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	91^55259-90^55259	108255	Robert Price	07/2015
4252	10^108251+85749	108252	Patrick De Geest	02/2021
4253	10^108251-50000000001	108251	Robert Price	12/2020
4254	10^108251-252081	108251	Patrick De Geest	02/2021
4255	4*10^108238-71	108239	Robert Price	12/2018
4256	3^226845+68	108233	Lelio R Paula	03/2017
4257	31836^2509+2509^31836	108227	Hans Havermann	10/2020
4258	5^154822-12866	108216	Enzo Doria	05/2014
4259	(9*2^359480+1)/5	108215	Lelio R Paula	03/2014
4260	2^359454-177	108207	Lelio R Paula	12/2011
4261	(19*10^108184+191)/3	108185	Robert Price	05/2019
4262	6^139022-59	108181	Lelio R Paula	02/2017
4263	(19*10^108176-43)/3	108177	Robert Price	05/2019
4264	2^359352-179	108176	Lelio R Paula	12/2011
4265	2^359338-1858781	108172	Enzo Doria	04/2016
4266	12^100230-97	108167	Lelio R Paula	03/2017
4267	27028^10043+10043^27028	108163	Hans Havermann	11/2020
4268	(25*2^359297-1)/137	108159	Lelio R Paula	03/2014
4269	(2^359262-509203)/9	108148	Lelio R Paula	12/2013
4270	26583^11702+11702^26583	108147	Hans Havermann	11/2020
4271	(3^226648-8)/352715633	108131	Lelio R Paula	12/2013
4272	6^138956-59	108129	Lelio R Paula	02/2017
4273	2^359184+30285	108126	Lelio R Paula	04/2017
4274	13^97059+10	108119	Lelio R Paula	03/2017
4275	2^359137-81	108112	Lelio R Paula	12/2011
4277	(15185*2^359105-1)/567	108103	Lelio R Paula	05/2015
4276	2^359110-11655	108103	Lelio R Paula	04/2017
4278	26227^13222+13222^26227	108090	Hans Havermann	10/2020
4279	8*6^138875+5	108067	Lelio R Paula	11/2014
4280	2^358987-216919	108066	Enzo Doria	05/2014
4281	(2^358977+2714)/2	108063	Stefano Morozzi	09/2020
4282	39^67918-67918^39	108062	Norbert Schneider	02/2017
4283	24^78283-1*78283^24	108048	Dylan Delgado	12/2019
4284	25282^18767+18767^25282	108040	Hans Havermann	11/2020
4285	2^358785-16933	108006	Enzo Doria	05/2013
4286	(2^358783+5)/33383	108000	Lelio R Paula	12/2013
4287	6^138770-77	107985	Lelio R Paula	02/2017
4288	(2^358727-1017)/94178479	107980	Lelio R Paula	12/2013
4289	10^107976+19	107977	Lelio R Paula	02/2017
4290	10^107976-202103	107976	Patrick De Geest	03/2017
4291	2^358684+75781	107975	Enzo Doria	04/2016
4292	24928^21411+21411^24928	107955	Hans Havermann	10/2020
4293	99^54094+2	107952	Lelio R Paula	06/2013
4294	(2^358583-9)/391	107942	Lelio R Paula	12/2013
4295	(2^358562+838)/2	107938	Stefano Morozzi	02/2021
4296	2^358538+55	107931	Lelio R Paula	12/2011
4297	2^358517-109009	107925	Enzo Doria	03/2014
4298	26395^12258+12258^26395	107914	Hans Havermann	10/2020
4299	3^226159+104	107906	Lelio R Paula	03/2017
4300	2^358310-11655	107863	Lelio R Paula	03/2017
4301	(68*10^107852-329)/9	107853	Robert Price	03/2021
4302	2^358275-112987	107852	Enzo Doria	07/2014
4303	3^226038+4	107848	Tyler NeSmith	01/2021
4304	2^358233-20005	107839	Enzo Doria	06/2013
4305	2^358194+175	107828	Lelio R Paula	12/2011
4306	107^53125-106	107812	Norbert Schneider	12/2016
4307	(25*10^107804+161)/3	107805	Robert Price	09/2019
4308	3^225922-2	107793	Lelio R Paula	10/2013
4309	12^99874-95	107783	Lelio R Paula	03/2017
4310	(2^358042+3042)/2	107782	Stefano Morozzi	09/2020
4311	2^358030-171	107778	Lelio R Paula	12/2011
4312	11^103488-4170	107772	Enzo Doria	12/2012
