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	(2^398398+774)/2	119930	Stefano Morozzi	09/2020
3002	(10^119880+179)/9	119880	Serge Batalov	12/2014
3003	(9*2^398145+1)/73	119853	Lelio R Paula	04/2014
3004	(10^119836+77)/3	119836	Robert Price	01/2018
3005	2^398029+1872527	119819	Enzo Doria	05/2016
3006	2^397897-113541	119779	Enzo Doria	08/2014
3007	(2^397696+1042)/2	119719	Stefano Morozzi	09/2020
3008	(19*10^119716+101)/3	119717	Robert Price	09/2019
3009	(21*2^397661-1)/27593	119705	Lelio R Paula	04/2014
3010	77*10^119688+3	119690	Robert Price	06/2020
3011	(2^397504+1698)/2	119661	Stefano Morozzi	09/2020
3012	(58^67853-1)/57	119653	Paul Bourdelais	09/2017
3013	2^397426+73849	119638	Enzo Doria	04/2016
3014	2^396933-112723	119489	Enzo Doria	06/2014
3015	11^114738-150	119488	Enzo Doria	10/2012
3016	(4*10^119474+149)/9	119474	Robert Price	04/2018
3017	2^396790-21	119446	Lelio R Paula	04/2013
3018	(2^396633-7)/5	119398	Lelio R Paula	04/2014
3019	(2^396577+2522)/2	119382	Stefano Morozzi	09/2020
3020	(2^396492+2230)/2	119356	Stefano Morozzi	01/2021
3022	105^59050+104	119352	Norbert Schneider	11/2016
3021	126^56824-125	119352	Norbert Schneider	12/2018
3023	139^55690-138	119345	Norbert Schneider	04/2019
3024	790^41179+41179^790	119322	Norbert Schneider	04/2019
3025	2^396374+73729	119321	Enzo Doria	04/2016
3026	88*10^119295+3	119297	Robert Price	05/2020
3027	2^396258-459491	119286	Enzo Doria	05/2015
3028	(2^396248+3126)/2	119283	Stefano Morozzi	09/2020
3029	2^396128-396128-1	119247	Karsten Bonath	06/2018
3030	(28*10^119206-67)/3	119207	Robert Price	10/2020
3031	(2^395986+5)/76881	119199	Lelio R Paula	04/2014
3032	(23*2^395942-1)/91	119190	Lelio R Paula	04/2014
3033	(2^395902+202)/2	119179	Stefano Morozzi	09/2020
3034	(2^395825+582)/2	119155	Stefano Morozzi	09/2020
3035	(2^395733+1130)/2	119128	Stefano Morozzi	09/2020
3036	(11*2^395548+1)/3	119073	Lelio R Paula	04/2014
3037	(30^80599+1)/31	119054	Robert Price	07/2013
3038	(43*10^119024-403)/9	119025	Robert Price	01/2019
3039	6*10^118964+43	118965	Robert Price	07/2020
3040	(8*10^118960+49)/3	118961	Robert Price	05/2020
3041	(194*10^118925-17)/3	118927	Robert Price	09/2020
3042	2^395062-109121	118926	Enzo Doria	04/2014
3043	2^395055-4627	118924	Yves Minet	05/2019
3044	(2^395054+702)/2	118923	Stefano Morozzi	09/2020
3045	(2^395011+2526)/2	118910	Stefano Morozzi	09/2020
3046	(2^394918+78557)/3	118882	Lelio R Paula	01/2015
3047	(2^394858+1018)/2	118864	Stefano Morozzi	09/2020
3048	(16*10^118852+77)/3	118853	Robert Price	03/2019
3049	(2^394739+3)/1883	118826	Lelio R Paula	04/2014
3050	10^118772-40000000001	118772	Robert Price	09/2020
3051	(2^394513+2034)/2	118760	Stefano Morozzi	09/2020
3052	2^394266+71389	118686	Enzo Doria	04/2016
3053	2^394215-51261	118671	Tony Prest / Never Odd Or Even	04/2018
3054	(2^394215-48793)/5/5	118670	Tony Prest / Never Odd Or Even	04/2018
3055	(2^394215-17063)/3/3/5	118669	Tony Prest / Never Odd Or Even	04/2018
3056	(2^394215-24393)/5/5/5/5/5	118668	Tony Prest / Never Odd Or Even	04/2018
3057	(2^394215-35885)/3/71/173	118666	Tony Prest / Never Odd Or Even	04/2018
3058	(2^394215-47925)/353/2269	118665	Tony Prest / Never Odd Or Even	04/2018
3059	(2^394215-62819)/3/3/3/3/3/3/3/7/21737/1082153/1953673	118650	Tony Prest / Never Odd Or Even	04/2018
