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 ?
4751	(9913*2^310557-1)/35	93490	Lelio R Paula	04/2015
4752	9*7^110614+2	93481	Lelio R Paula	11/2014
4753	2^310469-8295	93461	Lelio R Paula	03/2016
4754	2^310459-1159	93458	Yves Minet	11/2012
4755	6^120075-95	93437	Lelio R Paula	05/2016
4756	148^43041-147	93411	Norbert Schneider	05/2019
4757	2^310289+98327	93407	Yves Minet	11/2010
4758	2^310217-113143	93385	Enzo Doria	07/2014
4759	7^110494-68	93379	Lelio R Paula	04/2016
4760	2^310184-113093	93375	Enzo Doria	07/2014
4761	2^310180-110417	93374	Enzo Doria	05/2014
4762	gcd(V(1124905),5F(224981)(F(224981)-1)+1)	93372	Serge Batalov	04/2015
4763	3^195669+68	93358	Lelio R Paula	04/2016
4764	10^93356+91	93357	Robert Price	04/2011
4765	10^93356-28313	93356	Patrick De Geest	08/2013
4766	(85*10^93346+23)/9	93347	Robert Price	11/2015
4767	(3^195648-5)/3158276	93342	Lelio R Paula	04/2013
4768	3^195556+8680	93304	Lelio R Paula	04/2016
4769	2^309942-109991	93302	Enzo Doria	04/2014
4770	2^309926-1867301	93298	Enzo Doria	03/2016
4771	2^309924+85951	93297	Yves Minet	03/2011
4772	2^309896-4229	93288	Yves Minet	08/2018
4773	(86*10^93263-77)/9	93264	Robert Price	05/2016
4774	6^119836-125	93251	Lelio R Paula	05/2016
4775	(77*10^93249-257)/9	93250	Robert Price	10/2017
4776	3^195430-2	93244	Theodore Burton	02/2007
4777	(13*10^93236+47)/3	93237	Robert Price	01/2017
4778	(67*10^93226-7)/3	93228	Robert Price	10/2017
4779	(86*10^93217-221)/9	93218	Robert Price	06/2017
4780	2^309637-16329	93211	Enzo Doria	04/2013
4781	(41*10^93207+49)/9	93208	Robert Price	04/2016
4782	14^81312-57	93194	Lelio R Paula	06/2016
4783	41^57783-40	93192	Theodore Burton	02/2007
4784	3*10^93179-97	93180	Robert Price	08/2017
4785	5*7^110252-4	93175	Lelio R Paula	11/2014
4786	83061!4-512	93137	Robert Price	11/2019
4787	2^309380-27	93133	Lelio R Paula	11/2012
4788	23*10^93116-7	93118	Robert Price	03/2016
4789	(29*10^93082+1)/3	93083	Robert Price	11/2015
4790	(58*10^93062-13)/9	93063	Robert Price	09/2015
4791	2^309131+1869383	93058	Enzo Doria	05/2016
4792	2^309066-93	93039	Lelio R Paula	11/2012
4793	2^309063-113269	93038	Enzo Doria	07/2014
4794	3^194965+16	93022	Robert Price	10/2013
4795	2^308979+1869143	93012	Enzo Doria	05/2016
4796	5^133064+54	93008	Lelio R Paula	04/2016
4797	(2^308905-509203)/119	92988	Lelio R Paula	06/2013
4798	(94*10^92981-49)/99	92981	Ray Chandler	07/2011
4799	(2*10^92976-17)/3	92976	Robert Price	08/2014
4800	2^308809+37967	92961	Phil Moore	03/2008
4801	(3^194825+5)/11656	92952	Lelio R Paula	04/2013
4802	(2^308679+5)/1573	92919	Lelio R Paula	06/2013
4803	2^308650+513	92913	Lelio R Paula	02/2016
4804	5*7^109936+6	92908	Lelio R Paula	10/2014
4805	2*10^92897+89	92898	Robert Price	07/2016
4806	12^86073-29	92889	Lelio R Paula	06/2016
4807	2^308566-117	92888	Lelio R Paula	11/2012
4808	(17*10^92869-11)/3	92870	Robert Price	07/2015
4809	2^308459+75431	92856	Enzo Doria	04/2016
4810	2^308426-1866377	92846	Enzo Doria	03/2016
4811	(96^46831-1)/95	92830	Paul Bourdelais	09/2017
4812	2^308349-112111	92823	Enzo Doria	06/2014
4813	9*10^92821+19	92822	Robert Price	05/2016
