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	(2^383544+5)/3	115458	Lelio R Paula	03/2014
3252	89^59221-88^59221	115445	Robert Price	06/2015
3253	2^383347+1869413	115399	Enzo Doria	05/2016
3254	(103*10^115366+17)/3	115368	Robert Price	08/2020
3255	(2^383232+750)/2	115365	Stefano Morozzi	09/2020
3256	(2^383130-7)/131793	115329	Lelio R Paula	03/2014
3257	(12^106859+1)/13	115320	Paul Bourdelais	02/2010
3258	2^383039+1869509	115307	Enzo Doria	05/2016
3259	(13*2^382968+1)/7	115286	Lelio R Paula	04/2014
3260	(2^382945+2046)/2	115278	Stefano Morozzi	09/2020
3261	(2^382789+3182)/2	115231	Stefano Morozzi	09/2020
3262	6*10^115211+79	115212	Robert Price	09/2020
3263	(2^382722+3598)/2	115211	Stefano Morozzi	09/2020
3264	(2^382699+2090)/2	115204	Stefano Morozzi	09/2020
3265	2^382633+73697	115185	Enzo Doria	04/2016
3266	2^382509-113593	115147	Enzo Doria	08/2014
3267	2^382502-2791721	115145	Enzo Doria	03/2016
3268	(2^382495+1274)/2	115143	Stefano Morozzi	01/2021
3269	9^120590-120590	115073	Robert Price	03/2014
3270	2^382198+9	115054	Lelio R Paula	03/2013
3271	(89*10^115030-179)/9	115031	Robert Price	12/2019
3272	2^381883-59197	114959	Enzo Doria	10/2015
3273	(2^381820+1626)/2	114939	Stefano Morozzi	09/2020
3275	2^381806-4481	114936	Yves Minet	07/2011
3274	2^381808-1851507	114936	Enzo Doria	08/2015
3276	(2^381792+2502)/2	114931	Stefano Morozzi	09/2020
3277	2^381774-112373	114926	Enzo Doria	06/2014
3278	2^381555-109051	114860	Enzo Doria	04/2014
3279	2^381546-113501	114857	Enzo Doria	08/2014
3280	(7*10^114845-19)/3	114846	Robert Price	10/2020
3281	(2^381436+1182)/2	114824	Stefano Morozzi	09/2020
3282	3^240644+16	114817	Robert Price	04/2020
3283	2^381360-110429	114801	Enzo Doria	05/2014
3284	(17*10^114795+79)/3	114796	Robert Price	04/2019
3285	(66^63079+1)/67	114774	Paul Bourdelais	09/2017
3286	2^381252-115079	114769	Enzo Doria	06/2015
3287	(2^381251+3186)/2	114768	Stefano Morozzi	09/2020
3288	2^381209-29323	114756	Enzo Doria	07/2015
3289	569^41651-568^41651	114754	Jean-Louis Charton	11/2009
3290	2^381201+1873205	114753	Enzo Doria	06/2016
3291	(85*10^114737+293)/9	114738	Robert Price	12/2019
3292	(265*10^114736+17)/3	114738	Robert Price	03/2020
3293	(2^381062+2170)/2	114711	Stefano Morozzi	09/2020
3294	2^380974-112991	114685	Enzo Doria	07/2014
3295	88^58949-87	114626	Norbert Schneider	11/2015
3296	(2^380773+662)/2	114624	Stefano Morozzi	09/2020
3297	2^380700+91	114603	Lelio R Paula	03/2013
3298	(2^380632+2578)/2	114582	Stefano Morozzi	09/2020
3299	7*10^114577+27	114578	Robert Price	11/2020
3301	10^114575+3^114576	114576	Mike Oakes	09/2010
3300	10^114575+66561	114576	Patrick De Geest	02/2017
3302	10^114575-581081	114575	Patrick De Geest	02/2017
3303	2^380587-115315	114569	Enzo Doria	06/2015
3304	2^380513-216925	114546	Enzo Doria	05/2014
3305	2^380451-1840087	114528	Enzo Doria	06/2015
3306	(2^380426+1510)/2	114520	Stefano Morozzi	09/2020
3307	(15*2^380388-1)/539	114507	Lelio R Paula	04/2014
3308	2^380279-461347	114476	Enzo Doria	07/2015
3309	2^380021+1871147	114398	Enzo Doria	05/2016
3310	2^380005+1869707	114393	Enzo Doria	05/2016
3311	2^379958-113297	114379	Enzo Doria	07/2014
3312	(2^379897+1274)/2	114361	Stefano Morozzi	01/2021
3313	2^379881-109105	114356	Enzo Doria	04/2014
