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 ?
3270	10^100000+342909	100001	Milton L. Brown	12/2007
3251	10^100000+346579	100001	Robert Price	04/2012
3252	10^100000+829767	100001	Robert Price	05/2012
3253	10^100000+871899	100001	Robert Price	05/2012
3254	10^100000+1475997	100001	Robert Price	07/2012
3263	10^100000+1751769	100001	Robert Price	08/2012
3264	10^100000+2155489	100001	Robert Price	10/2012
3265	10^100000+2483527	100001	Robert Price	12/2012
3266	10^100000+2503087	100001	Robert Price	12/2012
3267	10^100000+2686179	100001	Robert Price	12/2012
3268	10^100000+2688933	100001	Robert Price	12/2012
3269	10^100000+3667159	100001	Robert Price	08/2013
3255	10^100000+5354043	100001	Robert Price	05/2016
3256	10^100000+5717979	100001	Robert Price	05/2016
3257	10^100000+6080631	100001	Robert Price	07/2016
3258	10^100000+6308469	100001	Robert Price	07/2016
3259	10^100000+6512023	100001	Robert Price	08/2016
3260	10^100000+6596557	100001	Robert Price	08/2016
3261	10^100000+7115409	100001	Robert Price	10/2016
3262	10^100000+7235803	100001	Robert Price	10/2016
3271	10^100000+7867333	100001	Robert Price	12/2016
3272	10^100000+8743093	100001	Robert Price	02/2017
3273	10^100000+8955391	100001	Robert Price	03/2017
3274	10^100000+9180019	100001	Robert Price	03/2017
3275	10^100000+9225987	100001	Robert Price	04/2017
3276	10^100000+9265587	100001	Robert Price	04/2017
3277	10^100000+9287049	100001	Robert Price	04/2017
3278	10^100000+9425053	100001	Robert Price	05/2017
3279	10^100000+9450769	100001	Robert Price	05/2017
3280	10^100000+9528747	100001	Robert Smith	05/2017
3281	10^100000+9548071	100001	Robert Price	06/2017
3282	10^100000+10064287	100001	Robert Price	08/2017
3283	10^100000+10229569	100001	Robert Price	10/2017
3285	10^99999+309403	100000	Daniel Heuer	01/2004
3284	10^100000-260199	100000	Patrick De Geest	01/2010
3286	10^99999-59511	99999	Patrick De Geest	07/2009
3287	2^332141-113073	99985	Enzo Doria	07/2014
3288	(3^209561+2)/728101255	99978	Lelio R Paula	09/2013
3289	2^332085+1865897	99968	Enzo Doria	03/2016
3290	(9787*2^332070-1)/936402369	99959	Lelio R Paula	05/2015
3291	2^332023+191	99949	Lelio R Paula	02/2011
3292	2^331938+71149	99924	Enzo Doria	04/2016
3293	2^331932-78795	99922	Lelio R Paula	09/2016
3294	2^331921+771	99919	Lelio R Paula	01/2013
3295	(3^209419-2)/5132755	99912	Lelio R Paula	09/2013
3296	2^331860-114989	99900	Enzo Doria	05/2015
3297	2^331746-11655	99866	Lelio R Paula	09/2016
3298	11^95891-28	99861	Lelio R Paula	08/2016
3299	(2^331694-5)/11	99849	Lelio R Paula	10/2013
3300	(3^209246+7)/64	99834	Lelio R Paula	09/2013
3301	25062^9617+9617^25062	99823	Hans Havermann	04/2018
3302	15^84866-52	99811	Lelio R Paula	08/2016
3303	13^89600+30	99810	Lelio R Paula	08/2016
3304	22950^22309+22309^22950	99798	Hans Havermann	03/2018
3305	5^142772-38	99794	Lelio R Paula	08/2016
3306	(23*2^331459+1)/475	99778	Lelio R Paula	11/2013
3307	2^331416-331416+1	99767	Robert Price	10/2014
3308	2^331256-57	99718	Lelio R Paula	12/2012
3309	28192^3443+3443^28192	99714	Hans Havermann	03/2018
3310	2^331185+737	99697	Lelio R Paula	01/2013
