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	2^638490-113507	192205	Enzo Doria	08/2014
3002	Phi(75881,561)	192120	Henri Lifchitz	12/2025
3003	2^638189-39943	192115	Enzo Doria	09/2015
3004	2^638110+1877119	192091	Enzo Doria	07/2016
3005	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
3006	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
3007	2^638066-2785211	192078	Enzo Doria	10/2015
3008	(35*10^191973-341)/9	191974	Robert Price	08/2021
3009	(112*10^191900+17)/3	191902	Robert Price	03/2020
3010	2^637475-115309	191900	Enzo Doria	07/2015
3011	(68*10^191754-113)/9	191755	Robert Price	03/2021
3012	2^636930-11	191736	Stefano Morozzi	07/2022
3013	(47*10^191732+259)/9	191733	Robert Price	03/2022
3014	41459^41522-41522^41459	191733	Norbert Schneider	04/2025
3015	2^636661+1876577	191655	Enzo Doria	07/2016
3016	(9^200807-2^200807)/7	191618	Jon Grantham	07/2023
3017	(34^125101-1)/33	191589	Paul Bourdelais	11/2017
3018	fibonacci(916540)-2	191546	Jon Grantham	08/2023
3019	2^636177-1855123	191509	Enzo Doria	09/2015
3020	2^636158-113627	191503	Enzo Doria	08/2014
3021	(37*25^136966+63)/4	191472	Curtis Bright	05/2015
3022	2^636035+79823	191466	Enzo Doria	06/2016
3023	2^636011-1860847	191459	Enzo Doria	11/2015
3024	2^635926-1860611	191433	Enzo Doria	11/2015
3025	3*2^635755+5	191382	Jon Grantham	07/2023
3026	3*10^191152-7	191153	Robert Price	08/2015
3027	2^634883-1865677	191119	Enzo Doria	02/2016
3028	2^634801+1871957	191095	Enzo Doria	05/2016
3029	(77*10^191080+157)/9	191081	Robert Price	05/2022
3030	(35*10^191073+1)/9	191074	Serge Batalov	07/2010
3031	9*10^191018-41	191019	Robert Price	08/2020
3032	2^634470-59861	190995	Enzo Doria	11/2015
3033	2^634368-29519	190964	Enzo Doria	08/2015
3034	(19*10^190935+11)/3	190936	Robert Price	07/2023
3035	2^634188-350609	190910	Enzo Doria	06/2015
3036	(65*10^190899+493)/9	190900	Robert Price	08/2021
3037	(62*10^190795-413)/9	190796	Robert Price	09/2021
3038	(26*10^190789-131)/3	190790	Robert Price	10/2019
3039	(13*10^190732-61)/3	190733	Robert Price	11/2018
3040	3*2^633524+5	190711	Jon Grantham	07/2023
3041	(7*10^190683+143)/3	190684	Robert Price	03/2018
3042	2^633088-113879	190579	Enzo Doria	10/2014
3043	2^633064+1874911	190572	Enzo Doria	06/2016
3044	5*3^399402+2^399402	190564	Jon Grantham	08/2023
3045	(43*10^190547+83)/9	190548	Robert Price	11/2018
3046	99*10^190543+7	190545	Robert Price	05/2021
3047	(299*10^190533+1)/3	190535	Robert Price	04/2020
3048	(1744*10^190519-1747)/3	190522	Robert Price	12/2020
3049	2^632815-15	190497	Stefano Morozzi	07/2022
3050	2^632795-351205	190491	Enzo Doria	06/2015
3051	41171^41272+41272^41171	190454	Norbert Schneider	05/2023
3052	(16*10^190420-19)/3	190421	Robert Price	02/2019
3053	(43*10^190351+101)/9	190352	Robert Price	11/2018
3054	2^632156+78391	190298	Enzo Doria	06/2016
3055	97*10^190295-3	190297	Robert Price	05/2020
3056	2^632082-1851971	190276	Enzo Doria	08/2015
3057	2^632020+1880311	190257	Enzo Doria	09/2016
3058	(5*10^190242-77)/9	190242	Robert Price	04/2021
3059	7*10^190210+13	190211	Robert Price	03/2021
3060	2^631637-462373	190142	Enzo Doria	08/2015
3061	2*10^190126-21	190127	Robert Price	09/2020
3062	(28*10^190105+191)/3	190106	Robert Price	02/2020
3063	2*10^190093+33	190094	Robert Price	11/2021
