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 ?
5001	10^90610-26573	90610	Patrick De Geest	07/2019
5002	10^90609-228173	90609	Patrick De Geest	07/2019
5003	2^300980-27	90605	Lelio R Paula	11/2012
5004	2*10^90597-7	90598	Dmitry Domanov	11/2010
5005	197^39485+2	90597	Lelio R Paula	06/2013
5006	7^107198+48	90593	Lelio R Paula	04/2016
5007	(86*10^90588+121)/9	90589	Robert Price	03/2017
5008	2^300923+53	90587	Lelio R Paula	11/2012
5009	2^300874+7	90573	Lelio R Paula	10/2012
5010	10^90567+9489	90568	Patrick De Geest	11/2018
5011	10^90567-231353	90567	Patrick De Geest	07/2019
5012	5^129568-56	90565	Lelio R Paula	04/2016
5013	2^300847-112831	90564	Enzo Doria	06/2014
5014	10^90562+790197	90563	Patrick De Geest	07/2019
5015	10^90562-2981	90562	Patrick De Geest	11/2018
5016	10^90549+3811	90550	Patrick De Geest	11/2018
5017	10^90549-630303	90549	Patrick De Geest	07/2019
5018	2^300790-4541	90547	Yves Minet	03/2019
5019	10^90532+8169	90533	Patrick De Geest	11/2018
5020	10^90531+9831	90532	Patrick De Geest	11/2018
5021	10^90532-154889	90532	Patrick De Geest	07/2019
5022	10^90531-1060589	90531	Patrick De Geest	07/2019
5023	2^300718+255255	90526	Lelio R Paula	02/2016
5024	10^90516+215917	90517	Patrick De Geest	07/2019
5025	10^90516-6783	90516	Patrick De Geest	11/2018
5026	10^90511+30177	90512	Patrick De Geest	07/2019
5027	10^90511-6977	90511	Patrick De Geest	11/2018
5028	2^300637+95	90501	Lelio R Paula	11/2012
5030	7^107087-24	90500	Lelio R Paula	04/2016
5029	10^90499+191547	90500	Patrick De Geest	07/2019
5031	10^90499-5823	90499	Patrick De Geest	11/2018
5033	(10^90499+3^90499)/13	90498	Robert Price	01/2013
5032	13^81241+90	90498	Lelio R Paula	06/2016
5034	10^90480+5131	90481	Patrick De Geest	11/2018
5035	10^90480-85721	90480	Patrick De Geest	07/2019
5036	6^116273-85	90478	Lelio R Paula	05/2016
5037	10^90473+3139	90474	Patrick De Geest	11/2018
5038	10^90473-150599	90473	Patrick De Geest	07/2019
5039	10^90470+2319	90471	Patrick De Geest	11/2018
5040	10^90470-71637	90470	Patrick De Geest	07/2019
5041	6^116256-17573	90465	Enzo Doria	02/2013
5042	2^300502+54615	90461	Lelio R Paula	02/2016
5043	(13*2^300487+1)/45	90456	Lelio R Paula	09/2013
5044	10^90453+141843	90454	Patrick De Geest	07/2019
5045	10^90453-3969	90453	Patrick De Geest	11/2018
5046	10^90440+1359	90441	Patrick De Geest	11/2018
5047	10^90440-18821	90440	Patrick De Geest	07/2019
5048	(3^189545-8)/5	90436	Lelio R Paula	01/2013
5049	(7*2^300406-1)/3	90432	Lelio R Paula	02/2014
5050	10^90430+3339	90431	Patrick De Geest	11/2018
5051	10^90430-63477	90430	Patrick De Geest	07/2019
5052	10^90414+229593	90415	Patrick De Geest	07/2019
5053	10^90414-1547	90414	Patrick De Geest	11/2018
5054	10^90404+47041	90405	Patrick De Geest	07/2019
5055	10^90404-6429	90404	Patrick De Geest	11/2018
5056	10^90401+2077	90402	Patrick De Geest	11/2018
5057	10^90401-368637	90401	Patrick De Geest	07/2019
5058	4*5^129332+3	90400	Lelio R Paula	10/2014
5059	10^90397+19783	90398	Patrick De Geest	07/2019
5060	10^90397-323	90397	Patrick De Geest	11/2018