3311	(4*10^99693+149)/9	99693	Robert Price	03/2017
3312	2^331154+1880527	99688	Enzo Doria	10/2016
3313	(19^77951+1)/20	99679	Paul Bourdelais	03/2010
3314	24354^12385+12385^24354	99679	Hans Havermann	03/2018
3315	2^331110+1870459	99675	Enzo Doria	05/2016
3316	5*2^331075+7	99665	Lelio R Paula	08/2014
3317	25776^7351+7351^25776	99659	Hans Havermann	02/2018
3318	(16*10^99656-31)/3	99657	Robert Price	03/2016
3319	2^330968+345	99632	Lelio R Paula	09/2016
3321	2*5^142528-7	99624	Lelio R Paula	11/2014
3320	2^330942+77329	99624	Enzo Doria	05/2016
3322	14^86914-99	99615	Lelio R Paula	08/2016
3323	(19*2^330902+1)/77	99611	Lelio R Paula	11/2013
3324	22971^21692+21692^22971	99610	Hans Havermann	03/2018
3325	2^330845+71687	99595	Enzo Doria	04/2016
3326	(23*2^330770+1)/3	99573	Lelio R Paula	11/2013
3327	24494^11613+11613^24494	99567	Hans Havermann	03/2018
3328	2^330735+8415	99562	Lelio R Paula	09/2016
3329	2^330720+74071	99557	Enzo Doria	04/2016
3330	31^66738-2	99531	Lelio R Paula	09/2013
3331	7*3^208567+4	99513	Lelio R Paula	08/2014
3332	(13*10^99508+47)/3	99509	Robert Price	01/2017
3333	2^330553+779	99507	Lelio R Paula	01/2013
3334	15^84606-94	99505	Lelio R Paula	08/2016
3335	6^127858+47	99493	Lelio R Paula	08/2016
3336	5^142337+48	99490	Lelio R Paula	08/2016
3337	7^117724-20	99489	Lelio R Paula	08/2016
3338	(29*10^99474-17)/3	99475	Erik Branger	09/2014
3339	(9*2^330407-1)/7	99463	Lelio R Paula	03/2014
3340	(68*10^99441+7)/3	99443	Robert Price	03/2016
3341	46^59791-45^59791	99418	Jean-Louis Charton	01/2013
3342	23839^14802+14802^23839	99417	Hans Havermann	02/2018
3343	(2*10^99408+529)/9	99408	Robert Price	01/2017
3344	53^57646-2	99398	Lelio R Paula	09/2013
3345	2^330165+1870025	99390	Enzo Doria	05/2016
3346	2^330142-155	99383	Lelio R Paula	12/2012
3347	2^330088-115259	99367	Enzo Doria	06/2015
3348	24216^12671+12671^24216	99354	Hans Havermann	01/2018
3349	(746*10^99303+1)/9	99305	Robert Price	02/2017
3350	3^208107+40	99293	Lelio R Paula	08/2016
3351	(5*2^329833-1)/369	99288	Lelio R Paula	02/2014
3352	8*3^208093+5	99287	Lelio R Paula	08/2014
3353	5^142043+56	99284	Lelio R Paula	08/2016
3354	22*10^99275+7	99277	Robert Price	04/2016
3355	2^329778+1876189	99274	Enzo Doria	07/2016
3356	(10^99239-13)/3	99239	Robert Price	02/2017
3357	3^207987+62	99236	Lelio R Paula	08/2016
3358	2^329638+49	99231	Lelio R Paula	12/2012
3359	7^117413-18	99226	Lelio R Paula	08/2016
3360	2^329586-458903	99216	Enzo Doria	04/2015
3361	2^329553+101	99206	Lelio R Paula	12/2012
3362	2^329551-112897	99205	Enzo Doria	06/2014
3363	(3^207925+7)/50	99204	Lelio R Paula	09/2013
3364	6^127458-17993	99182	Enzo Doria	03/2013
3365	27197^4428+4428^27197	99166	Hans Havermann	10/2017
3366	(46*10^99143-1)/9	99144	Robert Price	12/2014
3367	7*10^99133+69	99134	Robert Price	10/2017
3368	18^78968-3065	99127	Enzo Doria	03/2013
3369	25927^6654+6654^25927	99122	Hans Havermann	10/2017
3370	2^329259+189	99117	Lelio R Paula	12/2012
3371	8*10^99113+39	99114	Robert Price	01/2017
3372	6^127364+77	99109	Lelio R Paula	08/2016
3373	6^127285+13	99047	Lelio R Paula	08/2016