4313	2^357930-4547	107748	Yves Minet	03/2019
4314	2^357911-20089	107742	Enzo Doria	06/2013
4315	2^357885+12857	107735	Yves Minet	07/2010
4316	(248587#+9289)/(71327111512899)	107733	Makoto Morimoto	06/2019
4317	7^127473+40	107728	Lelio R Paula	03/2017
4318	5*2^357850+9	107725	Lelio R Paula	09/2014
4319	2^357786-291191	107705	Enzo Doria	06/2015
4320	28907^5320+5320^28907	107705	Hans Havermann	10/2020
4321	18^85798-23	107700	Lelio R Paula	04/2017
4322	3*10^107697+61	107698	Robert Price	09/2020
4323	(14*10^107694-83)/3	107695	Robert Price	12/2018
4324	2^357688-1854269	107675	Enzo Doria	09/2015
4325	2^357671-112225	107670	Enzo Doria	06/2014
4326	34323^1370+1370^34323	107662	Hans Havermann	11/2020
4327	2^357618-21005	107654	Enzo Doria	06/2013
4328	2^357615-17505	107653	Enzo Doria	05/2013
4329	26350^12171+12171^26350	107649	Hans Havermann	11/2020
4330	(30^72871-1)/29	107638	Robert Price	12/2011
4331	25021^20026+20026^25021	107631	Hans Havermann	11/2020
4332	2^357521+1870217	107625	Enzo Doria	05/2016
4333	2^357477-1203	107612	Lelio R Paula	03/2017
4334	26008^13693+13693^26008	107583	Hans Havermann	10/2020
4335	25432^16991+16991^25432	107583	Hans Havermann	10/2020
4336	(2^357371+3726)/2	107580	Stefano Morozzi	09/2020
4337	5^153894-18	107568	Lelio R Paula	02/2017
4338	2^357324-69059	107566	Enzo Doria	11/2015
4339	467^40296+40296^467	107563	Norbert Schneider	03/2019
4340	29446^4495+4495^29446	107559	Hans Havermann	10/2020
4341	2^357283-869688105	107553	Lelio R Paula	01/2017
4342	2^357280-16805	107552	Enzo Doria	05/2013
4343	10^107547+481719	107548	Patrick De Geest	03/2017
4344	10^107547-47	107547	Lelio R Paula	02/2017
4345	17^87396-32	107537	Lelio R Paula	04/2017
4346	(746*10^107505+1)/9	107507	Robert Price	03/2020
4347	(2^357125+1730)/2	107506	Stefano Morozzi	09/2020
4348	2^357081+107	107493	Lelio R Paula	12/2011
4349	2^357058-3911	107486	Yves Minet	04/2017
4350	3^225274+64	107484	Lelio R Paula	03/2017
4351	5*10^107482-57	107483	Robert Price	03/2021
4352	18^85619-95	107476	Lelio R Paula	04/2017
4353	(2^357013+2526)/2	107472	Stefano Morozzi	09/2020
4354	3^225248-130	107471	Lelio R Paula	03/2017
4355	(5*2^356961+1)/143	107455	Lelio R Paula	03/2014
4356	27029^9448+9448^27029	107450	Hans Havermann	11/2020
4357	2^356935-18085	107449	Enzo Doria	05/2013
4358	55396^87+87^55396	107442	Hans Havermann	10/2020
4359	10^107409+37	107410	Lelio R Paula	02/2017
4360	10^107409-329633	107409	Patrick De Geest	03/2017
4361	(2^356799+3134)/2	107407	Stefano Morozzi	09/2020
4362	2^356787-109027	107404	Enzo Doria	04/2014
4363	(2^356767+78557)/5	107397	Lelio R Paula	12/2013
4364	3*10^107389+77	107390	Robert Price	09/2018
4365	5^153622-42	107378	Lelio R Paula	02/2017
4366	2^356699-97305	107378	Lelio R Paula	03/2017
4367	2^356654+85	107364	Lelio R Paula	11/2011
4368	2^356641-19921	107360	Enzo Doria	06/2013
4369	5*10^107355+11	107356	Robert Price	08/2019
4370	2^356623-465	107355	Lelio R Paula	03/2017
4371	19^83945-92	107345	Lelio R Paula	02/2017
4372	25491^16246+16246^25491	107337	Hans Havermann	11/2020
4373	10^107334+28149	107335	Patrick De Geest	03/2017
4374	10^107334-83	107334	Lelio R Paula	02/2017
4375	2^356518+885	107323	Lelio R Paula	03/2017
4376	(59*10^107322+391)/9	107323	Robert Price	03/2021
