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	2^648988+1178971	195365	Enzo Doria	06/2016
3002	2^648975-114319	195361	Enzo Doria	02/2015
3003	(11*10^195350-137)/9	195351	Robert Price	01/2018
3004	2^648619-24835	195254	Enzo Doria	09/2013
3005	5*10^195250-21	195251	Robert Price	12/2021
3006	(14*10^195234-83)/3	195235	Robert Price	12/2018
3007	5*10^195221+81	195222	Robert Price	03/2019
3008	10^195143-5001	195143	Robert Price	12/2021
3009	2^648190-24737	195125	Enzo Doria	09/2013
3010	(57^111119+1)/58	195110	Paul Bourdelais	10/2017
3011	(29*10^195098-197)/3	195099	Robert Price	08/2021
3012	10^195060+89701	195061	Patrick De Geest	02/2021
3014	10^195060-40000000001	195060	Robert Price	09/2020
3013	10^195060-110337	195060	Patrick De Geest	02/2021
3015	56*10^195032-3	195034	Robert Price	03/2020
3016	11^187185-90	194934	Enzo Doria	09/2012
3017	2^647545-25	194931	Boyan Hu	12/2024
3018	2^647468+220141	194908	Enzo Doria	03/2024
3019	(83^101533-1)/91545628589416644493342	194827	Paul Vanderveen	06/2025
3020	(86*10^194818-437)/9	194819	Robert Price	03/2021
3021	7^230492-230492^7	194789	Henri Lifchitz	07/2024
3022	2^647068+77281	194787	Enzo Doria	05/2016
3023	2*10^194716-93	194717	Robert Price	12/2021
3024	15^165559-14^165559	194713	Jean-Louis Charton	03/2011
3025	F(931517)	194676	Henri Lifchitz	09/2008
3026	4*10^194668+49	194669	Robert Price	01/2019
3027	408^74564+407	194662	Alfred Reich	04/2026
3028	2^646589+1179407	194643	Enzo Doria	06/2016
3029	2^646289-114621	194553	Enzo Doria	05/2015
3030	2^646236-39659	194537	Enzo Doria	09/2015
3031	(16*10^194536+53)/3	194537	Robert Price	03/2019
3032	2^646161-59833	194514	Enzo Doria	11/2015
3033	(17*10^194502+31)/3	194503	Robert Price	01/2019
3034	(19*10^194428+287)/9	194429	Robert Price	10/2021
3035	2*10^194413+3	194414	Robert Price	07/2015
3036	2^645360-1848599	194273	Enzo Doria	08/2015
3037	22470^44641+44641^22470	194260	Norbert Schneider	08/2023
3038	(112*10^194150-1)/3	194152	Serge Batalov	12/2014
3039	Phi(293127,10)	194041	Makoto Kamada	12/2023
3040	2*10^193981-43	193982	Robert Price	04/2018
3041	2^644382+75169	193979	Enzo Doria	04/2016
3042	2^644304-1861409	193955	Enzo Doria	11/2015
3043	(29*10^193950-23)/3	193951	Robert Price	03/2022
3044	5*10^193907-9	193908	Robert Price	05/2015
3045	2^644043+1876703	193877	Enzo Doria	07/2016
3046	2*10^193841-63	193842	Robert Price	01/2022
3047	2^643735+1879733	193784	Enzo Doria	09/2016
3049	(5^277183+1)/6	193742	Paul Bourdelais	07/2010
3048	Phi(277183,-5)	193742	Henri Lifchitz	12/2025
3050	9*10^193712+71	193713	Robert Price	08/2020
3051	2^643216-286565	193628	Enzo Doria	07/2015
3052	2^643204+215011	193624	Enzo Doria	11/2023
3053	10^193566+1126339	193567	Patrick De Geest	09/2022
3055	10^193566-10000000001	193566	Robert Price	04/2021
3054	10^193566-454041	193566	Patrick De Geest	08/2021
3057	2^642888-24965	193529	Enzo Doria	09/2013
3056	2^642889+25367	193529	Enzo Doria	11/2023
3058	Phi(50157,p(50157))	193510	Henri Lifchitz	12/2025
3059	2^642448-114825	193397	Enzo Doria	05/2015
3060	2^642437-1856623	193393	Enzo Doria	10/2015
3061	2^642039-59797	193273	Enzo Doria	11/2015
3062	2^641987+39	193258	Jon Grantham	08/2023
3063	10^193230+513861	193231	Patrick De Geest	07/2018
3064	10^193230-8001	193230	Robert Price	03/2018
