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	10^92178-175509	92178	Patrick De Geest	07/2013
4252	2^306200+1185	92176	Lelio R Paula	02/2016
4253	2^306153+11	92162	Lelio R Paula	11/2012
4254	(2^306141-7)/5	92157	Lelio R Paula	06/2013
4255	(26*10^92152-23)/3	92153	Robert Price	08/2016
4256	(2*10^92152+67)/3	92152	Robert Price	04/2017
4257	410^92099+37^92099	92100	Mike Oakes	12/2010
4258	115^44684+114	92081	Norbert Schneider	07/2018
4259	(2^305867-2^152934+1)/5	92075		11/2006
4260	2^305851-109495	92071	Enzo Doria	04/2014
4261	12^85300+35	92055	Lelio R Paula	06/2016
4262	3^192911+92	92042	Lelio R Paula	04/2016
4263	2^305723-276271	92032	Enzo Doria	07/2015
4264	2^305676+93	92018	Donovan Johnson	06/2008
4265	3^192819+4	91999	Lelio R Paula	04/2013
4266	(38*10^91997-83)/99	91997	Ray Chandler	07/2011
4267	2^305539+72911	91977	Enzo Doria	04/2016
4268	(2^305427-5)/1297998213	91934	Lelio R Paula	06/2013
4269	85^47642+84	91922	Norbert Schneider	10/2015
4270	10^91920+187651	91921	Patrick De Geest	07/2013
4271	10^91920-39	91920	Robert Price	05/2011
4272	(22*10^91903+41)/9	91904	Robert Price	02/2015
4274	2^305275-27	91897	Lelio R Paula	11/2012
4273	3^192607-7726	91897	Enzo Doria	05/2014
4275	(7*10^91856-61)/9	91856	Erik Branger	12/2009
4276	(89*10^91839-53)/9	91840	Robert Price	11/2015
4277	8*5^131351+7	91812	Lelio R Paula	10/2014
4278	3^192426-68	91811	Lelio R Paula	04/2016
4279	2^304973+117	91807	Lelio R Paula	11/2012
4280	2^304939-1863727	91796	Enzo Doria	03/2016
4281	2^304902+8415	91785	Lelio R Paula	02/2016
4282	18^73119+61	91785	Lelio R Paula	06/2016
4283	(78557*2^304740+1)/159	91739	Lelio R Paula	06/2014
4284	2^304747+71355	91738	Lelio R Paula	02/2016
4285	8*3^192251+5	91728	Lelio R Paula	08/2014
4286	2^304674-87	91717	Lelio R Paula	11/2012
4287	(28*10^91715+701)/9	91716	Robert Price	11/2017
4288	(2^304698+9)/1362809953	91715	Lelio R Paula	06/2013
4289	(5*10^91707-119)/3	91708	Robert Price	04/2016
4290	2^304633-112771	91704	Enzo Doria	06/2014
4291	9*10^91693+23	91694	Robert Price	11/2017
4292	2^304578-16713	91688	Enzo Doria	05/2013
4293	6^117824-18713	91685	Enzo Doria	03/2013
4294	(17^74509-1)/16	91679	Paul Bourdelais	03/2010
4295	(2^304551-7)/8912231	91673	Lelio R Paula	06/2013
4296	(2^304532-3)/3013	91670	Lelio R Paula	06/2013
4297	2^304507-16645	91666	Enzo Doria	04/2013
4298	(29*2^304489+1)/31	91661	Lelio R Paula	09/2013
4299	2^304471-1836127	91655	Enzo Doria	04/2015
4300	2^304433+32769	91644	Lelio R Paula	02/2016
4301	2^304410-16625	91637	Enzo Doria	04/2013
4302	183^40500-2	91630	Lelio R Paula	10/2017
4303	(203*10^91613+1)/3	91615	Robert Price	09/2017
4304	4*5^131052+7	91603	Lelio R Paula	10/2014
4305	2^304278-4001	91597	Yves Minet	04/2017
4306	2^304272-1866377	91595	Enzo Doria	03/2016
4307	2^304268+19683	91594	Lelio R Paula	02/2016
4308	2^304162-161	91562	Lelio R Paula	11/2012
4309	5*7^108331+6	91552	Lelio R Paula	10/2014
4310	2^304082-2787821	91538	Enzo Doria	03/2016
4311	2^304015+64133	91518	David Broadhurst	06/2002
4312	(7*2^303963+1)/3	91503	Lelio R Paula	09/2013
4313	(2^303945-9)/3617	91494	Lelio R Paula	06/2013
