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 (> 50000)	Who ?	When ?
3251	(2^341388+47)/21014943	102761	Lelio R Paula	12/2013
3252	2^341355+21	102759	Lelio R Paula	08/2011
3253	2^341246+40755	102726	Lelio R Paula	11/2016
3254	(2^341256-5)/991699	102723	Lelio R Paula	12/2013
3255	7^121547+78	102720	Lelio R Paula	10/2016
3256	2^341223-461197	102719	Enzo Doria	06/2015
3258	2^341190-20577	102709	Enzo Doria	06/2013
3257	(27*2^341212+1)/84674449	102709	Lelio R Paula	12/2013
3259	6^131976-65	102698	Lelio R Paula	10/2016
3260	2^341134+2533	102692	Henri Lifchitz	09/2005
3261	13^92184-54	102688	Lelio R Paula	10/2016
3262	2^341116-20873	102687	Enzo Doria	06/2013
3263	2^341094-19953	102680	Enzo Doria	06/2013
3264	2^341053+129	102668	Lelio R Paula	08/2011
3266	(31*2^341006-1)/3	102655	Lelio R Paula	03/2014
3265	7^121471+94	102655	Lelio R Paula	10/2016
3268	2^341004-173	102653	Lelio R Paula	08/2011
3267	20^78901+3	102653	Lelio R Paula	10/2016
3269	5^146853-52	102646	Lelio R Paula	10/2016
3270	2^340969-216931	102642	Enzo Doria	05/2014
3271	122^49196+121	102641	Norbert Schneider	10/2018
3272	2^340952+1870021	102637	Enzo Doria	05/2016
3273	5*2^340940-3	102634	Lelio R Paula	08/2014
3274	(6^131891+1)/7	102631	Paul Bourdelais	01/2010
3275	(4*10^102612+83)/3	102613	Robert Price	02/2018
3276	75^54717+74	102598	Norbert Schneider	01/2015
3277	(17*10^102597+13)/3	102598	Robert Price	01/2019
3278	2^340806-20393	102593	Enzo Doria	06/2013
3279	(2^340790+5)/138267	102583	Lelio R Paula	12/2013
3280	6^131821+77	102577	Lelio R Paula	10/2016
3281	2^340688-29	102558	Henri Lifchitz	05/2005
3282	2^340685-109101	102557	Enzo Doria	04/2014
3283	65^56567-64	102552	Norbert Schneider	11/2014
3284	2^340547-108897	102515	Enzo Doria	03/2014
3285	7^121268+82	102484	Lelio R Paula	10/2016
3286	(6883*2^340443-1)/162401	102483	Lelio R Paula	05/2015
3287	2^340434-5955	102481	Lelio R Paula	11/2016
3288	(2^340381+47)/7	102465	Lelio R Paula	12/2013
3289	111^50095+110	102461	Norbert Schneider	04/2017
3290	2^340291-20301	102438	Enzo Doria	06/2013
3291	12^94915+89	102431	Lelio R Paula	10/2016
3292	2^340208-20373	102413	Enzo Doria	06/2013
3293	6^131598-17273	102404	Enzo Doria	02/2013
3294	2^340115-21181	102385	Enzo Doria	06/2013
3295	(55459*2^340090+1)/1591	102379	Lelio R Paula	07/2014
3296	89^52511-88^52511	102365	Robert Price	06/2015
3297	3^214539-112756	102362	Enzo Doria	07/2014
3298	2^340000-19877	102351	Enzo Doria	06/2013
3299	2^339990-114845	102348	Enzo Doria	05/2015
3300	(3^214516-2)/51383	102346	Lelio R Paula	12/2013
3301	20^78661-99	102341	Lelio R Paula	09/2016
3302	2^339951-19585	102336	Enzo Doria	05/2013
3303	(13*2^339943+1)/45	102333	Lelio R Paula	12/2013
3304	2^339889+29327	102317	Yves Minet	06/2010
3305	2^339834-109493	102301	Enzo Doria	04/2014
