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	8*10^105571+3	105572	Robert Price	08/2015
3002	2^350674-78557	105564	Jorge Menendez	03/2018
3003	2*5^151026-3	105563	Lelio R Paula	11/2014
3004	(2^350702+5)/34264674063	105562	Lelio R Paula	12/2013
3005	6^135647-5^135647	105554	Jean-Louis Charton	02/2009
3006	3^221211+236	105545	Lelio R Paula	11/2016
3007	(32*10^105530-77)/9	105531	Robert Price	06/2018
3008	10^105515+33	105516	Lelio R Paula	11/2016
3009	10^105515-41033	105515	Patrick De Geest	12/2016
3010	(29*2^350473-1)/267927	105499	Lelio R Paula	03/2014
3011	17^85732-72	105489	Lelio R Paula	01/2017
3012	2^350307-110329	105453	Enzo Doria	05/2014
3013	2^350253-20365	105437	Enzo Doria	06/2013
3014	(3*29^72089-1075)/4	105423	Curtis Bright	05/2015
3015	2^350139-109009	105403	Enzo Doria	04/2014
3016	3*5^150763+4	105380	Lelio R Paula	11/2014
3017	12^97643+91	105375	Lelio R Paula	02/2017
3018	6*5^150744-7	105367	Lelio R Paula	11/2014
3019	2^349996-112169	105360	Enzo Doria	06/2014
3020	11^101142-1080	105329	Enzo Doria	12/2012
3021	(68*10^105320-41)/9	105321	Robert Price	10/2013
3022	3^220712-9934	105307	Enzo Doria	05/2014
3023	7*10^105296+9	105297	Robert Price	09/2015
3024	2^349739+1873373	105282	Enzo Doria	06/2016
3025	7^124574+24	105278	Lelio R Paula	11/2016
3026	2^349708-20957	105273	Enzo Doria	06/2013
3027	2^349649-20469	105255	Enzo Doria	06/2013
3028	2^349607-20109	105243	Enzo Doria	06/2013
3029	2^349594-19085	105239	Enzo Doria	05/2013
3030	2^349530+1874479	105220	Enzo Doria	06/2016
3031	(3^220528+8)/8081	105215	Lelio R Paula	12/2013
3032	3^220464-112852	105189	Enzo Doria	07/2014
3033	2^349419-17349	105186	Enzo Doria	05/2013
3034	2^349400-2579	105180	Yves Minet	07/2014
3035	8*5^150471+3	105176	Lelio R Paula	11/2014
3036	655^37342+37342^655	105165	Norbert Schneider	08/2018
3037	13^94403+94	105160	Lelio R Paula	12/2016
3038	2^349301-112309	105151	Enzo Doria	06/2014
3039	9*2^349220+5	105127	Lelio R Paula	09/2014
3040	7*3^220317+8	105119	Lelio R Paula	09/2014
3041	7^124386+88	105119	Lelio R Paula	11/2016
3042	2^349171-19657	105111	Enzo Doria	06/2013
3043	(2^(6*58185+1)-5)/3	105093	Kevin Acres	11/2013
3044	(2^349111-5)/3	105093	Lelio R Paula	12/2013
3045	675^37142+37142^675	105087	Norbert Schneider	08/2018
3046	2^348981-2797573	105054	Enzo Doria	04/2016
3047	2^348869-6555	105021	Lelio R Paula	01/2017
3048	5^150217+78	104998	Lelio R Paula	11/2016
3049	2^348703-113005	104971	Enzo Doria	06/2014
3051	2^348612-809	104943	Yves Minet	05/2013
3050	(73*10^104942-1)/9	104943	Robert Price	01/2015
3052	2^348583-350407	104934	Enzo Doria	06/2015
3053	2^348531-949	104919	Yves Minet	05/2012
3054	20^80636-59	104910	Lelio R Paula	12/2016
3055	2^348437+35	104890	Lelio R Paula	09/2011
3056	2^348348+135	104864	Lelio R Paula	09/2011
3057	(2^348284+9)/25	104843	Lelio R Paula	12/2013
3058	75^55914-74	104843	Norbert Schneider	01/2015
3059	2^348268+255255	104840	Lelio R Paula	01/2017
3060	5^149985-52	104836	Lelio R Paula	11/2016
3061	2^348224-20249	104826	Enzo Doria	06/2013
3062	2^348212-20105	104823	Enzo Doria	06/2013
3063	20^80562+19	104814	Lelio R Paula	12/2016
3064	2*10^104811-87	104812	Robert Price	04/2018
