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	2^336369-19753	101258	Enzo Doria	05/2013
3252	2^336350-344291	101252	Enzo Doria	07/2015
3253	2^336243-108777	101220	Enzo Doria	03/2014
3254	(31*2^336189-1)/19	101204	Lelio R Paula	03/2014
3255	(78557*2^336178+1)/1268757	101199	Lelio R Paula	07/2014
3256	2^336150-20393	101192	Enzo Doria	06/2013
3257	2^336112-1865249	101180	Enzo Doria	03/2016
3258	2^336103-109015	101178	Enzo Doria	04/2014
3259	13^90809-96	101157	Lelio R Paula	10/2016
3260	19^79098-30	101147	Lelio R Paula	10/2016
3261	19^79095+88	101144	Lelio R Paula	10/2016
3262	15^85976+32	101116	Lelio R Paula	10/2016
3263	(3^211950+7)/28854513015920697088	101107	Lelio R Paula	11/2013
3264	(4^167933+17)/3	101106	Robert Price	02/2017
3265	2^335858+153	101104	Lelio R Paula	10/2009
3266	6^129918-35	101096	Lelio R Paula	10/2016
3267	3^211885-70	101095	Lelio R Paula	09/2016
3268	(29*2^335835-1)/550599	101093	Lelio R Paula	03/2014
3269	2^335818-20033	101092	Enzo Doria	06/2013
3270	2^335813-110083	101090	Enzo Doria	04/2014
3271	2^335804+2155	101088	Lelio R Paula	09/2016
3272	2^335784-16145	101082	Enzo Doria	04/2013
3273	11^97051+62	101069	Lelio R Paula	10/2016
3274	3*10^101065+11	101066	Robert Price	07/2018
3275	(2^335691-3)/26515	101049	Lelio R Paula	12/2013
3276	2^335658-94395	101044	Lelio R Paula	09/2016
3277	2^335586+169	101022	Lelio R Paula	10/2009
3278	(56^57787-1)/55	101021	Paul Bourdelais	08/2017
3279	(19*10^100997+737)/9	100998	Robert Price	07/2018
3280	47599!2+1024	100991	Robert Price	02/2015
3281	2^335468-18629	100986	Enzo Doria	05/2013
3282	2^335454-20961	100982	Enzo Doria	06/2013
3283	10^100978+61	100979	Lelio R Paula	09/2016
3284	10^100978-156437	100978	Patrick De Geest	11/2016
3285	(15*2^335417+1)/481	100970	Lelio R Paula	12/2013
3286	2^335403-1859167	100967	Enzo Doria	03/2016
3287	9*2^335364-5	100956	Lelio R Paula	08/2014
3288	2^335349+72287	100951	Enzo Doria	04/2016
3289	2^335329+16095	100945	Lelio R Paula	09/2016
3290	232823#+233663	100937	Makoto Morimoto	10/2017
3291	2^335237-20893	100917	Enzo Doria	06/2013
3292	2^335222-19337	100912	Enzo Doria	05/2013
3293	2^335222-109985	100912	Enzo Doria	04/2014
3294	2^335182-17237	100900	Enzo Doria	05/2013
3295	2^335043-16737	100858	Enzo Doria	05/2013
3296	(21181*2^335049+1)/1343811	100858	Lelio R Paula	07/2014
3297	2^335038-20633	100857	Enzo Doria	06/2013
3298	2^335031+1873373	100855	Enzo Doria	06/2016
3299	3^211354-8816	100842	Enzo Doria	05/2014
3300	2^334984-112757	100841	Enzo Doria	06/2014
3302	2^334857+48527	100803	Lelio R Paula	08/2011
3301	12^93406+29	100803	Lelio R Paula	10/2016
3303	(5*2^334825+1)/47	100792	Lelio R Paula	12/2013
3304	2^334809-13	100788	Lelio R Paula	04/2011
3305	(82*10^100780-1)/9	100781	Robert Price	12/2014
3306	(2^334779+47)/5	100778	Lelio R Paula	12/2013
3307	2^334751+2049	100771	Lelio R Paula	09/2016
3308	13^90443-98	100749	Lelio R Paula	10/2016
3309	(7*10^100737+71)/3	100738	Robert Price	05/2018
3310	(24737*2^334628+1)/3	100737	Lelio R Paula	07/2014
3311	15^85639-28	100720	Lelio R Paula	10/2016
3312	2^334562+577294575	100711	Lelio R Paula	09/2016
3313	4*3^211077-5	100710	Lelio R Paula	08/2014
3314	2^334524+145	100702	Lelio R Paula	07/2009
