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	41147^41147+30^30	189867	Henri Lifchitz	09/2024
3002	2^630359+1788953	189757	Enzo Doria	05/2016
3003	2^630228+1871971	189718	Enzo Doria	05/2016
3004	2^630108+781	189682	Lelio R Paula	08/2013
3005	2^629870-1867811	189610	Enzo Doria	04/2016
3006	(359^74189-1)/358	189558	Alexander Zhirkov	11/2017
3007	2^629326+2792929	189447	Enzo Doria	02/2016
3008	4*10^189401+13	189402	Robert Price	02/2021
3009	(10^189385-61)/3	189385	Serge Batalov	12/2014
3010	2^629036+1874011	189359	Enzo Doria	06/2016
3011	2^628930+80779	189327	Enzo Doria	07/2016
3012	(134*10^189309-11)/3	189311	Robert Price	01/2022
3013	9*10^189306-11	189307	Mischa Rodermond	04/2023
3014	3^396740-396740^3	189294	Henri Lifchitz	07/2024
3015	2^628582+1179439	189223	Enzo Doria	06/2016
3016	(44*10^188999-503)/9	189000	Robert Price	12/2018
3017	(16*10^188823+167)/3	188824	Robert Price	06/2019
3018	(10^188796+7)/4967/71933	188788	Alfred Reich	08/2021
3019	2^627037-2785843	188757	Enzo Doria	10/2015
3020	(10^188566+7)/311640753181661	188552	Alfred Reich	04/2022
3021	(16*10^188457+161)/3	188458	Robert Price	02/2019
3022	L(901657)	188436	Renaud Lifchitz	11/2008
3023	(19*10^188375+137)/3	188376	Robert Price	03/2022
3024	2^625651+74213	188340	Enzo Doria	04/2016
3025	2^625584-460919	188320	Enzo Doria	06/2015
3026	(8*10^188308-71)/9	188308	Serge Batalov	11/2022
3027	5^269399-3^269399-1	188302	Jon Grantham	08/2023
3028	(14*10^188218+139)/9	188219	Robert Price	11/2021
3029	40760^40821-40821^40760	188195	Norbert Schneider	07/2024
3030	(10^188164+359)/9	188164	Serge Batalov	12/2014
3031	2^624481-113611	187988	Enzo Doria	08/2014
3032	(2^624389+125582)/2	187960	Stefano Morozzi	09/2019
3033	(2^624389+166982)/2	187960	Stefano Morozzi	09/2019
3034	(2^624389+179886)/2	187960	Stefano Morozzi	09/2019
3035	(2^624387+64466)/2	187959	Stefano Morozzi	09/2019
3036	(2^624378+112990)/2	187957	Stefano Morozzi	09/2019
3037	(2^624380+161986)/2	187957	Stefano Morozzi	09/2019
3039	(2^624376+55762)/2	187956	Stefano Morozzi	09/2019
3038	(2^624377+169506)/2	187956	Stefano Morozzi	09/2019
3040	(2^624355+80178)/2	187950	Stefano Morozzi	09/2019
3041	(2^624351+61350)/2	187949	Stefano Morozzi	09/2019
3042	(2^624341+63462)/2	187946	Stefano Morozzi	09/2019
3043	(2^624344+135990)/2	187946	Stefano Morozzi	09/2019
3044	(2^624344+183898)/2	187946	Stefano Morozzi	09/2019
3046	(2^624340+126982)/2	187945	Stefano Morozzi	09/2019
3045	(2^624338+196110)/2	187945	Stefano Morozzi	09/2019
3047	(2^624337+105162)/2	187944	Stefano Morozzi	09/2019
3048	(2^624333+44594)/2	187943	Stefano Morozzi	09/2019
3049	(2^624321+88742)/2	187940	Stefano Morozzi	09/2019
3050	(2^624324+135178)/2	187940	Stefano Morozzi	09/2019
3051	(2^624317+14186)/2	187938	Stefano Morozzi	09/2019
3052	(2^624313+24450)/2	187937	Stefano Morozzi	09/2019
3053	(2^624309+184590)/2	187936	Stefano Morozzi	09/2019
3055	(2^624307+152658)/2	187935	Stefano Morozzi	09/2019
3054	(2^624307+185978)/2	187935	Stefano Morozzi	09/2019
3056	(2^624303+40814)/2	187934	Stefano Morozzi	09/2019
3057	(2^624304+99238)/2	187934	Stefano Morozzi	09/2019
3058	2^624077-112723	187866	Enzo Doria	07/2014
3059	2^624008+1874941	187846	Enzo Doria	06/2016
3060	2^623870+78679	187804	Enzo Doria	05/2016
3061	2^623714-114035	187757	Enzo Doria	11/2014