3065	2^348149-20053	104804	Enzo Doria	06/2013
3066	2^348095-171	104788	Lelio R Paula	09/2011
3067	2^348003-20377	104760	Enzo Doria	06/2013
3068	2^347994-741	104757	Lelio R Paula	12/2016
3069	(13*2^347972-1)/282309	104746	Lelio R Paula	03/2014
3070	2^347910-109937	104732	Enzo Doria	04/2014
3071	5^149794+28	104702	Lelio R Paula	11/2016
3072	105^51800-2	104698	Lelio R Paula	10/2017
3073	(16^86939+3^86939)/19	104684	Robert Price	06/2013
3074	(15^89009-1)/14	104682	Paul Bourdelais	03/2010
3075	2^347731-18609	104678	Enzo Doria	05/2013
3076	4*6^134519+7	104677	Lelio R Paula	11/2014
3077	2^347612-18545	104642	Enzo Doria	05/2013
3078	6^134465+95	104635	Lelio R Paula	11/2016
3079	2^347517-17301	104614	Enzo Doria	05/2013
3080	3^219222-310	104596	Lelio R Paula	11/2016
3081	(15*2^347399-1)/13	104578	Lelio R Paula	03/2014
3082	2^347372-17853	104570	Enzo Doria	05/2013
3083	2^347314+99	104552	Lelio R Paula	09/2011
3084	2^347300-22233	104548	Enzo Doria	06/2013
3085	2^347287-19845	104544	Enzo Doria	06/2013
3086	(31*2^347254-1)/891	104533	Lelio R Paula	03/2014
3087	5F(250091)(F(250091)-1)+1	104532	Serge Batalov	04/2015
3088	7*2^347239-3	104531	Lelio R Paula	09/2014
3089	(3^219098-8)/514147439969	104525	Lelio R Paula	12/2013
3090	5*3^219047+8	104513	Lelio R Paula	09/2014
3091	2^347148-109073	104502	Enzo Doria	04/2014
3092	2^347129-20145	104497	Enzo Doria	06/2013
3093	4*10^104461-57	104462	Robert Price	10/2018
3094	2^346923-19585	104435	Enzo Doria	05/2013
3095	(11*2^346864-1)/175	104416	Lelio R Paula	03/2014
3096	2^346854+346854^2+1	104414	Robert Price	06/2014
3097	2^346834+11715	104408	Lelio R Paula	04/2015
3098	79^55009+78	104387	Norbert Schneider	02/2015
3099	3^218744+58	104368	Lelio R Paula	11/2016
3100	2^346649+65	104352	Lelio R Paula	09/2011
3101	2^346638-17265	104349	Enzo Doria	05/2013
3102	5*10^104326+77	104327	Robert Price	12/2018
3104	2^346527-111817	104316	Enzo Doria	05/2014
3103	6^134055+101	104316	Lelio R Paula	11/2016
3105	6^134013+163	104283	Lelio R Paula	11/2016
3106	18^83049-89	104250	Lelio R Paula	01/2017
3107	2^346213+484049	104221	Enzo Doria	04/2017
3108	18^83021-91	104214	Lelio R Paula	01/2017
3109	10^104212+128779	104213	Patrick De Geest	05/2016
3110	10^104212+237447	104213	Patrick De Geest	05/2016
3111	10^104212+242139	104213	Patrick De Geest	05/2016
3112	10^104212+269199	104213	Patrick De Geest	05/2016
3113	(10^104212-71)/1	104212	Serge Batalov	12/2014
3114	2^346078+7695	104180	Lelio R Paula	12/2016
3115	2^346055-19537	104173	Enzo Doria	05/2013
3116	(3*2^346057+1)/77	104173	Lelio R Paula	12/2013
3117	2^346037-20125	104168	Enzo Doria	06/2013
3118	(34*10^104168-7)/9/13/551179	104162	Makoto Morimoto	05/2016
3119	6^133854-17993	104159	Enzo Doria	03/2013
3120	2^345990+1874239	104154	Enzo Doria	06/2016
3121	2^345988-20373	104153	Enzo Doria	06/2013
3122	(26*10^104132-503)/9	104133	Robert Price	07/2018
3123	3*5^148968+8	104125	Lelio R Paula	11/2014
3124	(7*10^104113+53)/3	104114	Robert Price	05/2018
3125	p(21253)#/2+8	104113	Robert Price	01/2017
3126	322^41507+41507^322	104094	Norbert Schneider	12/2014
3127	6^133768-17423	104092	Enzo Doria	03/2013
3128	2^345786-19557	104092	Enzo Doria	05/2013