3306	(11^98221-5^98221)/6	102286	Robert Price	01/2013
3307	3^214365+1820	102279	Lelio R Paula	10/2016
3308	(11*2^339705-1)/183	102261	Lelio R Paula	03/2014
3309	2^339694-16995	102259	Lelio R Paula	09/2016
3310	122^49008+121	102249	Norbert Schneider	10/2018
3311	7^120985-38	102245	Lelio R Paula	10/2016
3312	10^102244+122961	102245	Patrick De Geest	12/2016
3313	10^102244-27	102244	Lelio R Paula	09/2016
3314	7^120982-62	102242	Lelio R Paula	10/2016
3315	4*6^131382-5	102236	Lelio R Paula	11/2014
3316	2^339586-1091	102226	Yves Minet	11/2012
3317	11^98161-3072000	102225	Enzo Doria	12/2012
3318	9*7^120961-4	102225	Lelio R Paula	11/2014
3319	5*3^214250+2	102224	Serge Batalov	10/2010
3320	12^94713-59	102213	Lelio R Paula	10/2016
3321	12^94705+89	102204	Lelio R Paula	10/2016
3322	2^339407-177	102172	Lelio R Paula	08/2011
3323	4*10^102163-57	102164	Robert Price	10/2018
3324	2^339355+65	102157	Lelio R Paula	07/2011
3325	(2^339323+47)/880715	102141	Lelio R Paula	12/2013
3326	2^339168+21	102100	Lelio R Paula	07/2011
3327	2^339167-108807	102100	Enzo Doria	03/2014
3328	2^339156+163	102097	Lelio R Paula	08/2011
3329	24327^15668+15668^24327	102053	Hans Havermann	02/2019
3330	(2^338982-7)/1754517	102038	Lelio R Paula	12/2013
3331	2^338891-18885	102017	Enzo Doria	05/2013
3332	2^338829-113239	101998	Enzo Doria	07/2014
3333	2^338828-113297	101998	Enzo Doria	07/2014
3334	2^338796+93	101988	Donovan Johnson	06/2008
3335	lucasU(1373,1,32502)-lucasU(1373,1,32501)	101978	Mike Oakes	05/2009
3336	25295^10744+10744^25295	101969	Hans Havermann	01/2019
3337	25712^9243+9243^25712	101969	Hans Havermann	01/2019
3338	(71^55079-1)/70	101964	Paul Bourdelais	08/2017
3340	2^338682-19865	101954	Enzo Doria	06/2013
3339	(2^(112895*3+1)+243)/7	101954	Kevin Acres	12/2013
3341	28594^3673+3673^28594	101939	Hans Havermann	02/2019
3342	2^338568+37	101920	Lelio R Paula	07/2011
3343	2^338559-1858777	101917	Enzo Doria	04/2016
3344	(9*2^338520+1)/365	101904	Lelio R Paula	12/2013
3345	24502^14419+14419^24502	101903	Hans Havermann	01/2019
3346	2^338497-17041	101898	Enzo Doria	05/2013
3347	2^338475+54615	101892	Lelio R Paula	10/2016
3348	2^338426-19797	101877	Enzo Doria	06/2013
3349	2^338368-20369	101859	Enzo Doria	06/2013
3350	2^338366+74179	101859	Enzo Doria	04/2016
3351	27088^5755+5755^27088	101853	Hans Havermann	01/2019
3352	2^338280-19745	101833	Enzo Doria	06/2013
3353	(3*2^338236-1)/347	101818	Lelio R Paula	03/2014
3354	6^130841+103	101815	Lelio R Paula	10/2016
3355	2^338122-20117	101785	Enzo Doria	06/2013
3356	(2^338139+5)/905333	101785	Lelio R Paula	12/2013
3357	35^65917-7092	101781	Enzo Doria	03/2013
3358	2^338010-19833	101752	Enzo Doria	06/2013
3359	3^213215-76	101730	Lelio R Paula	09/2016
3360	23907^17998+17998^23907	101730	Hans Havermann	01/2019
