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	42^57867-41	93933	Norbert Schneider	08/2018
4252	2^311992-16209	93919	Enzo Doria	04/2013
4253	(85^48677+1)/86	93917	Paul Bourdelais	08/2017
4254	2^311965-39	93911	Lelio R Paula	11/2012
4255	2^311920-111689	93898	Enzo Doria	05/2014
4256	130^44414+129	93889	Norbert Schneider	01/2019
4257	7*10^93887-47	93888	Robert Price	02/2017
4258	12^86965-13	93851	Lelio R Paula	06/2016
4259	2^311705+16095	93833	Lelio R Paula	03/2016
4260	2^311665-81	93821	Lelio R Paula	11/2012
4261	730^32761+32761^730	93806	Norbert Schneider	09/2017
4262	11^90073+92	93802	Lelio R Paula	05/2016
4263	6*10^93792+41	93793	Robert Price	01/2017
4264	(2^311580+7)/591329	93790	Lelio R Paula	06/2013
4265	12^86900-77	93781	Lelio R Paula	06/2016
4266	2^311508-109769	93774	Enzo Doria	04/2014
4267	2^311486-1859621	93767	Enzo Doria	03/2016
4268	Phi(93811,10)/968129521/2109997013/3280113810431/639637782545831	93765	Kurt Beschorner	04/2015
4269	(10^93811-1)/(996812952121099970133280113810431639637782545831)	93765	Gord Palameta	10/2018
4270	2^311471+311469	93763	Renaud Lifchitz	01/2003
4271	(88*10^93760-1)/3	93762	Robert Price	10/2017
4272	2^311426+79459	93749	Enzo Doria	06/2016
4273	2^311294+5775	93709	Lelio R Paula	03/2016
4274	2^311252-1017	93697	Lelio R Paula	03/2016
4275	2^311247-112041	93695	Enzo Doria	06/2014
4276	7*10^93692-83	93693	Robert Price	09/2017
4277	2^311205-109645	93683	Enzo Doria	04/2014
4278	5^134027-84	93681	Lelio R Paula	04/2016
4279	(2^311148-1017)/557	93663	Lelio R Paula	06/2013
4280	(2^311027-2^155514+1)/5	93628		11/2006
4281	3^196192-28	93608	Robert Price	12/2013
4282	216091#+261433	93606	Makoto Morimoto	12/2015
4283	5^133917+68	93604	Lelio R Paula	04/2016
4284	2^310924-1709	93598	Yves Minet	03/2013
4285	(266*10^93577-11)/3	93579	Robert Price	09/2016
4286	(16*10^93577+161)/3	93578	Robert Price	05/2016
4287	3^196113-56	93570	Lelio R Paula	04/2016
4288	2^310806-110345	93562	Enzo Doria	05/2014
4289	3^196093+86	93561	Lelio R Paula	04/2016
4290	2^310780-2327	93555	Yves Minet	10/2013
4291	30^63332+41	93550	Lelio R Paula	08/2012
4292	(21181*2^310707+1)/21	93536	Lelio R Paula	06/2014
4293	8*5^133807+7	93528	Lelio R Paula	10/2014
4294	2^310686+8193	93526	Lelio R Paula	03/2016
4295	2^310646+63	93514	Lelio R Paula	11/2012
4296	(77*10^93508+31)/9	93509	Robert Price	10/2015
4297	(1000907^15583+1)/1000908	93499	Faysal YAtim	04/2009
4298	(2*10^93497+7)/9	93497	Erik Branger	03/2011
4299	3^195958-112852	93496	Enzo Doria	07/2014
4300	2^310583+16385	93495	Lelio R Paula	03/2016
4301	(9913*2^310557-1)/35	93490	Lelio R Paula	04/2015
4302	9*7^110614+2	93481	Lelio R Paula	11/2014
4303	2^310469-8295	93461	Lelio R Paula	03/2016
4304	2^310459-1159	93458	Yves Minet	11/2012
4305	6^120075-95	93437	Lelio R Paula	05/2016
4306	2^310289+98327	93407	Yves Minet	11/2010
4307	2^310217-113143	93385	Enzo Doria	07/2014
4308	7^110494-68	93379	Lelio R Paula	04/2016
4309	2^310184-113093	93375	Enzo Doria	07/2014
4310	2^310180-110417	93374	Enzo Doria	05/2014
4311	gcd(V(1124905),5F(224981)(F(224981)-1)+1)	93372	Serge Batalov	04/2015