3064	(68*10^190053-113)/9	190054	Robert Price	03/2021
3065	2^631183+213413	190006	Enzo Doria	09/2023
3066	2^631122-39251	189987	Enzo Doria	08/2015
3067	(26*10^189928-89)/9	189929	Robert Price	06/2018
3068	2^630839-97	189902	Yves Minet	07/2017
3069	99*10^189876-7	189878	Robert Price	07/2020
3070	41147^41147+30^30	189867	Henri Lifchitz	09/2024
3071	2^630359+1788953	189757	Enzo Doria	05/2016
3072	2^630228+1871971	189718	Enzo Doria	05/2016
3073	2^630108+781	189682	Lelio R Paula	08/2013
3074	2^629870-1867811	189610	Enzo Doria	04/2016
3075	(359^74189-1)/358	189558	Alexander Zhirkov	11/2017
3076	2^629326+2792929	189447	Enzo Doria	02/2016
3077	4*10^189401+13	189402	Robert Price	02/2021
3078	(10^189385-61)/3	189385	Serge Batalov	12/2014
3079	2^629036+1874011	189359	Enzo Doria	06/2016
3080	2^628930+80779	189327	Enzo Doria	07/2016
3081	(134*10^189309-11)/3	189311	Robert Price	01/2022
3082	9*10^189306-11	189307	Mischa Rodermond	04/2023
3083	3^396740-396740^3	189294	Henri Lifchitz	07/2024
3084	2^628582+1179439	189223	Enzo Doria	06/2016
3085	(44*10^188999-503)/9	189000	Robert Price	12/2018
3086	(16*10^188823+167)/3	188824	Robert Price	06/2019
3087	(10^188796+7)/4967/71933	188788	Alfred Reich	08/2021
3088	2^627037-2785843	188757	Enzo Doria	10/2015
3089	(10^188566+7)/311640753181661	188552	Alfred Reich	04/2022
3090	(16*10^188457+161)/3	188458	Robert Price	02/2019
3091	L(901657)	188436	Renaud Lifchitz	11/2008
3092	(19*10^188375+137)/3	188376	Robert Price	03/2022
3093	2^625651+74213	188340	Enzo Doria	04/2016
3094	2^625584-460919	188320	Enzo Doria	06/2015
3095	(8*10^188308-71)/9	188308	Serge Batalov	11/2022
3096	5^269399-3^269399-1	188302	Jon Grantham	08/2023
3097	(14*10^188218+139)/9	188219	Robert Price	11/2021
3098	40760^40821-40821^40760	188195	Norbert Schneider	07/2024
3099	(10^188164+359)/9	188164	Serge Batalov	12/2014
3100	2^624481-113611	187988	Enzo Doria	08/2014
3101	(2^624389+125582)/2	187960	Stefano Morozzi	09/2019
3102	(2^624389+166982)/2	187960	Stefano Morozzi	09/2019
3103	(2^624389+179886)/2	187960	Stefano Morozzi	09/2019
3104	(2^624387+64466)/2	187959	Stefano Morozzi	09/2019
3105	(2^624378+112990)/2	187957	Stefano Morozzi	09/2019
3106	(2^624380+161986)/2	187957	Stefano Morozzi	09/2019
3108	(2^624376+55762)/2	187956	Stefano Morozzi	09/2019
3107	(2^624377+169506)/2	187956	Stefano Morozzi	09/2019
3109	(2^624355+80178)/2	187950	Stefano Morozzi	09/2019
3110	(2^624351+61350)/2	187949	Stefano Morozzi	09/2019
3111	(2^624341+63462)/2	187946	Stefano Morozzi	09/2019
3112	(2^624344+135990)/2	187946	Stefano Morozzi	09/2019
3113	(2^624344+183898)/2	187946	Stefano Morozzi	09/2019
3115	(2^624340+126982)/2	187945	Stefano Morozzi	09/2019
3114	(2^624338+196110)/2	187945	Stefano Morozzi	09/2019
3116	(2^624337+105162)/2	187944	Stefano Morozzi	09/2019
3117	(2^624333+44594)/2	187943	Stefano Morozzi	09/2019
3118	(2^624321+88742)/2	187940	Stefano Morozzi	09/2019
3119	(2^624324+135178)/2	187940	Stefano Morozzi	09/2019
3120	(2^624317+14186)/2	187938	Stefano Morozzi	09/2019
3121	(2^624313+24450)/2	187937	Stefano Morozzi	09/2019
3122	(2^624309+184590)/2	187936	Stefano Morozzi	09/2019
3124	(2^624307+152658)/2	187935	Stefano Morozzi	09/2019
3123	(2^624307+185978)/2	187935	Stefano Morozzi	09/2019
3125	(2^624303+40814)/2	187934	Stefano Morozzi	09/2019