3374	(228581#+235862)/(2^31171*151)	99044	Makoto Morimoto	10/2017
3375	2^329007+73283	99041	Enzo Doria	04/2016
3376	5*3^207543-8	99024	Lelio R Paula	08/2014
3377	2^328885+149	99005	Lelio R Paula	12/2012
3378	23392^17075+17075^23392	99004	Hans Havermann	09/2017
3379	(2^328879-9)/119	99001	Lelio R Paula	10/2013
3380	5^141618+54	98987	Lelio R Paula	08/2016
3381	8*10^98982+51	98983	Robert Price	05/2017
3382	(21*2^328809-1)/7709	98979	Lelio R Paula	03/2014
3383	2^328794-2797601	98977	Enzo Doria	04/2016
3384	6^127176+5	98963	Lelio R Paula	11/2014
3385	24262^11989+11989^24262	98960	Hans Havermann	09/2017
3386	2^328700-109709	98949	Enzo Doria	04/2014
3387	46711!2-2^46711	98916	Robert Price	09/2015
3388	9*7^117037+4	98909	Lelio R Paula	11/2014
3389	(10^98890+149)/3	98890	Serge Batalov	12/2014
3390	22775^21978+21978^22775	98889	Hans Havermann	08/2017
3391	2^328497-216933	98888	Enzo Doria	05/2014
3392	2^328487+32769	98885	Lelio R Paula	08/2016
3393	3^207250-112358	98884	Enzo Doria	06/2014
3394	13^88754-90	98867	Lelio R Paula	08/2016
3395	2^328406+709	98861	Lelio R Paula	02/2013
3396	(17*2^328413-1)/16173	98860	Lelio R Paula	03/2014
3397	7^116976+76	98857	Lelio R Paula	08/2016
3398	2^328335+1155	98839	Lelio R Paula	08/2016
3400	(3*2^328311+1)/5	98832	Lelio R Paula	11/2013
3399	287^40210+40210^287	98832	Norbert Schneider	11/2014
3401	(2^328284+9)/1325	98821	Lelio R Paula	10/2013
3402	(21*2^328258+1)/2125	98814	Lelio R Paula	11/2013
3403	65^54491+48	98788	Lelio R Paula	04/2016
3404	3^207042+98	98785	Lelio R Paula	08/2016
3405	3^206977-112756	98754	Enzo Doria	07/2014
3406	7^116846-50	98747	Lelio R Paula	08/2016
3407	2^327967-28635	98728	Lelio R Paula	08/2016
3408	707^34642+34642^707	98710	Norbert Schneider	12/2017
3409	6^126850-47	98709	Lelio R Paula	08/2016
3410	8*6^126830-7	98694	Lelio R Paula	11/2014
3411	11^94770-270	98693	Enzo Doria	08/2012
3412	2^327832+43	98688	Lelio R Paula	12/2012
3413	2^327795+761	98677	Lelio R Paula	02/2013
3414	10^98669+147411	98670	Patrick De Geest	11/2016
3416	10^98669-9^(98669-1)	98669	Robert Price	05/2016
3415	10^98669-105249	98669	Patrick De Geest	11/2016
3417	2^327671-109801	98639	Enzo Doria	04/2014
3418	5^141090-14	98618	Lelio R Paula	08/2016
3419	20^75799+47	98617	Lelio R Paula	08/2016
3420	2^327515-1017	98592	Lelio R Paula	08/2016
3421	6^126692+97681	98586	Mike Oakes	04/2011
3422	2^327467-741	98578	Lelio R Paula	08/2016
3423	(2^327329+9)/19	98535	Lelio R Paula	10/2013
3424	7^116577-66	98519	Lelio R Paula	08/2016
3425	(3*2^327250+1)/7	98512	Lelio R Paula	11/2013
3426	(19*2^327192+1)/275	98494	Lelio R Paula	11/2013
3427	2^327162-66945	98486	Lelio R Paula	08/2016
3428	4*10^98472-3	98473	Erik Branger	11/2013
3429	(6883*2^327047-1)/77	98453	Lelio R Paula	05/2015
3430	(71*10^98446+1)/9	98447	Serge Batalov	11/2010
3431	13^88363+94	98432	Lelio R Paula	08/2016
3432	48^58543-47^58543	98425	Jean-Louis Charton	11/2005
3433	6^126481+41	98422	Lelio R Paula	08/2016
3434	78*10^98413-7	98415	Robert Price	05/2017
3435	7^116416+46	98383	Lelio R Paula	08/2016
3436	7^116407-24	98376	Lelio R Paula	07/2016
3438	2^326782-1860671	98372	Enzo Doria	03/2016
