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 (> 30000)	Who ?	When ?
3001	2^331938+71149	99924	Enzo Doria	04/2016
3002	2^331932-78795	99922	Lelio R Paula	09/2016
3003	2^331921+771	99919	Lelio R Paula	01/2013
3004	(3^209419-2)/5132755	99912	Lelio R Paula	09/2013
3005	2^331860-114989	99900	Enzo Doria	05/2015
3006	2^331746-11655	99866	Lelio R Paula	09/2016
3007	11^95891-28	99861	Lelio R Paula	08/2016
3008	(2^331694-5)/11	99849	Lelio R Paula	10/2013
3009	(3^209246+7)/64	99834	Lelio R Paula	09/2013
3010	15^84866-52	99811	Lelio R Paula	08/2016
3011	13^89600+30	99810	Lelio R Paula	08/2016
3012	5^142772-38	99794	Lelio R Paula	08/2016
3013	(23*2^331459+1)/475	99778	Lelio R Paula	11/2013
3014	2^331416-331416+1	99767	Robert Price	10/2014
3015	2^331256-57	99718	Lelio R Paula	12/2012
3016	2^331185+737	99697	Lelio R Paula	01/2013
3017	(4*10^99693+149)/9	99693	Robert Price	03/2017
3018	2^331154+1880527	99688	Enzo Doria	10/2016
3019	(19^77951+1)/20	99679	Paul Bourdelais	03/2010
3020	2^331110+1870459	99675	Enzo Doria	05/2016
3021	5*2^331075+7	99665	Lelio R Paula	08/2014
3022	(16*10^99656-31)/3	99657	Robert Price	03/2016
3023	2^330968+345	99632	Lelio R Paula	09/2016
3025	2*5^142528-7	99624	Lelio R Paula	11/2014
3024	2^330942+77329	99624	Enzo Doria	05/2016
3026	14^86914-99	99615	Lelio R Paula	08/2016
3027	(19*2^330902+1)/77	99611	Lelio R Paula	11/2013
3028	2^330845+71687	99595	Enzo Doria	04/2016
3029	(23*2^330770+1)/3	99573	Lelio R Paula	11/2013
3030	2^330735+8415	99562	Lelio R Paula	09/2016
3031	2^330720+74071	99557	Enzo Doria	04/2016
3032	31^66738-2	99531	Lelio R Paula	09/2013
3033	7*3^208567+4	99513	Lelio R Paula	08/2014
3034	(13*10^99508+47)/3	99509	Robert Price	01/2017
3035	2^330553+779	99507	Lelio R Paula	01/2013
3036	15^84606-94	99505	Lelio R Paula	08/2016
3037	6^127858+47	99493	Lelio R Paula	08/2016
3038	5^142337+48	99490	Lelio R Paula	08/2016
3039	7^117724-20	99489	Lelio R Paula	08/2016
3040	(29*10^99474-17)/3	99475	Erik Branger	09/2014
3041	(9*2^330407-1)/7	99463	Lelio R Paula	03/2014
3042	(68*10^99441+7)/3	99443	Robert Price	03/2016
3043	46^59791-45^59791	99418	Jean-Louis Charton	01/2013
3044	(2*10^99408+529)/9	99408	Robert Price	01/2017
3045	53^57646-2	99398	Lelio R Paula	09/2013
3046	2^330165+1870025	99390	Enzo Doria	05/2016
3047	2^330142-155	99383	Lelio R Paula	12/2012
3048	2^330088-115259	99367	Enzo Doria	06/2015
3049	(746*10^99303+1)/9	99305	Robert Price	02/2017
3050	3^208107+40	99293	Lelio R Paula	08/2016
3051	(5*2^329833-1)/369	99288	Lelio R Paula	02/2014
3052	8*3^208093+5	99287	Lelio R Paula	08/2014
3053	5^142043+56	99284	Lelio R Paula	08/2016
3054	22*10^99275+7	99277	Robert Price	04/2016
3055	2^329778+1876189	99274	Enzo Doria	07/2016
3056	(10^99239-13)/3	99239	Robert Price	02/2017
3057	3^207987+62	99236	Lelio R Paula	08/2016
3058	2^329638+49	99231	Lelio R Paula	12/2012
3059	7^117413-18	99226	Lelio R Paula	08/2016
3060	2^329586-458903	99216	Enzo Doria	04/2015
3061	2^329553+101	99206	Lelio R Paula	12/2012
3062	2^329551-112897	99205	Enzo Doria	06/2014
