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) !!!

Submit your PRPs

See the Top discoverers
See the Latest PRPs
Search by form


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	(47*10^191732+259)/9	191733	Robert Price	03/2022
3002	41459^41522-41522^41459	191733	Norbert Schneider	04/2025
3003	2^636661+1876577	191655	Enzo Doria	07/2016
3004	(9^200807-2^200807)/7	191618	Jon Grantham	07/2023
3005	(34^125101-1)/33	191589	Paul Bourdelais	11/2017
3006	fibonacci(916540)-2	191546	Jon Grantham	08/2023
3007	2^636177-1855123	191509	Enzo Doria	09/2015
3008	2^636158-113627	191503	Enzo Doria	08/2014
3009	(37*25^136966+63)/4	191472	Curtis Bright	05/2015
3010	2^636035+79823	191466	Enzo Doria	06/2016
3011	2^636011-1860847	191459	Enzo Doria	11/2015
3012	2^635926-1860611	191433	Enzo Doria	11/2015
3013	3*2^635755+5	191382	Jon Grantham	07/2023
3014	3*10^191152-7	191153	Robert Price	08/2015
3015	2^634883-1865677	191119	Enzo Doria	02/2016
3016	2^634801+1871957	191095	Enzo Doria	05/2016
3017	(77*10^191080+157)/9	191081	Robert Price	05/2022
3018	(35*10^191073+1)/9	191074	Serge Batalov	07/2010
3019	9*10^191018-41	191019	Robert Price	08/2020
3020	2^634470-59861	190995	Enzo Doria	11/2015
3021	2^634368-29519	190964	Enzo Doria	08/2015
3022	(19*10^190935+11)/3	190936	Robert Price	07/2023
3023	2^634188-350609	190910	Enzo Doria	06/2015
3024	(65*10^190899+493)/9	190900	Robert Price	08/2021
3025	(62*10^190795-413)/9	190796	Robert Price	09/2021
3026	(26*10^190789-131)/3	190790	Robert Price	10/2019
3027	(13*10^190732-61)/3	190733	Robert Price	11/2018
3028	3*2^633524+5	190711	Jon Grantham	07/2023
3029	(7*10^190683+143)/3	190684	Robert Price	03/2018
3030	2^633088-113879	190579	Enzo Doria	10/2014
3031	2^633064+1874911	190572	Enzo Doria	06/2016
3032	5*3^399402+2^399402	190564	Jon Grantham	08/2023
3033	(43*10^190547+83)/9	190548	Robert Price	11/2018
3034	99*10^190543+7	190545	Robert Price	05/2021
3035	(299*10^190533+1)/3	190535	Robert Price	04/2020
3036	(1744*10^190519-1747)/3	190522	Robert Price	12/2020
3037	2^632815-15	190497	Stefano Morozzi	07/2022
3038	2^632795-351205	190491	Enzo Doria	06/2015
3039	41171^41272+41272^41171	190454	Norbert Schneider	05/2023
3040	(16*10^190420-19)/3	190421	Robert Price	02/2019
3041	(43*10^190351+101)/9	190352	Robert Price	11/2018
3042	2^632156+78391	190298	Enzo Doria	06/2016
3043	97*10^190295-3	190297	Robert Price	05/2020
3044	2^632082-1851971	190276	Enzo Doria	08/2015
3045	2^632020+1880311	190257	Enzo Doria	09/2016
3046	(5*10^190242-77)/9	190242	Robert Price	04/2021
3047	7*10^190210+13	190211	Robert Price	03/2021
3048	2^631637-462373	190142	Enzo Doria	08/2015
3049	2*10^190126-21	190127	Robert Price	09/2020
3050	(28*10^190105+191)/3	190106	Robert Price	02/2020
3051	2*10^190093+33	190094	Robert Price	11/2021
3052	(68*10^190053-113)/9	190054	Robert Price	03/2021
3053	2^631183+213413	190006	Enzo Doria	09/2023
3054	2^631122-39251	189987	Enzo Doria	08/2015
3055	(26*10^189928-89)/9	189929	Robert Price	06/2018
3056	2^630839-97	189902	Yves Minet	07/2017
3057	99*10^189876-7	189878	Robert Price	07/2020
3058	41147^41147+30^30	189867	Henri Lifchitz	09/2024
3059	2^630359+1788953	189757	Enzo Doria	05/2016
3060	2^630228+1871971	189718	Enzo Doria	05/2016
3061	2^630108+781	189682	Lelio R Paula	08/2013
3062	2^629870-1867811	189610	Enzo Doria	04/2016