4312	3^195669+68	93358	Lelio R Paula	04/2016
4313	10^93356+91	93357	Robert Price	04/2011
4314	10^93356-28313	93356	Patrick De Geest	08/2013
4315	(85*10^93346+23)/9	93347	Robert Price	11/2015
4316	(3^195648-5)/3158276	93342	Lelio R Paula	04/2013
4317	3^195556+8680	93304	Lelio R Paula	04/2016
4318	2^309942-109991	93302	Enzo Doria	04/2014
4319	2^309926-1867301	93298	Enzo Doria	03/2016
4320	2^309924+85951	93297	Yves Minet	03/2011
4321	2^309896-4229	93288	Yves Minet	08/2018
4322	(86*10^93263-77)/9	93264	Robert Price	05/2016
4323	6^119836-125	93251	Lelio R Paula	05/2016
4324	(77*10^93249-257)/9	93250	Robert Price	10/2017
4325	3^195430-2	93244	Theodore Burton	02/2007
4326	(13*10^93236+47)/3	93237	Robert Price	01/2017
4327	(67*10^93226-7)/3	93228	Robert Price	10/2017
4328	(86*10^93217-221)/9	93218	Robert Price	06/2017
4329	2^309637-16329	93211	Enzo Doria	04/2013
4330	(41*10^93207+49)/9	93208	Robert Price	04/2016
4331	14^81312-57	93194	Lelio R Paula	06/2016
4332	41^57783-40	93192	Theodore Burton	02/2007
4333	3*10^93179-97	93180	Robert Price	08/2017
4334	5*7^110252-4	93175	Lelio R Paula	11/2014
4335	2^309380-27	93133	Lelio R Paula	11/2012
4336	23*10^93116-7	93118	Robert Price	03/2016
4337	(29*10^93082+1)/3	93083	Robert Price	11/2015
4338	(58*10^93062-13)/9	93063	Robert Price	09/2015
4339	2^309131+1869383	93058	Enzo Doria	05/2016
4340	2^309066-93	93039	Lelio R Paula	11/2012
4341	2^309063-113269	93038	Enzo Doria	07/2014
4342	3^194965+16	93022	Robert Price	10/2013
4343	2^308979+1869143	93012	Enzo Doria	05/2016
4344	5^133064+54	93008	Lelio R Paula	04/2016
4345	(2^308905-509203)/119	92988	Lelio R Paula	06/2013
4346	(94*10^92981-49)/99	92981	Ray Chandler	07/2011
4347	(2*10^92976-17)/3	92976	Robert Price	08/2014
4348	2^308809+37967	92961	Phil Moore	03/2008
4349	(3^194825+5)/11656	92952	Lelio R Paula	04/2013
4350	(2^308679+5)/1573	92919	Lelio R Paula	06/2013
4351	2^308650+513	92913	Lelio R Paula	02/2016
4352	5*7^109936+6	92908	Lelio R Paula	10/2014
4353	2*10^92897+89	92898	Robert Price	07/2016
4354	12^86073-29	92889	Lelio R Paula	06/2016
4355	2^308566-117	92888	Lelio R Paula	11/2012
4356	(17*10^92869-11)/3	92870	Robert Price	07/2015
4357	2^308459+75431	92856	Enzo Doria	04/2016
4358	2^308426-1866377	92846	Enzo Doria	03/2016
4359	(96^46831-1)/95	92830	Paul Bourdelais	09/2017
4360	2^308349-112111	92823	Enzo Doria	06/2014
4361	9*10^92821+19	92822	Robert Price	05/2016
4362	2^308337-75	92819	Lelio R Paula	11/2012
4363	4*3^194508+7	92805	Lelio R Paula	08/2014
4364	22*25^66379-113	92796	Curtis Bright	05/2015
4365	11^89101-1080	92790	Enzo Doria	12/2012
4366	2^308236-1867859	92789	Enzo Doria	04/2016
4367	12^85963+25	92770	Lelio R Paula	06/2016
4368	7^109750-66	92750	Lelio R Paula	04/2016
4369	9*10^92742+11	92743	Robert Kinser	01/2017
4370	(21*2^308046-1)/8857	92729	Lelio R Paula	02/2014
4371	2^307997-110655	92717	Enzo Doria	05/2014
4372	L(443609)	92709	Renaud Lifchitz	11/2003
4373	10^92691+9	92692	Robert Price	03/2011
4374	10^92691-252291	92691	Patrick De Geest	08/2013
4375	2^307879-2521	92681	Yves Minet	07/2014