3062	2^623651-1834251	187738	Enzo Doria	07/2015
3063	(7*10^187645+53)/3	187646	Robert Price	05/2018
3064	21650^43269+43269^21650	187591	Norbert Schneider	02/2023
3065	2^623146+1879609	187586	Enzo Doria	09/2016
3066	(401*10^187512+13)/9	187514	Robert Price	09/2021
3067	(5*10^187471+91)/3	187472	Robert Price	04/2018
3068	2^622500+81931	187392	Enzo Doria	08/2016
3069	(13*10^187382-157)/9	187383	Robert Price	05/2021
3070	2^622300-1861739	187331	Enzo Doria	12/2015
3071	(22*10^187317-91)/3	187318	Robert Price	02/2022
3072	(38*10^187281+349)/9	187282	Robert Price	10/2018
3073	2^622052+76771	187257	Enzo Doria	05/2016
3074	2^622005-24091	187243	Enzo Doria	08/2013
3075	7*10^187205-57	187206	Robert Price	06/2020
3076	2^621879-351787	187205	Enzo Doria	07/2015
3077	(5*10^187168-53)/3	187169	Robert Price	09/2020
3078	(23*10^187164-143)/3	187165	Robert Price	12/2019
3079	2^621700+79411	187151	Enzo Doria	06/2016
3080	2^621597+39	187120	Jon Grantham	08/2023
3081	Phi(271207,-5)	187112	Henri Lifchitz	12/2025
3082	(7*10^187101+131)/3	187102	Robert Price	06/2020
3083	(2*10^187062-71)/3	187062	Robert Price	12/2017
3084	V(1118570)	187013	Serge Batalov	07/2024
3085	2^620929-113203	186919	Enzo Doria	07/2014
3086	10^186842+168223	186843	Patrick De Geest	07/2018
3087	10^186842-8001	186842	Robert Price	03/2018
3088	V(1117640)/13411681/26823361/575709775681/989889277441	186814	Serge Batalov	07/2024
3089	2^620347-1777	186744	Lelio R Paula	07/2013
3090	(11*10^186659+133)/9	186660	Robert Price	04/2022
3091	11^179143-4170	186559	Enzo Doria	12/2012
3092	(13^186535)%(10^186535)	186535	Henri Lifchitz	05/2025
3094	(5^266863+1)/6	186529	Paul Bourdelais	07/2010
3093	Phi(266863,-5)	186529	Henri Lifchitz	12/2025
3095	2*10^186517+33	186518	Robert Price	11/2021
3096	2^619297-2792353	186427	Enzo Doria	02/2016
3097	(49*10^186409+383)/9	186410	Robert Price	04/2019
3098	2^618940-460139	186320	Enzo Doria	06/2015
3099	Phi(343570,2^5)	186109	Henri Lifchitz	12/2025
3100	2^618046+74179	186051	Enzo Doria	04/2016
3101	3*10^186019+11	186020	Robert Price	07/2018
3102	(16*10^185978-19)/3	185979	Robert Price	02/2019
3103	(22*10^185950-7)/3	185951	Robert Price	12/2022
3104	2*10^185930-3	185931	Robert Price	07/2015
3105	(82^97151+1)/83	185928	Paul Bourdelais	10/2017
3106	4*10^185905+91	185906	Robert Price	08/2018
3107	(34*10^185902-601)/9	185903	Robert Price	07/2022
3108	(19*10^185873+131)/3	185874	Robert Price	06/2020
3109	(37*10^185811+377)/9	185812	Robert Price	11/2018
3110	2^617250+9385	185811	Lelio R Paula	07/2013
3111	2^617130+9	185775	Stefano Morozzi	05/2021
3112	39^116749+2	185756	Robert Price	04/2015
3113	2^616924-39719	185713	Enzo Doria	09/2015
3114	2^616712+1867621	185649	Enzo Doria	04/2016
3115	(3^388897+2^388897)/5	185551	Jean-Louis Charton	09/2011
3116	8*10^185529-67	185530	Robert Price	08/2019
3117	(5*10^185520-11)/3	185521	Tyler Busby	02/2023
3118	5*2^616124+3	185473	Jon Grantham	07/2023
3119	2^615916+26791	185410	Enzo Doria	12/2023
3120	4*10^185355+9	185356	Robert Price	05/2015
3121	(16*10^185347+89)/3	185348	Robert Price	03/2021
3122	40247^40247-56^56	185327	Henri Lifchitz	08/2024
3123	2^615622+76639	185321	Enzo Doria	05/2016
3124	2^615591+1879223	185312	Enzo Doria	08/2016
3125	2^615587+217013	185311	Enzo Doria	12/2023