3126	(2^624304+99238)/2	187934	Stefano Morozzi	09/2019
3127	2^624077-112723	187866	Enzo Doria	07/2014
3128	2^624008+1874941	187846	Enzo Doria	06/2016
3129	2^623870+78679	187804	Enzo Doria	05/2016
3130	2^623714-114035	187757	Enzo Doria	11/2014
3131	2^623651-1834251	187738	Enzo Doria	07/2015
3132	(7*10^187645+53)/3	187646	Robert Price	05/2018
3133	21650^43269+43269^21650	187591	Norbert Schneider	02/2023
3134	2^623146+1879609	187586	Enzo Doria	09/2016
3135	(401*10^187512+13)/9	187514	Robert Price	09/2021
3136	(5*10^187471+91)/3	187472	Robert Price	04/2018
3137	2^622500+81931	187392	Enzo Doria	08/2016
3138	(13*10^187382-157)/9	187383	Robert Price	05/2021
3139	2^622300-1861739	187331	Enzo Doria	12/2015
3140	(22*10^187317-91)/3	187318	Robert Price	02/2022
3141	(38*10^187281+349)/9	187282	Robert Price	10/2018
3142	2^622052+76771	187257	Enzo Doria	05/2016
3143	2^622005-24091	187243	Enzo Doria	08/2013
3144	7*10^187205-57	187206	Robert Price	06/2020
3145	2^621879-351787	187205	Enzo Doria	07/2015
3146	(5*10^187168-53)/3	187169	Robert Price	09/2020
3147	(23*10^187164-143)/3	187165	Robert Price	12/2019
3148	2^621700+79411	187151	Enzo Doria	06/2016
3149	2^621597+39	187120	Jon Grantham	08/2023
3150	Phi(271207,-5)	187112	Henri Lifchitz	12/2025
3151	(7*10^187101+131)/3	187102	Robert Price	06/2020
3152	(2*10^187062-71)/3	187062	Robert Price	12/2017
3153	V(1118570)	187013	Serge Batalov	07/2024
3154	2^620929-113203	186919	Enzo Doria	07/2014
3155	10^186842+168223	186843	Patrick De Geest	07/2018
3156	10^186842-8001	186842	Robert Price	03/2018
3157	V(1117640)/13411681/26823361/575709775681/989889277441	186814	Serge Batalov	07/2024
3158	2^620347-1777	186744	Lelio R Paula	07/2013
3159	(11*10^186659+133)/9	186660	Robert Price	04/2022
3160	11^179143-4170	186559	Enzo Doria	12/2012
3161	(13^186535)%(10^186535)	186535	Henri Lifchitz	05/2025
3163	(5^266863+1)/6	186529	Paul Bourdelais	07/2010
3162	Phi(266863,-5)	186529	Henri Lifchitz	12/2025
3164	2*10^186517+33	186518	Robert Price	11/2021
3165	2^619297-2792353	186427	Enzo Doria	02/2016
3166	(49*10^186409+383)/9	186410	Robert Price	04/2019
3167	2^618940-460139	186320	Enzo Doria	06/2015
3168	Phi(343570,2^5)	186109	Henri Lifchitz	12/2025
3169	2^618046+74179	186051	Enzo Doria	04/2016
3170	3*10^186019+11	186020	Robert Price	07/2018
3171	(16*10^185978-19)/3	185979	Robert Price	02/2019
3172	(22*10^185950-7)/3	185951	Robert Price	12/2022
3173	2*10^185930-3	185931	Robert Price	07/2015
3174	(82^97151+1)/83	185928	Paul Bourdelais	10/2017
3175	4*10^185905+91	185906	Robert Price	08/2018
3176	(34*10^185902-601)/9	185903	Robert Price	07/2022
3177	(19*10^185873+131)/3	185874	Robert Price	06/2020
3178	(37*10^185811+377)/9	185812	Robert Price	11/2018
3179	2^617250+9385	185811	Lelio R Paula	07/2013
3180	2^617130+9	185775	Stefano Morozzi	05/2021
3181	39^116749+2	185756	Robert Price	04/2015
3182	2^616924-39719	185713	Enzo Doria	09/2015
3183	2^616712+1867621	185649	Enzo Doria	04/2016
3184	(3^388897+2^388897)/5	185551	Jean-Louis Charton	09/2011
3185	8*10^185529-67	185530	Robert Price	08/2019
3186	(5*10^185520-11)/3	185521	Tyler Busby	02/2023
3187	5*2^616124+3	185473	Jon Grantham	07/2023
3188	2^615916+26791	185410	Enzo Doria	12/2023
3189	4*10^185355+9	185356	Robert Price	05/2015
