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 (> 30000)	Who ?	When ?
3251	2^334524+145	100702	Lelio R Paula	07/2009
3252	(1017*2^334391-1)/3535	100662	Lelio R Paula	05/2015
3253	2^334294-113111	100633	Enzo Doria	07/2014
3254	6^129308-17723	100622	Enzo Doria	03/2013
3255	6^129305+95	100619	Lelio R Paula	10/2016
3256	2^334244-1167	100618	Lelio R Paula	09/2016
3257	(21*2^334050+1)/935	100558	Lelio R Paula	12/2013
3258	(78557*2^334018+1)/4326021	100548	Lelio R Paula	07/2014
3259	(35*10^100542+1)/9	100543	Serge Batalov	11/2010
3260	13^90251+24	100535	Lelio R Paula	10/2016
3261	2^333963+789	100533	Lelio R Paula	08/2011
3262	2^333919-1840087	100520	Enzo Doria	06/2015
3263	2^333911+72623	100518	Enzo Doria	04/2016
3264	18^80064-67	100503	Lelio R Paula	10/2016
3265	5^143742-48	100472	Lelio R Paula	10/2016
3266	2^333757-112123	100471	Enzo Doria	06/2014
3267	2^333603-108861	100425	Enzo Doria	03/2014
3268	9*7^118818-2	100414	Lelio R Paula	11/2014
3269	2^333546-17097	100408	Enzo Doria	05/2013
3270	17^81597+72	100401	Lelio R Paula	10/2016
3271	p(20559)#/2+8	100384	Robert Price	01/2017
3272	11^96390-24	100380	Lelio R Paula	10/2016
3273	4832563059*2^333333+30029	100353	Donovan Johnson	01/2008
3274	2^333354+763	100350	Lelio R Paula	08/2011
3275	2^333289-109483	100330	Enzo Doria	04/2014
3276	2^333240-2790209	100316	Enzo Doria	03/2016
3277	23601^17798+17798^23601	100314	Hans Havermann	05/2018
3278	(2^333227-2^166614+1)/5	100311		11/2006
3279	2^333225+719	100311	Lelio R Paula	08/2011
3280	2^333221-2785333	100310	Enzo Doria	10/2015
3281	76^53332-75	100308	Norbert Schneider	02/2015
3282	6^128892-17573	100298	Enzo Doria	03/2013
3283	2^333105-113215	100275	Enzo Doria	07/2014
3284	(31*2^333102+1)/2375	100272	Lelio R Paula	11/2013
3285	17^81476-74	100253	Lelio R Paula	10/2016
3286	23392^19207+19207^23392	100199	Hans Havermann	06/2018
3287	17^81417-16	100180	Theodore Burton	11/2005
3288	2^332739-113215	100165	Enzo Doria	07/2014
3289	2^332730-1865621	100162	Enzo Doria	03/2016
3290	91^51127-2	100160	Lelio R Paula	09/2013
3291	15^85159-32	100155	Lelio R Paula	10/2016
3292	6^128661+97	100118	Lelio R Paula	10/2016
3293	19^78285+40	100108	Lelio R Paula	07/2016
3294	6^128640+5	100102	Lelio R Paula	11/2014
3295	28562^3189+3189^28562	100072	Hans Havermann	05/2018
3296	6^128565-127	100044	Lelio R Paula	08/2016
3297	2^332309-133	100035	Lelio R Paula	02/2011
3298	2^332307+731	100035	Lelio R Paula	07/2011
3299	2^332301+12927	100033	Lelio R Paula	04/2013
3300	23406^18781+18781^23406	100031	Hans Havermann	04/2018
3301	12^92684-13	100023	Lelio R Paula	07/2016
3302	10^100002+236023	100003	Stefano Morozzi	05/2018
3303	10^100002+433741	100003	Stefano Morozzi	05/2018
3304	(10^100002-1)/9-10^33441	100002	Akihiko Yoshida	03/2018
3305	(10^100002-1)/9-10^44692	100002	Akihiko Yoshida	03/2018
3331	25206!+p(4114)	100001	Henri Lifchitz	09/2005
3332	25206!-p(5447)	100001	Henri Lifchitz	10/2005
3333	25206!-p(12402)	100001	Henri Lifchitz	04/2006
3334	25206!-p(16290)	100001	Henri Lifchitz	09/2006
3335	25206!-p(19647)	100001	Henri Lifchitz	02/2007
3336	2^332194+11473	100001	Henri Lifchitz	03/2007
3317	10^100000+342909	100001	Milton L. Brown	12/2007