5061	2^300249-16245	90384	Enzo Doria	04/2013
5062	(7*10^90371-313)/9	90371	Robert Price	11/2016
5063	10^90363+58677	90364	Patrick De Geest	07/2019
5064	10^90363-3557	90363	Patrick De Geest	11/2018
5065	10^90358+104641	90359	Patrick De Geest	07/2019
5067	2*6^116118+7	90358	Lelio R Paula	10/2014
5068	10^90358-4979	90358	Patrick De Geest	11/2018
5066	10^90357+112837	90358	Patrick De Geest	07/2019
5069	10^90357-189593	90357	Patrick De Geest	07/2019
5070	10^90356+53113	90357	Patrick De Geest	07/2019
5071	10^90356-7197	90356	Patrick De Geest	11/2018
5072	10^90353+603211	90354	Patrick De Geest	07/2019
5073	10^90353-1089	90353	Patrick De Geest	11/2018
5074	(24737*2^300101+1)/25	90343	Lelio R Paula	06/2014
5075	4*10^90334-21	90335	Robert Price	04/2016
5076	10^90322+137691	90323	Patrick De Geest	07/2019
5077	10^90322-9551	90322	Patrick De Geest	11/2018
5078	10^90316+9991	90317	Patrick De Geest	11/2018
5079	10^90316-45627	90316	Patrick De Geest	07/2019
5080	10^90315+32889	90316	Patrick De Geest	07/2019
5081	2^300019-110335	90315	Enzo Doria	05/2014
5082	10^90315-8561	90315	Patrick De Geest	11/2018
5083	FAB2(300001,5032)	90310	Robert Price	05/2019
5084	FAB2(300001,29405)	90310	Robert Price	05/2019
5085	2^299949-1005	90294	Lelio R Paula	11/2013
5086	10^90279+62457	90280	Patrick De Geest	07/2019
5087	10^90279-1551	90279	Patrick De Geest	09/2018
5088	2^299868-109613	90270	Enzo Doria	04/2014
5089	10^90259+359299	90260	Patrick De Geest	07/2019
5090	10^90259-9443	90259	Patrick De Geest	09/2018
5091	10^90252+102873	90253	Patrick De Geest	07/2019
5092	10^90252-8103	90252	Patrick De Geest	09/2018
5093	5*2^299799-3	90250	Lelio R Paula	08/2014
5094	13^81008-2	90239	Lelio R Paula	09/2013
5095	80697!4-256	90234	Robert Price	11/2019
5096	64^49957-63^49957	90232	Robert Price	07/2013
5097	10^90227+56281	90228	Patrick De Geest	06/2016
5100	2^299725+315	90227	Lelio R Paula	11/2013
5098	10^90227-1000000001	90227	Robert Price	05/2016
5099	10^90227-68763	90227	Patrick De Geest	06/2016
5101	5^129082+48	90225	Lelio R Paula	03/2016
5102	2^299699+195	90219	Lelio R Paula	10/2012
5103	(55*10^90211-1)/9	90212	Ray Chandler	02/2012
5104	10^90209+8971	90210	Patrick De Geest	09/2018
5105	10^90209-724797	90209	Patrick De Geest	07/2019
5106	10^90208+189531	90209	Patrick De Geest	07/2019
5107	10^90208-2247	90208	Patrick De Geest	09/2018
5108	116^43693-115	90203	Norbert Schneider	08/2018
5109	10^90202+3553	90203	Patrick De Geest	09/2018
5110	3^189053+280	90202	Lelio R Paula	04/2016
5111	10^90202-67793	90202	Patrick De Geest	07/2019
5112	2^299639-187	90201	Lelio R Paula	10/2012
5113	10^90199+254031	90200	Patrick De Geest	07/2019
5114	10^90199-2891	90199	Patrick De Geest	09/2018
5115	2^299631+183	90198	Lelio R Paula	10/2012
5116	10^90196+187539	90197	Patrick De Geest	07/2019
5117	10^90196-9683	90196	Patrick De Geest	09/2018
5118	10^90193+104973	90194	Patrick De Geest	07/2019
5119	10^90193-9809	90193	Patrick De Geest	09/2018
5120	(21*2^299611-1)/29	90192	Lelio R Paula	02/2014
