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	(19*10^104014-49)/3	104015	Robert Price	05/2019
3252	2^345504+723	104008	Lelio R Paula	09/2011
3253	2^345498-20037	104006	Enzo Doria	06/2013
3254	18^82854-37	104005	Lelio R Paula	01/2017
3255	2^345486-109065	104002	Enzo Doria	04/2014
3256	2^345487-1851507	104002	Enzo Doria	08/2015
3257	2^345476+777	103999	Lelio R Paula	09/2011
3258	4*10^103981-83	103982	Robert Price	10/2018
3259	(5*2^345321-1)/3	103953	Lelio R Paula	03/2014
3260	(2^345267-9)/539049127	103927	Lelio R Paula	12/2013
3261	(19*10^103907+77)/3	103908	Robert Price	05/2019
3262	(78557*2^345163+1)/78589	103905	Lelio R Paula	07/2014
3263	2^345106-112181	103888	Enzo Doria	06/2014
3264	2^345079+99	103880	Lelio R Paula	09/2011
3265	11^99736-1500	103865	Enzo Doria	12/2012
3266	2^344842-20157	103808	Enzo Doria	06/2013
3267	(47*2^344822+1)/1071	103801	Lelio R Paula	05/2015
3268	2^344802-20765	103796	Enzo Doria	06/2013
3269	2^344794-3821	103794	Yves Minet	05/2011
3270	2^344782-109103	103790	Enzo Doria	04/2014
3271	3^217521-112292	103784	Enzo Doria	06/2014
3272	2^344759-3505	103783	Lelio R Paula	11/2016
3273	2^344735-147	103776	Lelio R Paula	09/2011
3274	L(496533)-p(496533)	103770	Robert Price	02/2018
3275	2*10^103749-69	103750	Robert Price	03/2018
3276	(55459*2^344617+1)/3	103745	Lelio R Paula	07/2014
3277	2^344607-108891	103738	Enzo Doria	03/2014
3278	2^344541-19561	103718	Enzo Doria	05/2013
3279	(1017*2^344529-1)/569	103714	Lelio R Paula	05/2015
3280	(4*10^103703-1)/3	103704	Serge Batalov	08/2009
3281	2^344444-455	103688	Yves Minet	03/2012
3282	(1353^238539617^9)/10^307661	103673	Hans Havermann	06/2017
3283	2^344317-109933	103650	Enzo Doria	04/2014
3284	2^344309-1852033	103648	Enzo Doria	08/2015
3285	2^344213-21253	103619	Enzo Doria	06/2013
3286	2^344196-465	103614	Lelio R Paula	11/2016
3287	2^344187-20001	103611	Enzo Doria	06/2013
3288	(117191#+(355573#)/(117191#))/(200233679)	103602	Makoto Morimoto	10/2017
3289	20^79621-19^79621	103590	Jean-Louis Charton	03/2011
3290	Phi(155391,10)/1243129	103586	Maksym Voznyy	09/2015
3291	2^344085-20365	103580	Enzo Doria	06/2013
3292	5^148169+54	103566	Lelio R Paula	11/2016
3293	2^344017-108795	103560	Enzo Doria	03/2014
3294	2^343971-5077	103546	Lelio R Paula	09/2011
3295	(7*10^103531+71)/3	103532	Robert Price	05/2018
3296	2^343899+141	103524	Lelio R Paula	08/2011
3297	(2^343933+1)/(3*98294339989393)	103520	Gord Palameta	08/2018
3298	6^133029-67	103517	Lelio R Paula	11/2016
3299	(17*2^343877+1)/13625	103515	Lelio R Paula	12/2013
3300	(136*10^103474-1)/9	103476	Serge Batalov	12/2014
3301	5^148014-24	103458	Lelio R Paula	11/2016
3302	2^343604+9931	103436	Yves Minet	01/2011
3303	2^343601-21189	103435	Enzo Doria	06/2013
3304	2^343508-115229	103407	Enzo Doria	06/2015
3305	(509203*2^343491-1)/16147	103403	Lelio R Paula	05/2015
3306	3^216685-113056	103386	Enzo Doria	07/2014
3307	44^62903-43^62903	103379	Jean-Louis Charton	08/2012
3308	11^99262-20	103371	Lelio R Paula	12/2016
3309	(509203*2^343357-1)/5	103366	Lelio R Paula	05/2015
3310	2^343356-2791889	103361	Enzo Doria	03/2016
3311	(25*10^103360-241)/9	103361	Robert Price	05/2018
3312	Phi(104989,10)/2939693	103350	Maksym Voznyy	09/2015