4314	2^303930+1880527	91493	Enzo Doria	10/2016
4315	3^191684-68	91457	Lelio R Paula	04/2016
4316	(21*2^303813-1)/169	91456	Lelio R Paula	02/2014
4317	11^87797-120	91432	Enzo Doria	07/2012
4318	2^303698-1847231	91423	Enzo Doria	07/2015
4319	(38^28933-1)^2-2	91416	Norbert Schneider	06/2016
4320	2^303554+77299	91379	Enzo Doria	05/2016
4321	2^303542+12705	91376	Lelio R Paula	02/2016
4322	31^61269-2	91375	Lelio R Paula	09/2013
4323	2^303516-64875	91368	Lelio R Paula	02/2016
4324	(24737*2^303428+1)/3	91345	Lelio R Paula	06/2014
4325	(21181*2^303357+1)/32361	91320	Lelio R Paula	06/2014
4326	2^303344-2786969	91316	Enzo Doria	03/2016
4327	6^117346+65	91313	Lelio R Paula	05/2016
4328	2^303321+855	91309	Lelio R Paula	02/2016
4329	12^84606+47	91306	Lelio R Paula	06/2016
4330	2^303288+1874311	91299	Enzo Doria	06/2016
4331	197^39788-2	91293	Lelio R Paula	10/2017
4332	11^87663-1710	91292	Enzo Doria	12/2012
4333	2^303224+2533	91280	Henri Lifchitz	05/2005
4334	6^117302+143	91279	Lelio R Paula	05/2016
4335	3^191306-112880	91277	Enzo Doria	07/2014
4336	2^303207+12915	91275	Lelio R Paula	02/2016
4337	2^303191-111259	91270	Enzo Doria	05/2014
4338	10^91230+9^(91230+1)	91231	Robert Price	08/2016
4339	10^91230+7921	91231	Patrick De Geest	11/2016
4340	10^91230-911141	91230	Patrick De Geest	11/2016
4341	6^117232-17423	91225	Enzo Doria	02/2013
4342	7*10^91215+3	91216	Erik Branger	11/2009
4343	97*10^91205-3	91207	Robert Price	01/2017
4344	2^302979-161181	91206	Enzo Doria	04/2013
4345	2^302949+81	91197	Henri Lifchitz	02/2007
4346	4*6^117192-5	91194	Lelio R Paula	10/2014
4347	2^302918+99	91188	Lelio R Paula	11/2012
4348	2^302797+1869587	91151	Enzo Doria	05/2016
4349	265^37614+37614^265	91148	Norbert Schneider	01/2015
4350	7^107852+82	91146	Lelio R Paula	04/2016
4351	(38*10^91144-11)/9	91145	Robert Price	05/2015
4352	(55*10^91142+377)/9	91143	Robert Price	10/2017
4353	249^38030+38030^249	91128	Norbert Schneider	01/2015
4354	6^117094-211049	91117	Mike Oakes	05/2011
4355	2^302602-1867181	91093	Enzo Doria	03/2016
4356	(1017*2^302592-1)/53	91091	Lelio R Paula	04/2015
4357	15^77445-16	91083	Lelio R Paula	07/2016
4358	2^302505+81	91064	Henri Lifchitz	02/2007
4359	2^302496-112349	91061	Enzo Doria	06/2014
4360	17^73999-72	91052	Lelio R Paula	07/2016
4361	(16*10^91032+41)/3	91033	Robert Price	10/2017
4362	2^302332+577294575	91012	Lelio R Paula	08/2016
4363	2^302274+74209	90994	Enzo Doria	04/2016
4364	(311^36497-1)/310	90976	Eric Chen	09/2017
4365	(3^190668+2)/89	90970	Lelio R Paula	04/2013
4366	2^302188+90195	90968	Lelio R Paula	02/2016
4367	(53*10^90965-71)/9	90966	Robert Price	09/2015
4368	2^302113+74105	90946	Enzo Doria	04/2016
4369	2^302102-6555	90942	Lelio R Paula	02/2016
4371	156(10^(422731)-1)/101-1	90925	Robert Price	05/2014
4370	3^190568+38	90925	Lelio R Paula	04/2016
4372	2^302009-16449	90914	Enzo Doria	04/2013
4373	(17*2^301951-1)/165	90896	Lelio R Paula	02/2014
4374	3^190497+74	90891	Lelio R Paula	04/2016
4375	(24737*2^301896+1)/399	90882	Lelio R Paula	06/2014
4376	18^72397+89	90878	Lelio R Paula	06/2016