4814	2^308337-75	92819	Lelio R Paula	11/2012
4815	4*3^194508+7	92805	Lelio R Paula	08/2014
4816	22*25^66379-113	92796	Curtis Bright	05/2015
4817	11^89101-1080	92790	Enzo Doria	12/2012
4818	2^308236-1867859	92789	Enzo Doria	04/2016
4819	12^85963+25	92770	Lelio R Paula	06/2016
4820	7^109750-66	92750	Lelio R Paula	04/2016
4821	9*10^92742+11	92743	Robert Kinser	01/2017
4822	(21*2^308046-1)/8857	92729	Lelio R Paula	02/2014
4823	2^307997-110655	92717	Enzo Doria	05/2014
4824	L(443609)	92709	Renaud Lifchitz	11/2003
4825	10^92691+9	92692	Robert Price	03/2011
4826	10^92691-252291	92691	Patrick De Geest	08/2013
4827	2^307879-2521	92681	Yves Minet	07/2014
4828	(2^307780-7)/19959669	92644	Lelio R Paula	06/2013
4829	14^80831+47	92643	Lelio R Paula	06/2016
4830	15^78744+92	92611	Lelio R Paula	07/2016
4831	65^51083-64	92610	Norbert Schneider	11/2014
4832	131^43737-130	92604	Norbert Schneider	02/2019
4833	6^118996-16943	92597	Enzo Doria	02/2013
4834	(16*10^92591+41)/3	92592	Robert Price	10/2017
4835	(3^194014-7)/2	92568	Lelio R Paula	04/2013
4836	(63^51439+1)/64	92555	Paul Bourdelais	08/2017
4837	(26*10^92546-77)/3	92547	Robert Price	02/2017
4838	3^193954+340	92540	Lelio R Paula	04/2016
4839	2^307407-307407^2	92539	Henri Lifchitz	05/2005
4840	(17*10^92513-11)/3	92514	Robert Price	07/2015
4841	2^307318-4211	92512	Yves Minet	06/2011
4842	2^307280+193	92501	Lelio R Paula	11/2012
4843	20^71075-33	92471	Lelio R Paula	05/2016
4844	2^307126-78795	92455	Lelio R Paula	02/2016
4845	2^307125-49789	92454	Henri Lifchitz	08/2005
4846	2^307099+23	92447	Lelio R Paula	11/2012
4847	129^43798+128	92440	Norbert Schneider	01/2019
4848	Phi(277314,10)/3327769	92430	Makoto Kamada	05/2019
4849	7*10^92414-69	92415	Robert Price	01/2017
4850	(9787*2^306975-1)/2129155	92407	Lelio R Paula	04/2015
4851	2^306915+1873373	92391	Enzo Doria	06/2016
4852	2^306908+12915	92389	Lelio R Paula	02/2016
4853	19^72244-80	92383	Lelio R Paula	06/2016
4855	2^306849+75	92371	Lelio R Paula	11/2012
4854	(397*10^92369+53)/9	92371	Robert Price	11/2017
4856	2^306813-869688105	92360	Lelio R Paula	08/2016
4857	2^306672-109059	92318	Enzo Doria	04/2014
4858	6^118604-17063	92292	Enzo Doria	02/2013
4859	(31*2^306487-1)/2291	92260	Lelio R Paula	02/2014
4860	2^306467-1835611	92256	Enzo Doria	04/2015
4861	2^306433+76427	92246	Enzo Doria	05/2016
4862	2^306430-113313	92245	Enzo Doria	07/2014
4863	(23*10^92244-59)/9	92245	Robert Price	03/2017
4864	(47*2^306398+1)/1384803	92231	Lelio R Paula	04/2015
4865	(25*10^92186+59)/3	92187	Robert Price	05/2016
4866	2^306213-286183	92180	Enzo Doria	06/2015
4867	10^92178+61	92179	Robert Price	04/2011
4868	10^92178-175509	92178	Patrick De Geest	07/2013
4869	2^306200+1185	92176	Lelio R Paula	02/2016
4870	2^306153+11	92162	Lelio R Paula	11/2012
4871	(2^306141-7)/5	92157	Lelio R Paula	06/2013
4872	(26*10^92152-23)/3	92153	Robert Price	08/2016
4873	(2*10^92152+67)/3	92152	Robert Price	04/2017
4874	410^92099+37^92099	92100	Mike Oakes	12/2010
4875	115^44684+114	92081	Norbert Schneider	07/2018
4876	(2^305867-2^152934+1)/5	92075		11/2006
4877	2^305851-109495	92071	Enzo Doria	04/2014