4376	(2^307780-7)/19959669	92644	Lelio R Paula	06/2013
4377	14^80831+47	92643	Lelio R Paula	06/2016
4378	15^78744+92	92611	Lelio R Paula	07/2016
4379	65^51083-64	92610	Norbert Schneider	11/2014
4380	131^43737-130	92604	Norbert Schneider	02/2019
4381	6^118996-16943	92597	Enzo Doria	02/2013
4382	(16*10^92591+41)/3	92592	Robert Price	10/2017
4383	(3^194014-7)/2	92568	Lelio R Paula	04/2013
4384	(63^51439+1)/64	92555	Paul Bourdelais	08/2017
4385	(26*10^92546-77)/3	92547	Robert Price	02/2017
4386	3^193954+340	92540	Lelio R Paula	04/2016
4387	2^307407-307407^2	92539	Henri Lifchitz	05/2005
4388	(17*10^92513-11)/3	92514	Robert Price	07/2015
4389	2^307318-4211	92512	Yves Minet	06/2011
4390	2^307280+193	92501	Lelio R Paula	11/2012
4391	20^71075-33	92471	Lelio R Paula	05/2016
4392	2^307126-78795	92455	Lelio R Paula	02/2016
4393	2^307125-49789	92454	Henri Lifchitz	08/2005
4394	2^307099+23	92447	Lelio R Paula	11/2012
4395	129^43798+128	92440	Norbert Schneider	01/2019
4396	7*10^92414-69	92415	Robert Price	01/2017
4397	(9787*2^306975-1)/2129155	92407	Lelio R Paula	04/2015
4398	2^306915+1873373	92391	Enzo Doria	06/2016
4399	2^306908+12915	92389	Lelio R Paula	02/2016
4400	19^72244-80	92383	Lelio R Paula	06/2016
4401	2^306849+75	92371	Lelio R Paula	11/2012
4402	(397*10^92369+53)/9	92371	Robert Price	11/2017
4403	2^306813-869688105	92360	Lelio R Paula	08/2016
4404	2^306672-109059	92318	Enzo Doria	04/2014
4405	6^118604-17063	92292	Enzo Doria	02/2013
4406	(31*2^306487-1)/2291	92260	Lelio R Paula	02/2014
4407	2^306467-1835611	92256	Enzo Doria	04/2015
4408	2^306433+76427	92246	Enzo Doria	05/2016
4409	2^306430-113313	92245	Enzo Doria	07/2014
4410	(23*10^92244-59)/9	92245	Robert Price	03/2017
4411	(47*2^306398+1)/1384803	92231	Lelio R Paula	04/2015
4412	(25*10^92186+59)/3	92187	Robert Price	05/2016
4413	2^306213-286183	92180	Enzo Doria	06/2015
4414	10^92178+61	92179	Robert Price	04/2011
4415	10^92178-175509	92178	Patrick De Geest	07/2013
4416	2^306200+1185	92176	Lelio R Paula	02/2016
4417	2^306153+11	92162	Lelio R Paula	11/2012
4418	(2^306141-7)/5	92157	Lelio R Paula	06/2013
4419	(26*10^92152-23)/3	92153	Robert Price	08/2016
4420	(2*10^92152+67)/3	92152	Robert Price	04/2017
4421	410^92099+37^92099	92100	Mike Oakes	12/2010
4422	115^44684+114	92081	Norbert Schneider	07/2018
4423	(2^305867-2^152934+1)/5	92075		11/2006
4424	2^305851-109495	92071	Enzo Doria	04/2014
4425	12^85300+35	92055	Lelio R Paula	06/2016
4426	3^192911+92	92042	Lelio R Paula	04/2016
4427	2^305723-276271	92032	Enzo Doria	07/2015
4428	2^305676+93	92018	Donovan Johnson	06/2008
4429	3^192819+4	91999	Lelio R Paula	04/2013
4430	(38*10^91997-83)/99	91997	Ray Chandler	07/2011
4431	2^305539+72911	91977	Enzo Doria	04/2016
4432	(2^305427-5)/1297998213	91934	Lelio R Paula	06/2013
4433	85^47642+84	91922	Norbert Schneider	10/2015
4434	10^91920+187651	91921	Patrick De Geest	07/2013
4435	10^91920-39	91920	Robert Price	05/2011
4436	(22*10^91903+41)/9	91904	Robert Price	02/2015
4438	2^305275-27	91897	Lelio R Paula	11/2012
4437	3^192607-7726	91897	Enzo Doria	05/2014