3065	(62*10^193225-233)/9	193226	Robert Price	02/2022
3066	Phi(86312,13#)	193216	Henri Lifchitz	02/2026
3067	2^641692-286349	193169	Enzo Doria	07/2015
3068	2^641690-24737	193168	Enzo Doria	09/2013
3069	22268^44421+44421^22268	193129	Norbert Schneider	06/2023
3070	2^641514+1876549	193115	Enzo Doria	07/2016
3071	2^640888-2785619	192927	Enzo Doria	10/2015
3072	2^640874-2783741	192923	Enzo Doria	09/2015
3073	10^192922+192207	192923	Patrick De Geest	08/2021
3074	10^192922-7001	192922	Robert Price	04/2021
3075	2^640854+25	192917	Stefano Morozzi	05/2021
3076	34*10^192868-9	192870	Robert Price	06/2020
3077	(46*10^192841+683)/9	192842	Robert Price	03/2019
3078	2^640181+467	192714	Lelio R Paula	08/2013
3079	2^640072+27541	192681	Enzo Doria	01/2024
3080	(10^192700)/(192700^10)	192648	Henri Lifchitz	05/2025
3081	2^639536-1850249	192520	Enzo Doria	08/2015
3082	40714<>40712<>...<>1086421357911<>...<>40711<>40713	192464	Hans Havermann	12/2019
3083	5*10^192422-43	192423	Robert Price	01/2019
3084	2^639110-2792441	192392	Enzo Doria	02/2016
3085	(241^80761-1)/240	192372	Anonymous	04/2024
3086	2^638955-29827	192345	Enzo Doria	08/2015
3087	15^163539+14	192337	Alfred Reich	10/2023
3088	2^638713-2784223	192272	Enzo Doria	10/2015
3089	(10^192216+7)/149	192214	Alfred Reich	07/2021
3090	2^638490-113507	192205	Enzo Doria	08/2014
3091	Phi(75881,561)	192120	Henri Lifchitz	12/2025
3092	2^638189-39943	192115	Enzo Doria	09/2015
3093	2^638110+1877119	192091	Enzo Doria	07/2016
3094	MillsLike(2,1,4,12,4,22,12,114,4,138,142,2956,6388,5248,17532,96930,83782,1464,897448,300832)+82440	192083	Sergey Batalov	05/2024
3095	MillsLike(2,1,4,12,4,22,12,114,4,138,142,2956,6388,5248,17532,96930,83782,1464,897448,300832)	192083	Sergey Batalov	05/2024
3096	2^638066-2785211	192078	Enzo Doria	10/2015
3097	(35*10^191973-341)/9	191974	Robert Price	08/2021
3098	(112*10^191900+17)/3	191902	Robert Price	03/2020
3099	2^637475-115309	191900	Enzo Doria	07/2015
3100	(68*10^191754-113)/9	191755	Robert Price	03/2021
3101	2^636930-11	191736	Stefano Morozzi	07/2022
3102	(47*10^191732+259)/9	191733	Robert Price	03/2022
3103	41459^41522-41522^41459	191733	Norbert Schneider	04/2025
3104	2^636661+1876577	191655	Enzo Doria	07/2016
3105	(9^200807-2^200807)/7	191618	Jon Grantham	07/2023
3106	(34^125101-1)/33	191589	Paul Bourdelais	11/2017
3107	fibonacci(916540)-2	191546	Jon Grantham	08/2023
3108	2^636177-1855123	191509	Enzo Doria	09/2015
3109	2^636158-113627	191503	Enzo Doria	08/2014
3110	(37*25^136966+63)/4	191472	Curtis Bright	05/2015
3111	2^636035+79823	191466	Enzo Doria	06/2016
3112	2^636011-1860847	191459	Enzo Doria	11/2015
3113	2^635926-1860611	191433	Enzo Doria	11/2015
3114	3*2^635755+5	191382	Jon Grantham	07/2023
3115	3*10^191152-7	191153	Robert Price	08/2015
3116	2^634883-1865677	191119	Enzo Doria	02/2016
3117	2^634801+1871957	191095	Enzo Doria	05/2016
3118	(77*10^191080+157)/9	191081	Robert Price	05/2022
3119	(35*10^191073+1)/9	191074	Serge Batalov	07/2010
3120	9*10^191018-41	191019	Robert Price	08/2020
3121	2^634470-59861	190995	Enzo Doria	11/2015
3122	2^634368-29519	190964	Enzo Doria	08/2015
3123	(19*10^190935+11)/3	190936	Robert Price	07/2023
3124	2^634188-350609	190910	Enzo Doria	06/2015
3125	(65*10^190899+493)/9	190900	Robert Price	08/2021