4878	12^85300+35	92055	Lelio R Paula	06/2016
4879	((10^46026-1)1000/9+739)10^46026+(10^46026-1)/9	92055	Hans Havermann	05/2019
4880	3^192911+92	92042	Lelio R Paula	04/2016
4881	2^305723-276271	92032	Enzo Doria	07/2015
4882	2^305676+93	92018	Donovan Johnson	06/2008
4883	3^192819+4	91999	Lelio R Paula	04/2013
4884	(38*10^91997-83)/99	91997	Ray Chandler	07/2011
4885	2^305539+72911	91977	Enzo Doria	04/2016
4886	Phi(212014,10)	91960	Makoto Kamada	04/2019
4887	(2^305427-5)/1297998213	91934	Lelio R Paula	06/2013
4888	82077!4-128	91928	Robert Price	11/2019
4889	85^47642+84	91922	Norbert Schneider	10/2015
4890	10^91920+187651	91921	Patrick De Geest	07/2013
4891	10^91920-39	91920	Robert Price	05/2011
4892	(22*10^91903+41)/9	91904	Robert Price	02/2015
4894	2^305275-27	91897	Lelio R Paula	11/2012
4893	3^192607-7726	91897	Enzo Doria	05/2014
4895	(7*10^91856-61)/9	91856	Erik Branger	12/2009
4896	(89*10^91839-53)/9	91840	Robert Price	11/2015
4897	8*5^131351+7	91812	Lelio R Paula	10/2014
4898	3^192426-68	91811	Lelio R Paula	04/2016
4899	2^304973+117	91807	Lelio R Paula	11/2012
4900	2^304939-1863727	91796	Enzo Doria	03/2016
4901	2^304902+8415	91785	Lelio R Paula	02/2016
4902	18^73119+61	91785	Lelio R Paula	06/2016
4903	(78557*2^304740+1)/159	91739	Lelio R Paula	06/2014
4904	2^304747+71355	91738	Lelio R Paula	02/2016
4905	8*3^192251+5	91728	Lelio R Paula	08/2014
4906	2^304674-87	91717	Lelio R Paula	11/2012
4907	(28*10^91715+701)/9	91716	Robert Price	11/2017
4908	(2^304698+9)/1362809953	91715	Lelio R Paula	06/2013
4909	(5*10^91707-119)/3	91708	Robert Price	04/2016
4910	2^304633-112771	91704	Enzo Doria	06/2014
4911	9*10^91693+23	91694	Robert Price	11/2017
4912	2^304578-16713	91688	Enzo Doria	05/2013
4913	6^117824-18713	91685	Enzo Doria	03/2013
4914	(17^74509-1)/16	91679	Paul Bourdelais	03/2010
4915	(2^304551-7)/8912231	91673	Lelio R Paula	06/2013
4916	(2^304532-3)/3013	91670	Lelio R Paula	06/2013
4917	2^304507-16645	91666	Enzo Doria	04/2013
4918	(29*2^304489+1)/31	91661	Lelio R Paula	09/2013
4919	2^304471-1836127	91655	Enzo Doria	04/2015
4920	2^304433+32769	91644	Lelio R Paula	02/2016
4921	2^304410-16625	91637	Enzo Doria	04/2013
4922	183^40500-2	91630	Lelio R Paula	10/2017
4923	(203*10^91613+1)/3	91615	Robert Price	09/2017
4924	4*5^131052+7	91603	Lelio R Paula	10/2014
4925	2^304278-4001	91597	Yves Minet	04/2017
4926	2^304272-1866377	91595	Enzo Doria	03/2016
4927	2^304268+19683	91594	Lelio R Paula	02/2016
4928	2^304162-161	91562	Lelio R Paula	11/2012
4929	5*7^108331+6	91552	Lelio R Paula	10/2014
4930	2^304082-2787821	91538	Enzo Doria	03/2016
4931	2^304015+64133	91518	David Broadhurst	06/2002
4932	(7*2^303963+1)/3	91503	Lelio R Paula	09/2013
4933	(2^303945-9)/3617	91494	Lelio R Paula	06/2013
4934	2^303930+1880527	91493	Enzo Doria	10/2016
4935	3^191684-68	91457	Lelio R Paula	04/2016
4936	(21*2^303813-1)/169	91456	Lelio R Paula	02/2014
4937	11^87797-120	91432	Enzo Doria	07/2012
4938	2^303698-1847231	91423	Enzo Doria	07/2015
4939	(38^28933-1)^2-2	91416	Norbert Schneider	06/2016
4940	2^303554+77299	91379	Enzo Doria	05/2016