3313	2^343182-171	103309	Lelio R Paula	08/2011
3314	(23619^23619+23620^23620)/7187	103294	David Broadhurst	09/2009
3315	2^343079-1835611	103278	Enzo Doria	05/2015
3316	2^343063-1147	103273	Yves Minet	06/2013
3317	9*6^132689+7	103254	Lelio R Paula	11/2014
3318	2^342979-18085	103247	Enzo Doria	05/2013
3319	(16*10^103244-31)/3	103245	Robert Price	03/2019
3320	2^342966-16995	103244	Lelio R Paula	11/2016
3321	(16*10^103214-31)/3	103215	Robert Price	03/2019
3322	(37*10^103211+611)/9	103212	Robert Price	11/2018
3323	5^147650+16	103203	Lelio R Paula	11/2016
3324	gcd(Phi(852060,10),(10^42603+1)^3(10^42603+1-10^21302)+(10^85206+10^42603)(10^21302+1)+10^127809)	103201	Serge Batalov	04/2015
3325	2^342817+2707067	103199	Enzo Doria	03/2016
3326	43^63177-42	103198	Theodore Burton	02/2007
3327	2^342805-21025	103195	Enzo Doria	06/2013
3328	2^342714+12285	103168	Lelio R Paula	11/2016
3329	18^82178-4481	103156	Enzo Doria	03/2013
3330	2^342665-17349	103153	Enzo Doria	05/2013
3331	2^342612+175	103137	Lelio R Paula	08/2011
3332	5*2^342585-3	103130	Lelio R Paula	09/2014
3333	(16*10^103127+77)/3	103128	Robert Price	03/2019
3334	2^342503-19209	103104	Enzo Doria	05/2013
3335	2^342476+51	103096	Lelio R Paula	08/2011
3336	2^342460-18885	103091	Enzo Doria	05/2013
3337	7^121968+82	103075	Lelio R Paula	10/2016
3338	2^342392-108863	103071	Enzo Doria	03/2014
3339	3^216014+28	103065	Lelio R Paula	11/2016
3340	2^342353-108879	103059	Enzo Doria	03/2014
3341	10^103055+276081	103056	Patrick De Geest	12/2016
3342	10^103055-53	103055	Lelio R Paula	11/2016
3343	(58*10^103046+419)/9	103047	Robert Price	05/2019
3344	7^121933+4	103046	Lelio R Paula	11/2014
3345	19^80560-68	103017	Lelio R Paula	10/2016
3346	2^342209+76607	103016	Enzo Doria	05/2016
3348	328^40945+40945^328	103013	Norbert Schneider	12/2014
3347	12^95454-91	103013	Lelio R Paula	10/2016
3349	25833^9716+9716^25833	103009	Hans Havermann	01/2019
3350	65^56809-64^56809	102990	Robert Price	08/2013
3351	5^147338-6	102985	Lelio R Paula	11/2014
3352	2^342084-112739	102978	Enzo Doria	06/2014
3353	9*6^132330+7	102974	Lelio R Paula	11/2014
3354	2^342034-16737	102963	Enzo Doria	05/2013
3355	(9787*2^342011-1)/25	102959	Lelio R Paula	05/2015
3356	(3^215802-5)/124343756	102956	Lelio R Paula	12/2013
3357	2^341991-17421	102950	Enzo Doria	05/2013
3358	2^341969-112225	102943	Enzo Doria	06/2014
3359	(9787*2^341864-1)/3	102915	Lelio R Paula	05/2015
3361	2^341859+1869413	102910	Enzo Doria	05/2016
3360	10^102909+61	102910	Lelio R Paula	11/2016
3362	10^102909-67049	102909	Patrick De Geest	12/2016
3363	23814^20935+20935^23814	102898	Hans Havermann	02/2019
3364	28345^4264+4264^28345	102888	Hans Havermann	02/2019
3365	25665^10204+10204^25665	102886	Hans Havermann	02/2019
3366	26288^8181+8181^26288	102860	Hans Havermann	02/2019
3367	2^341659+1836773	102850	Enzo Doria	03/2016
3368	2^341608-110639	102835	Enzo Doria	05/2014
3369	10^102824+49	102825	Lelio R Paula	11/2016
3370	10^102824-168011	102824	Patrick De Geest	12/2016
3371	11^98708-8	102794	Lelio R Paula	10/2016
3372	2^341466+4429	102792	Lelio R Paula	09/2011
3373	2^341460-107	102790	Lelio R Paula	08/2011
3374	(2^341388+47)/21014943	102761	Lelio R Paula	12/2013