3063	(3^207925+7)/50	99204	Lelio R Paula	09/2013
3064	6^127458-17993	99182	Enzo Doria	03/2013
3065	(46*10^99143-1)/9	99144	Robert Price	12/2014
3066	18^78968-3065	99127	Enzo Doria	03/2013
3067	2^329259+189	99117	Lelio R Paula	12/2012
3068	8*10^99113+39	99114	Robert Price	01/2017
3069	6^127364+77	99109	Lelio R Paula	08/2016
3070	6^127285+13	99047	Lelio R Paula	08/2016
3071	2^329007+73283	99041	Enzo Doria	04/2016
3072	5*3^207543-8	99024	Lelio R Paula	08/2014
3073	2^328885+149	99005	Lelio R Paula	12/2012
3074	(2^328879-9)/119	99001	Lelio R Paula	10/2013
3075	5^141618+54	98987	Lelio R Paula	08/2016
3076	8*10^98982+51	98983	Robert Price	05/2017
3077	(21*2^328809-1)/7709	98979	Lelio R Paula	03/2014
3078	2^328794-2797601	98977	Enzo Doria	04/2016
3079	6^127176+5	98963	Lelio R Paula	11/2014
3080	2^328700-109709	98949	Enzo Doria	04/2014
3081	46711!2-2^46711	98916	Robert Price	09/2015
3082	9*7^117037+4	98909	Lelio R Paula	11/2014
3083	(10^98890+149)/3	98890	Serge Batalov	12/2014
3084	2^328497-216933	98888	Enzo Doria	05/2014
3085	2^328487+32769	98885	Lelio R Paula	08/2016
3086	3^207250-112358	98884	Enzo Doria	06/2014
3087	13^88754-90	98867	Lelio R Paula	08/2016
3088	2^328406+709	98861	Lelio R Paula	02/2013
3089	(17*2^328413-1)/16173	98860	Lelio R Paula	03/2014
3090	7^116976+76	98857	Lelio R Paula	08/2016
3091	2^328335+1155	98839	Lelio R Paula	08/2016
3092	(3*2^328311+1)/5	98832	Lelio R Paula	11/2013
3093	287^40210+40210^287	98832	Norbert Schneider	11/2014
3094	(2^328284+9)/1325	98821	Lelio R Paula	10/2013
3095	(21*2^328258+1)/2125	98814	Lelio R Paula	11/2013
3096	65^54491+48	98788	Lelio R Paula	04/2016
3097	3^207042+98	98785	Lelio R Paula	08/2016
3098	3^206977-112756	98754	Enzo Doria	07/2014
3099	7^116846-50	98747	Lelio R Paula	08/2016
3100	2^327967-28635	98728	Lelio R Paula	08/2016
3101	6^126850-47	98709	Lelio R Paula	08/2016
3102	8*6^126830-7	98694	Lelio R Paula	11/2014
3103	11^94770-270	98693	Enzo Doria	08/2012
3104	2^327832+43	98688	Lelio R Paula	12/2012
3105	2^327795+761	98677	Lelio R Paula	02/2013
3106	10^98669+147411	98670	Patrick De Geest	11/2016
3108	10^98669-9^(98669-1)	98669	Robert Price	05/2016
3107	10^98669-105249	98669	Patrick De Geest	11/2016
3109	2^327671-109801	98639	Enzo Doria	04/2014
3110	5^141090-14	98618	Lelio R Paula	08/2016
3111	20^75799+47	98617	Lelio R Paula	08/2016
3112	2^327515-1017	98592	Lelio R Paula	08/2016
3113	6^126692+97681	98586	Mike Oakes	04/2011
3114	2^327467-741	98578	Lelio R Paula	08/2016
3115	(2^327329+9)/19	98535	Lelio R Paula	10/2013
3116	7^116577-66	98519	Lelio R Paula	08/2016
3117	(3*2^327250+1)/7	98512	Lelio R Paula	11/2013
3118	(19*2^327192+1)/275	98494	Lelio R Paula	11/2013
3119	2^327162-66945	98486	Lelio R Paula	08/2016
3120	4*10^98472-3	98473	Erik Branger	11/2013
3121	(6883*2^327047-1)/77	98453	Lelio R Paula	05/2015
3122	(71*10^98446+1)/9	98447	Serge Batalov	11/2010
3123	13^88363+94	98432	Lelio R Paula	08/2016
3124	48^58543-47^58543	98425	Jean-Louis Charton	11/2005
3125	6^126481+41	98422	Lelio R Paula	08/2016