3063	(359^74189-1)/358	189558	Alexander Zhirkov	11/2017
3064	2^629326+2792929	189447	Enzo Doria	02/2016
3065	4*10^189401+13	189402	Robert Price	02/2021
3066	(10^189385-61)/3	189385	Serge Batalov	12/2014
3067	2^629036+1874011	189359	Enzo Doria	06/2016
3068	2^628930+80779	189327	Enzo Doria	07/2016
3069	(134*10^189309-11)/3	189311	Robert Price	01/2022
3070	9*10^189306-11	189307	Mischa Rodermond	04/2023
3071	3^396740-396740^3	189294	Henri Lifchitz	07/2024
3072	2^628582+1179439	189223	Enzo Doria	06/2016
3073	(44*10^188999-503)/9	189000	Robert Price	12/2018
3074	(16*10^188823+167)/3	188824	Robert Price	06/2019
3075	(10^188796+7)/4967/71933	188788	Alfred Reich	08/2021
3076	2^627037-2785843	188757	Enzo Doria	10/2015
3077	(10^188566+7)/311640753181661	188552	Alfred Reich	04/2022
3078	(16*10^188457+161)/3	188458	Robert Price	02/2019
3079	L(901657)	188436	Renaud Lifchitz	11/2008
3080	(19*10^188375+137)/3	188376	Robert Price	03/2022
3081	2^625651+74213	188340	Enzo Doria	04/2016
3082	2^625584-460919	188320	Enzo Doria	06/2015
3083	(8*10^188308-71)/9	188308	Serge Batalov	11/2022
3084	5^269399-3^269399-1	188302	Jon Grantham	08/2023
3085	(14*10^188218+139)/9	188219	Robert Price	11/2021
3086	40760^40821-40821^40760	188195	Norbert Schneider	07/2024
3087	(10^188164+359)/9	188164	Serge Batalov	12/2014
3088	2^624481-113611	187988	Enzo Doria	08/2014
3089	(2^624389+125582)/2	187960	Stefano Morozzi	09/2019
3090	(2^624389+166982)/2	187960	Stefano Morozzi	09/2019
3091	(2^624389+179886)/2	187960	Stefano Morozzi	09/2019
3092	(2^624387+64466)/2	187959	Stefano Morozzi	09/2019
3093	(2^624378+112990)/2	187957	Stefano Morozzi	09/2019
3094	(2^624380+161986)/2	187957	Stefano Morozzi	09/2019
3096	(2^624376+55762)/2	187956	Stefano Morozzi	09/2019
3095	(2^624377+169506)/2	187956	Stefano Morozzi	09/2019
3097	(2^624355+80178)/2	187950	Stefano Morozzi	09/2019
3098	(2^624351+61350)/2	187949	Stefano Morozzi	09/2019
3099	(2^624341+63462)/2	187946	Stefano Morozzi	09/2019
3100	(2^624344+135990)/2	187946	Stefano Morozzi	09/2019
3101	(2^624344+183898)/2	187946	Stefano Morozzi	09/2019
3103	(2^624340+126982)/2	187945	Stefano Morozzi	09/2019
3102	(2^624338+196110)/2	187945	Stefano Morozzi	09/2019
3104	(2^624337+105162)/2	187944	Stefano Morozzi	09/2019
3105	(2^624333+44594)/2	187943	Stefano Morozzi	09/2019
3106	(2^624321+88742)/2	187940	Stefano Morozzi	09/2019
3107	(2^624324+135178)/2	187940	Stefano Morozzi	09/2019
3108	(2^624317+14186)/2	187938	Stefano Morozzi	09/2019
3109	(2^624313+24450)/2	187937	Stefano Morozzi	09/2019
3110	(2^624309+184590)/2	187936	Stefano Morozzi	09/2019
3112	(2^624307+152658)/2	187935	Stefano Morozzi	09/2019
3111	(2^624307+185978)/2	187935	Stefano Morozzi	09/2019
3113	(2^624303+40814)/2	187934	Stefano Morozzi	09/2019
3114	(2^624304+99238)/2	187934	Stefano Morozzi	09/2019
3115	2^624077-112723	187866	Enzo Doria	07/2014
3116	2^624008+1874941	187846	Enzo Doria	06/2016
3117	2^623870+78679	187804	Enzo Doria	05/2016
3118	2^623714-114035	187757	Enzo Doria	11/2014
3119	2^623651-1834251	187738	Enzo Doria	07/2015
3120	(7*10^187645+53)/3	187646	Robert Price	05/2018
3121	21650^43269+43269^21650	187591	Norbert Schneider	02/2023
3122	2^623146+1879609	187586	Enzo Doria	09/2016
3123	(401*10^187512+13)/9	187514	Robert Price	09/2021
3124	(5*10^187471+91)/3	187472	Robert Price	04/2018