4377	(3*2^356506-1)/467	107317	Lelio R Paula	03/2014
4378	(2^356468+1162)/2	107308	Stefano Morozzi	09/2020
4379	2^356442-114713	107300	Enzo Doria	04/2015
4380	2^356425+72257	107295	Enzo Doria	04/2016
4381	2^356351-112237	107273	Enzo Doria	06/2014
4383	(6^137845-11)/5	107264	Paul Bourdelais	11/2011
4382	2^356322+74539	107264	Enzo Doria	04/2016
4384	2^356274+1874479	107250	Enzo Doria	06/2016
4385	24606^22819+22819^24606	107241	Hans Havermann	10/2020
4386	(2^356243+3686)/2	107240	Stefano Morozzi	09/2020
4387	20^82422-93	107234	Lelio R Paula	02/2017
4388	2^356157-20365	107214	Enzo Doria	06/2013
4389	8*10^107209+99	107210	Robert Price	03/2021
4390	2^356129-18949	107206	Enzo Doria	05/2013
4391	2^356100-109587	107197	Enzo Doria	04/2014
4392	(2^355978+3262)/2	107160	Stefano Morozzi	02/2021
4393	(31*2^355970+1)/5	107159	Lelio R Paula	03/2014
4394	2^355968-64875	107158	Lelio R Paula	01/2017
4395	2^355952+1870321	107153	Enzo Doria	05/2016
4396	27069^9088+9088^27069	107152	Hans Havermann	11/2020
4397	2^355915-117	107142	Lelio R Paula	11/2011
4398	(16*10^107140+77)/3	107141	Robert Price	03/2019
4399	24628^22369+22369^24628	107124	Hans Havermann	11/2020
4400	(19*2^355838-1)/15	107119	Lelio R Paula	03/2014
4401	3^224495-8	107112	Lelio R Paula	12/2013
4402	25077^18632+18632^25077	107086	Hans Havermann	10/2020
4403	7^126691-44	107067	Lelio R Paula	03/2017
4404	4^177830-8243	107065	Mike Oakes	02/2011
4405	(2^355562+1702)/2	107035	Stefano Morozzi	09/2020
4406	2^355524-21237	107024	Enzo Doria	06/2013
4408	(10223*2^355515+1)/4855	107022	Lelio R Paula	07/2014
4407	24843^20320+20320^24843	107022	Hans Havermann	10/2020
4409	2^355494-19901	107015	Enzo Doria	06/2013
4410	2^355454-869688105	107003	Lelio R Paula	01/2017
4411	4*10^106997+13	106998	Robert Price	02/2021
4412	2^355366+54615	106976	Lelio R Paula	01/2017
4413	(31*2^355346-1)/1563	106969	Lelio R Paula	03/2014
4415	2^355275-19861	106949	Enzo Doria	06/2013
4414	27503^7738+7738^27503	106949	Hans Havermann	11/2020
4416	(9179*2^355234-1)/1915	106937	Lelio R Paula	05/2015
4417	4*10^106914-93	106915	Robert Price	07/2020
4418	4*10^106892-3	106893	Robert Price	10/2015
4419	(66^58741+1)/67	106881	Paul Bourdelais	08/2017
4420	2^354946-3	106850	M. Frind & P. Underwood	08/2002
4421	(2^354945+3134)/2	106849	Stefano Morozzi	09/2020
4422	2^354873-18693	106828	Enzo Doria	05/2013
4423	(2^354831+3186)/2	106815	Stefano Morozzi	09/2020
4424	2^354828+4257	106814	Lelio R Paula	01/2017
4425	25216^17217+17217^25216	106814	Hans Havermann	10/2020
4426	(2^354799+1218)/2	106805	Stefano Morozzi	09/2020
4427	436^40459+40459^436	106791	Norbert Schneider	03/2019
4428	(21^80761+1)/22	106783	Paul Bourdelais	03/2010
4429	(115*10^106772-7)/9	106774	Robert Price	02/2020
4430	2^354640-354640+1	106758	Robert Price	10/2014
4431	(2^354603+2606)/2	106746	Stefano Morozzi	09/2020
4432	2^354585+95	106741	Lelio R Paula	10/2011
4433	2^354553+189	106732	Lelio R Paula	10/2011
4434	(2^354546+1338)/2	106729	Stefano Morozzi	02/2021
4435	2^354514-109031	106720	Enzo Doria	04/2014
4436	2^354509-109465	106718	Enzo Doria	04/2014
4437	(15*2^354478-1)/26983	106706	Lelio R Paula	03/2014
4438	Phi(217618,10)/899798636917	106693	Makoto Kamada	06/2019