3126	405^73192+404	190845	Alfred Reich	04/2026
3127	(62*10^190795-413)/9	190796	Robert Price	09/2021
3128	(26*10^190789-131)/3	190790	Robert Price	10/2019
3129	(13*10^190732-61)/3	190733	Robert Price	11/2018
3130	3*2^633524+5	190711	Jon Grantham	07/2023
3131	(7*10^190683+143)/3	190684	Robert Price	03/2018
3132	2^633088-113879	190579	Enzo Doria	10/2014
3133	2^633064+1874911	190572	Enzo Doria	06/2016
3134	5*3^399402+2^399402	190564	Jon Grantham	08/2023
3135	(43*10^190547+83)/9	190548	Robert Price	11/2018
3136	99*10^190543+7	190545	Robert Price	05/2021
3137	(299*10^190533+1)/3	190535	Robert Price	04/2020
3138	(1744*10^190519-1747)/3	190522	Robert Price	12/2020
3139	2^632815-15	190497	Stefano Morozzi	07/2022
3140	2^632795-351205	190491	Enzo Doria	06/2015
3141	41171^41272+41272^41171	190454	Norbert Schneider	05/2023
3142	(16*10^190420-19)/3	190421	Robert Price	02/2019
3143	(43*10^190351+101)/9	190352	Robert Price	11/2018
3144	2^632156+78391	190298	Enzo Doria	06/2016
3145	97*10^190295-3	190297	Robert Price	05/2020
3146	2^632082-1851971	190276	Enzo Doria	08/2015
3147	2^632020+1880311	190257	Enzo Doria	09/2016
3148	(5*10^190242-77)/9	190242	Robert Price	04/2021
3149	7*10^190210+13	190211	Robert Price	03/2021
3150	2^631637-462373	190142	Enzo Doria	08/2015
3151	2*10^190126-21	190127	Robert Price	09/2020
3152	(28*10^190105+191)/3	190106	Robert Price	02/2020
3153	2*10^190093+33	190094	Robert Price	11/2021
3154	(68*10^190053-113)/9	190054	Robert Price	03/2021
3155	2^631183+213413	190006	Enzo Doria	09/2023
3156	2^631122-39251	189987	Enzo Doria	08/2015
3157	(26*10^189928-89)/9	189929	Robert Price	06/2018
3158	2^630839-97	189902	Yves Minet	07/2017
3159	99*10^189876-7	189878	Robert Price	07/2020
3160	41147^41147+30^30	189867	Henri Lifchitz	09/2024
3161	2^630359+1788953	189757	Enzo Doria	05/2016
3162	2^630228+1871971	189718	Enzo Doria	05/2016
3163	2^630108+781	189682	Lelio R Paula	08/2013
3164	2^629870-1867811	189610	Enzo Doria	04/2016
3165	(359^74189-1)/358	189558	Alexander Zhirkov	11/2017
3166	2^629326+2792929	189447	Enzo Doria	02/2016
3167	4*10^189401+13	189402	Robert Price	02/2021
3168	(10^189385-61)/3	189385	Serge Batalov	12/2014
3169	2^629036+1874011	189359	Enzo Doria	06/2016
3170	2^628930+80779	189327	Enzo Doria	07/2016
3171	(134*10^189309-11)/3	189311	Robert Price	01/2022
3172	9*10^189306-11	189307	Mischa Rodermond	04/2023
3173	3^396740-396740^3	189294	Henri Lifchitz	07/2024
3174	2^628582+1179439	189223	Enzo Doria	06/2016
3175	(44*10^188999-503)/9	189000	Robert Price	12/2018
3176	(16*10^188823+167)/3	188824	Robert Price	06/2019
3177	(10^188796+7)/4967/71933	188788	Alfred Reich	08/2021
3178	2^627037-2785843	188757	Enzo Doria	10/2015
3179	(10^188566+7)/311640753181661	188552	Alfred Reich	04/2022
3180	(16*10^188457+161)/3	188458	Robert Price	02/2019
3181	L(901657)	188436	Renaud Lifchitz	11/2008
3182	(19*10^188375+137)/3	188376	Robert Price	03/2022
3183	2^625651+74213	188340	Enzo Doria	04/2016
3184	2^625584-460919	188320	Enzo Doria	06/2015
3185	(8*10^188308-71)/9	188308	Serge Batalov	11/2022
3186	5^269399-3^269399-1	188302	Jon Grantham	08/2023
3187	(14*10^188218+139)/9	188219	Robert Price	11/2021
3188	40760^40821-40821^40760	188195	Norbert Schneider	07/2024
3189	(10^188164+359)/9	188164	Serge Batalov	12/2014
