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	38496^1093+1093^38496	116975	Hans Havermann	02/2021
4252	3^245154-6256	116969	Enzo Doria	05/2014
4253	5*10^116966-43	116967	Robert Price	01/2019
4254	2^388536-113495	116961	Enzo Doria	08/2014
4255	(2^388512+382)/2	116954	Stefano Morozzi	02/2021
4256	2^388469-43	116941	Lelio R Paula	03/2013
4257	27417^18416+18416^27417	116939	Hans Havermann	02/2021
4258	(2^388438+1842)/2	116932	Stefano Morozzi	02/2021
4259	(7*2^388372-1)/111	116911	Lelio R Paula	04/2014
4260	(7*2^388335-1)/25	116900	Lelio R Paula	04/2014
4261	2^388180+93	116854	Donovan Johnson	07/2008
4262	(2^388167+2510)/2	116850	Stefano Morozzi	09/2020
4263	(85*10^116842+293)/9	116843	Robert Price	12/2019
4264	35296^2043+2043^35296	116840	Hans Havermann	02/2021
4265	(2^388081+7)/1179	116821	Lelio R Paula	03/2014
4266	38633^1056+1056^38633	116814	Hans Havermann	02/2021
4267	2^387946-113261	116784	Enzo Doria	07/2014
4268	28363^13056+13056^28363	116737	Hans Havermann	02/2021
4269	2^387745+75557	116723	Enzo Doria	04/2016
4270	(29*10^116719+313)/9	116720	Robert Price	04/2021
4271	29622^8699+8699^29622	116695	Hans Havermann	02/2021
4272	(206*10^116687-17)/9	116689	Robert Price	01/2020
4273	(7*10^116684+179)/3	116685	Robert Price	09/2018
4274	2^387554+71455	116666	Enzo Doria	04/2016
4275	(602*10^116647-71)/9	116649	Robert Price	12/2021
4276	(2^387447+78557)/365	116631	Lelio R Paula	12/2014
4277	(145*10^116610-1)/9	116612	Serge Batalov	12/2014
4278	(25*10^116601-331)/9	116602	Robert Price	08/2018
4279	(17*2^387284-1)/59	116584	Lelio R Paula	04/2014
4280	(2^387284+3726)/2	116584	Stefano Morozzi	09/2020
4281	2^387211+111546435	116563	Paul Bourdelais	10/2021
4282	10^116557+987654321	116558	Robert Price	12/2019
4283	10^116557+9141	116558	Patrick De Geest	02/2020
4284	10^116557-609431	116557	Patrick De Geest	02/2020
4285	(28*10^116546+41)/3	116547	Robert Price	07/2021
4286	(2^387123+1814)/2	116536	Stefano Morozzi	02/2021
4287	(2^387076+2046)/2	116522	Stefano Morozzi	09/2020
4288	(2^387073+2570)/2	116521	Stefano Morozzi	09/2020
4289	28846^10931+10931^28846	116500	Hans Havermann	02/2021
4290	10^116496+3593037	116497	Paul Bourdelais	10/2021
4291	(31*2^386968+1)/7	116490	Lelio R Paula	03/2014
4292	2^386947+1869143	116483	Enzo Doria	05/2016
4293	(30^78857-1)/29	116480	Robert Price	12/2011
4294	(2^386903-3)/5	116469	Lelio R Paula	03/2014
4295	28107^13892+13892^28107	116441	Hans Havermann	02/2021
4296	29110^9957+9957^29110	116386	Hans Havermann	02/2021
4297	26469^24838+24838^26469	116335	Hans Havermann	01/2021
4298	2^386389-1864783	116315	Enzo Doria	03/2016
4299	(31*2^386231-1)/1711	116266	Lelio R Paula	03/2014
4300	297^47012+47012^297	116250	Norbert Schneider	07/2018
4301	(35*10^116223-341)/9	116224	Robert Price	08/2021
4302	(2^386087-5)/40959	116220	Lelio R Paula	03/2014
4303	(2^386054+714)/2	116214	Stefano Morozzi	09/2020
4304	(10^116201+7)/39623	116197	Alfred Reich	06/2021
4305	2^385969-823	116189	Yves Minet	05/2012
4306	57^66162+2	116173	Lelio R Paula	08/2013
4307	2^385854+75049	116154	Enzo Doria	04/2016
4308	(2^385832+2590)/2	116147	Stefano Morozzi	09/2020
4309	2^385775-109587	116130	Enzo Doria	04/2014
4310	(14*10^116112-101)/3	116113	Robert Price	02/2019
4311	Phi(236354,10)/24817171	116109	Makoto Kamada	08/2019
4312	3*10^116107+23	116108	Robert Price	03/2022