3361	2^337930+63	101728	Lelio R Paula	07/2011
3362	2^337920+1869661	101725	Enzo Doria	05/2016
3363	24116^16509+16509^24116	101715	Hans Havermann	01/2019
3364	2^337859-19645	101706	Enzo Doria	05/2013
3365	2^337754+1869169	101675	Enzo Doria	05/2016
3366	3*10^101657-37	101658	Robert Price	07/2018
3367	(31*2^337677-1)/593	101650	Lelio R Paula	03/2014
3368	11^97605-24	101646	Lelio R Paula	10/2016
3369	8^112539-112539	101633	Robert Price	01/2014
3370	25694^9003+9003^25694	101605	Hans Havermann	12/2018
3371	2^337515-19869	101603	Enzo Doria	06/2013
3372	2^337473+719	101590	Lelio R Paula	08/2011
3373	(2^337485-509203)/656647157	101585	Lelio R Paula	12/2013
3374	2^337452-108815	101584	Enzo Doria	03/2014
3375	2^337453+1185	101584	Lelio R Paula	09/2016
3376	2^337410-113561	101571	Enzo Doria	08/2014
3377	2^337387+855	101564	Lelio R Paula	09/2016
3378	2^337367-17295	101558	Lelio R Paula	09/2016
3379	2^337342-109035	101551	Enzo Doria	04/2014
3380	23703^19238+19238^23703	101548	Hans Havermann	12/2018
3381	2^337267-19	101528	Lelio R Paula	07/2011
3382	2^337183-19989	101503	Enzo Doria	06/2013
3383	2^337149+72425	101492	Enzo Doria	04/2016
3384	24041^16642+16642^24041	101483	Hans Havermann	12/2018
3385	33982^969+969^33982	101482	Hans Havermann	12/2018
3386	2^337101-20241	101478	Enzo Doria	06/2013
3387	2^337035-20001	101458	Enzo Doria	06/2013
3388	2^337017-16995	101453	Lelio R Paula	09/2016
3389	2^336979-115315	101441	Enzo Doria	06/2015
3390	2^336970-20885	101439	Enzo Doria	06/2013
3391	2^336958+79	101435	Lelio R Paula	10/2009
3392	2^336942+169	101430	Lelio R Paula	10/2009
3393	(15185*2^336894-1)/7939	101416	Lelio R Paula	05/2015
3394	4*10^101415-89	101416	Robert Price	11/2018
3395	2^336871+257463	101409	Tony Prest / Never Odd Or Even	04/2016
3396	2^336871+318105	101409	Tony Prest / Never Odd Or Even	04/2016
3397	2^336871+1010813	101409	Tony Prest / Never Odd Or Even	04/2016
3398	2^336871+2302245	101409	Tony Prest / Never Odd Or Even	04/2016
3399	2^336871+389273	101409	Tony Prest / Never Odd Or Even	04/2016
3400	2^336871+1685475	101409	Tony Prest / Never Odd Or Even	04/2016
3401	2^336871+1068119	101409	Tony Prest / Never Odd Or Even	04/2016
3402	2^336871+586905	101409	Tony Prest / Never Odd Or Even	04/2016
3403	2^336871+674571	101409	Tony Prest / Never Odd Or Even	04/2016
3404	2^336871+707009	101409	Tony Prest / Never Odd Or Even	04/2016
3405	2^336871+1210299	101409	Tony Prest / Never Odd Or Even	04/2016
3406	2^336871+1921185	101409	Tony Prest / Never Odd Or Even	04/2016
3407	2^336871+2003973	101409	Tony Prest / Never Odd Or Even	04/2016
3408	2^336871+2656475	101409	Tony Prest / Never Odd Or Even	04/2016
3409	2^336871+2703023	101409	Tony Prest / Never Odd Or Even	04/2016
3410	2^336871+2704545	101409	Tony Prest / Never Odd Or Even	04/2016