3060	(2^394131+2214)/2	118645	Stefano Morozzi	09/2020
3061	(17*10^118635+13)/3	118636	Robert Price	01/2019
3062	5^169727+2	118635	Lelio R Paula	08/2013
3063	2^394034-3	118617	M. Frind & P. Underwood	09/2002
3064	(7*10^118607+179)/3	118608	Robert Price	09/2018
3065	3^248572-6242	118599	Enzo Doria	05/2014
3066	(3*2^393964-1)/181	118594	Lelio R Paula	04/2014
3067	7^140303-6	118570	Robert Price	11/2014
3068	(2^393864+2686)/2	118565	Stefano Morozzi	09/2020
3069	(2^393862+3150)/2	118564	Stefano Morozzi	09/2020
3070	(2^393849+3762)/2	118561	Stefano Morozzi	01/2021
3071	(2^393661+2666)/2	118504	Stefano Morozzi	09/2020
3072	(2^393650+1614)/2	118501	Stefano Morozzi	09/2020
3073	10^118485-50001	118485	Robert Price	08/2020
3074	(2^393528+1030)/2	118464	Stefano Morozzi	09/2020
3075	2^393427+75683	118434	Enzo Doria	04/2016
3076	2^393376-114749	118418	Enzo Doria	04/2015
3077	(2^393234+2010)/2	118375	Stefano Morozzi	09/2020
3078	(2^393205+3030)/2	118367	Stefano Morozzi	09/2020
3079	(2^393191+2174)/2	118362	Stefano Morozzi	09/2020
3080	2^393180+73	118359	Lelio R Paula	04/2013
3081	p(23881)#/2+256	118328	Robert Price	05/2017
3082	(10^118324+359)/9	118324	Serge Batalov	12/2014
3083	(2^393048+570)/2	118319	Stefano Morozzi	09/2020
3084	p(23879)#/2+64	118317	Robert Price	03/2017
3085	(238*10^118265-1)/3	118267	Robert Price	04/2020
3087	(53*10^118216+1)/9	118217	Serge Batalov	11/2010
3086	(2^392707+1710)/2	118217	Stefano Morozzi	09/2020
3088	(7*2^392697+1)/15	118214	Renaud Lifchitz	03/2011
3089	(157^53819-1)/156	118179	Alexander Zhirkov	06/2016
3090	(2^392567+2750)/2	118175	Stefano Morozzi	01/2021
3091	(19*2^392551+1)/3	118171	Lelio R Paula	04/2014
3092	2^392516-29219	118160	Enzo Doria	07/2015
3093	66*10^118155+7	118157	Robert Price	07/2020
3094	Phi(177231,10)	118152	Maksym Voznyy	09/2015
3095	2^392413-112123	118129	Enzo Doria	06/2014
3096	(2^392342+5)/27	118106	Lelio R Paula	04/2014
3097	(2^392333+1782)/2	118104	Stefano Morozzi	01/2021
3098	2^392300-1841429	118095	Enzo Doria	06/2015
3099	2^392220+75241	118070	Enzo Doria	04/2016
3100	10^118009+664447	118010	Patrick De Geest	07/2018
3101	10^118009-20001	118009	Robert Price	01/2018
3102	(14*10^117991+61)/3	117992	Robert Price	12/2018
3103	2^391933+5897	117984	Yves Minet	02/2011
3104	2^391912-1849259	117978	Enzo Doria	08/2015
3105	(2^391812+5)/14181	117944	Lelio R Paula	04/2014
3106	(7*10^117930-79)/9	117930	Robert Price	01/2021
3107	(46*10^117902+683)/9	117903	Robert Price	03/2019
3108	(7*2^391521+1)/285	117858	Lelio R Paula	04/2014
3109	2^391324+90901	117801	Yves Minet	02/2011
3110	2^391301-1859923	117794	Enzo Doria	03/2016
3111	2^391261-4131	117782	Yves Minet	02/2018
3112	(2^391211+554)/2	117766	Stefano Morozzi	09/2020
3113	38434^1157+1157^38434	117737	Hans Havermann	01/2021
3114	(2^391115-7)/11791	117734	Lelio R Paula	04/2014
3115	(85*10^117719+473)/9	117720	Robert Price	01/2020
3116	(2^391049+582)/2	117718	Stefano Morozzi	09/2020
3117	2^390960+1880881	117691	Enzo Doria	11/2016
3118	2^390897-1860553	117672	Enzo Doria	11/2015
3119	2^390889-115003	117670	Enzo Doria	06/2015
3120	2^390779-30337	117637	Paul Bourdelais	02/2012
3121	11^112916-780	117590	Enzo Doria	12/2012
3122	(2^390473+1002)/2	117544	Stefano Morozzi	09/2020
3123	(16^97613-5^97613)/11	117537	Robert Price	07/2013
3124	(2^390438+1774)/2	117534	Stefano Morozzi	01/2021
