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	5*3^399402+2^399402	190564	Jon Grantham	08/2023
3002	(43*10^190547+83)/9	190548	Robert Price	11/2018
3003	99*10^190543+7	190545	Robert Price	05/2021
3004	(299*10^190533+1)/3	190535	Robert Price	04/2020
3005	(1744*10^190519-1747)/3	190522	Robert Price	12/2020
3006	2^632815-15	190497	Stefano Morozzi	07/2022
3007	2^632795-351205	190491	Enzo Doria	06/2015
3008	41171^41272+41272^41171	190454	Norbert Schneider	05/2023
3009	(16*10^190420-19)/3	190421	Robert Price	02/2019
3010	(43*10^190351+101)/9	190352	Robert Price	11/2018
3011	2^632156+78391	190298	Enzo Doria	06/2016
3012	97*10^190295-3	190297	Robert Price	05/2020
3013	2^632082-1851971	190276	Enzo Doria	08/2015
3014	2^632020+1880311	190257	Enzo Doria	09/2016
3015	(5*10^190242-77)/9	190242	Robert Price	04/2021
3016	7*10^190210+13	190211	Robert Price	03/2021
3017	2^631637-462373	190142	Enzo Doria	08/2015
3018	2*10^190126-21	190127	Robert Price	09/2020
3019	(28*10^190105+191)/3	190106	Robert Price	02/2020
3020	2*10^190093+33	190094	Robert Price	11/2021
3021	(68*10^190053-113)/9	190054	Robert Price	03/2021
3022	2^631183+213413	190006	Enzo Doria	09/2023
3023	2^631122-39251	189987	Enzo Doria	08/2015
3024	(26*10^189928-89)/9	189929	Robert Price	06/2018
3025	2^630839-97	189902	Yves Minet	07/2017
3026	99*10^189876-7	189878	Robert Price	07/2020
3027	41147^41147+30^30	189867	Henri Lifchitz	09/2024
3028	2^630359+1788953	189757	Enzo Doria	05/2016
3029	2^630228+1871971	189718	Enzo Doria	05/2016
3030	2^630108+781	189682	Lelio R Paula	08/2013
3031	2^629870-1867811	189610	Enzo Doria	04/2016
3032	(359^74189-1)/358	189558	Alexander Zhirkov	11/2017
3033	2^629326+2792929	189447	Enzo Doria	02/2016
3034	4*10^189401+13	189402	Robert Price	02/2021
3035	(10^189385-61)/3	189385	Serge Batalov	12/2014
3036	2^629036+1874011	189359	Enzo Doria	06/2016
3037	2^628930+80779	189327	Enzo Doria	07/2016
3038	(134*10^189309-11)/3	189311	Robert Price	01/2022
3039	9*10^189306-11	189307	Mischa Rodermond	04/2023
3040	3^396740-396740^3	189294	Henri Lifchitz	07/2024
3041	2^628582+1179439	189223	Enzo Doria	06/2016
3042	(44*10^188999-503)/9	189000	Robert Price	12/2018
3043	(16*10^188823+167)/3	188824	Robert Price	06/2019
3044	(10^188796+7)/4967/71933	188788	Alfred Reich	08/2021
3045	2^627037-2785843	188757	Enzo Doria	10/2015
3046	(10^188566+7)/311640753181661	188552	Alfred Reich	04/2022
3047	(16*10^188457+161)/3	188458	Robert Price	02/2019
3048	L(901657)	188436	Renaud Lifchitz	11/2008
3049	(19*10^188375+137)/3	188376	Robert Price	03/2022
3050	2^625651+74213	188340	Enzo Doria	04/2016
3051	2^625584-460919	188320	Enzo Doria	06/2015
3052	(8*10^188308-71)/9	188308	Serge Batalov	11/2022
3053	5^269399-3^269399-1	188302	Jon Grantham	08/2023
3054	(14*10^188218+139)/9	188219	Robert Price	11/2021
3055	40760^40821-40821^40760	188195	Norbert Schneider	07/2024
3056	(10^188164+359)/9	188164	Serge Batalov	12/2014
3057	2^624481-113611	187988	Enzo Doria	08/2014
3058	(2^624389+125582)/2	187960	Stefano Morozzi	09/2019
3059	(2^624389+166982)/2	187960	Stefano Morozzi	09/2019
3060	(2^624389+179886)/2	187960	Stefano Morozzi	09/2019
3061	(2^624387+64466)/2	187959	Stefano Morozzi	09/2019
3062	(2^624378+112990)/2	187957	Stefano Morozzi	09/2019
3063	(2^624380+161986)/2	187957	Stefano Morozzi	09/2019