3411	2^336871+2766801	101409	Tony Prest / Never Odd Or Even	04/2016
3412	2^336871+2127735	101409	Tony Prest / Never Odd Or Even	04/2016
3413	(2^336871+821089)/3	101408	Tony Prest / Never Odd Or Even	05/2016
3414	(2^336871+119567)/5	101408	Tony Prest / Never Odd Or Even	05/2016
3415	(2^336871+398161)/3	101408	Tony Prest / Never Odd Or Even	05/2016
3416	(2^336871+625889)/7	101408	Tony Prest / Never Odd Or Even	05/2016
3417	24097^16150+16150^24097	101405	Hans Havermann	12/2018
3418	2^336842+94065	101400	Lelio R Paula	09/2016
3419	(2^336871+904417)/3/3/3/5/19/9287177/9690011663/29993043103	101378	Tony Prest / Never Odd Or Even	04/2016
3420	(2^336871+631971)/13/251/1601/294277/614362921/30324278867	101377	Tony Prest / Never Odd Or Even	04/2016
3421	(2^336871+1443541)/3/89/1655197/11018131/47972707/468862691879	101374	Tony Prest / Never Odd Or Even	04/2016
3422	(2^336871+689863)/3/11/109/137/1867/7151/20800501/29243857/127778489	101373	Tony Prest / Never Odd Or Even	04/2016
3423	(2^336871+219839)/191/643/3011/9479/117127/175750007/4578271757	101373	Tony Prest / Never Odd Or Even	04/2016
3424	(2^336871+272895)/19/661/977572033/95853078653/520779768241	101373	Tony Prest / Never Odd Or Even	04/2016
3425	(2^336871+1023429)/2311/415873/991889/3630648341/207732189179	101373	Tony Prest / Never Odd Or Even	04/2016
3426	10^101369+203811	101370	Patrick De Geest	11/2016
3427	10^101369-99	101369	Lelio R Paula	09/2016
3428	(2^336871+1832627)/5/5/23/181/4397/91373/3746673331/115602484097/279351383917	101363	Tony Prest / Never Odd Or Even	04/2016
3429	2^336701-113563	101358	Enzo Doria	08/2014
3430	2^336644-109023	101340	Enzo Doria	04/2014
3431	2^336601-21081	101327	Enzo Doria	06/2013
3432	20^77869+63	101310	Lelio R Paula	09/2016
3433	(13*2^336523-1)/19	101304	Lelio R Paula	03/2014
3435	6^130179-137	101299	Lelio R Paula	10/2016
3434	(2^336506+lucasV(1,2,336506)+1)/2	101299	Mike Oakes	11/2016
3436	(24737*2^336485+1)/7285	101293	Lelio R Paula	07/2014
3437	(2^336448+9)/497405	101276	Lelio R Paula	12/2013
3438	2^336369-19753	101258	Enzo Doria	05/2013
3439	23842^17653+17653^23842	101253	Hans Havermann	11/2018
3440	2^336350-344291	101252	Enzo Doria	07/2015
3441	2^336243-108777	101220	Enzo Doria	03/2014
3442	(31*2^336189-1)/19	101204	Lelio R Paula	03/2014
3443	23535^19954+19954^23535	101202	Hans Havermann	11/2018
3444	(78557*2^336178+1)/1268757	101199	Lelio R Paula	07/2014
3445	2^336150-20393	101192	Enzo Doria	06/2013
3446	23996^16473+16473^23996	101186	Hans Havermann	11/2018
3447	2^336112-1865249	101180	Enzo Doria	03/2016
3448	2^336103-109015	101178	Enzo Doria	04/2014
3449	13^90809-96	101157	Lelio R Paula	10/2016
3450	26199^7258+7258^26199	101150	Hans Havermann	11/2018
3451	19^79098-30	101147	Lelio R Paula	10/2016
3452	19^79095+88	101144	Lelio R Paula	10/2016