3190	(16*10^185347+89)/3	185348	Robert Price	03/2021
3191	40247^40247-56^56	185327	Henri Lifchitz	08/2024
3192	2^615622+76639	185321	Enzo Doria	05/2016
3193	2^615591+1879223	185312	Enzo Doria	08/2016
3194	2^615587+217013	185311	Enzo Doria	12/2023
3195	2^615503+1876643	185285	Enzo Doria	07/2016
3196	5^265007-4^265007	185232	Jean-Louis Charton	02/2013
3198	(4*10^185221-91)/3	185222	Robert Price	03/2018
3197	(7*10^185221+131)/3	185222	Robert Price	06/2020
3199	(62*10^185216-413)/9	185217	Robert Price	09/2021
3200	(232*10^185180+17)/3	185182	Robert Price	04/2021
3201	56*10^185139-3	185141	Robert Price	03/2020
3202	(28*10^185105+47)/3	185106	Robert Price	02/2021
3203	2^614783-2790097	185069	Enzo Doria	12/2015
3204	2^614745-29323	185057	Enzo Doria	07/2015
3205	(((((((((((2^3+3)^3+30)^3+6)^3+80)^3+12)^3+450)^3+894)^3+3636)^3+70756)^3+97220)^3+66768)^3+300840	185052	Serge Batalov	07/2013
3206	(49*10^184993-67)/9	184994	Robert Price	03/2019
3207	(5*10^184954-191)/3	184955	Robert Price	05/2021
3208	(14*10^184950+211)/9	184951	Robert Price	04/2018
3209	2^614360+215221	184941	Enzo Doria	11/2023
3210	2^614315+81353	184928	Enzo Doria	08/2016
3211	2^614294-1849961	184921	Enzo Doria	08/2015
3212	2^614266+1877809	184913	Enzo Doria	08/2016
3213	(185*10^184878-11)/3	184880	Robert Price	10/2020
3214	91*10^184867-9	184869	Robert Price	06/2021
3215	(37^117841-1)/581320056003516	184784	Paul Vanderveen	06/2025
3216	39803^40170-40170^39803	184779	Norbert Schneider	05/2024
3217	(14789^44521-1)/(14789^211-1)	184770	Ryan Propper	11/2023
3218	(85*10^184768+77)/9	184769	Robert Price	07/2022
3219	2^613715-1860727	184747	Enzo Doria	11/2015
3220	(4*10^184730+89)/3	184731	Robert Price	08/2021
3221	2*10^184723+41	184724	Robert Price	05/2018
3222	(49*10^184703+293)/9	184704	Robert Price	03/2021
3223	2^613487-349987	184678	Enzo Doria	07/2015
3224	(95^93377+1)/96	184672	Paul Bourdelais	11/2017
3225	14^161089-161089^14	184629	Serge Batalov	05/2016
3226	40008^40109-40109^40008	184588	Norbert Schneider	05/2024
3227	2^613033-114621	184542	Enzo Doria	05/2015
3228	3*2^612759+5	184460	Jon Grantham	07/2023
3229	2^612587+213413	184408	Enzo Doria	09/2023
3231	(9^193247+1)/10	184404	Paul Bourdelais	02/2010
3230	Phi(193247,-9)	184404	Henri Lifchitz	12/2025
3232	2^612424+212341	184358	Enzo Doria	08/2023
3233	2^612341-1604809	184334	Enzo Doria	05/2015
3234	(11*10^184308-161)/3	184309	Robert Price	11/2021
3235	(2^611999-1)/18464214225958267477777390354183	184199	Dario Alpern	06/2017
3236	(14*10^184150+37)/3	184151	Robert Price	12/2018
3237	2^611731-4837	184150	Yves Minet	08/2018
3238	3*10^184124-7	184125	Robert Price	08/2015
3239	2^611644+29371	184124	Enzo Doria	02/2024
3240	9*10^184122-11	184123	Mischa Rodermond	04/2023
3241	2^611628-24537	184119	Enzo Doria	08/2013
3242	3*10^184110+13	184111	Robert Price	07/2018
3243	(14280^44521-1)/(14280^211-1)	184097	Ryan Propper	11/2023
3244	(194*10^184093+1)/3	184095	Robert Price	01/2022
3245	2^611460+71881	184068	Enzo Doria	04/2016
3246	4*10^184004-63	184005	Robert Price	10/2018
3247	2^611111+84083	183963	Boyan Hu	05/2024
3248	2^610982-1867301	183924	Enzo Doria	03/2016
3249	(10^183917+1)/11/9952852373	183906	Alfred Reich	02/2024
3250	3*10^183872-49	183873	Robert Price	07/2018

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