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 (> 30000)	Who ?	When ?
3001	2^348212-20105	104823	Enzo Doria	06/2013
3002	20^80562+19	104814	Lelio R Paula	12/2016
3003	2*10^104811-87	104812	Robert Price	04/2018
3004	2^348149-20053	104804	Enzo Doria	06/2013
3005	2^348095-171	104788	Lelio R Paula	09/2011
3006	2^348003-20377	104760	Enzo Doria	06/2013
3007	2^347994-741	104757	Lelio R Paula	12/2016
3008	(13*2^347972-1)/282309	104746	Lelio R Paula	03/2014
3009	2^347910-109937	104732	Enzo Doria	04/2014
3010	5^149794+28	104702	Lelio R Paula	11/2016
3011	105^51800-2	104698	Lelio R Paula	10/2017
3012	(16^86939+3^86939)/19	104684	Robert Price	06/2013
3013	(15^89009-1)/14	104682	Paul Bourdelais	03/2010
3014	2^347731-18609	104678	Enzo Doria	05/2013
3015	4*6^134519+7	104677	Lelio R Paula	11/2014
3016	2^347612-18545	104642	Enzo Doria	05/2013
3017	6^134465+95	104635	Lelio R Paula	11/2016
3018	2^347517-17301	104614	Enzo Doria	05/2013
3019	3^219222-310	104596	Lelio R Paula	11/2016
3020	(15*2^347399-1)/13	104578	Lelio R Paula	03/2014
3021	2^347372-17853	104570	Enzo Doria	05/2013
3022	2^347314+99	104552	Lelio R Paula	09/2011
3023	2^347300-22233	104548	Enzo Doria	06/2013
3024	2^347287-19845	104544	Enzo Doria	06/2013
3025	(31*2^347254-1)/891	104533	Lelio R Paula	03/2014
3026	5F(250091)(F(250091)-1)+1	104532	Serge Batalov	04/2015
3027	7*2^347239-3	104531	Lelio R Paula	09/2014
3028	(3^219098-8)/514147439969	104525	Lelio R Paula	12/2013
3029	5*3^219047+8	104513	Lelio R Paula	09/2014
3030	2^347148-109073	104502	Enzo Doria	04/2014
3031	2^347129-20145	104497	Enzo Doria	06/2013
3032	4*10^104461-57	104462	Robert Price	10/2018
3033	2^346923-19585	104435	Enzo Doria	05/2013
3034	(11*2^346864-1)/175	104416	Lelio R Paula	03/2014
3035	2^346854+346854^2+1	104414	Robert Price	06/2014
3036	2^346834+11715	104408	Lelio R Paula	04/2015
3037	79^55009+78	104387	Norbert Schneider	02/2015
3038	3^218744+58	104368	Lelio R Paula	11/2016
3039	2^346649+65	104352	Lelio R Paula	09/2011
3040	2^346638-17265	104349	Enzo Doria	05/2013
3042	2^346527-111817	104316	Enzo Doria	05/2014
3041	6^134055+101	104316	Lelio R Paula	11/2016
3043	6^134013+163	104283	Lelio R Paula	11/2016
3044	18^83049-89	104250	Lelio R Paula	01/2017
3045	2^346213+484049	104221	Enzo Doria	04/2017
3046	18^83021-91	104214	Lelio R Paula	01/2017
3047	10^104212+128779	104213	Patrick De Geest	05/2016
3048	10^104212+237447	104213	Patrick De Geest	05/2016
3049	10^104212+242139	104213	Patrick De Geest	05/2016
3050	10^104212+269199	104213	Patrick De Geest	05/2016
3051	(10^104212-71)/1	104212	Serge Batalov	12/2014
3052	2^346078+7695	104180	Lelio R Paula	12/2016
3054	2^346055-19537	104173	Enzo Doria	05/2013
3053	(3*2^346057+1)/77	104173	Lelio R Paula	12/2013
3055	2^346037-20125	104168	Enzo Doria	06/2013
3056	(34*10^104168-7)/9/13/551179	104162	Makoto Morimoto	05/2016
3057	6^133854-17993	104159	Enzo Doria	03/2013
3058	2^345990+1874239	104154	Enzo Doria	06/2016
3059	2^345988-20373	104153	Enzo Doria	06/2013
3060	(26*10^104132-503)/9	104133	Robert Price	07/2018
3061	3*5^148968+8	104125	Lelio R Paula	11/2014
3062	(7*10^104113+53)/3	104114	Robert Price	05/2018