3126	2^615503+1876643	185285	Enzo Doria	07/2016
3127	5^265007-4^265007	185232	Jean-Louis Charton	02/2013
3128	(4*10^185221-91)/3	185222	Robert Price	03/2018
3129	(7*10^185221+131)/3	185222	Robert Price	06/2020
3130	(62*10^185216-413)/9	185217	Robert Price	09/2021
3131	(232*10^185180+17)/3	185182	Robert Price	04/2021
3132	56*10^185139-3	185141	Robert Price	03/2020
3133	(28*10^185105+47)/3	185106	Robert Price	02/2021
3134	2^614783-2790097	185069	Enzo Doria	12/2015
3135	2^614745-29323	185057	Enzo Doria	07/2015
3136	(((((((((((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
3137	(49*10^184993-67)/9	184994	Robert Price	03/2019
3138	(5*10^184954-191)/3	184955	Robert Price	05/2021
3139	(14*10^184950+211)/9	184951	Robert Price	04/2018
3140	2^614360+215221	184941	Enzo Doria	11/2023
3141	2^614315+81353	184928	Enzo Doria	08/2016
3142	2^614294-1849961	184921	Enzo Doria	08/2015
3143	2^614266+1877809	184913	Enzo Doria	08/2016
3144	(185*10^184878-11)/3	184880	Robert Price	10/2020
3145	91*10^184867-9	184869	Robert Price	06/2021
3146	(37^117841-1)/581320056003516	184784	Paul Vanderveen	06/2025
3147	39803^40170-40170^39803	184779	Norbert Schneider	05/2024
3148	(14789^44521-1)/(14789^211-1)	184770	Ryan Propper	11/2023
3149	(85*10^184768+77)/9	184769	Robert Price	07/2022
3150	2^613715-1860727	184747	Enzo Doria	11/2015
3151	(4*10^184730+89)/3	184731	Robert Price	08/2021
3152	2*10^184723+41	184724	Robert Price	05/2018
3153	(49*10^184703+293)/9	184704	Robert Price	03/2021
3154	2^613487-349987	184678	Enzo Doria	07/2015
3155	(95^93377+1)/96	184672	Paul Bourdelais	11/2017
3156	14^161089-161089^14	184629	Serge Batalov	05/2016
3157	40008^40109-40109^40008	184588	Norbert Schneider	05/2024
3158	2^613033-114621	184542	Enzo Doria	05/2015
3159	3*2^612759+5	184460	Jon Grantham	07/2023
3160	2^612587+213413	184408	Enzo Doria	09/2023
3162	(9^193247+1)/10	184404	Paul Bourdelais	02/2010
3161	Phi(193247,-9)	184404	Henri Lifchitz	12/2025
3163	2^612424+212341	184358	Enzo Doria	08/2023
3164	2^612341-1604809	184334	Enzo Doria	05/2015
3165	(11*10^184308-161)/3	184309	Robert Price	11/2021
3166	(2^611999-1)/18464214225958267477777390354183	184199	Dario Alpern	06/2017
3167	(14*10^184150+37)/3	184151	Robert Price	12/2018
3168	2^611731-4837	184150	Yves Minet	08/2018
3169	3*10^184124-7	184125	Robert Price	08/2015
3170	2^611644+29371	184124	Enzo Doria	02/2024
3171	9*10^184122-11	184123	Mischa Rodermond	04/2023
3172	2^611628-24537	184119	Enzo Doria	08/2013
3173	3*10^184110+13	184111	Robert Price	07/2018
3174	(14280^44521-1)/(14280^211-1)	184097	Ryan Propper	11/2023
3175	(194*10^184093+1)/3	184095	Robert Price	01/2022
3176	2^611460+71881	184068	Enzo Doria	04/2016
3177	4*10^184004-63	184005	Robert Price	10/2018
3178	2^611111+84083	183963	Boyan Hu	05/2024
3179	2^610982-1867301	183924	Enzo Doria	03/2016
3180	(10^183917+1)/11/9952852373	183906	Alfred Reich	02/2024
3181	3*10^183872-49	183873	Robert Price	07/2018
3182	2^610597+1178897	183809	Enzo Doria	05/2016
3183	(8*10^183773-269)/9	183773	Robert Price	09/2021
3184	(65*10^183768-29)/9	183769	Robert Price	01/2021
3185	(17*10^183764+31)/3	183765	Robert Price	01/2019
3186	(28*10^183760-1)/9	183761	Serge Batalov	10/2014
3187	2^610401+1277	183750	Lelio R Paula	07/2013
3188	2^610356-1849019	183736	Enzo Doria	08/2015