4313	28729^10990+10990^28729	116094	Hans Havermann	02/2021
4314	2^385622+71839	116084	Enzo Doria	04/2016
4315	2^385564+781	116067	Lelio R Paula	01/2012
4316	(2^385565+1562)/2	116067	Stefano Morozzi	09/2020
4317	(2^385563+378)/2	116066	Stefano Morozzi	02/2021
4318	(2^385557+2214)/2	116064	Stefano Morozzi	09/2020
4319	29431^8776+8776^29431	116056	Hans Havermann	01/2021
4320	(266*10^116024-17)/3	116026	Robert Price	07/2020
4321	30263^6820+6820^30263	116022	Hans Havermann	02/2021
4322	2^385410+71893	116020	Enzo Doria	04/2016
4323	38225^1084+1084^38225	116014	Hans Havermann	02/2021
4324	26548^23433+23433^26548	116011	Hans Havermann	02/2021
4325	(25*2^385091+1)/27	115924	Lelio R Paula	04/2014
4326	(11*10^115910-131)/3	115911	Robert Price	09/2018
4327	2^384953-111943	115883	Paul Bourdelais	02/2012
4328	43^70942-2	115882	Lelio R Paula	04/2014
4329	(94*10^115879-7)/3	115881	Robert Price	03/2020
4330	7*10^115863+3	115864	Robert Price	08/2015
4331	2^384834+93	115847	Donovan Johnson	07/2008
4332	2^384809+71297	115840	Enzo Doria	04/2016
4333	(55*10^115829+323)/9	115830	Robert Price	10/2021
4334	(7*2^384759-1)/5	115825	Lelio R Paula	04/2014
4335	31348^4951+4951^31348	115822	Hans Havermann	02/2021
4336	(793*10^115810+53)/9	115812	Robert Price	01/2022
4337	(71*10^115810-17)/9	115811	Ray Chandler	08/2011
4338	(97*10^115794-1)/3	115796	Serge Batalov	12/2014
4339	31115^5266+5266^31115	115794	Hans Havermann	02/2021
4340	2*10^115784-27	115785	Robert Price	05/2018
4341	10^115773+126739	115774	Patrick De Geest	04/2018
4343	10^115773-1000000001	115773	Robert Price	03/2018
4342	10^115773-396221	115773	Patrick De Geest	04/2018
4344	(2^384582+778)/2	115771	Stefano Morozzi	09/2020
4345	30537^6178+6178^30537	115762	Hans Havermann	01/2021
4346	2^384530+1874305	115756	Enzo Doria	06/2016
4347	(3*2^384524-1)/7631	115750	Lelio R Paula	03/2014
4348	28275^12406+12406^28275	115748	Hans Havermann	01/2021
4349	(44*10^115697-413)/9	115698	Robert Price	03/2019
4350	31408^4825+4825^31408	115692	Hans Havermann	02/2021
4351	(2^384317+1026)/2	115691	Stefano Morozzi	09/2020
4352	2^384312+81091	115690	Yves Minet	02/2010
4353	(2^384265+2150)/2	115675	Stefano Morozzi	09/2020
4354	(2^384246+2182)/2	115670	Stefano Morozzi	09/2020
4355	(4*10^115668-79)/3	115669	Robert Price	02/2018
4356	(2^384193+242)/2	115654	Stefano Morozzi	09/2020
4357	(266947#+1267)/(7^2*181)	115647	Makoto Morimoto	06/2019
4358	(266947#+273808)/(2109157)	115646	Makoto Morimoto	10/2017
4359	18^92125-92125^18	115642	Dylan Delgado	08/2019
4360	3^242337-4042	115625	Enzo Doria	05/2014
4361	(2^383931+674)/2	115575	Stefano Morozzi	09/2020
4362	7*10^115561+79	115562	Robert Price	07/2019
4363	(2^383872+3046)/2	115557	Stefano Morozzi	09/2020
4364	(11*2^383859-13)/15	115553	Renaud Lifchitz	03/2011
4365	2^383780-3149	115530	Yves Minet	10/2014
4366	(41*10^115523-383)/9	115524	Robert Price	11/2018
4367	27316^16923+16923^27316	115506	Hans Havermann	02/2021
4368	(2^383618+618)/2	115481	Stefano Morozzi	09/2020
4369	2^383560-455	115464	Yves Minet	03/2012
4370	(2^383544+5)/3	115458	Lelio R Paula	03/2014
4371	(22*10^115454+119)/3	115455	Robert Price	04/2021
4372	89^59221-88^59221	115445	Robert Price	06/2015
4373	2^383347+1869413	115399	Enzo Doria	05/2016
4374	(103*10^115366+17)/3	115368	Robert Price	08/2020
4375	(2^383232+750)/2	115365	Stefano Morozzi	09/2020