3375	2^341355+21	102759	Lelio R Paula	08/2011
3376	2^341246+40755	102726	Lelio R Paula	11/2016
3377	(2^341256-5)/991699	102723	Lelio R Paula	12/2013
3378	7^121547+78	102720	Lelio R Paula	10/2016
3379	2^341223-461197	102719	Enzo Doria	06/2015
3380	27838^4893+4893^27838	102711	Hans Havermann	03/2019
3382	2^341190-20577	102709	Enzo Doria	06/2013
3381	(27*2^341212+1)/84674449	102709	Lelio R Paula	12/2013
3383	6^131976-65	102698	Lelio R Paula	10/2016
3384	2^341134+2533	102692	Henri Lifchitz	09/2005
3385	13^92184-54	102688	Lelio R Paula	10/2016
3386	2^341116-20873	102687	Enzo Doria	06/2013
3387	2^341094-19953	102680	Enzo Doria	06/2013
3388	23761^20950+20950^23761	102676	Hans Havermann	03/2019
3389	2^341053+129	102668	Lelio R Paula	08/2011
3391	(31*2^341006-1)/3	102655	Lelio R Paula	03/2014
3390	7^121471+94	102655	Lelio R Paula	10/2016
3393	2^341004-173	102653	Lelio R Paula	08/2011
3392	20^78901+3	102653	Lelio R Paula	10/2016
3394	5^146853-52	102646	Lelio R Paula	10/2016
3395	2^340969-216931	102642	Enzo Doria	05/2014
3396	122^49196+121	102641	Norbert Schneider	10/2018
3397	2^340952+1870021	102637	Enzo Doria	05/2016
3398	5*2^340940-3	102634	Lelio R Paula	08/2014
3399	(6^131891+1)/7	102631	Paul Bourdelais	01/2010
3400	25876^9239+9239^25876	102615	Hans Havermann	02/2019
3401	(4*10^102612+83)/3	102613	Robert Price	02/2018
3402	75^54717+74	102598	Norbert Schneider	01/2015
3403	(17*10^102597+13)/3	102598	Robert Price	01/2019
3404	2^340806-20393	102593	Enzo Doria	06/2013
3405	(2^340790+5)/138267	102583	Lelio R Paula	12/2013
3406	6^131821+77	102577	Lelio R Paula	10/2016
3407	2^340688-29	102558	Henri Lifchitz	05/2005
3408	2^340685-109101	102557	Enzo Doria	04/2014
3409	65^56567-64	102552	Norbert Schneider	11/2014
3410	26230^8121+8121^26230	102550	Hans Havermann	03/2019
3411	2^340547-108897	102515	Enzo Doria	03/2014
3412	25592^10119+10119^25592	102500	Hans Havermann	02/2019
3413	7^121268+82	102484	Lelio R Paula	10/2016
3414	(6883*2^340443-1)/162401	102483	Lelio R Paula	05/2015
3415	2^340434-5955	102481	Lelio R Paula	11/2016
3416	(2^340381+47)/7	102465	Lelio R Paula	12/2013
3417	111^50095+110	102461	Norbert Schneider	04/2017
3418	2^340291-20301	102438	Enzo Doria	06/2013
3419	12^94915+89	102431	Lelio R Paula	10/2016
3420	24466^15349+15349^24466	102417	Hans Havermann	03/2019
3421	2^340208-20373	102413	Enzo Doria	06/2013
3422	6^131598-17273	102404	Enzo Doria	02/2013
3423	2^340115-21181	102385	Enzo Doria	06/2013
3424	(55459*2^340090+1)/1591	102379	Lelio R Paula	07/2014
3425	89^52511-88^52511	102365	Robert Price	06/2015
3426	3^214539-112756	102362	Enzo Doria	07/2014
3427	2^340000-19877	102351	Enzo Doria	06/2013
3428	2^339990-114845	102348	Enzo Doria	05/2015
3429	(3^214516-2)/51383	102346	Lelio R Paula	12/2013
3430	20^78661-99	102341	Lelio R Paula	09/2016
3431	2^339951-19585	102336	Enzo Doria	05/2013
3432	(13*2^339943+1)/45	102333	Lelio R Paula	12/2013
3433	2^339889+29327	102317	Yves Minet	06/2010
3434	26348^7641+7641^26348	102314	Hans Havermann	03/2019
3435	2^339834-109493	102301	Enzo Doria	04/2014
3436	(16*10^102299-19)/3	102300	Robert Price	02/2019
3437	(11^98221-5^98221)/6	102286	Robert Price	01/2013
3438	3^214365+1820	102279	Lelio R Paula	10/2016