3125	(2^390418+1722)/2	117528	Stefano Morozzi	09/2020
3126	(2^390403+654)/2	117523	Stefano Morozzi	09/2020
3127	(2^390343+2246)/2	117505	Stefano Morozzi	01/2021
3128	(17*2^390272+1)/1983	117482	Lelio R Paula	04/2014
3129	31^78759-30	117459	Theodore Burton	02/2007
3130	(2^390176+1222)/2	117455	Stefano Morozzi	09/2020
3131	(2^390133+1242)/2	117442	Stefano Morozzi	09/2020
3132	(2^390013+2634)/2	117406	Stefano Morozzi	09/2020
3133	3*10^117402+61	117403	Robert Price	09/2020
3134	2^389998+37	117402	Lelio R Paula	03/2013
3135	(2^389977+314)/2	117395	Stefano Morozzi	09/2020
3136	(2^389921+342)/2	117378	Stefano Morozzi	01/2021
3137	(2^389768+1582)/2	117332	Stefano Morozzi	09/2020
3138	29^80192-1*80192^29	117273	Dylan Delgado	12/2019
3139	(13*10^117249+161)/3	117250	Robert Price	11/2018
3140	2^389478+43	117245	Lelio R Paula	03/2013
3141	(298*10^117229-7)/3	117231	Robert Price	06/2020
3142	(2^389416+342)/2	117226	Stefano Morozzi	01/2021
3143	(29*2^389351-1)/9	117207	Lelio R Paula	04/2014
3144	5*10^117205+23	117206	Robert Price	03/2019
3145	(2^389341-7)/3865	117200	Lelio R Paula	03/2014
3146	(2^389276+2650)/2	117184	Stefano Morozzi	09/2020
3147	10^117142+209223	117143	Patrick De Geest	04/2018
3149	10^117142-1000000001	117142	Robert Price	03/2018
3148	10^117142-966057	117142	Patrick De Geest	04/2018
3150	10^117135+360577	117136	Patrick De Geest	07/2018
3151	10^117135-401	117135	Robert Price	01/2018
3152	4*10^117123+79	117124	Robert Price	08/2018
3153	2^389033-12797413	117111	Enzo Doria	04/2016
3154	(2^388987+2634)/2	117097	Stefano Morozzi	09/2020
3155	2^388960-109505	117089	Enzo Doria	04/2014
3156	7*10^117082-57	117083	Robert Price	06/2020
3157	(2^388928-5)/569	117077	Lelio R Paula	03/2014
3158	2^388888-1529	117067	Yves Minet	01/2013
3159	10^117059+28879	117060	Patrick De Geest	05/2016
3160	(10^117059-71)/1	117059	Serge Batalov	12/2014
3161	(2^388854+3630)/2	117057	Stefano Morozzi	09/2020
3162	(2^388842+2098)/2	117053	Stefano Morozzi	09/2020
3163	(2^388789+3150)/2	117037	Stefano Morozzi	09/2020
3164	(693^41189-1)/692	117005	Michael Stocker	05/2020
3165	(26*10^116999-503)/9	117000	Robert Price	07/2018
3166	(2^388609+1554)/2	116983	Stefano Morozzi	09/2020
3167	3^245154-6256	116969	Enzo Doria	05/2014
3168	5*10^116966-43	116967	Robert Price	01/2019
3169	2^388536-113495	116961	Enzo Doria	08/2014
3170	2^388469-43	116941	Lelio R Paula	03/2013
3171	(7*2^388372-1)/111	116911	Lelio R Paula	04/2014
3172	(7*2^388335-1)/25	116900	Lelio R Paula	04/2014
3173	2^388180+93	116854	Donovan Johnson	07/2008
3174	(2^388167+2510)/2	116850	Stefano Morozzi	09/2020
3175	(85*10^116842+293)/9	116843	Robert Price	12/2019
3176	(2^388081+7)/1179	116821	Lelio R Paula	03/2014
3177	2^387946-113261	116784	Enzo Doria	07/2014
3178	2^387745+75557	116723	Enzo Doria	04/2016
3179	(206*10^116687-17)/9	116689	Robert Price	01/2020
3180	(7*10^116684+179)/3	116685	Robert Price	09/2018
3181	2^387554+71455	116666	Enzo Doria	04/2016
3182	(2^387447+78557)/365	116631	Lelio R Paula	12/2014
3183	(145*10^116610-1)/9	116612	Serge Batalov	12/2014
3184	(25*10^116601-331)/9	116602	Robert Price	08/2018
3185	(17*2^387284-1)/59	116584	Lelio R Paula	04/2014
3186	(2^387284+3726)/2	116584	Stefano Morozzi	09/2020
3187	10^116557+987654321	116558	Robert Price	12/2019