3437	17^79948+58	98372	Lelio R Paula	08/2016
3439	3^206143-98	98356	Lelio R Paula	08/2016
3440	8*5^140705+7	98350	Lelio R Paula	11/2014
3441	2^326585+11	98312	Lelio R Paula	12/2012
3442	2^326582-459161	98311	Enzo Doria	05/2015
3443	(2^326548+9)/5	98301	Lelio R Paula	10/2013
3444	2^326538+71659	98298	Enzo Doria	04/2016
3445	15^83575-58	98292	Lelio R Paula	08/2016
3446	10^98288+3	98289	Robert Price	03/2011
3447	10^98288-117017	98288	Patrick De Geest	11/2011
3448	(44*10^98284-719)/9	98285	Robert Price	12/2017
3449	2^326421-2797573	98263	Enzo Doria	04/2016
3450	2^326401+16095	98257	Lelio R Paula	07/2016
3451	7^116240-116240^7	98235	Norbert Schneider	05/2017
3452	17^79826-78	98222	Lelio R Paula	08/2016
3453	2^326268-809	98217	Yves Minet	04/2011
3454	(418*10^98199+23)/9	98201	Robert Price	08/2017
3455	12*10^98198-7	98200	Robert Price	11/2017
3456	15^83496-76	98199	Lelio R Paula	08/2016
3457	(10223*2^326179+1)/6125	98190	Lelio R Paula	07/2014
3458	9*5^140471-4	98186	Lelio R Paula	11/2014
3459	2^326069-2383	98157	Yves Minet	10/2013
3460	2^325973+1185	98128	Lelio R Paula	07/2016
3461	(25*2^325949-1)/17	98121	Lelio R Paula	02/2014
3462	2^325945-1847269	98120	Enzo Doria	07/2015
3463	8*10^98111-67	98112	Robert Price	10/2017
3464	2^325866+15	98096	Lelio R Paula	12/2012
3465	2^325765+1974305	98066	Enzo Doria	06/2016
3466	2^325733-58695	98056	Lelio R Paula	07/2016
3467	2^325717-3645	98051	Lelio R Paula	07/2016
3468	(23*2^325583-1)/21	98011	Lelio R Paula	02/2014
3469	(7*10^98007-13)/3	98008	Robert Price	06/2016
3470	2^325512-459959	97989	Enzo Doria	05/2015
3471	(3^205354-8)/17	97978	Lelio R Paula	09/2013
3472	2^325433+76817	97966	Enzo Doria	05/2016
3473	5*10^97963+81	97964	Robert Price	08/2017
3474	2^325390-109061	97953	Enzo Doria	04/2014
3475	13^87921+24	97940	Lelio R Paula	08/2016
3476	961^32831-960^32831	97926	Jean-Louis Charton	02/2011
3477	2^325215+12909	97900	Lelio R Paula	07/2016
3478	7*10^97874-69	97875	Robert Price	01/2017
3479	(17^79537+5^79537)/22	97865	Robert Price	06/2013
3480	15^83212+22	97865	Lelio R Paula	08/2016
3481	2^325087-109057	97861	Enzo Doria	04/2014
3482	2^325074+1870657	97858	Enzo Doria	05/2016
3484	2^325066-2111	97855	Yves Minet	08/2013
3483	CopelandErdos(97855)	97855	Eric W. Weisstein	10/2015
3485	18^77944-89	97841	Lelio R Paula	07/2016
3486	6^125720-17663	97830	Enzo Doria	02/2013
3487	2^324972-2069	97827	Yves Minet	05/2013
3488	2^324944-2788319	97818	Enzo Doria	03/2016
3490	4*10^97799-9	97800	Erik Branger	11/2013
3489	2^324882+577294575	97800	Lelio R Paula	09/2016
3491	2^324863-1867921	97794	Enzo Doria	04/2016
3492	6^125662-18473	97785	Enzo Doria	03/2013
3493	12^90604+11	97779	Lelio R Paula	07/2016
3494	5^139830+24	97737	Lelio R Paula	04/2016
3495	2^324612+1155	97718	Lelio R Paula	07/2016
3496	19^76404-44	97702	Lelio R Paula	07/2016
3497	2^324505-2983	97686	Yves Minet	04/2011
3498	(31*2^324496-1)/45	97683	Lelio R Paula	02/2014
3499	6^125488-17843	97649	Enzo Doria	02/2013
3500	7^115515-2	97622	Lelio R Paula	09/2013

Find by discoverer :

PRP Records

Probable Primes Top 10000

(205869 PRPs in the top)