3439	31978^1579+1579^31978	102278	Hans Havermann	03/2019
3440	(11*2^339705-1)/183	102261	Lelio R Paula	03/2014
3441	2^339694-16995	102259	Lelio R Paula	09/2016
3442	(56*10^102255+691)/9	102256	Robert Price	05/2019
3443	122^49008+121	102249	Norbert Schneider	10/2018
3444	7^120985-38	102245	Lelio R Paula	10/2016
3445	10^102244+122961	102245	Patrick De Geest	12/2016
3446	10^102244-27	102244	Lelio R Paula	09/2016
3447	7^120982-62	102242	Lelio R Paula	10/2016
3448	4*6^131382-5	102236	Lelio R Paula	11/2014
3449	2^339586-1091	102226	Yves Minet	11/2012
3450	11^98161-3072000	102225	Enzo Doria	12/2012
3451	9*7^120961-4	102225	Lelio R Paula	11/2014
3452	5*3^214250+2	102224	Serge Batalov	10/2010
3453	12^94713-59	102213	Lelio R Paula	10/2016
3454	12^94705+89	102204	Lelio R Paula	10/2016
3455	2^339407-177	102172	Lelio R Paula	08/2011
3456	4*10^102163-57	102164	Robert Price	10/2018
3457	2^339355+65	102157	Lelio R Paula	07/2011
3458	(2^339323+47)/880715	102141	Lelio R Paula	12/2013
3460	2^339168+21	102100	Lelio R Paula	07/2011
3459	2^339167-108807	102100	Enzo Doria	03/2014
3461	2^339156+163	102097	Lelio R Paula	08/2011
3462	2^339081-4543	102074	Yves Minet	03/2019
3463	24327^15668+15668^24327	102053	Hans Havermann	02/2019
3464	25080^11711+11711^25080	102041	Hans Havermann	02/2019
3465	(2^338982-7)/1754517	102038	Lelio R Paula	12/2013
3466	2^338891-18885	102017	Enzo Doria	05/2013
3467	2^338829-113239	101998	Enzo Doria	07/2014
3468	2^338828-113297	101998	Enzo Doria	07/2014
3469	2^338796+93	101988	Donovan Johnson	06/2008
3470	lucasU(1373,1,32502)-lucasU(1373,1,32501)	101978	Mike Oakes	05/2009
3471	25295^10744+10744^25295	101969	Hans Havermann	01/2019
3472	25712^9243+9243^25712	101969	Hans Havermann	01/2019
3473	(71^55079-1)/70	101964	Paul Bourdelais	08/2017
3475	2^338682-19865	101954	Enzo Doria	06/2013
3474	(2^(112895*3+1)+243)/7	101954	Kevin Acres	12/2013
3476	28594^3673+3673^28594	101939	Hans Havermann	02/2019
3477	2^338568+37	101920	Lelio R Paula	07/2011
3478	2^338559-1858777	101917	Enzo Doria	04/2016
3479	(9*2^338520+1)/365	101904	Lelio R Paula	12/2013
3480	24502^14419+14419^24502	101903	Hans Havermann	01/2019
3481	2^338497-17041	101898	Enzo Doria	05/2013
3482	2^338475+54615	101892	Lelio R Paula	10/2016
3483	2^338426-19797	101877	Enzo Doria	06/2013
3484	2^338368-20369	101859	Enzo Doria	06/2013
3485	2^338366+74179	101859	Enzo Doria	04/2016
3486	27088^5755+5755^27088	101853	Hans Havermann	01/2019
3487	2^338280-19745	101833	Enzo Doria	06/2013
3488	(3*2^338236-1)/347	101818	Lelio R Paula	03/2014
3489	6^130841+103	101815	Lelio R Paula	10/2016
3490	2^338122-20117	101785	Enzo Doria	06/2013
3491	(2^338139+5)/905333	101785	Lelio R Paula	12/2013
3492	35^65917-7092	101781	Enzo Doria	03/2013
3493	2^338010-19833	101752	Enzo Doria	06/2013
3494	3^213215-76	101730	Lelio R Paula	09/2016
3495	23907^17998+17998^23907	101730	Hans Havermann	01/2019
3496	2^337930+63	101728	Lelio R Paula	07/2011
3497	2^337920+1869661	101725	Enzo Doria	05/2016
3498	24116^16509+16509^24116	101715	Hans Havermann	01/2019
3499	2^337859-19645	101706	Enzo Doria	05/2013
3500	2^337754+1869169	101675	Enzo Doria	05/2016

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