3190	2^624481-113611	187988	Enzo Doria	08/2014
3191	(2^624389+125582)/2	187960	Stefano Morozzi	09/2019
3192	(2^624389+166982)/2	187960	Stefano Morozzi	09/2019
3193	(2^624389+179886)/2	187960	Stefano Morozzi	09/2019
3194	(2^624387+64466)/2	187959	Stefano Morozzi	09/2019
3195	(2^624378+112990)/2	187957	Stefano Morozzi	09/2019
3196	(2^624380+161986)/2	187957	Stefano Morozzi	09/2019
3198	(2^624376+55762)/2	187956	Stefano Morozzi	09/2019
3197	(2^624377+169506)/2	187956	Stefano Morozzi	09/2019
3199	(2^624355+80178)/2	187950	Stefano Morozzi	09/2019
3200	(2^624351+61350)/2	187949	Stefano Morozzi	09/2019
3201	(2^624341+63462)/2	187946	Stefano Morozzi	09/2019
3202	(2^624344+135990)/2	187946	Stefano Morozzi	09/2019
3203	(2^624344+183898)/2	187946	Stefano Morozzi	09/2019
3205	(2^624340+126982)/2	187945	Stefano Morozzi	09/2019
3204	(2^624338+196110)/2	187945	Stefano Morozzi	09/2019
3206	(2^624337+105162)/2	187944	Stefano Morozzi	09/2019
3207	(2^624333+44594)/2	187943	Stefano Morozzi	09/2019
3208	(2^624321+88742)/2	187940	Stefano Morozzi	09/2019
3209	(2^624324+135178)/2	187940	Stefano Morozzi	09/2019
3210	(2^624317+14186)/2	187938	Stefano Morozzi	09/2019
3211	(2^624313+24450)/2	187937	Stefano Morozzi	09/2019
3212	(2^624309+184590)/2	187936	Stefano Morozzi	09/2019
3214	(2^624307+152658)/2	187935	Stefano Morozzi	09/2019
3213	(2^624307+185978)/2	187935	Stefano Morozzi	09/2019
3215	(2^624303+40814)/2	187934	Stefano Morozzi	09/2019
3216	(2^624304+99238)/2	187934	Stefano Morozzi	09/2019
3217	2^624077-112723	187866	Enzo Doria	07/2014
3218	2^624008+1874941	187846	Enzo Doria	06/2016
3219	2^623870+78679	187804	Enzo Doria	05/2016
3220	2^623714-114035	187757	Enzo Doria	11/2014
3221	2^623651-1834251	187738	Enzo Doria	07/2015
3222	(7*10^187645+53)/3	187646	Robert Price	05/2018
3223	21650^43269+43269^21650	187591	Norbert Schneider	02/2023
3224	2^623146+1879609	187586	Enzo Doria	09/2016
3225	(401*10^187512+13)/9	187514	Robert Price	09/2021
3226	(5*10^187471+91)/3	187472	Robert Price	04/2018
3227	2^622500+81931	187392	Enzo Doria	08/2016
3228	(13*10^187382-157)/9	187383	Robert Price	05/2021
3229	2^622300-1861739	187331	Enzo Doria	12/2015
3230	(22*10^187317-91)/3	187318	Robert Price	02/2022
3231	(38*10^187281+349)/9	187282	Robert Price	10/2018
3232	2^622052+76771	187257	Enzo Doria	05/2016
3233	2^622005-24091	187243	Enzo Doria	08/2013
3234	7*10^187205-57	187206	Robert Price	06/2020
3235	2^621879-351787	187205	Enzo Doria	07/2015
3236	(5*10^187168-53)/3	187169	Robert Price	09/2020
3237	(23*10^187164-143)/3	187165	Robert Price	12/2019
3238	2^621700+79411	187151	Enzo Doria	06/2016
3239	2^621597+39	187120	Jon Grantham	08/2023
3240	Phi(271207,-5)	187112	Henri Lifchitz	12/2025
3241	(7*10^187101+131)/3	187102	Robert Price	06/2020
3242	(2*10^187062-71)/3	187062	Robert Price	12/2017
3243	V(1118570)	187013	Serge Batalov	07/2024
3244	2^620929-113203	186919	Enzo Doria	07/2014
3245	10^186842+168223	186843	Patrick De Geest	07/2018
3246	10^186842-8001	186842	Robert Price	03/2018
3247	V(1117640)/13411681/26823361/575709775681/989889277441	186814	Serge Batalov	07/2024
3248	2^620347-1777	186744	Lelio R Paula	07/2013
3249	(11*10^186659+133)/9	186660	Robert Price	04/2022
3250	11^179143-4170	186559	Enzo Doria	12/2012

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