3065	(2^624376+55762)/2	187956	Stefano Morozzi	09/2019
3064	(2^624377+169506)/2	187956	Stefano Morozzi	09/2019
3066	(2^624355+80178)/2	187950	Stefano Morozzi	09/2019
3067	(2^624351+61350)/2	187949	Stefano Morozzi	09/2019
3068	(2^624341+63462)/2	187946	Stefano Morozzi	09/2019
3069	(2^624344+135990)/2	187946	Stefano Morozzi	09/2019
3070	(2^624344+183898)/2	187946	Stefano Morozzi	09/2019
3072	(2^624340+126982)/2	187945	Stefano Morozzi	09/2019
3071	(2^624338+196110)/2	187945	Stefano Morozzi	09/2019
3073	(2^624337+105162)/2	187944	Stefano Morozzi	09/2019
3074	(2^624333+44594)/2	187943	Stefano Morozzi	09/2019
3075	(2^624321+88742)/2	187940	Stefano Morozzi	09/2019
3076	(2^624324+135178)/2	187940	Stefano Morozzi	09/2019
3077	(2^624317+14186)/2	187938	Stefano Morozzi	09/2019
3078	(2^624313+24450)/2	187937	Stefano Morozzi	09/2019
3079	(2^624309+184590)/2	187936	Stefano Morozzi	09/2019
3081	(2^624307+152658)/2	187935	Stefano Morozzi	09/2019
3080	(2^624307+185978)/2	187935	Stefano Morozzi	09/2019
3082	(2^624303+40814)/2	187934	Stefano Morozzi	09/2019
3083	(2^624304+99238)/2	187934	Stefano Morozzi	09/2019
3084	2^624077-112723	187866	Enzo Doria	07/2014
3085	2^624008+1874941	187846	Enzo Doria	06/2016
3086	2^623870+78679	187804	Enzo Doria	05/2016
3087	2^623714-114035	187757	Enzo Doria	11/2014
3088	2^623651-1834251	187738	Enzo Doria	07/2015
3089	(7*10^187645+53)/3	187646	Robert Price	05/2018
3090	21650^43269+43269^21650	187591	Norbert Schneider	02/2023
3091	2^623146+1879609	187586	Enzo Doria	09/2016
3092	(401*10^187512+13)/9	187514	Robert Price	09/2021
3093	(5*10^187471+91)/3	187472	Robert Price	04/2018
3094	2^622500+81931	187392	Enzo Doria	08/2016
3095	(13*10^187382-157)/9	187383	Robert Price	05/2021
3096	2^622300-1861739	187331	Enzo Doria	12/2015
3097	(22*10^187317-91)/3	187318	Robert Price	02/2022
3098	(38*10^187281+349)/9	187282	Robert Price	10/2018
3099	2^622052+76771	187257	Enzo Doria	05/2016
3100	2^622005-24091	187243	Enzo Doria	08/2013
3101	7*10^187205-57	187206	Robert Price	06/2020
3102	2^621879-351787	187205	Enzo Doria	07/2015
3103	(5*10^187168-53)/3	187169	Robert Price	09/2020
3104	(23*10^187164-143)/3	187165	Robert Price	12/2019
3105	2^621700+79411	187151	Enzo Doria	06/2016
3106	2^621597+39	187120	Jon Grantham	08/2023
3107	Phi(271207,-5)	187112	Henri Lifchitz	12/2025
3108	(7*10^187101+131)/3	187102	Robert Price	06/2020
3109	(2*10^187062-71)/3	187062	Robert Price	12/2017
3110	V(1118570)	187013	Serge Batalov	07/2024
3111	2^620929-113203	186919	Enzo Doria	07/2014
3112	10^186842+168223	186843	Patrick De Geest	07/2018
3113	10^186842-8001	186842	Robert Price	03/2018
3114	V(1117640)/13411681/26823361/575709775681/989889277441	186814	Serge Batalov	07/2024
3115	2^620347-1777	186744	Lelio R Paula	07/2013
3116	(11*10^186659+133)/9	186660	Robert Price	04/2022
3117	11^179143-4170	186559	Enzo Doria	12/2012
3118	(13^186535)%(10^186535)	186535	Henri Lifchitz	05/2025
3120	(5^266863+1)/6	186529	Paul Bourdelais	07/2010
3119	Phi(266863,-5)	186529	Henri Lifchitz	12/2025
3121	2*10^186517+33	186518	Robert Price	11/2021
3122	2^619297-2792353	186427	Enzo Doria	02/2016
3123	(49*10^186409+383)/9	186410	Robert Price	04/2019
3124	2^618940-460139	186320	Enzo Doria	06/2015
3125	Phi(343570,2^5)	186109	Henri Lifchitz	12/2025
