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 ?
4251	(2^381251+3186)/2	114768	Stefano Morozzi	09/2020
4252	2^381209-29323	114756	Enzo Doria	07/2015
4253	2^381207-111546435	114755	Paul Bourdelais	10/2021
4254	569^41651-568^41651	114754	Jean-Louis Charton	11/2009
4255	2^381201+1873205	114753	Enzo Doria	06/2016
4256	(85*10^114737+293)/9	114738	Robert Price	12/2019
4257	(265*10^114736+17)/3	114738	Robert Price	03/2020
4258	(2^381062+2170)/2	114711	Stefano Morozzi	09/2020
4259	2^380974-112991	114685	Enzo Doria	07/2014
4260	37097^1234+1234^37097	114679	Hans Havermann	02/2021
4261	88^58949-87	114626	Norbert Schneider	11/2015
4262	(2^380773+662)/2	114624	Stefano Morozzi	09/2020
4263	29913^6782+6782^29913	114608	Hans Havermann	02/2021
4264	2^380700+91	114603	Lelio R Paula	03/2013
4265	(2^380632+2578)/2	114582	Stefano Morozzi	09/2020
4266	7*10^114577+27	114578	Robert Price	11/2020
4268	10^114575+3^114576	114576	Mike Oakes	09/2010
4267	10^114575+66561	114576	Patrick De Geest	02/2017
4269	10^114575-581081	114575	Patrick De Geest	02/2017
4270	2^380587-115315	114569	Enzo Doria	06/2015
4271	31874^3927+3927^31874	114558	Hans Havermann	02/2021
4272	2^380513-216925	114546	Enzo Doria	05/2014
4273	2^380451-1840087	114528	Enzo Doria	06/2015
4274	(2^380426+1510)/2	114520	Stefano Morozzi	09/2020
4275	(15*2^380388-1)/539	114507	Lelio R Paula	04/2014
4276	2^380279-461347	114476	Enzo Doria	07/2015
4277	27121^16590+16590^27121	114447	Hans Havermann	01/2021
4278	25966^25555+25555^25966	114445	Hans Havermann	01/2021
4279	(11*10^114400+529)/9	114401	Robert Price	09/2021
4280	2^380021+1871147	114398	Enzo Doria	05/2016
4281	2^380005+1869707	114393	Enzo Doria	05/2016
4282	2^379958-113297	114379	Enzo Doria	07/2014
4283	(2^379897+1274)/2	114361	Stefano Morozzi	01/2021
4284	2^379881-109105	114356	Enzo Doria	04/2014
4285	(21*2^379857-1)/13	114349	Lelio R Paula	03/2014
4286	(4*10^114340+83)/3	114341	Robert Price	02/2018
4287	(26*10^114317-77)/3	114318	Robert Price	11/2019
4288	(4*10^114296+149)/9	114296	Robert Price	04/2018
4289	88^58773-87	114284	Norbert Schneider	11/2015
4290	27764^13065+13065^27764	114280	Hans Havermann	01/2021
4291	2^379529-2790283	114250	Enzo Doria	03/2016
4292	2^379522+1869115	114248	Enzo Doria	05/2016
4293	(145*10^114226-1)/9	114228	Serge Batalov	12/2014
4294	2^379317-115033	114186	Enzo Doria	06/2015
4295	(22*10^114178+47)/3	114179	Robert Price	06/2021
4296	(17*2^379246-1)/17407	114162	Lelio R Paula	03/2014
4297	(2^379192+226)/2	114148	Stefano Morozzi	09/2020
4298	6*10^114091+23	114092	Robert Price	09/2020
4299	(4*10^114076+143)/3	114077	Robert Price	03/2018
4300	(2^378820+3226)/2	114036	Stefano Morozzi	01/2021
4301	(2^378754+2058)/2	114017	Stefano Morozzi	09/2020
4302	(46*10^113969+683)/9	113970	Robert Price	03/2019
4303	(83*10^113969+133)/9	113970	Robert Price	08/2021
4304	32226^3439+3439^32226	113966	Hans Havermann	02/2021
4305	78*10^113954-7	113956	Robert Price	10/2020
4306	2*10^113941+9	113942	Dmitry Domanov	11/2010
4307	10^113933+145897	113934	Patrick De Geest	02/2021
4310	(2^378478+1642)/2	113933	Stefano Morozzi	09/2020
4308	10^113933-8000000001	113933	Robert Price	11/2020
4309	10^113933-66167	113933	Patrick De Geest	02/2021
4311	2339662057597*10^113903+9	113916	Robert Price	03/2021
4312	4*10^113905+91	113906	Robert Price	08/2018