4941	2^303542+12705	91376	Lelio R Paula	02/2016
4942	31^61269-2	91375	Lelio R Paula	09/2013
4943	2^303516-64875	91368	Lelio R Paula	02/2016
4944	(24737*2^303428+1)/3	91345	Lelio R Paula	06/2014
4945	(21181*2^303357+1)/32361	91320	Lelio R Paula	06/2014
4946	2^303344-2786969	91316	Enzo Doria	03/2016
4947	6^117346+65	91313	Lelio R Paula	05/2016
4948	2^303321+855	91309	Lelio R Paula	02/2016
4949	12^84606+47	91306	Lelio R Paula	06/2016
4950	2^303288+1874311	91299	Enzo Doria	06/2016
4951	197^39788-2	91293	Lelio R Paula	10/2017
4952	11^87663-1710	91292	Enzo Doria	12/2012
4953	2^303224+2533	91280	Henri Lifchitz	05/2005
4954	6^117302+143	91279	Lelio R Paula	05/2016
4955	3^191306-112880	91277	Enzo Doria	07/2014
4956	2^303207+12915	91275	Lelio R Paula	02/2016
4957	2^303191-111259	91270	Enzo Doria	05/2014
4958	81539!4+32	91267	Robert Price	09/2019
4960	10^91230+9^(91230+1)	91231	Robert Price	08/2016
4959	10^91230+7921	91231	Patrick De Geest	11/2016
4962	10^91230-911141	91230	Patrick De Geest	11/2016
4961	10^91229+348793	91230	Patrick De Geest	07/2019
4963	10^91229-2471	91229	Patrick De Geest	01/2019
4964	2996^26241+26241^2996	91228	Norbert Schneider	01/2020
4966	10^91225+5271	91226	Patrick De Geest	01/2019
4965	2816^26445+26445^2816	91226	Norbert Schneider	02/2020
4968	6^117232-17423	91225	Enzo Doria	02/2013
4967	10^91225-147219	91225	Patrick De Geest	07/2019
4969	7*10^91215+3	91216	Erik Branger	11/2009
4970	10^91215+230611	91216	Patrick De Geest	07/2019
4971	10^91215-4539	91215	Patrick De Geest	01/2019
4972	10^91210+2421	91211	Patrick De Geest	01/2019
4973	10^91210-1737	91210	Patrick De Geest	01/2019
4974	97*10^91205-3	91207	Robert Price	01/2017
4975	2^302979-161181	91206	Enzo Doria	04/2013
4976	2^302949+81	91197	Henri Lifchitz	02/2007
4977	10^91194+200361	91195	Patrick De Geest	07/2019
4979	4*6^117192-5	91194	Lelio R Paula	10/2014
4978	10^91194-8663	91194	Patrick De Geest	01/2019
4980	2^302918+99	91188	Lelio R Paula	11/2012
4981	10^91186+268111	91187	Patrick De Geest	07/2019
4982	10^91186-7763	91186	Patrick De Geest	01/2019
4983	10^91181+550471	91182	Patrick De Geest	07/2019
4984	10^91181-1367	91181	Patrick De Geest	01/2019
4985	10^91178+71883	91179	Patrick De Geest	07/2019
4986	10^91178-4719	91178	Patrick De Geest	01/2019
4987	10^91165+3043	91166	Patrick De Geest	01/2019
4988	10^91165-399413	91165	Patrick De Geest	07/2019
4989	10^91156+3861	91157	Patrick De Geest	01/2019
4990	10^91156-231497	91156	Patrick De Geest	07/2019
4991	2^302797+1869587	91151	Enzo Doria	05/2016
4992	265^37614+37614^265	91148	Norbert Schneider	01/2015
4993	7^107852+82	91146	Lelio R Paula	04/2016
4994	(38*10^91144-11)/9	91145	Robert Price	05/2015
4995	(55*10^91142+377)/9	91143	Robert Price	10/2017
4996	10^91128+9961	91129	Patrick De Geest	01/2019
4998	249^38030+38030^249	91128	Norbert Schneider	01/2015
4997	10^91128-189153	91128	Patrick De Geest	07/2019
4999	6^117094-211049	91117	Mike Oakes	05/2011
5000	2^302602-1867181	91093	Enzo Doria	03/2016

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PRP Records

Probable Primes Top 10000

(259919 PRPs in the top)