3350	10^100000+346579	100001	Robert Price	04/2012
3351	10^100000+829767	100001	Robert Price	05/2012
3352	10^100000+871899	100001	Robert Price	05/2012
3353	10^100000+1475997	100001	Robert Price	07/2012
3337	10^100000+1751769	100001	Robert Price	08/2012
3338	10^100000+2155489	100001	Robert Price	10/2012
3339	10^100000+2483527	100001	Robert Price	12/2012
3340	10^100000+2503087	100001	Robert Price	12/2012
3341	10^100000+2686179	100001	Robert Price	12/2012
3342	10^100000+2688933	100001	Robert Price	12/2012
3343	10^100000+3667159	100001	Robert Price	08/2013
3347	10^100000+3938473	100001	Robert Price	05/2015
3348	10^100000+3979761	100001	Robert Price	05/2015
3349	10^100000+4293973	100001	Robert Price	09/2015
3344	10^100000+4858267	100001	Robert Price	12/2015
3345	10^100000+5113299	100001	Robert Price	02/2016
3346	10^100000+5169411	100001	Robert Price	02/2016
3309	10^100000+5354043	100001	Robert Price	05/2016
3310	10^100000+5717979	100001	Robert Price	05/2016
3311	10^100000+6080631	100001	Robert Price	07/2016
3312	10^100000+6308469	100001	Robert Price	07/2016
3313	10^100000+6512023	100001	Robert Price	08/2016
3314	10^100000+6596557	100001	Robert Price	08/2016
3315	10^100000+7115409	100001	Robert Price	10/2016
3316	10^100000+7235803	100001	Robert Price	10/2016
3318	10^100000+7867333	100001	Robert Price	12/2016
3319	10^100000+8743093	100001	Robert Price	02/2017
3320	10^100000+8955391	100001	Robert Price	03/2017
3321	10^100000+9180019	100001	Robert Price	03/2017
3322	10^100000+9225987	100001	Robert Price	04/2017
3323	10^100000+9265587	100001	Robert Price	04/2017
3324	10^100000+9287049	100001	Robert Price	04/2017
3325	10^100000+9425053	100001	Robert Price	05/2017
3326	10^100000+9450769	100001	Robert Price	05/2017
3327	10^100000+9528747	100001	Robert Smith	05/2017
3328	10^100000+9548071	100001	Robert Price	06/2017
3329	10^100000+10064287	100001	Robert Price	08/2017
3330	10^100000+10229569	100001	Robert Price	10/2017
3306	10^100000+11187931	100001	Robert Price	03/2018
3307	10^100000+11264721	100001	Robert Price	04/2018
3308	10^100000+11477661	100001	Robert Price	05/2018
3355	10^99999+309403	100000	Daniel Heuer	01/2004
3354	10^100000-260199	100000	Patrick De Geest	01/2010
3356	10^99999-59511	99999	Patrick De Geest	07/2009
3357	2^332141-113073	99985	Enzo Doria	07/2014
3358	(3^209561+2)/728101255	99978	Lelio R Paula	09/2013
3359	23827^15702+15702^23827	99978	Hans Havermann	04/2018
3360	2^332085+1865897	99968	Enzo Doria	03/2016
3361	(9787*2^332070-1)/936402369	99959	Lelio R Paula	05/2015
3362	2^332023+191	99949	Lelio R Paula	02/2011
3363	2^331938+71149	99924	Enzo Doria	04/2016
3364	2^331932-78795	99922	Lelio R Paula	09/2016
3365	2^331921+771	99919	Lelio R Paula	01/2013
3366	(3^209419-2)/5132755	99912	Lelio R Paula	09/2013
3367	2^331860-114989	99900	Enzo Doria	05/2015
3368	2^331746-11655	99866	Lelio R Paula	09/2016
3369	11^95891-28	99861	Lelio R Paula	08/2016
3370	(2^331694-5)/11	99849	Lelio R Paula	10/2013
3371	(3^209246+7)/64	99834	Lelio R Paula	09/2013
3372	25062^9617+9617^25062	99823	Hans Havermann	04/2018
3373	15^84866-52	99811	Lelio R Paula	08/2016
3374	13^89600+30	99810	Lelio R Paula	08/2016