3063	p(21253)#/2+8	104113	Robert Price	01/2017
3064	322^41507+41507^322	104094	Norbert Schneider	12/2014
3065	6^133768-17423	104092	Enzo Doria	03/2013
3066	2^345786-19557	104092	Enzo Doria	05/2013
3067	171^46606-2	104072	Lelio R Paula	10/2017
3068	2^345704-149	104068	Lelio R Paula	09/2011
3069	6^133704-17273	104042	Enzo Doria	02/2013
3070	(3*2^345590-1)/23	104033	Lelio R Paula	03/2014
3071	(19*2^345590+1)/33859	104030	Lelio R Paula	12/2013
3072	2^345547+11	104021	Lelio R Paula	09/2011
3073	2^345504+723	104008	Lelio R Paula	09/2011
3074	2^345498-20037	104006	Enzo Doria	06/2013
3075	18^82854-37	104005	Lelio R Paula	01/2017
3076	2^345486-109065	104002	Enzo Doria	04/2014
3077	2^345487-1851507	104002	Enzo Doria	08/2015
3078	2^345476+777	103999	Lelio R Paula	09/2011
3079	4*10^103981-83	103982	Robert Price	10/2018
3080	(5*2^345321-1)/3	103953	Lelio R Paula	03/2014
3081	(2^345267-9)/539049127	103927	Lelio R Paula	12/2013
3082	(78557*2^345163+1)/78589	103905	Lelio R Paula	07/2014
3083	2^345106-112181	103888	Enzo Doria	06/2014
3084	2^345079+99	103880	Lelio R Paula	09/2011
3085	11^99736-1500	103865	Enzo Doria	12/2012
3086	2^344842-20157	103808	Enzo Doria	06/2013
3087	(47*2^344822+1)/1071	103801	Lelio R Paula	05/2015
3088	2^344802-20765	103796	Enzo Doria	06/2013
3089	2^344794-3821	103794	Yves Minet	05/2011
3090	2^344782-109103	103790	Enzo Doria	04/2014
3091	3^217521-112292	103784	Enzo Doria	06/2014
3092	2^344759-3505	103783	Lelio R Paula	11/2016
3093	2^344735-147	103776	Lelio R Paula	09/2011
3094	L(496533)-p(496533)	103770	Robert Price	02/2018
3095	2*10^103749-69	103750	Robert Price	03/2018
3096	(55459*2^344617+1)/3	103745	Lelio R Paula	07/2014
3097	2^344607-108891	103738	Enzo Doria	03/2014
3098	2^344541-19561	103718	Enzo Doria	05/2013
3099	(1017*2^344529-1)/569	103714	Lelio R Paula	05/2015
3100	(4*10^103703-1)/3	103704	Serge Batalov	08/2009
3101	2^344444-455	103688	Yves Minet	03/2012
3102	(1353^238539617^9)/10^307661	103673	Hans Havermann	06/2017
3103	2^344317-109933	103650	Enzo Doria	04/2014
3104	2^344309-1852033	103648	Enzo Doria	08/2015
3105	2^344213-21253	103619	Enzo Doria	06/2013
3106	2^344196-465	103614	Lelio R Paula	11/2016
3107	2^344187-20001	103611	Enzo Doria	06/2013
3108	(117191#+(355573#)/(117191#))/(200233679)	103602	Makoto Morimoto	10/2017
3109	20^79621-19^79621	103590	Jean-Louis Charton	03/2011
3110	Phi(155391,10)/1243129	103586	Maksym Voznyy	09/2015
3111	2^344085-20365	103580	Enzo Doria	06/2013
3112	5^148169+54	103566	Lelio R Paula	11/2016
3113	2^344017-108795	103560	Enzo Doria	03/2014
3114	2^343971-5077	103546	Lelio R Paula	09/2011
3115	(7*10^103531+71)/3	103532	Robert Price	05/2018
3116	2^343899+141	103524	Lelio R Paula	08/2011
3117	(2^343933+1)/(3*98294339989393)	103520	Gord Palameta	08/2018
3118	6^133029-67	103517	Lelio R Paula	11/2016
3119	(17*2^343877+1)/13625	103515	Lelio R Paula	12/2013
3120	(136*10^103474-1)/9	103476	Serge Batalov	12/2014
3121	5^148014-24	103458	Lelio R Paula	11/2016
3122	2^343604+9931	103436	Yves Minet	01/2011
3123	2^343601-21189	103435	Enzo Doria	06/2013
3124	2^343508-115229	103407	Enzo Doria	06/2015
3125	(509203*2^343491-1)/16147	103403	Lelio R Paula	05/2015