3314	(21*2^379857-1)/13	114349	Lelio R Paula	03/2014
3315	(4*10^114340+83)/3	114341	Robert Price	02/2018
3316	(26*10^114317-77)/3	114318	Robert Price	11/2019
3317	(4*10^114296+149)/9	114296	Robert Price	04/2018
3318	88^58773-87	114284	Norbert Schneider	11/2015
3319	2^379529-2790283	114250	Enzo Doria	03/2016
3320	2^379522+1869115	114248	Enzo Doria	05/2016
3321	(145*10^114226-1)/9	114228	Serge Batalov	12/2014
3322	2^379317-115033	114186	Enzo Doria	06/2015
3323	(17*2^379246-1)/17407	114162	Lelio R Paula	03/2014
3324	(2^379192+226)/2	114148	Stefano Morozzi	09/2020
3325	6*10^114091+23	114092	Robert Price	09/2020
3326	(4*10^114076+143)/3	114077	Robert Price	03/2018
3327	(2^378820+3226)/2	114036	Stefano Morozzi	01/2021
3328	(2^378754+2058)/2	114017	Stefano Morozzi	09/2020
3329	(46*10^113969+683)/9	113970	Robert Price	03/2019
3330	78*10^113954-7	113956	Robert Price	10/2020
3331	2*10^113941+9	113942	Dmitry Domanov	11/2010
3333	(2^378478+1642)/2	113933	Stefano Morozzi	09/2020
3332	10^113933-8000000001	113933	Robert Price	11/2020
3334	4*10^113905+91	113906	Robert Price	08/2018
3335	10^113894-10000001	113894	Robert Price	09/2020
3336	4*10^113874-21	113875	Robert Price	09/2018
3337	2^378272-16565	113872	Enzo Doria	04/2013
3338	2^378217-109075	113855	Enzo Doria	04/2014
3339	2^378198+67	113849	Lelio R Paula	03/2013
3340	2^378173-3249	113842	Yves Minet	12/2014
3341	(2^378155-5)/6597	113833	Lelio R Paula	03/2014
3342	92941#+(355049#)/(92941#)	113830	Makoto Morimoto	10/2017
3343	2^378128-262977	113828	Enzo Doria	05/2014
3344	2^378123-113215	113827	Enzo Doria	07/2014
3345	6^146274-18893	113824	Enzo Doria	03/2013
3346	2^378078+75	113813	Lelio R Paula	03/2013
3347	2^377940+63	113772	Lelio R Paula	03/2013
3348	2^377941-2785843	113772	Enzo Doria	04/2016
3349	2^377810+1875109	113733	Enzo Doria	09/2016
3350	2^377803-1838635	113731	Enzo Doria	05/2015
3351	2^377799+52223	113729	Yves Minet	08/2010
3352	11^109190-270	113710	Enzo Doria	12/2012
3353	7*10^113693+9	113694	Robert Price	09/2015
3354	13899^27442+27442^13899	113692	Norbert Schneider	12/2020
3355	(82*10^113681+161)/9	113682	Robert Price	10/2019
3356	26121^22478+22478^26121	113673	Hans Havermann	01/2021
3357	4*10^113658+49	113659	Robert Price	01/2019
3358	(2*10^113631+529)/9	113631	Robert Price	01/2018
3359	2^377408-2798279	113612	Enzo Doria	04/2016
3360	13706^27459+27459^13706	113596	Norbert Schneider	12/2020
3361	5*10^113586+57	113587	Robert Price	12/2018
3362	2^377222+93679	113556	Yves Minet	02/2011
3363	262147#+316847	113552	Makoto Morimoto	02/2016
3364	(2^377131+2018)/2	113528	Stefano Morozzi	09/2020
3365	2^377026-458903	113497	Enzo Doria	04/2015
3366	(2^377014+2202)/2	113493	Stefano Morozzi	09/2020
3367	(2^376967+258)/2	113479	Stefano Morozzi	09/2020
3368	(29*10^113468-17)/3	113469	Robert Price	09/2019
3369	35^73477-34^73477	113454	Robert Price	05/2012
3370	(14*10^113451-89)/3	113452	Robert Price	05/2020
3371	2^376790+27	113426	Lelio R Paula	03/2013
3372	2^376786-112701	113424	Enzo Doria	06/2014
3373	2^376731+21	113408	Lelio R Paula	03/2013
3374	9*10^113394-73	113395	Robert Price	01/2021
3376	2^376634+1871245	113379	Enzo Doria	05/2016
3375	(4^188318+17)/3	113379	Robert Price	02/2017