3315	(1017*2^334391-1)/3535	100662	Lelio R Paula	05/2015
3316	2^334294-113111	100633	Enzo Doria	07/2014
3317	6^129308-17723	100622	Enzo Doria	03/2013
3318	6^129305+95	100619	Lelio R Paula	10/2016
3319	2^334244-1167	100618	Lelio R Paula	09/2016
3320	(21*2^334050+1)/935	100558	Lelio R Paula	12/2013
3321	24885^10984+10984^24885	100555	Hans Havermann	07/2018
3322	(78557*2^334018+1)/4326021	100548	Lelio R Paula	07/2014
3323	(35*10^100542+1)/9	100543	Serge Batalov	11/2010
3324	23578^18367+18367^23578	100538	Hans Havermann	07/2018
3325	13^90251+24	100535	Lelio R Paula	10/2016
3326	2^333963+789	100533	Lelio R Paula	08/2011
3327	2^333919-1840087	100520	Enzo Doria	06/2015
3328	2^333911+72623	100518	Enzo Doria	04/2016
3329	24605^12168+12168^24605	100517	Hans Havermann	08/2018
3330	18^80064-67	100503	Lelio R Paula	10/2016
3331	5^143742-48	100472	Lelio R Paula	10/2016
3332	24095^14784+14784^24095	100472	Hans Havermann	08/2018
3333	2^333757-112123	100471	Enzo Doria	06/2014
3334	27358^4693+4693^27358	100444	Hans Havermann	07/2018
3335	2^333603-108861	100425	Enzo Doria	03/2014
3336	9*7^118818-2	100414	Lelio R Paula	11/2014
3337	2^333546-17097	100408	Enzo Doria	05/2013
3338	17^81597+72	100401	Lelio R Paula	10/2016
3339	p(20559)#/2+8	100384	Robert Price	01/2017
3340	11^96390-24	100380	Lelio R Paula	10/2016
3341	4832563059*2^333333+30029	100353	Donovan Johnson	01/2008
3342	23565^18136+18136^23565	100353	Hans Havermann	07/2018
3343	2^333354+763	100350	Lelio R Paula	08/2011
3344	2^333289-109483	100330	Enzo Doria	04/2014
3345	2^333240-2790209	100316	Enzo Doria	03/2016
3346	23601^17798+17798^23601	100314	Hans Havermann	05/2018
3348	(2^333227-2^166614+1)/5	100311		11/2006
3347	2^333225+719	100311	Lelio R Paula	08/2011
3349	2^333221-2785333	100310	Enzo Doria	10/2015
3350	76^53332-75	100308	Norbert Schneider	02/2015
3351	6^128892-17573	100298	Enzo Doria	03/2013
3352	2^333105-113215	100275	Enzo Doria	07/2014
3353	(31*2^333102+1)/2375	100272	Lelio R Paula	11/2013
3354	17^81476-74	100253	Lelio R Paula	10/2016
3355	23392^19207+19207^23392	100199	Hans Havermann	06/2018
3356	17^81417-16	100180	Theodore Burton	11/2005
3357	2^332739-113215	100165	Enzo Doria	07/2014
3358	2^332730-1865621	100162	Enzo Doria	03/2016
3359	91^51127-2	100160	Lelio R Paula	09/2013
3360	15^85159-32	100155	Lelio R Paula	10/2016
3361	6^128661+97	100118	Lelio R Paula	10/2016
3362	19^78285+40	100108	Lelio R Paula	07/2016
3363	6^128640+5	100102	Lelio R Paula	11/2014
3364	28562^3189+3189^28562	100072	Hans Havermann	05/2018
3365	6^128565-127	100044	Lelio R Paula	08/2016
3366	2^332309-133	100035	Lelio R Paula	02/2011
3367	2^332307+731	100035	Lelio R Paula	07/2011
3368	2^332301+12927	100033	Lelio R Paula	04/2013
3369	23406^18781+18781^23406	100031	Hans Havermann	04/2018
3370	12^92684-13	100023	Lelio R Paula	07/2016
3371	10^100002+236023	100003	Stefano Morozzi	05/2018
3372	10^100002+433741	100003	Stefano Morozzi	05/2018
3373	(10^100002-1)/9-10^33441	100002	Akihiko Yoshida	03/2018
3374	(10^100002-1)/9-10^44692	100002	Akihiko Yoshida	03/2018
3375	10^100002-249519	100002	Patrick De Geest	07/2018
3376	10^100001+314199	100002	Patrick De Geest	07/2018