3453	15^85976+32	101116	Lelio R Paula	10/2016
3454	2^335872-2776215	101108	Tony Prest / Never Odd Or Even	01/2019
3455	(3^211950+7)/28854513015920697088	101107	Lelio R Paula	11/2013
3456	(4^167933+17)/3	101106	Robert Price	02/2017
3458	2^335858+153	101104	Lelio R Paula	10/2009
3457	(2^335872-2776871)/5/5/479	101104	Tony Prest / Never Odd Or Even	01/2019
3459	(2^335872-2758787)/23/31/20809	101101	Tony Prest / Never Odd Or Even	01/2019
3460	(2^335872-2795083)/3/3/113/283/148367	101097	Tony Prest / Never Odd Or Even	01/2019
3461	6^129918-35	101096	Lelio R Paula	10/2016
3462	3^211885-70	101095	Lelio R Paula	09/2016
3464	(29*2^335835-1)/550599	101093	Lelio R Paula	03/2014
3463	(2^335872-2794771)/3/5/5/61/232312440293	101093	Tony Prest / Never Odd Or Even	01/2019
3465	2^335818-20033	101092	Enzo Doria	06/2013
3466	2^335813-110083	101090	Enzo Doria	04/2014
3467	2^335804+2155	101088	Lelio R Paula	09/2016
3468	(2^335872-2756679)/7/7/7/13/31/4987/437653/8734021	101087	Tony Prest / Never Odd Or Even	01/2019
3469	2^335784-16145	101082	Enzo Doria	04/2013
3470	11^97051+62	101069	Lelio R Paula	10/2016
3471	3*10^101065+11	101066	Robert Price	07/2018
3472	27820^4293+4293^27820	101064	Hans Havermann	10/2018
3473	(2^335691-3)/26515	101049	Lelio R Paula	12/2013
3474	2^335658-94395	101044	Lelio R Paula	09/2016
3475	24514^13215+13215^24514	101024	Hans Havermann	11/2018
3476	2^335586+169	101022	Lelio R Paula	10/2009
3477	(56^57787-1)/55	101021	Paul Bourdelais	08/2017
3478	(19*10^100997+737)/9	100998	Robert Price	07/2018
3479	47599!2+1024	100991	Robert Price	02/2015
3480	2^335468-18629	100986	Enzo Doria	05/2013
3481	2^335454-20961	100982	Enzo Doria	06/2013
3482	10^100978+61	100979	Lelio R Paula	09/2016
3483	10^100978-156437	100978	Patrick De Geest	11/2016
3484	(15*2^335417+1)/481	100970	Lelio R Paula	12/2013
3485	2^335403-1859167	100967	Enzo Doria	03/2016
3486	23599^18976+18976^23599	100962	Hans Havermann	10/2018
3487	9*2^335364-5	100956	Lelio R Paula	08/2014
3488	2^335349+72287	100951	Enzo Doria	04/2016
3489	2^335329+16095	100945	Lelio R Paula	09/2016
3490	232823#+233663	100937	Makoto Morimoto	10/2017
3491	2^335237-20893	100917	Enzo Doria	06/2013
3492	2^335222-19337	100912	Enzo Doria	05/2013
3493	2^335222-109985	100912	Enzo Doria	04/2014
3494	2^335182-17237	100900	Enzo Doria	05/2013
3495	2^335043-16737	100858	Enzo Doria	05/2013
3496	(21181*2^335049+1)/1343811	100858	Lelio R Paula	07/2014
3497	2^335038-20633	100857	Enzo Doria	06/2013
3498	2^335031+1873373	100855	Enzo Doria	06/2016
3499	23489^19650+19650^23489	100847	Hans Havermann	10/2018
3500	3^211354-8816	100842	Enzo Doria	05/2014

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Probable Primes Top 10000

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