3189	(63^102103+1)/64	183717	Paul Bourdelais	10/2017
3190	23*10^183710-7	183712	Robert Price	02/2020
3191	(2^610289+1)/(3*528882550291)	183704	Gord Palameta	08/2018
3192	(4*10^183659+149)/9	183659	Robert Price	04/2018
3193	(4*10^183657+41)/9	183657	Serge Batalov	11/2022
3194	(11^176327-1)/31738870	183619	Paul Vanderveen	05/2025
3195	7*10^183596+39	183597	Robert Price	01/2023
3196	2^609846-1834251	183582	Enzo Doria	07/2015
3197	10^183546+1547323	183547	Patrick De Geest	02/2021
3199	10^183546-800000001	183546	Robert Price	09/2020
3198	10^183546-584297	183546	Patrick De Geest	02/2021
3200	7*10^183511+39	183512	Robert Price	01/2023
3201	(23*10^183477-71)/3	183478	Robert Price	07/2020
3202	11^176176-240	183469	Enzo Doria	11/2012
3203	(41^113749+1)/42	183451	Paul Bourdelais	11/2017
3204	6*10^183429+53	183430	Robert Price	05/2020
3205	(28*10^183403+191)/3	183404	Robert Price	02/2020
3206	U(1096855)	183383	Serge Batalov	07/2024
3207	(5^262337-1)/363486427756606700767551233751524443601036	183325	Paul Vanderveen	05/2025
3208	(101^91463+1)/102	183320	Paul Bourdelais	11/2017
3209	2^608965-113989	183317	Enzo Doria	10/2014
3210	A005165(43592)	183312	Serge Batalov	07/2017
3211	(61*10^183294+119)/9	183295	Robert Price	05/2019
3212	2^608814-461261	183272	Enzo Doria	06/2015
3213	(163*10^183227-1)/9	183229	Serge Batalov	12/2014
3214	2^608541-608541^2	183190	Henri Lifchitz	02/2018
3215	2^608293+143807	183115	Enzo Doria	10/2016
3216	2^608164-462419	183076	Enzo Doria	08/2015
3217	2^607950-1862303	183012	Enzo Doria	12/2015
3218	5*3^383376+2^383376	182918	Jon Grantham	08/2023
3219	(46*10^182896+683)/9	182897	Robert Price	03/2019
3220	(2*10^182787+73)/3	182787	Robert Price	09/2020
3221	2^607101+1871987	182756	Enzo Doria	05/2016
3222	2^606869-69175	182686	Enzo Doria	11/2015
3223	8*10^182671+71	182672	Robert Price	05/2022
3224	(23*10^182666-71)/3	182667	Robert Price	07/2020
3225	3*10^182614-11	182615	Robert Price	07/2018
3226	2^606560-357	182593	Enzo Doria	05/2014
3227	66*10^182420+7	182422	Robert Price	07/2020
3228	2^605687+1866983	182330	Enzo Doria	03/2016
3229	2^605655-114445	182321	Enzo Doria	02/2015
3230	94*10^182291-3	182293	Robert Price	05/2020
3231	(20^140053+1)/21	182212	Paul Bourdelais	04/2010
3232	(14*10^182177-221)/9	182178	Robert Price	04/2018
3233	2^605174-112751	182176	Enzo Doria	06/2014
3234	(905^61609-1)/904	182154	Anonymous	05/2024
3235	2^604761+1874507	182052	Enzo Doria	06/2016
3236	2^604705+1871957	182035	Enzo Doria	05/2016
3237	(14*10^182000+229)/9	182001	Robert Price	03/2018
3238	(10^181996+41)/3	181996	Robert Price	12/2017
3239	(17*10^181979+91)/9	181980	Robert Price	02/2022
3240	(10^181960+3)/7	181960	Jinyuan Wang	11/2024
3241	(5*10^181950-101)/3	181951	Robert Price	04/2018
3242	2^603915+75233	181797	Enzo Doria	04/2016
3243	39470^39537+39537^39470	181723	Norbert Schneider	12/2022
3244	(10^181710+7)/563747/2019847	181698	Alfred Reich	08/2021
3245	7*10^181594-57	181595	Robert Price	06/2020
3246	8*10^181580+29	181581	Robert Price	11/2021
3247	(83*10^181544+61)/9	181545	Serge Batalov	01/2023
3248	(2*10^181457+7)/9	181457	Rytis Slatkevicius	01/2023
3249	3*10^181445+23	181446	Robert Price	03/2022
3250	(194*10^181369-11)/3	181371	Robert Price	09/2020

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