4313	10^113894+76609	113895	Patrick De Geest	02/2021
4315	10^113894-10000001	113894	Robert Price	09/2020
4314	10^113894-373947	113894	Patrick De Geest	02/2021
4316	33933^2270+2270^33933	113881	Hans Havermann	02/2021
4317	4*10^113874-21	113875	Robert Price	09/2018
4318	2^378272-16565	113872	Enzo Doria	04/2013
4319	2^378217-109075	113855	Enzo Doria	04/2014
4320	2^378198+67	113849	Lelio R Paula	03/2013
4321	2^378173-3249	113842	Yves Minet	12/2014
4322	(2^378155-5)/6597	113833	Lelio R Paula	03/2014
4323	92941#+(355049#)/(92941#)	113830	Makoto Morimoto	10/2017
4324	30030^6173+6173^30030	113829	Hans Havermann	01/2021
4325	2^378128-262977	113828	Enzo Doria	05/2014
4326	2^378123-113215	113827	Enzo Doria	07/2014
4327	6^146274-18893	113824	Enzo Doria	03/2013
4328	34596^1949+1949^34596	113815	Hans Havermann	02/2021
4329	2^378078+75	113813	Lelio R Paula	03/2013
4330	(28*10^113810+449)/9	113811	Robert Price	11/2021
4331	26273^21448+21448^26273	113799	Hans Havermann	02/2021
4332	2^377966+255255	113780	Paul Bourdelais	10/2021
4333	2^377940+63	113772	Lelio R Paula	03/2013
4334	2^377941-2785843	113772	Enzo Doria	04/2016
4335	2^377810+1875109	113733	Enzo Doria	09/2016
4336	2^377803-1838635	113731	Enzo Doria	05/2015
4337	2^377799+52223	113729	Yves Minet	08/2010
4338	(2^377791+3258)/2	113727	Stefano Morozzi	02/2021
4339	11^109190-270	113710	Enzo Doria	12/2012
4340	28206^10739+10739^28206	113698	Hans Havermann	01/2021
4341	7*10^113693+9	113694	Robert Price	09/2015
4342	13899^27442+27442^13899	113692	Norbert Schneider	12/2020
4343	(82*10^113681+161)/9	113682	Robert Price	10/2019
4344	26121^22478+22478^26121	113673	Hans Havermann	01/2021
4345	4*10^113658+49	113659	Robert Price	01/2019
4346	(10^113656+7)/40231/6439001	113645	Alfred Reich	06/2021
4347	(2*10^113631+529)/9	113631	Robert Price	01/2018
4348	2^377408-2798279	113612	Enzo Doria	04/2016
4349	13706^27459+27459^13706	113596	Norbert Schneider	12/2020
4350	5*10^113586+57	113587	Robert Price	12/2018
4351	(2^377242+2794)/2	113561	Stefano Morozzi	02/2021
4352	2^377222+93679	113556	Yves Minet	02/2011
4354	262147#+316847	113552	Makoto Morimoto	02/2016
4353	27172^15101+15101^27172	113552	Hans Havermann	01/2021
4355	(2^377131+2018)/2	113528	Stefano Morozzi	09/2020
4356	2^377026-458903	113497	Enzo Doria	04/2015
4357	(2^377014+2202)/2	113493	Stefano Morozzi	09/2020
4358	34791^1828+1828^34791	113488	Hans Havermann	02/2021
4359	(2^376967+258)/2	113479	Stefano Morozzi	09/2020
4360	(29*10^113468-17)/3	113469	Robert Price	09/2019
4361	35^73477-34^73477	113454	Robert Price	05/2012
4362	(14*10^113451-89)/3	113452	Robert Price	05/2020
4363	2^376790+27	113426	Lelio R Paula	03/2013
4364	2^376786-112701	113424	Enzo Doria	06/2014
4365	2^376731+21	113408	Lelio R Paula	03/2013
4366	9*10^113394-73	113395	Robert Price	01/2021
4367	29660^6651+6651^29660	113387	Hans Havermann	01/2021
4369	2^376634+1871245	113379	Enzo Doria	05/2016
4368	(4^188318+17)/3	113379	Robert Price	02/2017
4370	E(29532)/492842728006750534663978950979381235	113367	Thomas Ritschel	01/2021
4371	2^376576-344369	113361	Enzo Doria	07/2015
4372	2^376549-4543	113353	Yves Minet	03/2019
4373	(17*2^376526-1)/223	113345	Lelio R Paula	03/2014
4374	(27*2^376441-1)/811	113319	Lelio R Paula	03/2014
4375	(2^376350+3538)/2	113293	Stefano Morozzi	09/2020
4376	27265^14272+14272^27265	113273	Hans Havermann	02/2021