3126	78*10^98413-7	98415	Robert Price	05/2017
3127	7^116416+46	98383	Lelio R Paula	08/2016
3128	7^116407-24	98376	Lelio R Paula	07/2016
3130	2^326782-1860671	98372	Enzo Doria	03/2016
3129	17^79948+58	98372	Lelio R Paula	08/2016
3131	3^206143-98	98356	Lelio R Paula	08/2016
3132	8*5^140705+7	98350	Lelio R Paula	11/2014
3133	2^326585+11	98312	Lelio R Paula	12/2012
3134	2^326582-459161	98311	Enzo Doria	05/2015
3135	(2^326548+9)/5	98301	Lelio R Paula	10/2013
3136	2^326538+71659	98298	Enzo Doria	04/2016
3137	15^83575-58	98292	Lelio R Paula	08/2016
3138	10^98288+3	98289	Robert Price	03/2011
3139	10^98288-117017	98288	Patrick De Geest	11/2011
3140	2^326421-2797573	98263	Enzo Doria	04/2016
3141	2^326401+16095	98257	Lelio R Paula	07/2016
3142	17^79826-78	98222	Lelio R Paula	08/2016
3143	2^326268-809	98217	Yves Minet	04/2011
3144	15^83496-76	98199	Lelio R Paula	08/2016
3145	(10223*2^326179+1)/6125	98190	Lelio R Paula	07/2014
3146	9*5^140471-4	98186	Lelio R Paula	11/2014
3147	2^326069-2383	98157	Yves Minet	10/2013
3148	2^325973+1185	98128	Lelio R Paula	07/2016
3149	(25*2^325949-1)/17	98121	Lelio R Paula	02/2014
3150	2^325945-1847269	98120	Enzo Doria	07/2015
3151	2^325866+15	98096	Lelio R Paula	12/2012
3152	2^325765+1974305	98066	Enzo Doria	06/2016
3153	2^325733-58695	98056	Lelio R Paula	07/2016
3154	2^325717-3645	98051	Lelio R Paula	07/2016
3155	(23*2^325583-1)/21	98011	Lelio R Paula	02/2014
3156	(7*10^98007-13)/3	98008	Robert Price	06/2016
3157	2^325512-459959	97989	Enzo Doria	05/2015
3158	(3^205354-8)/17	97978	Lelio R Paula	09/2013
3159	2^325433+76817	97966	Enzo Doria	05/2016
3160	2^325390-109061	97953	Enzo Doria	04/2014
3161	13^87921+24	97940	Lelio R Paula	08/2016
3162	961^32831-960^32831	97926	Jean-Louis Charton	02/2011
3163	2^325215+12909	97900	Lelio R Paula	07/2016
3164	7*10^97874-69	97875	Robert Price	01/2017
3165	(17^79537+5^79537)/22	97865	Robert Price	06/2013
3166	15^83212+22	97865	Lelio R Paula	08/2016
3167	2^325087-109057	97861	Enzo Doria	04/2014
3168	2^325074+1870657	97858	Enzo Doria	05/2016
3170	2^325066-2111	97855	Yves Minet	08/2013
3169	CopelandErdos(97855)	97855	Eric W. Weisstein	10/2015
3171	18^77944-89	97841	Lelio R Paula	07/2016
3172	6^125720-17663	97830	Enzo Doria	02/2013
3173	2^324972-2069	97827	Yves Minet	05/2013
3174	2^324944-2788319	97818	Enzo Doria	03/2016
3176	4*10^97799-9	97800	Erik Branger	11/2013
3175	2^324882+577294575	97800	Lelio R Paula	09/2016
3177	2^324863-1867921	97794	Enzo Doria	04/2016
3178	6^125662-18473	97785	Enzo Doria	03/2013
3179	12^90604+11	97779	Lelio R Paula	07/2016
3180	5^139830+24	97737	Lelio R Paula	04/2016
3181	2^324612+1155	97718	Lelio R Paula	07/2016
3182	19^76404-44	97702	Lelio R Paula	07/2016
3183	2^324505-2983	97686	Yves Minet	04/2011
3184	(31*2^324496-1)/45	97683	Lelio R Paula	02/2014
3185	6^125488-17843	97649	Enzo Doria	02/2013
3186	7^115515-2	97622	Lelio R Paula	09/2013
3187	6^125418-5	97595	Lelio R Paula	11/2014
3188	2^324076+1155	97557	Lelio R Paula	07/2016
3189	(2^324074+9)/13	97555	Lelio R Paula	10/2013
3190	(55459*2^323993+1)/21	97536	Lelio R Paula	07/2014