3126	3^216685-113056	103386	Enzo Doria	07/2014
3127	44^62903-43^62903	103379	Jean-Louis Charton	08/2012
3128	11^99262-20	103371	Lelio R Paula	12/2016
3129	(509203*2^343357-1)/5	103366	Lelio R Paula	05/2015
3131	2^343356-2791889	103361	Enzo Doria	03/2016
3130	(25*10^103360-241)/9	103361	Robert Price	05/2018
3132	Phi(104989,10)/2939693	103350	Maksym Voznyy	09/2015
3133	2^343182-171	103309	Lelio R Paula	08/2011
3134	(23619^23619+23620^23620)/7187	103294	David Broadhurst	09/2009
3135	2^343079-1835611	103278	Enzo Doria	05/2015
3136	2^343063-1147	103273	Yves Minet	06/2013
3137	9*6^132689+7	103254	Lelio R Paula	11/2014
3138	2^342979-18085	103247	Enzo Doria	05/2013
3139	2^342966-16995	103244	Lelio R Paula	11/2016
3140	(37*10^103211+611)/9	103212	Robert Price	11/2018
3141	5^147650+16	103203	Lelio R Paula	11/2016
3142	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
3143	2^342817+2707067	103199	Enzo Doria	03/2016
3144	43^63177-42	103198	Theodore Burton	02/2007
3145	2^342805-21025	103195	Enzo Doria	06/2013
3146	2^342714+12285	103168	Lelio R Paula	11/2016
3147	18^82178-4481	103156	Enzo Doria	03/2013
3148	2^342665-17349	103153	Enzo Doria	05/2013
3149	2^342612+175	103137	Lelio R Paula	08/2011
3150	5*2^342585-3	103130	Lelio R Paula	09/2014
3151	2^342503-19209	103104	Enzo Doria	05/2013
3152	2^342476+51	103096	Lelio R Paula	08/2011
3153	2^342460-18885	103091	Enzo Doria	05/2013
3154	7^121968+82	103075	Lelio R Paula	10/2016
3155	2^342392-108863	103071	Enzo Doria	03/2014
3156	3^216014+28	103065	Lelio R Paula	11/2016
3157	2^342353-108879	103059	Enzo Doria	03/2014
3158	10^103055+276081	103056	Patrick De Geest	12/2016
3159	10^103055-53	103055	Lelio R Paula	11/2016
3160	7^121933+4	103046	Lelio R Paula	11/2014
3161	19^80560-68	103017	Lelio R Paula	10/2016
3162	2^342209+76607	103016	Enzo Doria	05/2016
3164	328^40945+40945^328	103013	Norbert Schneider	12/2014
3163	12^95454-91	103013	Lelio R Paula	10/2016
3165	65^56809-64^56809	102990	Robert Price	08/2013
3166	5^147338-6	102985	Lelio R Paula	11/2014
3167	2^342084-112739	102978	Enzo Doria	06/2014
3168	9*6^132330+7	102974	Lelio R Paula	11/2014
3169	2^342034-16737	102963	Enzo Doria	05/2013
3170	(9787*2^342011-1)/25	102959	Lelio R Paula	05/2015
3171	(3^215802-5)/124343756	102956	Lelio R Paula	12/2013
3172	2^341991-17421	102950	Enzo Doria	05/2013
3173	2^341969-112225	102943	Enzo Doria	06/2014
3174	(9787*2^341864-1)/3	102915	Lelio R Paula	05/2015
3175	2^341859+1869413	102910	Enzo Doria	05/2016
3176	10^102909+61	102910	Lelio R Paula	11/2016
3177	10^102909-67049	102909	Patrick De Geest	12/2016
3178	2^341659+1836773	102850	Enzo Doria	03/2016
3179	2^341608-110639	102835	Enzo Doria	05/2014
3180	10^102824+49	102825	Lelio R Paula	11/2016
3181	10^102824-168011	102824	Patrick De Geest	12/2016
3182	11^98708-8	102794	Lelio R Paula	10/2016
3183	2^341466+4429	102792	Lelio R Paula	09/2011
3184	2^341460-107	102790	Lelio R Paula	08/2011
3185	(2^341388+47)/21014943	102761	Lelio R Paula	12/2013
3186	2^341355+21	102759	Lelio R Paula	08/2011
3187	2^341246+40755	102726	Lelio R Paula	11/2016
3188	(2^341256-5)/991699	102723	Lelio R Paula	12/2013