3391	25206!+p(4114)	100001	Henri Lifchitz	09/2005
3392	25206!-p(5447)	100001	Henri Lifchitz	10/2005
3393	25206!-p(12402)	100001	Henri Lifchitz	04/2006
3394	25206!-p(16290)	100001	Henri Lifchitz	09/2006
3395	25206!-p(19647)	100001	Henri Lifchitz	02/2007
3396	2^332194+11473	100001	Henri Lifchitz	03/2007
3390	10^100000+342909	100001	Milton L. Brown	12/2007
3411	10^100000+346579	100001	Robert Price	04/2012
3412	10^100000+829767	100001	Robert Price	05/2012
3413	10^100000+871899	100001	Robert Price	05/2012
3414	10^100000+1475997	100001	Robert Price	07/2012
3383	10^100000+1751769	100001	Robert Price	08/2012
3384	10^100000+2155489	100001	Robert Price	10/2012
3385	10^100000+2483527	100001	Robert Price	12/2012
3386	10^100000+2503087	100001	Robert Price	12/2012
3387	10^100000+2686179	100001	Robert Price	12/2012
3388	10^100000+2688933	100001	Robert Price	12/2012
3389	10^100000+3667159	100001	Robert Price	08/2013
3397	10^100000+3938473	100001	Robert Price	05/2015
3398	10^100000+3979761	100001	Robert Price	05/2015
3399	10^100000+4293973	100001	Robert Price	09/2015
3400	10^100000+4858267	100001	Robert Price	12/2015
3401	10^100000+5113299	100001	Robert Price	02/2016
3402	10^100000+5169411	100001	Robert Price	02/2016
3403	10^100000+5354043	100001	Robert Price	05/2016
3404	10^100000+5717979	100001	Robert Price	05/2016
3405	10^100000+6080631	100001	Robert Price	07/2016
3406	10^100000+6308469	100001	Robert Price	07/2016
3407	10^100000+6512023	100001	Robert Price	08/2016
3408	10^100000+6596557	100001	Robert Price	08/2016
3409	10^100000+7115409	100001	Robert Price	10/2016
3410	10^100000+7235803	100001	Robert Price	10/2016
3415	10^100000+7867333	100001	Robert Price	12/2016
3416	10^100000+8743093	100001	Robert Price	02/2017
3417	10^100000+8955391	100001	Robert Price	03/2017
3418	10^100000+9180019	100001	Robert Price	03/2017
3419	10^100000+9225987	100001	Robert Price	04/2017
3420	10^100000+9265587	100001	Robert Price	04/2017
3421	10^100000+9287049	100001	Robert Price	04/2017
3422	10^100000+9425053	100001	Robert Price	05/2017
3423	10^100000+9450769	100001	Robert Price	05/2017
3424	10^100000+9528747	100001	Robert Smith	05/2017
3425	10^100000+9548071	100001	Robert Price	06/2017
3426	10^100000+10064287	100001	Robert Price	08/2017
3427	10^100000+10229569	100001	Robert Price	10/2017
3377	10^100000+11187931	100001	Robert Price	03/2018
3378	10^100000+11264721	100001	Robert Price	04/2018
3379	10^100000+11477661	100001	Robert Price	05/2018
3380	10^100000+11644653	100001	Robert Price	07/2018
3381	10^100001-431439	100001	Patrick De Geest	07/2018
3382	10^100000+11769399	100001	Robert Price	08/2018
3428	10^99999+309403	100000	Daniel Heuer	01/2004
3429	10^100000-260199	100000	Patrick De Geest	01/2010
3430	10^99999-59511	99999	Patrick De Geest	07/2009
3431	2^332141-113073	99985	Enzo Doria	07/2014
3432	(3^209561+2)/728101255	99978	Lelio R Paula	09/2013
3433	23827^15702+15702^23827	99978	Hans Havermann	04/2018
3434	2^332085+1865897	99968	Enzo Doria	03/2016
3435	(9787*2^332070-1)/936402369	99959	Lelio R Paula	05/2015
3436	2^332023+191	99949	Lelio R Paula	02/2011
3437	2^331938+71149	99924	Enzo Doria	04/2016
3438	2^331932-78795	99922	Lelio R Paula	09/2016