3191	13^87557-12^87557	97534	Jean-Louis Charton	12/2008
3192	2^323946+73939	97518	Enzo Doria	04/2016
3193	2^323937+1866947	97515	Enzo Doria	03/2016
3194	6^125290-18533	97495	Enzo Doria	03/2013
3195	2^323845+101	97488	Lelio R Paula	12/2012
3196	18^77662+65	97487	Lelio R Paula	07/2016
3197	2^323772+76771	97466	Enzo Doria	05/2016
3198	2^323765-112213	97463	Enzo Doria	06/2014
3199	2^323720-6555	97450	Lelio R Paula	07/2016
3200	2^323694-1860401	97442	Enzo Doria	03/2016
3201	20^74886+3	97429	Lelio R Paula	06/2016
3203	3*10^97399+73	97400	Robert Price	04/2016
3202	7^115252-50	97400	Lelio R Paula	07/2016
3204	224737#+393581	97389	Nicolas PALAU	12/2016
3205	(26*10^97353+31)/3	97354	Robert Price	07/2016
3206	61^54517-60^54517	97331	Jean-Louis Charton	09/2005
3207	6^125021-85	97286	Lelio R Paula	08/2016
3208	2^323164-47355	97283	Lelio R Paula	07/2016
3209	(3^203902+4)/36051015157	97276	Lelio R Paula	09/2013
3210	2^323054-6555	97249	Lelio R Paula	07/2016
3211	(31*10^97242+41)/9	97243	Robert Price	04/2015
3212	GoldenRatioPrime[97241]	97241	Eric W. Weisstein	06/2009
3213	12^90098-41	97233	Lelio R Paula	07/2016
3214	2^322928-216929	97212	Enzo Doria	05/2014
3215	(7*2^322896-1)/57	97201	Lelio R Paula	02/2014
3216	(2^322897+5)/3146107489	97193	Lelio R Paula	10/2013
3217	2^322725+75761	97150	Enzo Doria	04/2016
3218	(13*2^322686+1)/119	97138	Lelio R Paula	11/2013
3219	(41*10^97085+373)/9	97086	Robert Price	04/2017
3220	2^322413+77	97056	Lelio R Paula	12/2012
3221	2^322406+177	97054	Lelio R Paula	12/2012
3222	(14*10^97044+31)/9	97045	Robert Price	02/2015
3223	2^322302+255255	97023	Lelio R Paula	07/2016
3224	2^322196-113093	96991	Enzo Doria	07/2014
3225	2^322000-1861469	96932	Enzo Doria	03/2016
3226	2^321971-112747	96923	Enzo Doria	06/2014
3227	11^93062-92	96915	Lelio R Paula	06/2016
3228	(11*2^321841-7)/15	96884	Renaud Lifchitz	03/2011
3229	3^203051+34	96880	Lelio R Paula	05/2016
3230	(64*10^96863-1)/27	96864	Serge Batalov	05/2010
3231	2^321716-2786939	96847	Enzo Doria	03/2016
3232	2^321701-113053	96842	Enzo Doria	07/2014
3233	2^321700-28635	96842	Lelio R Paula	06/2016
3234	(5*2^321691-1)/27	96838	Lelio R Paula	02/2014
3235	6^124433-124433	96828	Robert Price	01/2014
3236	2^321631+69	96821	Lelio R Paula	12/2012
3237	(13*2^321606+1)/119	96813	Lelio R Paula	11/2013
3238	(46*10^96798-1)/9	96799	Serge Batalov	10/2014
3239	(59*10^96798+31)/9	96799	Robert Price	09/2015
3240	223319#+231223	96790	Makoto Morimoto	02/2016
3241	2^321519-28635	96787	Lelio R Paula	06/2016
3242	2^321487-1867237	96778	Enzo Doria	03/2016
3243	2^321461-63	96770	Lelio R Paula	12/2012
3244	2^321439+123	96763	Lelio R Paula	12/2012
3245	2^321434+709	96762	Lelio R Paula	02/2013
3246	14^84413+89	96749	Lelio R Paula	07/2016
3247	(28*10^96743+71)/9	96744	Serge Batalov	12/2008
3248	13^86847+96	96743	Lelio R Paula	06/2016
3249	9*2^321336-7	96733	Lelio R Paula	08/2014
3250	(209*10^96722-17)/3	96724	Robert Price	05/2017

Find by discoverer :

PRP Records

Probable Primes Top 10000

(173006 PRPs in the top)