5121	2^299567+113	90179	Lelio R Paula	10/2012
5122	2^299550+189	90174	Lelio R Paula	10/2012
5123	10^90170+376063	90171	Patrick De Geest	07/2019
5124	10^90170-6749	90170	Patrick De Geest	09/2018
5125	(2^299535+3)/29	90168	Lelio R Paula	01/2013
5126	10^90160+271947	90161	Patrick De Geest	07/2019
5127	10^90160-5613	90160	Patrick De Geest	09/2018
5128	(97*10^90155-1)/3	90157	Serge Batalov	12/2014
5130	3^188938+8680	90147	Lelio R Paula	04/2016
5129	10^90146+160209	90147	Patrick De Geest	07/2019
5131	10^90146-2027	90146	Patrick De Geest	09/2018
5132	6^115840-55	90142	Lelio R Paula	05/2016
5133	(5*10^90142-473)/9	90142	Robert Price	12/2017
5134	8*7^106659+5	90139	Lelio R Paula	10/2014
5136	2^299406-16653	90131	Enzo Doria	05/2013
5135	(317057^16384+1)/2	90131	Richard Fischer	10/2019
5137	10^90128+288673	90129	Patrick De Geest	07/2019
5138	208049#+(216091#)/(208049#)	90128	Makoto Morimoto	04/2016
5139	10^90128-8387	90128	Patrick De Geest	09/2018
5140	(F(5)^128941-F(4)^128941)/F(3)	90126	Wayne Halsdorf	03/2012
5141	6^115819-53	90125	Lelio R Paula	05/2016
5142	10^90123+6313	90124	Patrick De Geest	09/2018
5144	6^115816-16853	90123	Enzo Doria	02/2013
5143	10^90123-22617	90123	Patrick De Geest	07/2019
5145	6^115813-23	90121	Lelio R Paula	05/2016
5146	(22*10^90110+161)/3	90111	Robert Price	02/2017
5148	(2^299330-509203)/69	90106	Lelio R Paula	01/2013
5147	10^90105+915759	90106	Patrick De Geest	07/2019
5150	10^90105-767	90105	Patrick De Geest	09/2018
5149	10^90104+48189	90105	Patrick De Geest	07/2019
5151	10^90104-7703	90104	Patrick De Geest	09/2018
5152	10^90103+9159	90104	Patrick De Geest	09/2018
5153	10^90103-208457	90103	Patrick De Geest	07/2019
5154	10^90102+73011	90103	Patrick De Geest	07/2019
5155	10^90102-602433	90102	Patrick De Geest	07/2019
5156	10^90101+1225537	90102	Patrick De Geest	07/2019
5157	10^90101-3207	90101	Patrick De Geest	09/2018
5158	(29*10^90096-17)/3	90097	Erik Branger	09/2014
5159	10^90089+143181	90090	Patrick De Geest	07/2019
5160	10^90089-3573	90089	Patrick De Geest	09/2018
5161	2^299247+1870529	90083	Enzo Doria	05/2016
5162	10^90079+1609	90080	Patrick De Geest	09/2018
5163	10^90079-230043	90079	Patrick De Geest	07/2019
5164	2^299229-2797783	90077	Enzo Doria	04/2016
5165	2^299220-16317	90075	Enzo Doria	04/2013
5166	11^86491-1350	90072	Enzo Doria	12/2012
5167	10^90071+52333	90072	Patrick De Geest	07/2019
5168	10^90071-1233	90071	Patrick De Geest	09/2018
5169	(314401^16384+1)/2	90071	Richard Fischer	10/2019
5170	10^90069+158527	90070	Patrick De Geest	07/2019
5171	10^90069-7841	90069	Patrick De Geest	09/2018
5172	(31*10^90064-1)/3	90066	Robert Price	03/2017
5173	10^90060+149431	90061	Patrick De Geest	07/2019
5174	10^90060-839	90060	Patrick De Geest	09/2018
5175	10^90052+2361	90053	Patrick De Geest	09/2018
5176	10^90052-90929	90052	Patrick De Geest	07/2019
5177	10^90047+619	90048	Patrick De Geest	09/2018
5178	10^90047-151071	90047	Patrick De Geest	07/2019
5179	L(430949)/861899/1440387561539	90045	Serge Batalov	07/2017
5180	2^299112+73951	90042	Enzo Doria	04/2016
