-1)/13	104578	Lelio R Paula	03/2014
3198	2^347372-17853	104570	Enzo Doria	05/2013
3199	2^347314+99	104552	Lelio R Paula	09/2011
3200	2^347300-22233	104548	Enzo Doria	06/2013
3201	2^347287-19845	104544	Enzo Doria	06/2013
3202	(31*2^347254-1)/891	104533	Lelio R Paula	03/2014
3203	5F(250091)(F(250091)-1)+1	104532	Serge Batalov	04/2015
3204	7*2^347239-3	104531	Lelio R Paula	09/2014
3205	(3^219098-8)/514147439969	104525	Lelio R Paula	12/2013
3206	5*3^219047+8	104513	Lelio R Paula	09/2014
3207	2^347148-109073	104502	Enzo Doria	04/2014
3208	2^347129-20145	104497	Enzo Doria	06/2013
3209	4*10^104461-57	104462	Robert Price	10/2018
3210	2^346923-19585	104435	Enzo Doria	05/2013
3211	(11*2^346864-1)/175	104416	Lelio R Paula	03/2014
3212	2^346854+346854^2+1	104414	Robert Price	06/2014
3213	2^346834+11715	104408	Lelio R Paula	04/2015
3214	79^55009+78	104387	Norbert Schneider	02/2015
3215	3^218744+58	104368	Lelio R Paula	11/2016
3216	2^346649+65	104352	Lelio R Paula	09/2011
3217	2^346638-17265	104349	Enzo Doria	05/2013
3218	5*10^104326+77	104327	Robert Price	12/2018
3220	2^346527-111817	104316	Enzo Doria	05/2014
3219	6^134055+101	104316	Lelio R Paula	11/2016
3221	6^134013+163	104283	Lelio R Paula	11/2016
3222	18^83049-89	104250	Lelio R Paula	01/2017
3223	2^346213+484049	104221	Enzo Doria	04/2017
3224	18^83021-91	104214	Lelio R Paula	01/2017
3225	10^104212+128779	104213	Patrick De Geest	05/2016
3226	10^104212+237447	104213	Patrick De Geest	05/2016
3227	10^104212+242139	104213	Patrick De Geest	05/2016
3228	10^104212+269199	104213	Patrick De Geest	05/2016
3229	(10^104212-71)/1	104212	Serge Batalov	12/2014
3230	2^346078+7695	104180	Lelio R Paula	12/2016
3231	2^346055-19537	104173	Enzo Doria	05/2013
3232	(3*2^346057+1)/77	104173	Lelio R Paula	12/2013
3233	2^346037-20125	104168	Enzo Doria	06/2013
3234	(34*10^104168-7)/9/13/551179	104162	Makoto Morimoto	05/2016
3235	6^133854-17993	104159	Enzo Doria	03/2013
3236	2^345990+1874239	104154	Enzo Doria	06/2016
3237	2^345988-20373	104153	Enzo Doria	06/2013
3238	(26*10^104132-503)/9	104133	Robert Price	07/2018
3239	3*5^148968+8	104125	Lelio R Paula	11/2014
3240	(7*10^104113+53)/3	104114	Robert Price	05/2018
3241	p(21253)#/2+8	104113	Robert Price	01/2017
3242	322^41507+41507^322	104094	Norbert Schneider	12/2014
3243	6^133768-17423	104092	Enzo Doria	03/2013
3244	2^345786-19557	104092	Enzo Doria	05/2013
3245	171^46606-2	104072	Lelio R Paula	10/2017
3246	2^345704-149	104068	Lelio R Paula	09/2011
3247	6^133704-17273	104042	Enzo Doria	02/2013
3248	(3*2^345590-1)/23	104033	Lelio R Paula	03/2014
3249	(19*2^345590+1)/33859	104030	Lelio R Paula	12/2013
3250	2^345547+11	104021	Lelio R Paula	09/2011

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PRP Records

Probable Primes Top 10000

(252932 PRPs in the top)