3129	171^46606-2	104072	Lelio R Paula	10/2017
3130	2^345704-149	104068	Lelio R Paula	09/2011
3131	6^133704-17273	104042	Enzo Doria	02/2013
3132	(3*2^345590-1)/23	104033	Lelio R Paula	03/2014
3133	(19*2^345590+1)/33859	104030	Lelio R Paula	12/2013
3134	2^345547+11	104021	Lelio R Paula	09/2011
3135	2^345504+723	104008	Lelio R Paula	09/2011
3136	2^345498-20037	104006	Enzo Doria	06/2013
3137	18^82854-37	104005	Lelio R Paula	01/2017
3138	2^345486-109065	104002	Enzo Doria	04/2014
3139	2^345487-1851507	104002	Enzo Doria	08/2015
3140	2^345476+777	103999	Lelio R Paula	09/2011
3141	4*10^103981-83	103982	Robert Price	10/2018
3142	(5*2^345321-1)/3	103953	Lelio R Paula	03/2014
3143	(2^345267-9)/539049127	103927	Lelio R Paula	12/2013
3144	(78557*2^345163+1)/78589	103905	Lelio R Paula	07/2014
3145	2^345106-112181	103888	Enzo Doria	06/2014
3146	2^345079+99	103880	Lelio R Paula	09/2011
3147	11^99736-1500	103865	Enzo Doria	12/2012
3148	2^344842-20157	103808	Enzo Doria	06/2013
3149	(47*2^344822+1)/1071	103801	Lelio R Paula	05/2015
3150	2^344802-20765	103796	Enzo Doria	06/2013
3151	2^344794-3821	103794	Yves Minet	05/2011
3152	2^344782-109103	103790	Enzo Doria	04/2014
3153	3^217521-112292	103784	Enzo Doria	06/2014
3154	2^344759-3505	103783	Lelio R Paula	11/2016
3155	2^344735-147	103776	Lelio R Paula	09/2011
3156	L(496533)-p(496533)	103770	Robert Price	02/2018
3157	2*10^103749-69	103750	Robert Price	03/2018
3158	(55459*2^344617+1)/3	103745	Lelio R Paula	07/2014
3159	2^344607-108891	103738	Enzo Doria	03/2014
3160	2^344541-19561	103718	Enzo Doria	05/2013
3161	(1017*2^344529-1)/569	103714	Lelio R Paula	05/2015
3162	(4*10^103703-1)/3	103704	Serge Batalov	08/2009
3163	2^344444-455	103688	Yves Minet	03/2012
3164	(1353^238539617^9)/10^307661	103673	Hans Havermann	06/2017
3165	2^344317-109933	103650	Enzo Doria	04/2014
3166	2^344309-1852033	103648	Enzo Doria	08/2015
3167	2^344213-21253	103619	Enzo Doria	06/2013
3168	2^344196-465	103614	Lelio R Paula	11/2016
3169	2^344187-20001	103611	Enzo Doria	06/2013
3170	(117191#+(355573#)/(117191#))/(200233679)	103602	Makoto Morimoto	10/2017
3171	20^79621-19^79621	103590	Jean-Louis Charton	03/2011
3172	Phi(155391,10)/1243129	103586	Maksym Voznyy	09/2015
3173	2^344085-20365	103580	Enzo Doria	06/2013
3174	5^148169+54	103566	Lelio R Paula	11/2016
3175	2^344017-108795	103560	Enzo Doria	03/2014
3176	2^343971-5077	103546	Lelio R Paula	09/2011
3177	(7*10^103531+71)/3	103532	Robert Price	05/2018
3178	2^343899+141	103524	Lelio R Paula	08/2011
3179	(2^343933+1)/(3*98294339989393)	103520	Gord Palameta	08/2018
3180	6^133029-67	103517	Lelio R Paula	11/2016
3181	(17*2^343877+1)/13625	103515	Lelio R Paula	12/2013
3182	(136*10^103474-1)/9	103476	Serge Batalov	12/2014
3183	5^148014-24	103458	Lelio R Paula	11/2016
3184	2^343604+9931	103436	Yves Minet	01/2011
3185	2^343601-21189	103435	Enzo Doria	06/2013
3186	2^343508-115229	103407	Enzo Doria	06/2015
3187	(509203*2^343491-1)/16147	103403	Lelio R Paula	05/2015
3188	3^216685-113056	103386	Enzo Doria	07/2014
3189	44^62903-43^62903	103379	Jean-Louis Charton	08/2012
3190	11^99262-20	103371	Lelio R Paula	12/2016