3375	22950^22309+22309^22950	99798	Hans Havermann	03/2018
3376	5^142772-38	99794	Lelio R Paula	08/2016
3377	(23*2^331459+1)/475	99778	Lelio R Paula	11/2013
3378	2^331416-331416+1	99767	Robert Price	10/2014
3379	2^331256-57	99718	Lelio R Paula	12/2012
3380	28192^3443+3443^28192	99714	Hans Havermann	03/2018
3381	2^331185+737	99697	Lelio R Paula	01/2013
3382	(4*10^99693+149)/9	99693	Robert Price	03/2017
3383	2^331154+1880527	99688	Enzo Doria	10/2016
3385	(19^77951+1)/20	99679	Paul Bourdelais	03/2010
3384	24354^12385+12385^24354	99679	Hans Havermann	03/2018
3386	2^331110+1870459	99675	Enzo Doria	05/2016
3387	5*2^331075+7	99665	Lelio R Paula	08/2014
3388	25776^7351+7351^25776	99659	Hans Havermann	02/2018
3389	(16*10^99656-31)/3	99657	Robert Price	03/2016
3390	2^330968+345	99632	Lelio R Paula	09/2016
3392	2*5^142528-7	99624	Lelio R Paula	11/2014
3391	2^330942+77329	99624	Enzo Doria	05/2016
3393	14^86914-99	99615	Lelio R Paula	08/2016
3394	(19*2^330902+1)/77	99611	Lelio R Paula	11/2013
3395	22971^21692+21692^22971	99610	Hans Havermann	03/2018
3396	2^330845+71687	99595	Enzo Doria	04/2016
3397	(23*2^330770+1)/3	99573	Lelio R Paula	11/2013
3398	24494^11613+11613^24494	99567	Hans Havermann	03/2018
3399	2^330735+8415	99562	Lelio R Paula	09/2016
3400	2^330720+74071	99557	Enzo Doria	04/2016
3401	31^66738-2	99531	Lelio R Paula	09/2013
3402	7*3^208567+4	99513	Lelio R Paula	08/2014
3403	(13*10^99508+47)/3	99509	Robert Price	01/2017
3404	2^330553+779	99507	Lelio R Paula	01/2013
3405	15^84606-94	99505	Lelio R Paula	08/2016
3406	6^127858+47	99493	Lelio R Paula	08/2016
3407	5^142337+48	99490	Lelio R Paula	08/2016
3408	7^117724-20	99489	Lelio R Paula	08/2016
3409	(29*10^99474-17)/3	99475	Erik Branger	09/2014
3410	(9*2^330407-1)/7	99463	Lelio R Paula	03/2014
3411	(68*10^99441+7)/3	99443	Robert Price	03/2016
3412	46^59791-45^59791	99418	Jean-Louis Charton	01/2013
3413	23839^14802+14802^23839	99417	Hans Havermann	02/2018
3414	(2*10^99408+529)/9	99408	Robert Price	01/2017
3415	53^57646-2	99398	Lelio R Paula	09/2013
3416	2^330165+1870025	99390	Enzo Doria	05/2016
3417	2^330142-155	99383	Lelio R Paula	12/2012
3418	2^330088-115259	99367	Enzo Doria	06/2015
3419	24216^12671+12671^24216	99354	Hans Havermann	01/2018
3420	(746*10^99303+1)/9	99305	Robert Price	02/2017
3421	3^208107+40	99293	Lelio R Paula	08/2016
3422	(5*2^329833-1)/369	99288	Lelio R Paula	02/2014
3423	8*3^208093+5	99287	Lelio R Paula	08/2014
3424	5^142043+56	99284	Lelio R Paula	08/2016
3425	22*10^99275+7	99277	Robert Price	04/2016
3426	2^329778+1876189	99274	Enzo Doria	07/2016
3427	(10^99239-13)/3	99239	Robert Price	02/2017
3428	3^207987+62	99236	Lelio R Paula	08/2016
3429	2^329638+49	99231	Lelio R Paula	12/2012
3430	7^117413-18	99226	Lelio R Paula	08/2016
3431	2^329586-458903	99216	Enzo Doria	04/2015
3432	2^329553+101	99206	Lelio R Paula	12/2012
3433	2^329551-112897	99205	Enzo Doria	06/2014
3434	(3^207925+7)/50	99204	Lelio R Paula	09/2013
3435	6^127458-17993	99182	Enzo Doria	03/2013
3436	27197^4428+4428^27197	99166	Hans Havermann	10/2017
3437	(46*10^99143-1)/9	99144	Robert Price	12/2014
3438	7*10^99133+69	99134	Robert Price	10/2017