4377	32174^3315+3315^32174	113269	Hans Havermann	02/2021
4378	(2*10^113248+73)/3	113248	Robert Price	09/2020
4379	2^376128-21237	113226	Enzo Doria	06/2013
4380	5*10^113224-81	113225	Robert Price	01/2019
4381	10^113220+51409	113221	Patrick De Geest	02/2021
4383	10^113220-1000001	113220	Robert Price	08/2020
4382	10^113220-61779	113220	Patrick De Geest	02/2021
4384	(2^376102+1578)/2	113218	Stefano Morozzi	09/2020
4385	(2^375996+3102)/2	113186	Stefano Morozzi	09/2020
4386	37258^1091+1091^37258	113184	Hans Havermann	02/2021
4387	(94*10^113176+11)/3	113178	Robert Price	04/2020
4388	(46*10^113162+521)/9	113163	Robert Price	02/2019
4389	(2^375885+3614)/2	113153	Stefano Morozzi	09/2020
4390	(2^375873+2006)/2	113149	Stefano Morozzi	09/2020
4391	(8*10^113135-269)/9	113135	Robert Price	09/2021
4392	(2^375726+694)/2	113105	Stefano Morozzi	09/2020
4393	26050^21959+21959^26050	113100	Hans Havermann	02/2021
4394	2^375638-1787171	113079	Enzo Doria	03/2016
4395	(2^375563+2178)/2	113056	Stefano Morozzi	09/2020
4396	2^375537+4847	113048	Yves Minet	02/2011
4397	(17^91837+16^91837)/33	113000	Robert Price	08/2013
4398	5F(270343)(F(270343)+1)+1	112997	Serge Batalov	04/2015
4399	2^375350-3221	112992	Yves Minet	07/2011
4400	(13*2^375306+1)/7	112979	Lelio R Paula	03/2014
4401	2^375305+76757	112979	Enzo Doria	05/2016
4402	2^375258+1874989	112964	Enzo Doria	07/2016
4403	(29^77237-1)/28	112950	Robert Price	04/2012
4404	26620^17483+17483^26620	112939	Hans Havermann	01/2021
4405	2^375154+74959	112933	Enzo Doria	04/2016
4406	(266*10^112930-17)/3	112932	Robert Price	07/2020
4407	(2^375134+778)/2	112927	Stefano Morozzi	09/2020
4408	(85*10^112919+293)/9	112920	Robert Price	12/2019
4409	29412^6899+6899^29412	112907	Hans Havermann	02/2021
4410	(191*10^112903-17)/3	112905	Robert Price	11/2021
4411	(2^375022+1210)/2	112893	Stefano Morozzi	09/2020
4412	25992^22039+22039^25992	112889	Hans Havermann	02/2021
4413	2^374993-2787163	112885	Enzo Doria	11/2015
4414	(697*10^112869+23)/9	112871	Robert Price	04/2021
4415	30420^5111+5111^30420	112813	Hans Havermann	02/2021
4416	13699^27268+27268^13699	112800	Norbert Schneider	12/2020
4417	123^53970+2	112793	Lelio R Paula	06/2013
4418	28942^7887+7887^28942	112785	Hans Havermann	01/2021
4419	2^374640-4685	112778	Yves Minet	05/2019
4420	57290^93+93^57290	112775	Hans Havermann	01/2021
4421	(2^374556+682)/2	112753	Stefano Morozzi	09/2020
4422	p(22852)#/2+512	112745	Robert Price	05/2017
4423	(11*10^112742-131)/3	112743	Robert Price	09/2018
4424	2^374441-21049	112718	Enzo Doria	06/2013
4425	4*10^112706-93	112707	Robert Price	07/2020
4426	(2^374321+1)/3	112682	H.&R. Lifchitz	12/2000
4427	(2^374213+1766)/2	112650	Stefano Morozzi	09/2020
4428	(2^374094+2674)/2	112614	Stefano Morozzi	09/2020
4429	(13^101089-1)/12	112607	Paul Bourdelais	03/2010
4430	3^236011-8828	112606	Enzo Doria	05/2014
4431	31854^3427+3427^31854	112602	Hans Havermann	02/2021
4432	(85*10^112530-373)/9	112531	Robert Price	05/2021
4433	(2^373748+1090)/2	112510	Stefano Morozzi	09/2020
4434	(2^373727+1806)/2	112503	Stefano Morozzi	01/2021
4435	27618^11821+11821^27618	112479	Hans Havermann	01/2021
4436	26343^18580+18580^26343	112460	Hans Havermann	01/2021
4437	39^70666+2	112435	Lelio R Paula	11/2013
4438	(134*10^112400+7)/3	112402	Robert Price	02/2020