3191	(509203*2^343357-1)/5	103366	Lelio R Paula	05/2015
3193	2^343356-2791889	103361	Enzo Doria	03/2016
3192	(25*10^103360-241)/9	103361	Robert Price	05/2018
3194	Phi(104989,10)/2939693	103350	Maksym Voznyy	09/2015
3195	2^343182-171	103309	Lelio R Paula	08/2011
3196	(23619^23619+23620^23620)/7187	103294	David Broadhurst	09/2009
3197	2^343079-1835611	103278	Enzo Doria	05/2015
3198	2^343063-1147	103273	Yves Minet	06/2013
3199	9*6^132689+7	103254	Lelio R Paula	11/2014
3200	2^342979-18085	103247	Enzo Doria	05/2013
3201	2^342966-16995	103244	Lelio R Paula	11/2016
3202	(37*10^103211+611)/9	103212	Robert Price	11/2018
3203	5^147650+16	103203	Lelio R Paula	11/2016
3204	gcd(Phi(852060,10),(10^42603+1)^3(10^42603+1-10^21302)+(10^85206+10^42603)(10^21302+1)+10^127809)	103201	Serge Batalov	04/2015
3205	2^342817+2707067	103199	Enzo Doria	03/2016
3206	43^63177-42	103198	Theodore Burton	02/2007
3207	2^342805-21025	103195	Enzo Doria	06/2013
3208	2^342714+12285	103168	Lelio R Paula	11/2016
3209	18^82178-4481	103156	Enzo Doria	03/2013
3210	2^342665-17349	103153	Enzo Doria	05/2013
3211	2^342612+175	103137	Lelio R Paula	08/2011
3212	5*2^342585-3	103130	Lelio R Paula	09/2014
3213	2^342503-19209	103104	Enzo Doria	05/2013
3214	2^342476+51	103096	Lelio R Paula	08/2011
3215	2^342460-18885	103091	Enzo Doria	05/2013
3216	7^121968+82	103075	Lelio R Paula	10/2016
3217	2^342392-108863	103071	Enzo Doria	03/2014
3218	3^216014+28	103065	Lelio R Paula	11/2016
3219	2^342353-108879	103059	Enzo Doria	03/2014
3220	10^103055+276081	103056	Patrick De Geest	12/2016
3221	10^103055-53	103055	Lelio R Paula	11/2016
3222	7^121933+4	103046	Lelio R Paula	11/2014
3223	19^80560-68	103017	Lelio R Paula	10/2016
3224	2^342209+76607	103016	Enzo Doria	05/2016
3226	328^40945+40945^328	103013	Norbert Schneider	12/2014
3225	12^95454-91	103013	Lelio R Paula	10/2016
3227	25833^9716+9716^25833	103009	Hans Havermann	01/2019
3228	65^56809-64^56809	102990	Robert Price	08/2013
3229	5^147338-6	102985	Lelio R Paula	11/2014
3230	2^342084-112739	102978	Enzo Doria	06/2014
3231	9*6^132330+7	102974	Lelio R Paula	11/2014
3232	2^342034-16737	102963	Enzo Doria	05/2013
3233	(9787*2^342011-1)/25	102959	Lelio R Paula	05/2015
3234	(3^215802-5)/124343756	102956	Lelio R Paula	12/2013
3235	2^341991-17421	102950	Enzo Doria	05/2013
3236	2^341969-112225	102943	Enzo Doria	06/2014
3237	(9787*2^341864-1)/3	102915	Lelio R Paula	05/2015
3238	2^341859+1869413	102910	Enzo Doria	05/2016
3239	10^102909+61	102910	Lelio R Paula	11/2016
3240	10^102909-67049	102909	Patrick De Geest	12/2016
3241	23814^20935+20935^23814	102898	Hans Havermann	02/2019
3242	28345^4264+4264^28345	102888	Hans Havermann	02/2019
3243	25665^10204+10204^25665	102886	Hans Havermann	02/2019
3244	2^341659+1836773	102850	Enzo Doria	03/2016
3245	2^341608-110639	102835	Enzo Doria	05/2014
3246	10^102824+49	102825	Lelio R Paula	11/2016
3247	10^102824-168011	102824	Patrick De Geest	12/2016
3248	11^98708-8	102794	Lelio R Paula	10/2016
3249	2^341466+4429	102792	Lelio R Paula	09/2011
3250	2^341460-107	102790	Lelio R Paula	08/2011

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Probable Primes Top 10000

(252538 PRPs in the top)