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	(14*10^195234-83)/3	195235	Robert Price	12/2018
3002	5*10^195221+81	195222	Robert Price	03/2019
3003	10^195143-5001	195143	Robert Price	12/2021
3004	2^648190-24737	195125	Enzo Doria	09/2013
3005	(57^111119+1)/58	195110	Paul Bourdelais	10/2017
3006	(29*10^195098-197)/3	195099	Robert Price	08/2021
3007	10^195060+89701	195061	Patrick De Geest	02/2021
3009	10^195060-40000000001	195060	Robert Price	09/2020
3008	10^195060-110337	195060	Patrick De Geest	02/2021
3010	56*10^195032-3	195034	Robert Price	03/2020
3011	11^187185-90	194934	Enzo Doria	09/2012
3012	2^647545-25	194931	Boyan Hu	12/2024
3013	2^647468+220141	194908	Enzo Doria	03/2024
3014	(83^101533-1)/91545628589416644493342	194827	Paul Vanderveen	06/2025
3015	(86*10^194818-437)/9	194819	Robert Price	03/2021
3016	7^230492-230492^7	194789	Henri Lifchitz	07/2024
3017	2^647068+77281	194787	Enzo Doria	05/2016
3018	2*10^194716-93	194717	Robert Price	12/2021
3019	15^165559-14^165559	194713	Jean-Louis Charton	03/2011
3020	F(931517)	194676	Henri Lifchitz	09/2008
3021	4*10^194668+49	194669	Robert Price	01/2019
3022	408^74564+407	194662	Alfred Reich	04/2026
3023	2^646589+1179407	194643	Enzo Doria	06/2016
3024	2^646289-114621	194553	Enzo Doria	05/2015
3025	2^646236-39659	194537	Enzo Doria	09/2015
3026	(16*10^194536+53)/3	194537	Robert Price	03/2019
3027	2^646161-59833	194514	Enzo Doria	11/2015
3028	(17*10^194502+31)/3	194503	Robert Price	01/2019
3029	(19*10^194428+287)/9	194429	Robert Price	10/2021
3030	2*10^194413+3	194414	Robert Price	07/2015
3031	2^645360-1848599	194273	Enzo Doria	08/2015
3032	22470^44641+44641^22470	194260	Norbert Schneider	08/2023
3033	(112*10^194150-1)/3	194152	Serge Batalov	12/2014
3034	Phi(293127,10)	194041	Makoto Kamada	12/2023
3035	2*10^193981-43	193982	Robert Price	04/2018
3036	2^644382+75169	193979	Enzo Doria	04/2016
3037	2^644304-1861409	193955	Enzo Doria	11/2015
3038	(29*10^193950-23)/3	193951	Robert Price	03/2022
3039	5*10^193907-9	193908	Robert Price	05/2015
3040	2^644043+1876703	193877	Enzo Doria	07/2016
3041	2*10^193841-63	193842	Robert Price	01/2022
3042	2^643735+1879733	193784	Enzo Doria	09/2016
3044	(5^277183+1)/6	193742	Paul Bourdelais	07/2010
3043	Phi(277183,-5)	193742	Henri Lifchitz	12/2025
3045	9*10^193712+71	193713	Robert Price	08/2020
3046	2^643216-286565	193628	Enzo Doria	07/2015
3047	2^643204+215011	193624	Enzo Doria	11/2023
3048	10^193566+1126339	193567	Patrick De Geest	09/2022
3050	10^193566-10000000001	193566	Robert Price	04/2021
3049	10^193566-454041	193566	Patrick De Geest	08/2021
3052	2^642888-24965	193529	Enzo Doria	09/2013
3051	2^642889+25367	193529	Enzo Doria	11/2023
3053	Phi(50157,p(50157))	193510	Henri Lifchitz	12/2025
3054	2^642448-114825	193397	Enzo Doria	05/2015
3055	2^642437-1856623	193393	Enzo Doria	10/2015
3056	2^642039-59797	193273	Enzo Doria	11/2015
3057	2^641987+39	193258	Jon Grantham	08/2023
3058	10^193230+513861	193231	Patrick De Geest	07/2018
3059	10^193230-8001	193230	Robert Price	03/2018
3060	(62*10^193225-233)/9	193226	Robert Price	02/2022
3061	Phi(86312,13#)	193216	Henri Lifchitz	02/2026
3062	2^641692-286349	193169	Enzo Doria	07/2015
3063	2^641690-24737	193168	Enzo Doria	09/2013