4376	(2^383130-7)/131793	115329	Lelio R Paula	03/2014
4377	(12^106859+1)/13	115320	Paul Bourdelais	02/2010
4378	29961^7060+7060^29961	115315	Hans Havermann	01/2021
4380	2^383039+1869509	115307	Enzo Doria	05/2016
4379	32918^3183+3183^32918	115307	Hans Havermann	01/2021
4381	36964^1315+1315^36964	115288	Hans Havermann	02/2021
4382	(13*2^382968+1)/7	115286	Lelio R Paula	04/2014
4383	(22*10^115282+29)/3	115283	Robert Price	02/2021
4384	(2^382945+2046)/2	115278	Stefano Morozzi	09/2020
4385	(2^382789+3182)/2	115231	Stefano Morozzi	09/2020
4386	30416^6141+6141^30416	115224	Hans Havermann	02/2021
4387	6*10^115211+79	115212	Robert Price	09/2020
4388	(2^382722+3598)/2	115211	Stefano Morozzi	09/2020
4389	27987^13078+13078^27987	115210	Hans Havermann	02/2021
4390	(2^382699+2090)/2	115204	Stefano Morozzi	09/2020
4391	2^382633+73697	115185	Enzo Doria	04/2016
4392	2^382509-113593	115147	Enzo Doria	08/2014
4393	2^382502-2791721	115145	Enzo Doria	03/2016
4394	(2^382495+1274)/2	115143	Stefano Morozzi	01/2021
4395	26752^20065+20065^26752	115099	Hans Havermann	02/2021
4396	26383^23008+23008^26383	115080	Hans Havermann	02/2021
4397	9^120590-120590	115073	Robert Price	03/2014
4398	28203^12016+12016^28203	115062	Hans Havermann	02/2021
4399	2^382198+9	115054	Lelio R Paula	03/2013
4400	30101^6630+6630^30101	115032	Hans Havermann	01/2021
4401	(89*10^115030-179)/9	115031	Robert Price	12/2019
4402	(2^381935+2774)/2	114974	Stefano Morozzi	02/2021
4403	27300^16271+16271^27300	114972	Hans Havermann	02/2021
4404	2^381883-59197	114959	Enzo Doria	10/2015
4405	27423^15542+15542^27423	114944	Hans Havermann	02/2021
4406	(2^381820+1626)/2	114939	Stefano Morozzi	09/2020
4408	2^381806-4481	114936	Yves Minet	07/2011
4407	2^381808-1851507	114936	Enzo Doria	08/2015
4409	(2^381792+2502)/2	114931	Stefano Morozzi	09/2020
4410	2^381774-112373	114926	Enzo Doria	06/2014
4411	26341^22980+22980^26341	114883	Hans Havermann	01/2021
4412	2^381555-109051	114860	Enzo Doria	04/2014
4413	2^381546-113501	114857	Enzo Doria	08/2014
4414	(7*10^114845-19)/3	114846	Robert Price	10/2020
4415	26675^20178+20178^26675	114833	Hans Havermann	02/2021
4416	(2^381436+1182)/2	114824	Stefano Morozzi	09/2020
4417	3^240644+16	114817	Robert Price	04/2020
4418	2^381360-110429	114801	Enzo Doria	05/2014
4419	(17*10^114795+79)/3	114796	Robert Price	04/2019
4420	(66^63079+1)/67	114774	Paul Bourdelais	09/2017
4421	2^381252-115079	114769	Enzo Doria	06/2015
4422	(2^381251+3186)/2	114768	Stefano Morozzi	09/2020
4423	2^381209-29323	114756	Enzo Doria	07/2015
4424	2^381207-111546435	114755	Paul Bourdelais	10/2021
4425	569^41651-568^41651	114754	Jean-Louis Charton	11/2009
4426	2^381201+1873205	114753	Enzo Doria	06/2016
4427	(85*10^114737+293)/9	114738	Robert Price	12/2019
4428	(265*10^114736+17)/3	114738	Robert Price	03/2020
4429	(2^381062+2170)/2	114711	Stefano Morozzi	09/2020
4430	2^380974-112991	114685	Enzo Doria	07/2014
4431	37097^1234+1234^37097	114679	Hans Havermann	02/2021
4432	88^58949-87	114626	Norbert Schneider	11/2015
4433	(2^380773+662)/2	114624	Stefano Morozzi	09/2020
4434	29913^6782+6782^29913	114608	Hans Havermann	02/2021
4435	(331*10^114605-7)/9	114607	Robert Price	04/2022
4436	2^380700+91	114603	Lelio R Paula	03/2013
4437	(2^380632+2578)/2	114582	Stefano Morozzi	09/2020