3377	E(29532)/492842728006750534663978950979381235	113367	Thomas Ritschel	01/2021
3378	2^376576-344369	113361	Enzo Doria	07/2015
3379	2^376549-4543	113353	Yves Minet	03/2019
3380	(17*2^376526-1)/223	113345	Lelio R Paula	03/2014
3381	(27*2^376441-1)/811	113319	Lelio R Paula	03/2014
3382	(2^376350+3538)/2	113293	Stefano Morozzi	09/2020
3383	(2*10^113248+73)/3	113248	Robert Price	09/2020
3384	2^376128-21237	113226	Enzo Doria	06/2013
3385	5*10^113224-81	113225	Robert Price	01/2019
3386	10^113220-1000001	113220	Robert Price	08/2020
3387	(2^376102+1578)/2	113218	Stefano Morozzi	09/2020
3388	(2^375996+3102)/2	113186	Stefano Morozzi	09/2020
3389	(94*10^113176+11)/3	113178	Robert Price	04/2020
3390	(46*10^113162+521)/9	113163	Robert Price	02/2019
3391	(2^375885+3614)/2	113153	Stefano Morozzi	09/2020
3392	(2^375873+2006)/2	113149	Stefano Morozzi	09/2020
3393	(2^375726+694)/2	113105	Stefano Morozzi	09/2020
3394	2^375638-1787171	113079	Enzo Doria	03/2016
3395	(2^375563+2178)/2	113056	Stefano Morozzi	09/2020
3396	2^375537+4847	113048	Yves Minet	02/2011
3397	(17^91837+16^91837)/33	113000	Robert Price	08/2013
3398	5F(270343)(F(270343)+1)+1	112997	Serge Batalov	04/2015
3399	2^375350-3221	112992	Yves Minet	07/2011
3400	(13*2^375306+1)/7	112979	Lelio R Paula	03/2014
3401	2^375305+76757	112979	Enzo Doria	05/2016
3402	2^375258+1874989	112964	Enzo Doria	07/2016
3403	(29^77237-1)/28	112950	Robert Price	04/2012
3404	2^375154+74959	112933	Enzo Doria	04/2016
3405	(266*10^112930-17)/3	112932	Robert Price	07/2020
3406	(2^375134+778)/2	112927	Stefano Morozzi	09/2020
3407	(85*10^112919+293)/9	112920	Robert Price	12/2019
3408	(2^375022+1210)/2	112893	Stefano Morozzi	09/2020
3409	2^374993-2787163	112885	Enzo Doria	11/2015
3410	13699^27268+27268^13699	112800	Norbert Schneider	12/2020
3411	123^53970+2	112793	Lelio R Paula	06/2013
3412	2^374640-4685	112778	Yves Minet	05/2019
3413	(2^374556+682)/2	112753	Stefano Morozzi	09/2020
3414	p(22852)#/2+512	112745	Robert Price	05/2017
3415	(11*10^112742-131)/3	112743	Robert Price	09/2018
3416	2^374441-21049	112718	Enzo Doria	06/2013
3417	4*10^112706-93	112707	Robert Price	07/2020
3418	(2^374321+1)/3	112682	H.&R. Lifchitz	12/2000
3419	(2^374213+1766)/2	112650	Stefano Morozzi	09/2020
3420	(2^374094+2674)/2	112614	Stefano Morozzi	09/2020
3421	(13^101089-1)/12	112607	Paul Bourdelais	03/2010
3422	3^236011-8828	112606	Enzo Doria	05/2014
3423	(2^373748+1090)/2	112510	Stefano Morozzi	09/2020
3424	(2^373727+1806)/2	112503	Stefano Morozzi	01/2021
3425	26343^18580+18580^26343	112460	Hans Havermann	01/2021
3426	39^70666+2	112435	Lelio R Paula	11/2013
3427	(134*10^112400+7)/3	112402	Robert Price	02/2020
3428	(2^373365+326)/2	112394	Stefano Morozzi	09/2020
3429	(2^373350-7)/3	112390	Lelio R Paula	03/2014
3430	2^373306-1840931	112377	Enzo Doria	06/2015
3431	(2^373262+270)/2	112363	Stefano Morozzi	09/2020
3432	(142*10^112352-7)/9	112354	Robert Price	12/2019
3433	2^373117+1872107	112320	Enzo Doria	05/2016
3434	(2^373083+2226)/2	112309	Stefano Morozzi	01/2021
3435	27963^10376+10376^27963	112301	Hans Havermann	01/2021
3436	2^373040+2792761	112297	Enzo Doria	03/2016
3437	EPrime(112280)	112280	Eric W. Weisstein	10/2010
3438	2^372950+7	112270	Lelio R Paula	03/2013