3126	2^618046+74179	186051	Enzo Doria	04/2016
3127	3*10^186019+11	186020	Robert Price	07/2018
3128	(16*10^185978-19)/3	185979	Robert Price	02/2019
3129	(22*10^185950-7)/3	185951	Robert Price	12/2022
3130	2*10^185930-3	185931	Robert Price	07/2015
3131	(82^97151+1)/83	185928	Paul Bourdelais	10/2017
3132	4*10^185905+91	185906	Robert Price	08/2018
3133	(34*10^185902-601)/9	185903	Robert Price	07/2022
3134	(19*10^185873+131)/3	185874	Robert Price	06/2020
3135	(37*10^185811+377)/9	185812	Robert Price	11/2018
3136	2^617250+9385	185811	Lelio R Paula	07/2013
3137	2^617130+9	185775	Stefano Morozzi	05/2021
3138	39^116749+2	185756	Robert Price	04/2015
3139	2^616924-39719	185713	Enzo Doria	09/2015
3140	2^616712+1867621	185649	Enzo Doria	04/2016
3141	(3^388897+2^388897)/5	185551	Jean-Louis Charton	09/2011
3142	8*10^185529-67	185530	Robert Price	08/2019
3143	(5*10^185520-11)/3	185521	Tyler Busby	02/2023
3144	5*2^616124+3	185473	Jon Grantham	07/2023
3145	2^615916+26791	185410	Enzo Doria	12/2023
3146	4*10^185355+9	185356	Robert Price	05/2015
3147	(16*10^185347+89)/3	185348	Robert Price	03/2021
3148	40247^40247-56^56	185327	Henri Lifchitz	08/2024
3149	2^615622+76639	185321	Enzo Doria	05/2016
3150	2^615591+1879223	185312	Enzo Doria	08/2016
3151	2^615587+217013	185311	Enzo Doria	12/2023
3152	2^615503+1876643	185285	Enzo Doria	07/2016
3153	5^265007-4^265007	185232	Jean-Louis Charton	02/2013
3155	(4*10^185221-91)/3	185222	Robert Price	03/2018
3154	(7*10^185221+131)/3	185222	Robert Price	06/2020
3156	(62*10^185216-413)/9	185217	Robert Price	09/2021
3157	(232*10^185180+17)/3	185182	Robert Price	04/2021
3158	56*10^185139-3	185141	Robert Price	03/2020
3159	(28*10^185105+47)/3	185106	Robert Price	02/2021
3160	2^614783-2790097	185069	Enzo Doria	12/2015
3161	2^614745-29323	185057	Enzo Doria	07/2015
3162	(((((((((((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
3163	(49*10^184993-67)/9	184994	Robert Price	03/2019
3164	(5*10^184954-191)/3	184955	Robert Price	05/2021
3165	(14*10^184950+211)/9	184951	Robert Price	04/2018
3166	2^614360+215221	184941	Enzo Doria	11/2023
3167	2^614315+81353	184928	Enzo Doria	08/2016
3168	2^614294-1849961	184921	Enzo Doria	08/2015
3169	2^614266+1877809	184913	Enzo Doria	08/2016
3170	(185*10^184878-11)/3	184880	Robert Price	10/2020
3171	91*10^184867-9	184869	Robert Price	06/2021
3172	(37^117841-1)/581320056003516	184784	Paul Vanderveen	06/2025
3173	39803^40170-40170^39803	184779	Norbert Schneider	05/2024
3174	(14789^44521-1)/(14789^211-1)	184770	Ryan Propper	11/2023
3175	(85*10^184768+77)/9	184769	Robert Price	07/2022
3176	2^613715-1860727	184747	Enzo Doria	11/2015
3177	(4*10^184730+89)/3	184731	Robert Price	08/2021
3178	2*10^184723+41	184724	Robert Price	05/2018
3179	(49*10^184703+293)/9	184704	Robert Price	03/2021
3180	2^613487-349987	184678	Enzo Doria	07/2015
3181	(95^93377+1)/96	184672	Paul Bourdelais	11/2017
3182	14^161089-161089^14	184629	Serge Batalov	05/2016
3183	40008^40109-40109^40008	184588	Norbert Schneider	05/2024
3184	2^613033-114621	184542	Enzo Doria	05/2015
3185	3*2^612759+5	184460	Jon Grantham	07/2023
3186	2^612587+213413	184408	Enzo Doria	09/2023
3188	(9^193247+1)/10	184404	Paul Bourdelais	02/2010
3187	Phi(193247,-9)	184404	Henri Lifchitz	12/2025