4377	6^116769-47	90864	Lelio R Paula	05/2016
4378	2^301712-465	90825	Lelio R Paula	02/2016
4379	2^301693-69	90819	Lelio R Paula	11/2012
4380	2^301683-301683^2	90816	Henri Lifchitz	05/2005
4381	10^90800-6453	90800	Patrick De Geest	11/2018
4382	11^87187-1710	90796	Enzo Doria	12/2012
4383	5*10^90793+21	90794	Robert Price	01/2017
4384	(22*10^90792-13)/9	90793	Robert Price	03/2015
4385	2^301591-1615	90788	Lelio R Paula	02/2016
4386	(52^52901+1)/53	90777	Paul Bourdelais	08/2017
4387	2^301546-109037	90775	Enzo Doria	04/2014
4388	10^90772+4029	90773	Patrick De Geest	11/2018
4389	10^90770-431	90770	Patrick De Geest	11/2018
4390	14^79195-3	90768	Lelio R Paula	06/2016
4391	10^90766+877	90767	Patrick De Geest	11/2018
4392	2^301517-1861693	90766	Enzo Doria	11/2015
4393	10^90765-4797	90765	Patrick De Geest	11/2018
4394	10^90757+7573	90758	Patrick De Geest	11/2018
4395	10^90756-8727	90756	Patrick De Geest	11/2018
4396	10^90749+823	90750	Patrick De Geest	11/2018
4398	2^301460-173	90749	Lelio R Paula	11/2012
4397	10^90748+4213	90749	Patrick De Geest	11/2018
4399	10^90747-9279	90747	Patrick De Geest	11/2018
4400	(85*10^90745-103)/9	90746	Robert Price	10/2017
4401	10^90726+4077	90727	Patrick De Geest	11/2018
4402	10^90721+181	90722	Patrick De Geest	11/2018
4403	2^301312-89	90704	Lelio R Paula	11/2012
4404	10^90696+6349	90697	Patrick De Geest	11/2018
4405	2^301285-129	90696	Lelio R Paula	11/2012
4406	2^301282-109991	90695	Enzo Doria	04/2014
4407	10^90690+8877	90691	Patrick De Geest	11/2018
4408	10^90683-2577	90683	Patrick De Geest	11/2018
4409	2^301228-1854269	90679	Enzo Doria	09/2015
4410	(151*10^90669-1)/3	90671	Robert Price	04/2017
4411	(32*10^90669+13)/9	90670	Robert Price	04/2015
4412	10^90669+9793	90670	Patrick De Geest	11/2018
4413	10^90665-3087	90665	Patrick De Geest	11/2018
4414	10^90662-9519	90662	Patrick De Geest	11/2018
4415	10^90661+2373	90662	Patrick De Geest	11/2018
4416	3*5^129698+8	90656	Lelio R Paula	10/2014
4417	F(433781)	90655	Henri Lifchitz	09/2003
4418	19^70891+82	90653	Lelio R Paula	06/2016
4419	(29*2^301124-1)/13	90648	Lelio R Paula	02/2014
4420	10^90636-3101	90636	Patrick De Geest	11/2018
4421	7*3^189953-8	90632	Lelio R Paula	08/2014
4422	10^90626-1131	90626	Patrick De Geest	11/2018
4423	11^87022-1800	90625	Enzo Doria	12/2012
4424	10^90623+861	90624	Patrick De Geest	11/2018
4425	(2^301042+47)/12036969	90616	Lelio R Paula	06/2013
4426	2^301004-2786939	90612	Enzo Doria	03/2016
4427	10^90611-9737	90611	Patrick De Geest	11/2018
4428	10^90609+6823	90610	Patrick De Geest	11/2018
4429	2^300980-27	90605	Lelio R Paula	11/2012
4430	2*10^90597-7	90598	Dmitry Domanov	11/2010
4431	197^39485+2	90597	Lelio R Paula	06/2013
4432	7^107198+48	90593	Lelio R Paula	04/2016
4433	(86*10^90588+121)/9	90589	Robert Price	03/2017
4434	2^300923+53	90587	Lelio R Paula	11/2012
4435	2^300874+7	90573	Lelio R Paula	10/2012
4436	10^90567+9489	90568	Patrick De Geest	11/2018
4437	5^129568-56	90565	Lelio R Paula	04/2016
4438	2^300847-112831	90564	Enzo Doria	06/2014
4439	10^90562-2981	90562	Patrick De Geest	11/2018
4440	10^90549+3811	90550	Patrick De Geest	11/2018