3439	2^372945+1872167	112268	Enzo Doria	05/2016
3440	(2^372754+3094)/2	112210	Stefano Morozzi	09/2020
3441	6*10^112208+43	112209	Robert Price	07/2020
3442	(2^372728+3058)/2	112203	Stefano Morozzi	09/2020
3443	2^372695+72113	112193	Enzo Doria	04/2016
3444	2^372689-2563	112191	Yves Minet	07/2014
3445	2^372638-1859441	112176	Enzo Doria	03/2016
3446	3^235074-113056	112159	Enzo Doria	07/2014
3447	-E(29242)/489848365125303139750087	112140	Thomas Ritschel	01/2021
3448	(2^372428+3742)/2	112112	Stefano Morozzi	01/2021
3449	131^52949-130	112108	Norbert Schneider	02/2019
3450	(91*10^112098-1)/9	112100	Robert Price	04/2015
3451	2^372310-85061	112077	Paul Bourdelais	02/2012
3452	(10^112067+53)/9	112067	Serge Batalov	07/2015
3453	(2^372237+2082)/2	112055	Stefano Morozzi	09/2020
3454	75^59760+2	112054	Lelio R Paula	08/2013
3455	(2^372200+1710)/2	112044	Stefano Morozzi	09/2020
3456	(2^372181+2250)/2	112038	Stefano Morozzi	01/2021
3457	(2^372161+2574)/2	112032	Stefano Morozzi	09/2020
3458	8*10^112018-49	112019	Robert Price	08/2019
3460	2^372108+74221	112016	Enzo Doria	04/2016
3459	(2^372109+2046)/2	112016	Stefano Morozzi	09/2020
3461	(184*10^112007-1)/3	112009	Robert Price	02/2020
3462	5*10^112003+81	112004	Robert Price	03/2019
3463	215^48018+48018^215	112000	Norbert Schneider	10/2018
3464	2^371970-459491	111975	Enzo Doria	05/2015
3465	41^69427-40^69427	111971	Robert Price	07/2012
3466	(2^371782+358)/2	111918	Stefano Morozzi	01/2021
3467	(10^111902+71)/9	111902	Serge Batalov	07/2015
3468	(2^371625+1610)/2	111870	Stefano Morozzi	09/2020
3469	2^371440-112865	111815	Enzo Doria	06/2014
3470	2^371426-459161	111811	Enzo Doria	05/2015
3471	(94*10^111770+11)/3	111772	Robert Price	04/2020
3472	2^371276-461267	111766	Enzo Doria	07/2015
3473	6*10^111760+43	111761	Robert Price	07/2020
3474	98079!4-1024	111747	Robert Price	11/2019
3475	(2^371186+3162)/2	111738	Stefano Morozzi	09/2020
3476	2^371098-113261	111712	Enzo Doria	07/2014
3477	(7*10^111706-61)/9	111706	Erik Branger	01/2011
3478	2^371044+1869391	111696	Enzo Doria	05/2016
3479	26310^17581+17581^26310	111688	Hans Havermann	01/2021
3480	88^57416+87	111645	Norbert Schneider	11/2015
3481	2^370829-109693	111631	Enzo Doria	04/2014
3482	15^94906-2	111619	Lelio R Paula	11/2013
3483	(2^370726+1198)/2	111600	Stefano Morozzi	09/2020
3484	2^370695-4627	111591	Yves Minet	05/2019
3485	7*10^111579-87	111580	Robert Price	06/2020
3487	2^370643-37	111575	Yves Minet	01/2012
3486	(2^370655-5)/2439	111575	Lelio R Paula	03/2014
3488	2^370610-3911	111565	Yves Minet	04/2017
3489	286^45405+45405^286	111532	Norbert Schneider	04/2015
3490	4*5^159563-9	111531	Lelio R Paula	11/2014
3491	(4^185225+23)/3	111517	Robert Price	10/2018
3492	2^370393-2797093	111500	Enzo Doria	03/2016
3493	(21*2^370382-1)/629	111495	Lelio R Paula	03/2014
3494	(2^370371+554)/2	111493	Stefano Morozzi	09/2020
3495	2^370292-2791979	111469	Enzo Doria	03/2016
3496	2^370177-461551	111435	Enzo Doria	07/2015
3497	(2^370169+1706)/2	111432	Stefano Morozzi	09/2020
3498	109^54683-108	111413	Norbert Schneider	02/2017
3499	(2^370043+1010)/2	111394	Stefano Morozzi	09/2020
3500	32961^2396+2396^32961	111392	Hans Havermann	10/2020

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