3439	2^331921+771	99919	Lelio R Paula	01/2013
3440	(3^209419-2)/5132755	99912	Lelio R Paula	09/2013
3441	2^331860-114989	99900	Enzo Doria	05/2015
3442	2^331746-11655	99866	Lelio R Paula	09/2016
3443	11^95891-28	99861	Lelio R Paula	08/2016
3444	(2^331694-5)/11	99849	Lelio R Paula	10/2013
3445	(3^209246+7)/64	99834	Lelio R Paula	09/2013
3446	25062^9617+9617^25062	99823	Hans Havermann	04/2018
3447	15^84866-52	99811	Lelio R Paula	08/2016
3448	13^89600+30	99810	Lelio R Paula	08/2016
3449	22950^22309+22309^22950	99798	Hans Havermann	03/2018
3450	5^142772-38	99794	Lelio R Paula	08/2016
3451	(23*2^331459+1)/475	99778	Lelio R Paula	11/2013
3452	2^331416-331416+1	99767	Robert Price	10/2014
3453	2^331256-57	99718	Lelio R Paula	12/2012
3454	28192^3443+3443^28192	99714	Hans Havermann	03/2018
3455	2^331185+737	99697	Lelio R Paula	01/2013
3456	(4*10^99693+149)/9	99693	Robert Price	03/2017
3457	2^331154+1880527	99688	Enzo Doria	10/2016
3459	(19^77951+1)/20	99679	Paul Bourdelais	03/2010
3458	24354^12385+12385^24354	99679	Hans Havermann	03/2018
3460	2^331110+1870459	99675	Enzo Doria	05/2016
3461	5*2^331075+7	99665	Lelio R Paula	08/2014
3462	25776^7351+7351^25776	99659	Hans Havermann	02/2018
3463	(16*10^99656-31)/3	99657	Robert Price	03/2016
3464	2^330968+345	99632	Lelio R Paula	09/2016
3466	2*5^142528-7	99624	Lelio R Paula	11/2014
3465	2^330942+77329	99624	Enzo Doria	05/2016
3467	14^86914-99	99615	Lelio R Paula	08/2016
3468	(19*2^330902+1)/77	99611	Lelio R Paula	11/2013
3469	22971^21692+21692^22971	99610	Hans Havermann	03/2018
3470	2^330845+71687	99595	Enzo Doria	04/2016
3471	(23*2^330770+1)/3	99573	Lelio R Paula	11/2013
3472	24494^11613+11613^24494	99567	Hans Havermann	03/2018
3473	2^330735+8415	99562	Lelio R Paula	09/2016
3474	2^330720+74071	99557	Enzo Doria	04/2016
3475	31^66738-2	99531	Lelio R Paula	09/2013
3476	7*3^208567+4	99513	Lelio R Paula	08/2014
3477	(13*10^99508+47)/3	99509	Robert Price	01/2017
3478	2^330553+779	99507	Lelio R Paula	01/2013
3479	15^84606-94	99505	Lelio R Paula	08/2016
3480	6^127858+47	99493	Lelio R Paula	08/2016
3481	5^142337+48	99490	Lelio R Paula	08/2016
3482	7^117724-20	99489	Lelio R Paula	08/2016
3483	(29*10^99474-17)/3	99475	Erik Branger	09/2014
3484	(9*2^330407-1)/7	99463	Lelio R Paula	03/2014
3485	(68*10^99441+7)/3	99443	Robert Price	03/2016
3486	46^59791-45^59791	99418	Jean-Louis Charton	01/2013
3487	23839^14802+14802^23839	99417	Hans Havermann	02/2018
3488	(2*10^99408+529)/9	99408	Robert Price	01/2017
3489	53^57646-2	99398	Lelio R Paula	09/2013
3490	2^330165+1870025	99390	Enzo Doria	05/2016
3491	2^330142-155	99383	Lelio R Paula	12/2012
3492	2^330088-115259	99367	Enzo Doria	06/2015
3493	24216^12671+12671^24216	99354	Hans Havermann	01/2018
3494	(746*10^99303+1)/9	99305	Robert Price	02/2017
3495	3^208107+40	99293	Lelio R Paula	08/2016
3496	(5*2^329833-1)/369	99288	Lelio R Paula	02/2014
3497	8*3^208093+5	99287	Lelio R Paula	08/2014
3498	5^142043+56	99284	Lelio R Paula	08/2016
3499	22*10^99275+7	99277	Robert Price	04/2016
3500	2^329778+1876189	99274	Enzo Doria	07/2016

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PRP Records

Probable Primes Top 10000

(218736 PRPs in the top)