3064	22268^44421+44421^22268	193129	Norbert Schneider	06/2023
3065	2^641514+1876549	193115	Enzo Doria	07/2016
3066	2^640888-2785619	192927	Enzo Doria	10/2015
3067	2^640874-2783741	192923	Enzo Doria	09/2015
3068	10^192922+192207	192923	Patrick De Geest	08/2021
3069	10^192922-7001	192922	Robert Price	04/2021
3070	2^640854+25	192917	Stefano Morozzi	05/2021
3071	34*10^192868-9	192870	Robert Price	06/2020
3072	(46*10^192841+683)/9	192842	Robert Price	03/2019
3073	2^640181+467	192714	Lelio R Paula	08/2013
3074	2^640072+27541	192681	Enzo Doria	01/2024
3075	(10^192700)/(192700^10)	192648	Henri Lifchitz	05/2025
3076	2^639536-1850249	192520	Enzo Doria	08/2015
3077	40714<>40712<>...<>1086421357911<>...<>40711<>40713	192464	Hans Havermann	12/2019
3078	5*10^192422-43	192423	Robert Price	01/2019
3079	2^639110-2792441	192392	Enzo Doria	02/2016
3080	(241^80761-1)/240	192372	Anonymous	04/2024
3081	2^638955-29827	192345	Enzo Doria	08/2015
3082	15^163539+14	192337	Alfred Reich	10/2023
3083	2^638713-2784223	192272	Enzo Doria	10/2015
3084	(10^192216+7)/149	192214	Alfred Reich	07/2021
3085	2^638490-113507	192205	Enzo Doria	08/2014
3086	Phi(75881,561)	192120	Henri Lifchitz	12/2025
3087	2^638189-39943	192115	Enzo Doria	09/2015
3088	2^638110+1877119	192091	Enzo Doria	07/2016
3089	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
3090	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
3091	2^638066-2785211	192078	Enzo Doria	10/2015
3092	(35*10^191973-341)/9	191974	Robert Price	08/2021
3093	(112*10^191900+17)/3	191902	Robert Price	03/2020
3094	2^637475-115309	191900	Enzo Doria	07/2015
3095	(68*10^191754-113)/9	191755	Robert Price	03/2021
3096	2^636930-11	191736	Stefano Morozzi	07/2022
3097	(47*10^191732+259)/9	191733	Robert Price	03/2022
3098	41459^41522-41522^41459	191733	Norbert Schneider	04/2025
3099	2^636661+1876577	191655	Enzo Doria	07/2016
3100	(9^200807-2^200807)/7	191618	Jon Grantham	07/2023
3101	(34^125101-1)/33	191589	Paul Bourdelais	11/2017
3102	fibonacci(916540)-2	191546	Jon Grantham	08/2023
3103	2^636177-1855123	191509	Enzo Doria	09/2015
3104	2^636158-113627	191503	Enzo Doria	08/2014
3105	(37*25^136966+63)/4	191472	Curtis Bright	05/2015
3106	2^636035+79823	191466	Enzo Doria	06/2016
3107	2^636011-1860847	191459	Enzo Doria	11/2015
3108	2^635926-1860611	191433	Enzo Doria	11/2015
3109	3*2^635755+5	191382	Jon Grantham	07/2023
3110	3*10^191152-7	191153	Robert Price	08/2015
3111	2^634883-1865677	191119	Enzo Doria	02/2016
3112	2^634801+1871957	191095	Enzo Doria	05/2016
3113	(77*10^191080+157)/9	191081	Robert Price	05/2022
3114	(35*10^191073+1)/9	191074	Serge Batalov	07/2010
3115	9*10^191018-41	191019	Robert Price	08/2020
3116	2^634470-59861	190995	Enzo Doria	11/2015
3117	2^634368-29519	190964	Enzo Doria	08/2015
3118	(19*10^190935+11)/3	190936	Robert Price	07/2023
3119	2^634188-350609	190910	Enzo Doria	06/2015
3120	(65*10^190899+493)/9	190900	Robert Price	08/2021
3121	405^73192+404	190845	Alfred Reich	04/2026
3122	(62*10^190795-413)/9	190796	Robert Price	09/2021
3123	(26*10^190789-131)/3	190790	Robert Price	10/2019
3124	(13*10^190732-61)/3	190733	Robert Price	11/2018
3125	3*2^633524+5	190711	Jon Grantham	07/2023
3126	(7*10^190683+143)/3	190684	Robert Price	03/2018
3127	2^633088-113879	190579	Enzo Doria	10/2014