3125	2^622500+81931	187392	Enzo Doria	08/2016
3126	(13*10^187382-157)/9	187383	Robert Price	05/2021
3127	2^622300-1861739	187331	Enzo Doria	12/2015
3128	(22*10^187317-91)/3	187318	Robert Price	02/2022
3129	(38*10^187281+349)/9	187282	Robert Price	10/2018
3130	2^622052+76771	187257	Enzo Doria	05/2016
3131	2^622005-24091	187243	Enzo Doria	08/2013
3132	7*10^187205-57	187206	Robert Price	06/2020
3133	2^621879-351787	187205	Enzo Doria	07/2015
3134	(5*10^187168-53)/3	187169	Robert Price	09/2020
3135	(23*10^187164-143)/3	187165	Robert Price	12/2019
3136	2^621700+79411	187151	Enzo Doria	06/2016
3137	2^621597+39	187120	Jon Grantham	08/2023
3138	Phi(271207,-5)	187112	Henri Lifchitz	12/2025
3139	(7*10^187101+131)/3	187102	Robert Price	06/2020
3140	(2*10^187062-71)/3	187062	Robert Price	12/2017
3141	V(1118570)	187013	Serge Batalov	07/2024
3142	2^620929-113203	186919	Enzo Doria	07/2014
3143	10^186842+168223	186843	Patrick De Geest	07/2018
3144	10^186842-8001	186842	Robert Price	03/2018
3145	V(1117640)/13411681/26823361/575709775681/989889277441	186814	Serge Batalov	07/2024
3146	2^620347-1777	186744	Lelio R Paula	07/2013
3147	(11*10^186659+133)/9	186660	Robert Price	04/2022
3148	11^179143-4170	186559	Enzo Doria	12/2012
3149	(13^186535)%(10^186535)	186535	Henri Lifchitz	05/2025
3151	(5^266863+1)/6	186529	Paul Bourdelais	07/2010
3150	Phi(266863,-5)	186529	Henri Lifchitz	12/2025
3152	2*10^186517+33	186518	Robert Price	11/2021
3153	2^619297-2792353	186427	Enzo Doria	02/2016
3154	(49*10^186409+383)/9	186410	Robert Price	04/2019
3155	2^618940-460139	186320	Enzo Doria	06/2015
3156	Phi(343570,2^5)	186109	Henri Lifchitz	12/2025
3157	2^618046+74179	186051	Enzo Doria	04/2016
3158	3*10^186019+11	186020	Robert Price	07/2018
3159	(16*10^185978-19)/3	185979	Robert Price	02/2019
3160	(22*10^185950-7)/3	185951	Robert Price	12/2022
3161	2*10^185930-3	185931	Robert Price	07/2015
3162	(82^97151+1)/83	185928	Paul Bourdelais	10/2017
3163	4*10^185905+91	185906	Robert Price	08/2018
3164	(34*10^185902-601)/9	185903	Robert Price	07/2022
3165	(19*10^185873+131)/3	185874	Robert Price	06/2020
3166	(37*10^185811+377)/9	185812	Robert Price	11/2018
3167	2^617250+9385	185811	Lelio R Paula	07/2013
3168	2^617130+9	185775	Stefano Morozzi	05/2021
3169	39^116749+2	185756	Robert Price	04/2015
3170	2^616924-39719	185713	Enzo Doria	09/2015
3171	2^616712+1867621	185649	Enzo Doria	04/2016
3172	(3^388897+2^388897)/5	185551	Jean-Louis Charton	09/2011
3173	8*10^185529-67	185530	Robert Price	08/2019
3174	(5*10^185520-11)/3	185521	Tyler Busby	02/2023
3175	5*2^616124+3	185473	Jon Grantham	07/2023
3176	2^615916+26791	185410	Enzo Doria	12/2023
3177	4*10^185355+9	185356	Robert Price	05/2015
3178	(16*10^185347+89)/3	185348	Robert Price	03/2021
3179	40247^40247-56^56	185327	Henri Lifchitz	08/2024
3180	2^615622+76639	185321	Enzo Doria	05/2016
3181	2^615591+1879223	185312	Enzo Doria	08/2016
3182	2^615587+217013	185311	Enzo Doria	12/2023
3183	2^615503+1876643	185285	Enzo Doria	07/2016
3184	5^265007-4^265007	185232	Jean-Louis Charton	02/2013
3186	(4*10^185221-91)/3	185222	Robert Price	03/2018
3185	(7*10^185221+131)/3	185222	Robert Price	06/2020
3187	(62*10^185216-413)/9	185217	Robert Price	09/2021
3188	(232*10^185180+17)/3	185182	Robert Price	04/2021