3439	18^78968-3065	99127	Enzo Doria	03/2013
3440	25927^6654+6654^25927	99122	Hans Havermann	10/2017
3441	2^329259+189	99117	Lelio R Paula	12/2012
3442	8*10^99113+39	99114	Robert Price	01/2017
3443	6^127364+77	99109	Lelio R Paula	08/2016
3444	6^127285+13	99047	Lelio R Paula	08/2016
3445	(228581#+235862)/(2^31171*151)	99044	Makoto Morimoto	10/2017
3446	2^329007+73283	99041	Enzo Doria	04/2016
3447	5*3^207543-8	99024	Lelio R Paula	08/2014
3448	2^328885+149	99005	Lelio R Paula	12/2012
3449	23392^17075+17075^23392	99004	Hans Havermann	09/2017
3450	(2^328879-9)/119	99001	Lelio R Paula	10/2013
3451	5^141618+54	98987	Lelio R Paula	08/2016
3452	8*10^98982+51	98983	Robert Price	05/2017
3453	(21*2^328809-1)/7709	98979	Lelio R Paula	03/2014
3454	2^328794-2797601	98977	Enzo Doria	04/2016
3455	6^127176+5	98963	Lelio R Paula	11/2014
3456	24262^11989+11989^24262	98960	Hans Havermann	09/2017
3457	2^328700-109709	98949	Enzo Doria	04/2014
3458	46711!2-2^46711	98916	Robert Price	09/2015
3459	9*7^117037+4	98909	Lelio R Paula	11/2014
3460	(10^98890+149)/3	98890	Serge Batalov	12/2014
3461	22775^21978+21978^22775	98889	Hans Havermann	08/2017
3462	2^328497-216933	98888	Enzo Doria	05/2014
3463	2^328487+32769	98885	Lelio R Paula	08/2016
3464	3^207250-112358	98884	Enzo Doria	06/2014
3465	13^88754-90	98867	Lelio R Paula	08/2016
3466	2^328406+709	98861	Lelio R Paula	02/2013
3467	(17*2^328413-1)/16173	98860	Lelio R Paula	03/2014
3468	7^116976+76	98857	Lelio R Paula	08/2016
3469	2^328335+1155	98839	Lelio R Paula	08/2016
3470	(3*2^328311+1)/5	98832	Lelio R Paula	11/2013
3471	287^40210+40210^287	98832	Norbert Schneider	11/2014
3472	(2^328284+9)/1325	98821	Lelio R Paula	10/2013
3473	(21*2^328258+1)/2125	98814	Lelio R Paula	11/2013
3474	65^54491+48	98788	Lelio R Paula	04/2016
3475	3^207042+98	98785	Lelio R Paula	08/2016
3476	3^206977-112756	98754	Enzo Doria	07/2014
3477	7^116846-50	98747	Lelio R Paula	08/2016
3478	2^327967-28635	98728	Lelio R Paula	08/2016
3479	707^34642+34642^707	98710	Norbert Schneider	12/2017
3480	6^126850-47	98709	Lelio R Paula	08/2016
3481	8*6^126830-7	98694	Lelio R Paula	11/2014
3482	11^94770-270	98693	Enzo Doria	08/2012
3483	2^327832+43	98688	Lelio R Paula	12/2012
3484	2^327795+761	98677	Lelio R Paula	02/2013
3485	10^98669+147411	98670	Patrick De Geest	11/2016
3487	10^98669-9^(98669-1)	98669	Robert Price	05/2016
3486	10^98669-105249	98669	Patrick De Geest	11/2016
3488	2^327671-109801	98639	Enzo Doria	04/2014
3489	5^141090-14	98618	Lelio R Paula	08/2016
3490	20^75799+47	98617	Lelio R Paula	08/2016
3491	2^327515-1017	98592	Lelio R Paula	08/2016
3492	6^126692+97681	98586	Mike Oakes	04/2011
3493	2^327467-741	98578	Lelio R Paula	08/2016
3494	(2^327329+9)/19	98535	Lelio R Paula	10/2013
3495	7^116577-66	98519	Lelio R Paula	08/2016
3496	(3*2^327250+1)/7	98512	Lelio R Paula	11/2013
3497	(19*2^327192+1)/275	98494	Lelio R Paula	11/2013
3498	2^327162-66945	98486	Lelio R Paula	08/2016
3499	4*10^98472-3	98473	Erik Branger	11/2013
3500	(6883*2^327047-1)/77	98453	Lelio R Paula	05/2015

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PRP Records

Probable Primes Top 10000

(212140 PRPs in the top)