4439	(7*10^91856-61)/9	91856	Erik Branger	12/2009
4440	(89*10^91839-53)/9	91840	Robert Price	11/2015
4441	8*5^131351+7	91812	Lelio R Paula	10/2014
4442	3^192426-68	91811	Lelio R Paula	04/2016
4443	2^304973+117	91807	Lelio R Paula	11/2012
4444	2^304939-1863727	91796	Enzo Doria	03/2016
4445	2^304902+8415	91785	Lelio R Paula	02/2016
4446	18^73119+61	91785	Lelio R Paula	06/2016
4447	(78557*2^304740+1)/159	91739	Lelio R Paula	06/2014
4448	2^304747+71355	91738	Lelio R Paula	02/2016
4449	8*3^192251+5	91728	Lelio R Paula	08/2014
4450	2^304674-87	91717	Lelio R Paula	11/2012
4451	(28*10^91715+701)/9	91716	Robert Price	11/2017
4452	(2^304698+9)/1362809953	91715	Lelio R Paula	06/2013
4453	(5*10^91707-119)/3	91708	Robert Price	04/2016
4454	2^304633-112771	91704	Enzo Doria	06/2014
4455	9*10^91693+23	91694	Robert Price	11/2017
4456	2^304578-16713	91688	Enzo Doria	05/2013
4457	6^117824-18713	91685	Enzo Doria	03/2013
4458	(17^74509-1)/16	91679	Paul Bourdelais	03/2010
4459	(2^304551-7)/8912231	91673	Lelio R Paula	06/2013
4460	(2^304532-3)/3013	91670	Lelio R Paula	06/2013
4461	2^304507-16645	91666	Enzo Doria	04/2013
4462	(29*2^304489+1)/31	91661	Lelio R Paula	09/2013
4463	2^304471-1836127	91655	Enzo Doria	04/2015
4464	2^304433+32769	91644	Lelio R Paula	02/2016
4465	2^304410-16625	91637	Enzo Doria	04/2013
4466	183^40500-2	91630	Lelio R Paula	10/2017
4467	(203*10^91613+1)/3	91615	Robert Price	09/2017
4468	4*5^131052+7	91603	Lelio R Paula	10/2014
4469	2^304278-4001	91597	Yves Minet	04/2017
4470	2^304272-1866377	91595	Enzo Doria	03/2016
4471	2^304268+19683	91594	Lelio R Paula	02/2016
4472	2^304162-161	91562	Lelio R Paula	11/2012
4473	5*7^108331+6	91552	Lelio R Paula	10/2014
4474	2^304082-2787821	91538	Enzo Doria	03/2016
4475	2^304015+64133	91518	David Broadhurst	06/2002
4476	(7*2^303963+1)/3	91503	Lelio R Paula	09/2013
4477	(2^303945-9)/3617	91494	Lelio R Paula	06/2013
4478	2^303930+1880527	91493	Enzo Doria	10/2016
4479	3^191684-68	91457	Lelio R Paula	04/2016
4480	(21*2^303813-1)/169	91456	Lelio R Paula	02/2014
4481	11^87797-120	91432	Enzo Doria	07/2012
4482	2^303698-1847231	91423	Enzo Doria	07/2015
4483	(38^28933-1)^2-2	91416	Norbert Schneider	06/2016
4484	2^303554+77299	91379	Enzo Doria	05/2016
4485	2^303542+12705	91376	Lelio R Paula	02/2016
4486	31^61269-2	91375	Lelio R Paula	09/2013
4487	2^303516-64875	91368	Lelio R Paula	02/2016
4488	(24737*2^303428+1)/3	91345	Lelio R Paula	06/2014
4489	(21181*2^303357+1)/32361	91320	Lelio R Paula	06/2014
4490	2^303344-2786969	91316	Enzo Doria	03/2016
4491	6^117346+65	91313	Lelio R Paula	05/2016
4492	2^303321+855	91309	Lelio R Paula	02/2016
4493	12^84606+47	91306	Lelio R Paula	06/2016
4494	2^303288+1874311	91299	Enzo Doria	06/2016
4495	197^39788-2	91293	Lelio R Paula	10/2017
4496	11^87663-1710	91292	Enzo Doria	12/2012
4497	2^303224+2533	91280	Henri Lifchitz	05/2005
4498	6^117302+143	91279	Lelio R Paula	05/2016
4499	3^191306-112880	91277	Enzo Doria	07/2014
4500	2^303207+12915	91275	Lelio R Paula	02/2016

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Probable Primes Top 10000

(252675 PRPs in the top)