4439	15^90710+28	106684	Lelio R Paula	04/2017
4440	7^126237+34	106683	Lelio R Paula	03/2017
4441	2^354385-115315	106681	Enzo Doria	06/2015
4442	2^354327-19305	106664	Enzo Doria	06/2013
4443	(35*10^106649+1)/9	106650	Serge Batalov	11/2010
4444	10^106636+97	106637	Lelio R Paula	02/2017
4445	10^106636-22923	106636	Patrick De Geest	03/2017
4446	2^354220-57	106631	Lelio R Paula	10/2011
4447	(68*10^106628-329)/9	106629	Robert Price	03/2021
4448	(29*10^106620-77)/3	106621	Robert Price	02/2020
4449	(746*10^106618+1)/9	106620	Robert Price	03/2020
4450	2*10^106613+29	106614	Robert Price	02/2021
4451	2^354157-17041	106612	Enzo Doria	05/2013
4452	12^98778+73	106600	Lelio R Paula	02/2017
4453	33333^1576+1576^33333	106585	Hans Havermann	11/2020
4454	2^354064+1870651	106584	Enzo Doria	05/2016
4455	24568^21779+21779^24568	106577	Hans Havermann	11/2020
4456	2^353992-57	106563	Lelio R Paula	10/2011
4457	9*10^106559+59	106560	Robert Price	01/2020
4458	7*10^106553+27	106554	Robert Price	11/2020
4459	28847^4938+4938^28847	106548	Hans Havermann	10/2020
4460	NSW(139160)	106535	Robert Price	12/2018
4461	(7*10^106516+113)/3	106517	Robert Price	02/2018
4462	2^353832-1853849	106515	Enzo Doria	09/2015
4463	(7^126037-1)/6	106513	Paul Bourdelais	09/2008
4464	2^353794-18453	106503	Enzo Doria	05/2013
4465	(2^353761+2094)/2	106493	Stefano Morozzi	09/2020
4466	2^353728+7695	106483	Lelio R Paula	01/2017
4467	26476^10509+10509^26476	106475	Hans Havermann	10/2020
4468	2^353672-303	106466	Yves Minet	02/2012
4469	6^136811+101	106460	Lelio R Paula	02/2017
4470	2^353641+1871981	106457	Enzo Doria	05/2016
4471	(8*10^106454-29)/3	106455	Robert Price	07/2018
4472	27845^6654+6654^27845	106454	Hans Havermann	11/2020
4473	25316^16017+16017^25316	106444	Hans Havermann	11/2020
4474	2^353553+54615	106431	Lelio R Paula	01/2017
4475	2^353544-18897	106428	Enzo Doria	05/2013
4476	28894^4823+4823^28894	106426	Hans Havermann	11/2020
4477	25696^13829+13829^25696	106402	Hans Havermann	11/2020
4478	6^136729-133	106396	Lelio R Paula	02/2017
4479	2^353418+1605	106390	Lelio R Paula	01/2017
4480	2^353387+65	106381	Lelio R Paula	10/2011
4481	2^353372+74311	106376	Enzo Doria	04/2016
4482	2^353344-3693	106368	Yves Minet	03/2017
4484	2^353277-20089	106347	Enzo Doria	06/2013
4483	2^353275+72173	106347	Enzo Doria	04/2016
4485	2^353268-17705	106345	Enzo Doria	05/2013
4486	2^353267-19857	106344	Enzo Doria	06/2013
4487	(46*10^106343+143)/9	106344	Robert Price	01/2019
4488	(2^353189+3054)/2	106321	Stefano Morozzi	09/2020
4489	35087^1072+1072^35087	106321	Hans Havermann	10/2020
4490	(2^353184+1290)/2	106319	Stefano Morozzi	01/2021
4491	26985^8684+8684^26985	106287	Hans Havermann	10/2020
4492	(2^353051+606)/2	106279	Stefano Morozzi	09/2020
4493	222748^3+3^222748	106278	Anatoly F. Selevich	12/2010
4494	(9179*2^353019-1)/9	106273	Lelio R Paula	05/2015
4495	2^353025+72257	106272	Enzo Doria	04/2016
4498	2^352932-20345	106244	Enzo Doria	06/2013
4496	(2^353011-3)/745325861246794515484535	106244	Lelio R Paula	12/2013
4497	25628^13983+13983^25628	106244	Hans Havermann	10/2020
4499	2^352883-187	106229	Lelio R Paula	10/2011
4500	20^81649-19^81649	106228	Jean-Louis Charton	03/2011

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