3189	56*10^185139-3	185141	Robert Price	03/2020
3190	(28*10^185105+47)/3	185106	Robert Price	02/2021
3191	2^614783-2790097	185069	Enzo Doria	12/2015
3192	2^614745-29323	185057	Enzo Doria	07/2015
3193	(((((((((((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
3194	(49*10^184993-67)/9	184994	Robert Price	03/2019
3195	(5*10^184954-191)/3	184955	Robert Price	05/2021
3196	(14*10^184950+211)/9	184951	Robert Price	04/2018
3197	2^614360+215221	184941	Enzo Doria	11/2023
3198	2^614315+81353	184928	Enzo Doria	08/2016
3199	2^614294-1849961	184921	Enzo Doria	08/2015
3200	2^614266+1877809	184913	Enzo Doria	08/2016
3201	(185*10^184878-11)/3	184880	Robert Price	10/2020
3202	91*10^184867-9	184869	Robert Price	06/2021
3203	(37^117841-1)/581320056003516	184784	Paul Vanderveen	06/2025
3204	39803^40170-40170^39803	184779	Norbert Schneider	05/2024
3205	(14789^44521-1)/(14789^211-1)	184770	Ryan Propper	11/2023
3206	(85*10^184768+77)/9	184769	Robert Price	07/2022
3207	2^613715-1860727	184747	Enzo Doria	11/2015
3208	(4*10^184730+89)/3	184731	Robert Price	08/2021
3209	2*10^184723+41	184724	Robert Price	05/2018
3210	(49*10^184703+293)/9	184704	Robert Price	03/2021
3211	2^613487-349987	184678	Enzo Doria	07/2015
3212	(95^93377+1)/96	184672	Paul Bourdelais	11/2017
3213	14^161089-161089^14	184629	Serge Batalov	05/2016
3214	40008^40109-40109^40008	184588	Norbert Schneider	05/2024
3215	2^613033-114621	184542	Enzo Doria	05/2015
3216	3*2^612759+5	184460	Jon Grantham	07/2023
3217	2^612587+213413	184408	Enzo Doria	09/2023
3219	(9^193247+1)/10	184404	Paul Bourdelais	02/2010
3218	Phi(193247,-9)	184404	Henri Lifchitz	12/2025
3220	2^612424+212341	184358	Enzo Doria	08/2023
3221	2^612341-1604809	184334	Enzo Doria	05/2015
3222	(11*10^184308-161)/3	184309	Robert Price	11/2021
3223	(2^611999-1)/18464214225958267477777390354183	184199	Dario Alpern	06/2017
3224	(14*10^184150+37)/3	184151	Robert Price	12/2018
3225	2^611731-4837	184150	Yves Minet	08/2018
3226	3*10^184124-7	184125	Robert Price	08/2015
3227	2^611644+29371	184124	Enzo Doria	02/2024
3228	9*10^184122-11	184123	Mischa Rodermond	04/2023
3229	2^611628-24537	184119	Enzo Doria	08/2013
3230	3*10^184110+13	184111	Robert Price	07/2018
3231	(14280^44521-1)/(14280^211-1)	184097	Ryan Propper	11/2023
3232	(194*10^184093+1)/3	184095	Robert Price	01/2022
3233	2^611460+71881	184068	Enzo Doria	04/2016
3234	4*10^184004-63	184005	Robert Price	10/2018
3235	2^611111+84083	183963	Boyan Hu	05/2024
3236	2^610982-1867301	183924	Enzo Doria	03/2016
3237	(10^183917+1)/11/9952852373	183906	Alfred Reich	02/2024
3238	3*10^183872-49	183873	Robert Price	07/2018
3239	2^610597+1178897	183809	Enzo Doria	05/2016
3240	(8*10^183773-269)/9	183773	Robert Price	09/2021
3241	(65*10^183768-29)/9	183769	Robert Price	01/2021
3242	(17*10^183764+31)/3	183765	Robert Price	01/2019
3243	(28*10^183760-1)/9	183761	Serge Batalov	10/2014
3244	2^610401+1277	183750	Lelio R Paula	07/2013
3245	2^610356-1849019	183736	Enzo Doria	08/2015
3246	(63^102103+1)/64	183717	Paul Bourdelais	10/2017
3247	23*10^183710-7	183712	Robert Price	02/2020
3248	(2^610289+1)/(3*528882550291)	183704	Gord Palameta	08/2018
3249	(4*10^183659+149)/9	183659	Robert Price	04/2018
3250	(4*10^183657+41)/9	183657	Serge Batalov	11/2022

Find by discoverer :

PRP Records

Probable Primes Top 10000

(302588 PRPs in the top)