3128	2^633064+1874911	190572	Enzo Doria	06/2016
3129	5*3^399402+2^399402	190564	Jon Grantham	08/2023
3130	(43*10^190547+83)/9	190548	Robert Price	11/2018
3131	99*10^190543+7	190545	Robert Price	05/2021
3132	(299*10^190533+1)/3	190535	Robert Price	04/2020
3133	(1744*10^190519-1747)/3	190522	Robert Price	12/2020
3134	2^632815-15	190497	Stefano Morozzi	07/2022
3135	2^632795-351205	190491	Enzo Doria	06/2015
3136	41171^41272+41272^41171	190454	Norbert Schneider	05/2023
3137	(16*10^190420-19)/3	190421	Robert Price	02/2019
3138	(43*10^190351+101)/9	190352	Robert Price	11/2018
3139	2^632156+78391	190298	Enzo Doria	06/2016
3140	97*10^190295-3	190297	Robert Price	05/2020
3141	2^632082-1851971	190276	Enzo Doria	08/2015
3142	2^632020+1880311	190257	Enzo Doria	09/2016
3143	(5*10^190242-77)/9	190242	Robert Price	04/2021
3144	7*10^190210+13	190211	Robert Price	03/2021
3145	2^631637-462373	190142	Enzo Doria	08/2015
3146	2*10^190126-21	190127	Robert Price	09/2020
3147	(28*10^190105+191)/3	190106	Robert Price	02/2020
3148	2*10^190093+33	190094	Robert Price	11/2021
3149	(68*10^190053-113)/9	190054	Robert Price	03/2021
3150	2^631183+213413	190006	Enzo Doria	09/2023
3151	2^631122-39251	189987	Enzo Doria	08/2015
3152	(26*10^189928-89)/9	189929	Robert Price	06/2018
3153	2^630839-97	189902	Yves Minet	07/2017
3154	99*10^189876-7	189878	Robert Price	07/2020
3155	41147^41147+30^30	189867	Henri Lifchitz	09/2024
3156	2^630359+1788953	189757	Enzo Doria	05/2016
3157	2^630228+1871971	189718	Enzo Doria	05/2016
3158	2^630108+781	189682	Lelio R Paula	08/2013
3159	2^629870-1867811	189610	Enzo Doria	04/2016
3160	(359^74189-1)/358	189558	Alexander Zhirkov	11/2017
3161	2^629326+2792929	189447	Enzo Doria	02/2016
3162	4*10^189401+13	189402	Robert Price	02/2021
3163	(10^189385-61)/3	189385	Serge Batalov	12/2014
3164	2^629036+1874011	189359	Enzo Doria	06/2016
3165	2^628930+80779	189327	Enzo Doria	07/2016
3166	(134*10^189309-11)/3	189311	Robert Price	01/2022
3167	9*10^189306-11	189307	Mischa Rodermond	04/2023
3168	3^396740-396740^3	189294	Henri Lifchitz	07/2024
3169	2^628582+1179439	189223	Enzo Doria	06/2016
3170	(44*10^188999-503)/9	189000	Robert Price	12/2018
3171	(16*10^188823+167)/3	188824	Robert Price	06/2019
3172	(10^188796+7)/4967/71933	188788	Alfred Reich	08/2021
3173	2^627037-2785843	188757	Enzo Doria	10/2015
3174	(10^188566+7)/311640753181661	188552	Alfred Reich	04/2022
3175	(16*10^188457+161)/3	188458	Robert Price	02/2019
3176	L(901657)	188436	Renaud Lifchitz	11/2008
3177	(19*10^188375+137)/3	188376	Robert Price	03/2022
3178	2^625651+74213	188340	Enzo Doria	04/2016
3179	2^625584-460919	188320	Enzo Doria	06/2015
3180	(8*10^188308-71)/9	188308	Serge Batalov	11/2022
3181	5^269399-3^269399-1	188302	Jon Grantham	08/2023
3182	(14*10^188218+139)/9	188219	Robert Price	11/2021
3183	40760^40821-40821^40760	188195	Norbert Schneider	07/2024
3184	(10^188164+359)/9	188164	Serge Batalov	12/2014
3185	2^624481-113611	187988	Enzo Doria	08/2014
3186	(2^624389+125582)/2	187960	Stefano Morozzi	09/2019
3187	(2^624389+166982)/2	187960	Stefano Morozzi	09/2019
3188	(2^624389+179886)/2	187960	Stefano Morozzi	09/2019
3189	(2^624387+64466)/2	187959	Stefano Morozzi	09/2019
3190	(2^624378+112990)/2	187957	Stefano Morozzi	09/2019