3189	2^612424+212341	184358	Enzo Doria	08/2023
3190	2^612341-1604809	184334	Enzo Doria	05/2015
3191	(11*10^184308-161)/3	184309	Robert Price	11/2021
3192	(2^611999-1)/18464214225958267477777390354183	184199	Dario Alpern	06/2017
3193	(14*10^184150+37)/3	184151	Robert Price	12/2018
3194	2^611731-4837	184150	Yves Minet	08/2018
3195	3*10^184124-7	184125	Robert Price	08/2015
3196	2^611644+29371	184124	Enzo Doria	02/2024
3197	9*10^184122-11	184123	Mischa Rodermond	04/2023
3198	2^611628-24537	184119	Enzo Doria	08/2013
3199	3*10^184110+13	184111	Robert Price	07/2018
3200	(14280^44521-1)/(14280^211-1)	184097	Ryan Propper	11/2023
3201	(194*10^184093+1)/3	184095	Robert Price	01/2022
3202	2^611460+71881	184068	Enzo Doria	04/2016
3203	4*10^184004-63	184005	Robert Price	10/2018
3204	2^611111+84083	183963	Boyan Hu	05/2024
3205	2^610982-1867301	183924	Enzo Doria	03/2016
3206	(10^183917+1)/11/9952852373	183906	Alfred Reich	02/2024
3207	3*10^183872-49	183873	Robert Price	07/2018
3208	2^610597+1178897	183809	Enzo Doria	05/2016
3209	(8*10^183773-269)/9	183773	Robert Price	09/2021
3210	(65*10^183768-29)/9	183769	Robert Price	01/2021
3211	(17*10^183764+31)/3	183765	Robert Price	01/2019
3212	(28*10^183760-1)/9	183761	Serge Batalov	10/2014
3213	2^610401+1277	183750	Lelio R Paula	07/2013
3214	2^610356-1849019	183736	Enzo Doria	08/2015
3215	(63^102103+1)/64	183717	Paul Bourdelais	10/2017
3216	23*10^183710-7	183712	Robert Price	02/2020
3217	(2^610289+1)/(3*528882550291)	183704	Gord Palameta	08/2018
3218	(4*10^183659+149)/9	183659	Robert Price	04/2018
3219	(4*10^183657+41)/9	183657	Serge Batalov	11/2022
3220	(11^176327-1)/31738870	183619	Paul Vanderveen	05/2025
3221	7*10^183596+39	183597	Robert Price	01/2023
3222	2^609846-1834251	183582	Enzo Doria	07/2015
3223	10^183546+1547323	183547	Patrick De Geest	02/2021
3225	10^183546-800000001	183546	Robert Price	09/2020
3224	10^183546-584297	183546	Patrick De Geest	02/2021
3226	7*10^183511+39	183512	Robert Price	01/2023
3227	(23*10^183477-71)/3	183478	Robert Price	07/2020
3228	11^176176-240	183469	Enzo Doria	11/2012
3229	(41^113749+1)/42	183451	Paul Bourdelais	11/2017
3230	6*10^183429+53	183430	Robert Price	05/2020
3231	(28*10^183403+191)/3	183404	Robert Price	02/2020
3232	U(1096855)	183383	Serge Batalov	07/2024
3233	(5^262337-1)/363486427756606700767551233751524443601036	183325	Paul Vanderveen	05/2025
3234	(101^91463+1)/102	183320	Paul Bourdelais	11/2017
3235	2^608965-113989	183317	Enzo Doria	10/2014
3236	A005165(43592)	183312	Serge Batalov	07/2017
3237	(61*10^183294+119)/9	183295	Robert Price	05/2019
3238	2^608814-461261	183272	Enzo Doria	06/2015
3239	(163*10^183227-1)/9	183229	Serge Batalov	12/2014
3240	2^608541-608541^2	183190	Henri Lifchitz	02/2018
3241	2^608293+143807	183115	Enzo Doria	10/2016
3242	2^608164-462419	183076	Enzo Doria	08/2015
3243	2^607950-1862303	183012	Enzo Doria	12/2015
3244	5*3^383376+2^383376	182918	Jon Grantham	08/2023
3245	(46*10^182896+683)/9	182897	Robert Price	03/2019
3246	(2*10^182787+73)/3	182787	Robert Price	09/2020
3247	2^607101+1871987	182756	Enzo Doria	05/2016
3248	2^606869-69175	182686	Enzo Doria	11/2015
3249	8*10^182671+71	182672	Robert Price	05/2022
3250	(23*10^182666-71)/3	182667	Robert Price	07/2020

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