4441	10^90532+8169	90533	Patrick De Geest	11/2018
4442	10^90531+9831	90532	Patrick De Geest	11/2018
4443	2^300718+255255	90526	Lelio R Paula	02/2016
4444	10^90516-6783	90516	Patrick De Geest	11/2018
4445	10^90511-6977	90511	Patrick De Geest	11/2018
4446	2^300637+95	90501	Lelio R Paula	11/2012
4447	7^107087-24	90500	Lelio R Paula	04/2016
4448	10^90499-5823	90499	Patrick De Geest	11/2018
4450	(10^90499+3^90499)/13	90498	Robert Price	01/2013
4449	13^81241+90	90498	Lelio R Paula	06/2016
4451	10^90480+5131	90481	Patrick De Geest	11/2018
4452	6^116273-85	90478	Lelio R Paula	05/2016
4453	10^90473+3139	90474	Patrick De Geest	11/2018
4454	10^90470+2319	90471	Patrick De Geest	11/2018
4455	6^116256-17573	90465	Enzo Doria	02/2013
4456	2^300502+54615	90461	Lelio R Paula	02/2016
4457	(13*2^300487+1)/45	90456	Lelio R Paula	09/2013
4458	10^90453-3969	90453	Patrick De Geest	11/2018
4459	10^90440+1359	90441	Patrick De Geest	11/2018
4460	(3^189545-8)/5	90436	Lelio R Paula	01/2013
4461	(7*2^300406-1)/3	90432	Lelio R Paula	02/2014
4462	10^90430+3339	90431	Patrick De Geest	11/2018
4463	10^90414-1547	90414	Patrick De Geest	11/2018
4464	10^90404-6429	90404	Patrick De Geest	11/2018
4465	10^90401+2077	90402	Patrick De Geest	11/2018
4466	4*5^129332+3	90400	Lelio R Paula	10/2014
4467	10^90397-323	90397	Patrick De Geest	11/2018
4468	2^300249-16245	90384	Enzo Doria	04/2013
4469	(7*10^90371-313)/9	90371	Robert Price	11/2016
4470	10^90363-3557	90363	Patrick De Geest	11/2018
4472	2*6^116118+7	90358	Lelio R Paula	10/2014
4471	10^90358-4979	90358	Patrick De Geest	11/2018
4473	10^90356-7197	90356	Patrick De Geest	11/2018
4474	10^90353-1089	90353	Patrick De Geest	11/2018
4475	(24737*2^300101+1)/25	90343	Lelio R Paula	06/2014
4476	4*10^90334-21	90335	Robert Price	04/2016
4477	10^90322-9551	90322	Patrick De Geest	11/2018
4478	10^90316+9991	90317	Patrick De Geest	11/2018
4480	2^300019-110335	90315	Enzo Doria	05/2014
4479	10^90315-8561	90315	Patrick De Geest	11/2018
4481	2^299949-1005	90294	Lelio R Paula	11/2013
4482	10^90279-1551	90279	Patrick De Geest	09/2018
4483	2^299868-109613	90270	Enzo Doria	04/2014
4484	10^90259-9443	90259	Patrick De Geest	09/2018
4485	10^90252-8103	90252	Patrick De Geest	09/2018
4486	5*2^299799-3	90250	Lelio R Paula	08/2014
4487	13^81008-2	90239	Lelio R Paula	09/2013
4488	64^49957-63^49957	90232	Robert Price	07/2013
4489	10^90227+56281	90228	Patrick De Geest	06/2016
4492	2^299725+315	90227	Lelio R Paula	11/2013
4490	10^90227-1000000001	90227	Robert Price	05/2016
4491	10^90227-68763	90227	Patrick De Geest	06/2016
4493	5^129082+48	90225	Lelio R Paula	03/2016
4494	2^299699+195	90219	Lelio R Paula	10/2012
4495	(55*10^90211-1)/9	90212	Ray Chandler	02/2012
4496	10^90209+8971	90210	Patrick De Geest	09/2018
4497	10^90208-2247	90208	Patrick De Geest	09/2018
4498	116^43693-115	90203	Norbert Schneider	08/2018
4499	10^90202+3553	90203	Patrick De Geest	09/2018
4500	3^189053+280	90202	Lelio R Paula	04/2016

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Probable Primes Top 10000

(252402 PRPs in the top)