3191	(2^624380+161986)/2	187957	Stefano Morozzi	09/2019
3193	(2^624376+55762)/2	187956	Stefano Morozzi	09/2019
3192	(2^624377+169506)/2	187956	Stefano Morozzi	09/2019
3194	(2^624355+80178)/2	187950	Stefano Morozzi	09/2019
3195	(2^624351+61350)/2	187949	Stefano Morozzi	09/2019
3196	(2^624341+63462)/2	187946	Stefano Morozzi	09/2019
3197	(2^624344+135990)/2	187946	Stefano Morozzi	09/2019
3198	(2^624344+183898)/2	187946	Stefano Morozzi	09/2019
3200	(2^624340+126982)/2	187945	Stefano Morozzi	09/2019
3199	(2^624338+196110)/2	187945	Stefano Morozzi	09/2019
3201	(2^624337+105162)/2	187944	Stefano Morozzi	09/2019
3202	(2^624333+44594)/2	187943	Stefano Morozzi	09/2019
3203	(2^624321+88742)/2	187940	Stefano Morozzi	09/2019
3204	(2^624324+135178)/2	187940	Stefano Morozzi	09/2019
3205	(2^624317+14186)/2	187938	Stefano Morozzi	09/2019
3206	(2^624313+24450)/2	187937	Stefano Morozzi	09/2019
3207	(2^624309+184590)/2	187936	Stefano Morozzi	09/2019
3209	(2^624307+152658)/2	187935	Stefano Morozzi	09/2019
3208	(2^624307+185978)/2	187935	Stefano Morozzi	09/2019
3210	(2^624303+40814)/2	187934	Stefano Morozzi	09/2019
3211	(2^624304+99238)/2	187934	Stefano Morozzi	09/2019
3212	2^624077-112723	187866	Enzo Doria	07/2014
3213	2^624008+1874941	187846	Enzo Doria	06/2016
3214	2^623870+78679	187804	Enzo Doria	05/2016
3215	2^623714-114035	187757	Enzo Doria	11/2014
3216	2^623651-1834251	187738	Enzo Doria	07/2015
3217	(7*10^187645+53)/3	187646	Robert Price	05/2018
3218	21650^43269+43269^21650	187591	Norbert Schneider	02/2023
3219	2^623146+1879609	187586	Enzo Doria	09/2016
3220	(401*10^187512+13)/9	187514	Robert Price	09/2021
3221	(5*10^187471+91)/3	187472	Robert Price	04/2018
3222	2^622500+81931	187392	Enzo Doria	08/2016
3223	(13*10^187382-157)/9	187383	Robert Price	05/2021
3224	2^622300-1861739	187331	Enzo Doria	12/2015
3225	(22*10^187317-91)/3	187318	Robert Price	02/2022
3226	(38*10^187281+349)/9	187282	Robert Price	10/2018
3227	2^622052+76771	187257	Enzo Doria	05/2016
3228	2^622005-24091	187243	Enzo Doria	08/2013
3229	7*10^187205-57	187206	Robert Price	06/2020
3230	2^621879-351787	187205	Enzo Doria	07/2015
3231	(5*10^187168-53)/3	187169	Robert Price	09/2020
3232	(23*10^187164-143)/3	187165	Robert Price	12/2019
3233	2^621700+79411	187151	Enzo Doria	06/2016
3234	2^621597+39	187120	Jon Grantham	08/2023
3235	Phi(271207,-5)	187112	Henri Lifchitz	12/2025
3236	(7*10^187101+131)/3	187102	Robert Price	06/2020
3237	(2*10^187062-71)/3	187062	Robert Price	12/2017
3238	V(1118570)	187013	Serge Batalov	07/2024
3239	2^620929-113203	186919	Enzo Doria	07/2014
3240	10^186842+168223	186843	Patrick De Geest	07/2018
3241	10^186842-8001	186842	Robert Price	03/2018
3242	V(1117640)/13411681/26823361/575709775681/989889277441	186814	Serge Batalov	07/2024
3243	2^620347-1777	186744	Lelio R Paula	07/2013
3244	(11*10^186659+133)/9	186660	Robert Price	04/2022
3245	11^179143-4170	186559	Enzo Doria	12/2012
3246	(13^186535)%(10^186535)	186535	Henri Lifchitz	05/2025
3248	(5^266863+1)/6	186529	Paul Bourdelais	07/2010
3247	Phi(266863,-5)	186529	Henri Lifchitz	12/2025
3249	2*10^186517+33	186518	Robert Price	11/2021
3250	2^619297-2792353	186427	Enzo Doria	02/2016

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