3189	7^121547+78	102720	Lelio R Paula	10/2016
3190	2^341223-461197	102719	Enzo Doria	06/2015
3192	2^341190-20577	102709	Enzo Doria	06/2013
3191	(27*2^341212+1)/84674449	102709	Lelio R Paula	12/2013
3193	6^131976-65	102698	Lelio R Paula	10/2016
3194	2^341134+2533	102692	Henri Lifchitz	09/2005
3195	13^92184-54	102688	Lelio R Paula	10/2016
3196	2^341116-20873	102687	Enzo Doria	06/2013
3197	2^341094-19953	102680	Enzo Doria	06/2013
3198	2^341053+129	102668	Lelio R Paula	08/2011
3199	(31*2^341006-1)/3	102655	Lelio R Paula	03/2014
3200	7^121471+94	102655	Lelio R Paula	10/2016
3202	2^341004-173	102653	Lelio R Paula	08/2011
3201	20^78901+3	102653	Lelio R Paula	10/2016
3203	5^146853-52	102646	Lelio R Paula	10/2016
3204	2^340969-216931	102642	Enzo Doria	05/2014
3205	122^49196+121	102641	Norbert Schneider	10/2018
3206	2^340952+1870021	102637	Enzo Doria	05/2016
3207	5*2^340940-3	102634	Lelio R Paula	08/2014
3208	(6^131891+1)/7	102631	Paul Bourdelais	01/2010
3209	(4*10^102612+83)/3	102613	Robert Price	02/2018
3210	75^54717+74	102598	Norbert Schneider	01/2015
3211	2^340806-20393	102593	Enzo Doria	06/2013
3212	(2^340790+5)/138267	102583	Lelio R Paula	12/2013
3213	6^131821+77	102577	Lelio R Paula	10/2016
3214	2^340688-29	102558	Henri Lifchitz	05/2005
3215	2^340685-109101	102557	Enzo Doria	04/2014
3216	65^56567-64	102552	Norbert Schneider	11/2014
3217	2^340547-108897	102515	Enzo Doria	03/2014
3218	7^121268+82	102484	Lelio R Paula	10/2016
3219	(6883*2^340443-1)/162401	102483	Lelio R Paula	05/2015
3220	2^340434-5955	102481	Lelio R Paula	11/2016
3221	(2^340381+47)/7	102465	Lelio R Paula	12/2013
3222	111^50095+110	102461	Norbert Schneider	04/2017
3223	2^340291-20301	102438	Enzo Doria	06/2013
3224	12^94915+89	102431	Lelio R Paula	10/2016
3225	2^340208-20373	102413	Enzo Doria	06/2013
3226	6^131598-17273	102404	Enzo Doria	02/2013
3227	2^340115-21181	102385	Enzo Doria	06/2013
3228	(55459*2^340090+1)/1591	102379	Lelio R Paula	07/2014
3229	89^52511-88^52511	102365	Robert Price	06/2015
3230	3^214539-112756	102362	Enzo Doria	07/2014
3231	2^340000-19877	102351	Enzo Doria	06/2013
3232	2^339990-114845	102348	Enzo Doria	05/2015
3233	(3^214516-2)/51383	102346	Lelio R Paula	12/2013
3234	20^78661-99	102341	Lelio R Paula	09/2016
3235	2^339951-19585	102336	Enzo Doria	05/2013
3236	(13*2^339943+1)/45	102333	Lelio R Paula	12/2013
3237	2^339889+29327	102317	Yves Minet	06/2010
3238	2^339834-109493	102301	Enzo Doria	04/2014
3239	(11^98221-5^98221)/6	102286	Robert Price	01/2013
3240	3^214365+1820	102279	Lelio R Paula	10/2016
3241	(11*2^339705-1)/183	102261	Lelio R Paula	03/2014
3242	2^339694-16995	102259	Lelio R Paula	09/2016
3243	122^49008+121	102249	Norbert Schneider	10/2018
3245	7^120985-38	102245	Lelio R Paula	10/2016
3244	10^102244+122961	102245	Patrick De Geest	12/2016
3246	10^102244-27	102244	Lelio R Paula	09/2016
3247	7^120982-62	102242	Lelio R Paula	10/2016
3248	4*6^131382-5	102236	Lelio R Paula	11/2014
3249	2^339586-1091	102226	Yves Minet	11/2012
3250	11^98161-3072000	102225	Enzo Doria	12/2012

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Probable Primes Top 10000

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