3188	10^116557+9141	116558	Patrick De Geest	02/2020
3189	10^116557-609431	116557	Patrick De Geest	02/2020
3190	(2^387076+2046)/2	116522	Stefano Morozzi	09/2020
3191	(2^387073+2570)/2	116521	Stefano Morozzi	09/2020
3192	(31*2^386968+1)/7	116490	Lelio R Paula	03/2014
3193	2^386947+1869143	116483	Enzo Doria	05/2016
3194	(30^78857-1)/29	116480	Robert Price	12/2011
3195	(2^386903-3)/5	116469	Lelio R Paula	03/2014
3196	2^386389-1864783	116315	Enzo Doria	03/2016
3197	(31*2^386231-1)/1711	116266	Lelio R Paula	03/2014
3198	297^47012+47012^297	116250	Norbert Schneider	07/2018
3199	(2^386087-5)/40959	116220	Lelio R Paula	03/2014
3200	(2^386054+714)/2	116214	Stefano Morozzi	09/2020
3201	2^385969-823	116189	Yves Minet	05/2012
3202	57^66162+2	116173	Lelio R Paula	08/2013
3203	2^385854+75049	116154	Enzo Doria	04/2016
3204	(2^385832+2590)/2	116147	Stefano Morozzi	09/2020
3205	2^385775-109587	116130	Enzo Doria	04/2014
3206	(14*10^116112-101)/3	116113	Robert Price	02/2019
3207	Phi(236354,10)/24817171	116109	Makoto Kamada	08/2019
3208	2^385622+71839	116084	Enzo Doria	04/2016
3210	2^385564+781	116067	Lelio R Paula	01/2012
3209	(2^385565+1562)/2	116067	Stefano Morozzi	09/2020
3211	(2^385557+2214)/2	116064	Stefano Morozzi	09/2020
3212	(266*10^116024-17)/3	116026	Robert Price	07/2020
3213	2^385410+71893	116020	Enzo Doria	04/2016
3214	(25*2^385091+1)/27	115924	Lelio R Paula	04/2014
3215	(11*10^115910-131)/3	115911	Robert Price	09/2018
3216	2^384953-111943	115883	Paul Bourdelais	02/2012
3217	43^70942-2	115882	Lelio R Paula	04/2014
3218	(94*10^115879-7)/3	115881	Robert Price	03/2020
3219	7*10^115863+3	115864	Robert Price	08/2015
3220	2^384834+93	115847	Donovan Johnson	07/2008
3221	2^384809+71297	115840	Enzo Doria	04/2016
3222	(7*2^384759-1)/5	115825	Lelio R Paula	04/2014
3223	(71*10^115810-17)/9	115811	Ray Chandler	08/2011
3224	(97*10^115794-1)/3	115796	Serge Batalov	12/2014
3225	2*10^115784-27	115785	Robert Price	05/2018
3226	10^115773+126739	115774	Patrick De Geest	04/2018
3228	10^115773-1000000001	115773	Robert Price	03/2018
3227	10^115773-396221	115773	Patrick De Geest	04/2018
3229	(2^384582+778)/2	115771	Stefano Morozzi	09/2020
3230	2^384530+1874305	115756	Enzo Doria	06/2016
3231	(3*2^384524-1)/7631	115750	Lelio R Paula	03/2014
3232	(44*10^115697-413)/9	115698	Robert Price	03/2019
3233	(2^384317+1026)/2	115691	Stefano Morozzi	09/2020
3234	2^384312+81091	115690	Yves Minet	02/2010
3235	(2^384265+2150)/2	115675	Stefano Morozzi	09/2020
3236	(2^384246+2182)/2	115670	Stefano Morozzi	09/2020
3237	(4*10^115668-79)/3	115669	Robert Price	02/2018
3238	(2^384193+242)/2	115654	Stefano Morozzi	09/2020
3239	(266947#+1267)/(7^2*181)	115647	Makoto Morimoto	06/2019
3240	(266947#+273808)/(2109157)	115646	Makoto Morimoto	10/2017
3241	18^92125-92125^18	115642	Dylan Delgado	08/2019
3242	3^242337-4042	115625	Enzo Doria	05/2014
3243	(2^383931+674)/2	115575	Stefano Morozzi	09/2020
3244	7*10^115561+79	115562	Robert Price	07/2019
3245	(2^383872+3046)/2	115557	Stefano Morozzi	09/2020
3246	(11*2^383859-13)/15	115553	Renaud Lifchitz	03/2011
3247	2^383780-3149	115530	Yves Minet	10/2014
3248	(41*10^115523-383)/9	115524	Robert Price	11/2018
3249	(2^383618+618)/2	115481	Stefano Morozzi	09/2020
3250	2^383560-455	115464	Yves Minet	03/2012

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