4438	7*10^114577+27	114578	Robert Price	11/2020
4440	10^114575+3^114576	114576	Mike Oakes	09/2010
4439	10^114575+66561	114576	Patrick De Geest	02/2017
4441	10^114575-581081	114575	Patrick De Geest	02/2017
4442	2^380587-115315	114569	Enzo Doria	06/2015
4443	31874^3927+3927^31874	114558	Hans Havermann	02/2021
4444	2^380513-216925	114546	Enzo Doria	05/2014
4445	2^380451-1840087	114528	Enzo Doria	06/2015
4446	(2^380426+1510)/2	114520	Stefano Morozzi	09/2020
4447	(15*2^380388-1)/539	114507	Lelio R Paula	04/2014
4448	2^380279-461347	114476	Enzo Doria	07/2015
4449	(331*10^114454-7)/9	114456	Robert Price	04/2022
4450	27121^16590+16590^27121	114447	Hans Havermann	01/2021
4451	25966^25555+25555^25966	114445	Hans Havermann	01/2021
4452	(11*10^114400+529)/9	114401	Robert Price	09/2021
4453	2^380021+1871147	114398	Enzo Doria	05/2016
4454	2^380005+1869707	114393	Enzo Doria	05/2016
4455	2^379958-113297	114379	Enzo Doria	07/2014
4456	(2^379897+1274)/2	114361	Stefano Morozzi	01/2021
4457	2^379881-109105	114356	Enzo Doria	04/2014
4458	(21*2^379857-1)/13	114349	Lelio R Paula	03/2014
4459	(4*10^114340+83)/3	114341	Robert Price	02/2018
4460	(26*10^114317-77)/3	114318	Robert Price	11/2019
4461	(4*10^114296+149)/9	114296	Robert Price	04/2018
4462	88^58773-87	114284	Norbert Schneider	11/2015
4463	27764^13065+13065^27764	114280	Hans Havermann	01/2021
4464	2^379529-2790283	114250	Enzo Doria	03/2016
4465	2^379522+1869115	114248	Enzo Doria	05/2016
4466	(145*10^114226-1)/9	114228	Serge Batalov	12/2014
4467	2^379317-115033	114186	Enzo Doria	06/2015
4468	(22*10^114178+47)/3	114179	Robert Price	06/2021
4469	(17*2^379246-1)/17407	114162	Lelio R Paula	03/2014
4470	(2^379192+226)/2	114148	Stefano Morozzi	09/2020
4471	6*10^114091+23	114092	Robert Price	09/2020
4472	(4*10^114076+143)/3	114077	Robert Price	03/2018
4473	(2^378820+3226)/2	114036	Stefano Morozzi	01/2021
4474	(2^378754+2058)/2	114017	Stefano Morozzi	09/2020
4476	(46*10^113969+683)/9	113970	Robert Price	03/2019
4475	(83*10^113969+133)/9	113970	Robert Price	08/2021
4477	32226^3439+3439^32226	113966	Hans Havermann	02/2021
4478	(77*10^113963-149)/9	113964	Robert Price	03/2022
4479	78*10^113954-7	113956	Robert Price	10/2020
4480	2*10^113941+9	113942	Dmitry Domanov	11/2010
4481	10^113933+145897	113934	Patrick De Geest	02/2021
4484	(2^378478+1642)/2	113933	Stefano Morozzi	09/2020
4482	10^113933-8000000001	113933	Robert Price	11/2020
4483	10^113933-66167	113933	Patrick De Geest	02/2021
4485	2339662057597*10^113903+9	113916	Robert Price	03/2021
4486	4*10^113905+91	113906	Robert Price	08/2018
4487	10^113894+76609	113895	Patrick De Geest	02/2021
4489	10^113894-10000001	113894	Robert Price	09/2020
4488	10^113894-373947	113894	Patrick De Geest	02/2021
4490	33933^2270+2270^33933	113881	Hans Havermann	02/2021
4491	4*10^113874-21	113875	Robert Price	09/2018
4492	2^378272-16565	113872	Enzo Doria	04/2013
4493	2^378217-109075	113855	Enzo Doria	04/2014
4494	2^378198+67	113849	Lelio R Paula	03/2013
4495	2^378173-3249	113842	Yves Minet	12/2014
4496	(2^378155-5)/6597	113833	Lelio R Paula	03/2014
4497	92941#+(355049#)/(92941#)	113830	Makoto Morimoto	10/2017
4498	30030^6173+6173^30030	113829	Hans Havermann	01/2021
4499	2^378128-262977	113828	Enzo Doria	05/2014
4500	2^378123-113215	113827	Enzo Doria	07/2014

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