4439	(2^373365+326)/2	112394	Stefano Morozzi	09/2020
4440	(2^373350-7)/3	112390	Lelio R Paula	03/2014
4441	2^373306-1840931	112377	Enzo Doria	06/2015
4442	(2^373262+270)/2	112363	Stefano Morozzi	09/2020
4443	34409^1842+1842^34409	112356	Hans Havermann	02/2021
4444	(142*10^112352-7)/9	112354	Robert Price	12/2019
4445	25580^24633+24633^25580	112336	Hans Havermann	01/2021
4446	2^373117+1872107	112320	Enzo Doria	05/2016
4447	(2^373083+2226)/2	112309	Stefano Morozzi	01/2021
4448	27963^10376+10376^27963	112301	Hans Havermann	01/2021
4449	2^373040+2792761	112297	Enzo Doria	03/2016
4450	EPrime(112280)	112280	Eric W. Weisstein	10/2010
4451	2^372950+7	112270	Lelio R Paula	03/2013
4452	2^372945+1872167	112268	Enzo Doria	05/2016
4453	36274^1243+1243^36274	112249	Hans Havermann	02/2021
4454	(55*10^112246+629)/9	112247	Robert Price	01/2022
4455	(2^372872+3798)/2	112246	Stefano Morozzi	02/2021
4456	25513^25060+25060^25513	112232	Hans Havermann	02/2021
4457	(2^372754+3094)/2	112210	Stefano Morozzi	09/2020
4458	6*10^112208+43	112209	Robert Price	07/2020
4459	(2^372728+3058)/2	112203	Stefano Morozzi	09/2020
4460	32061^3158+3158^32061	112195	Hans Havermann	02/2021
4461	2^372695+72113	112193	Enzo Doria	04/2016
4462	2^372689-2563	112191	Yves Minet	07/2014
4463	2^372638-1859441	112176	Enzo Doria	03/2016
4464	3^235074-113056	112159	Enzo Doria	07/2014
4465	-E(29242)/489848365125303139750087	112140	Thomas Ritschel	01/2021
4466	(2^372514+1822)/2	112138	Stefano Morozzi	02/2021
4467	29468^6387+6387^29468	112135	Hans Havermann	02/2021
4468	(2^372428+3742)/2	112112	Stefano Morozzi	01/2021
4469	25375^25454-25454^25375	112110	Norbert Schneider	01/2021
4470	131^52949-130	112108	Norbert Schneider	02/2019
4471	(91*10^112098-1)/9	112100	Robert Price	04/2015
4472	2^372310-85061	112077	Paul Bourdelais	02/2012
4473	(10^112067+53)/9	112067	Serge Batalov	07/2015
4474	(2^372237+2082)/2	112055	Stefano Morozzi	09/2020
4475	75^59760+2	112054	Lelio R Paula	08/2013
4476	(2^372200+1710)/2	112044	Stefano Morozzi	09/2020
4477	(10^112048+7)/8747/373157	112039	Alfred Reich	06/2021
4478	(2^372181+2250)/2	112038	Stefano Morozzi	01/2021
4479	(2^372161+2574)/2	112032	Stefano Morozzi	09/2020
4480	8*10^112018-49	112019	Robert Price	08/2019
4482	2^372108+74221	112016	Enzo Doria	04/2016
4481	(2^372109+2046)/2	112016	Stefano Morozzi	09/2020
4483	8*10^112011-73	112012	Robert Price	01/2022
4484	(184*10^112007-1)/3	112009	Robert Price	02/2020
4485	5*10^112003+81	112004	Robert Price	03/2019
4486	215^48018+48018^215	112000	Norbert Schneider	10/2018
4487	25549^24148+24148^25549	111979	Hans Havermann	02/2021
4488	2^371970-459491	111975	Enzo Doria	05/2015
4489	41^69427-40^69427	111971	Robert Price	07/2012
4490	(2^371782+358)/2	111918	Stefano Morozzi	01/2021
4491	(34*10^111902-547)/9	111903	Robert Price	03/2021
4492	(10^111902+71)/9	111902	Serge Batalov	07/2015
4493	(2^371625+1610)/2	111870	Stefano Morozzi	09/2020
4494	29080^7027+7027^29080	111865	Hans Havermann	01/2021
4495	31307^3730+3730^31307	111820	Hans Havermann	02/2021
4496	2^371440-112865	111815	Enzo Doria	06/2014
4497	2^371426-459161	111811	Enzo Doria	05/2015
4498	25768^21771+21771^25768	111779	Hans Havermann	02/2021
4499	28022^9747+9747^28022	111777	Hans Havermann	02/2021
4500	(94*10^111770+11)/3	111772	Robert Price	04/2020

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