5181	8^99702+7^(99702-1)	90040	Robert Price	02/2016
5182	10^90038+157803	90039	Patrick De Geest	07/2019
5183	10^90038-9687	90038	Patrick De Geest	09/2018
5184	5*10^90033+3	90034	Dmitry Domanov	11/2010
5185	10^90030+225813	90031	Patrick De Geest	07/2019
5186	10^90030-1461	90030	Patrick De Geest	09/2018
5187	243^37738+37738^243	90029	Norbert Schneider	01/2015
5188	10^90025+70569	90026	Patrick De Geest	07/2019
5189	10^90025-8703	90025	Patrick De Geest	09/2018
5190	2^299048-113297	90023	Enzo Doria	07/2014
5191	10^90015+849	90016	Patrick De Geest	09/2018
5192	10^90015-228387	90015	Patrick De Geest	07/2019
5193	10^90010+6811	90011	Patrick De Geest	09/2018
5194	10^90010-183597	90010	Patrick De Geest	11/2018
5195	10^90009+58321	90010	Patrick De Geest	11/2018
5196	10^90008+847	90009	Patrick De Geest	09/2018
5197	10^90009-356013	90009	Patrick De Geest	11/2018
5199	3^188648+92	90008	Lelio R Paula	12/2015
5198	10^90008-706049	90008	Patrick De Geest	11/2018
5200	5*2^298991+7	90006	Lelio R Paula	08/2014
5201	(25*2^298997+1)/3267	90005	Lelio R Paula	01/2013
5202	10^90000+8869	90001	Patrick De Geest	12/2009
5204	10^89999+82939	90000	Dirk Augustin	04/2007
5203	10^90000-140343	90000	Patrick De Geest	12/2009
5205	10^89999-194891	89999	Patrick De Geest	11/2009
5206	19^70365-78	89980	Lelio R Paula	12/2015
5207	NaturalLogarithmOf2(89973)	89973	Eric W. Weisstein	10/2015
5208	2^298852-64875	89964	Lelio R Paula	11/2013
5209	18^71659+37	89952	Lelio R Paula	12/2015
5210	(2908*29^61501-3)/7	89942	Curtis Bright	05/2015
5211	17^73067+20	89906	Lelio R Paula	11/2015
5212	2^298637-99	89899	Lelio R Paula	10/2012
5213	9^94188+38^94188-24^94188-3*2^94188	89879	Mike Oakes	01/2011
5214	9*10^89858+19	89859	Robert Price	05/2016
5215	2^298501+1870067	89858	Enzo Doria	05/2016
5216	11^86280-98	89852	Lelio R Paula	11/2015
5217	2^298473-110059	89850	Enzo Doria	04/2014
5218	19^70263-32	89850	Lelio R Paula	12/2015
5219	(299*10^89836-17)/3	89838	Robert Price	01/2017
5220	3^188286+14	89836	Robert Price	09/2013
5221	gcd(V(1091095),5F(218219)(F(218219)+1)+1)	89822	Serge Batalov	04/2015
5222	2^298367+58905	89818	Lelio R Paula	11/2013
5223	2^298319-109657	89803	Enzo Doria	04/2014
5224	8*10^89800+81	89801	Robert Price	05/2017
5225	18^71505-91	89759	Lelio R Paula	12/2015
5226	(7^106187+1)/8	89738	Paul Bourdelais	04/2008
5227	2^298079-109531	89731	Enzo Doria	04/2014
5228	117^43380+116	89718	Norbert Schneider	08/2018
5229	(22699*2^298016+1)/385	89714	Lelio R Paula	06/2014
5230	156(10^(422427)-1)/101-1	89709	Robert Price	05/2014
5231	2^298003-66945	89708	Lelio R Paula	11/2013
5232	(23*10^89705-83)/3	89706	Robert Price	09/2017
5233	17^72900-54	89700	Lelio R Paula	11/2015
5234	3*2^297956+5	89695	Lelio R Paula	08/2014
5235	20^68938-11	89691	Lelio R Paula	01/2016
5236	89*10^89687-7	89689	Robert Price	03/2017
5237	(297847^16384+1)/2	89686	Richard Fischer	08/2019
5238	2^297923+77783	89684	Enzo Doria	05/2016
5239	11^86107-24576000	89672	Enzo Doria	02/2013
5240	2^297878-111911	89671	Enzo Doria	05/2014
5241	7^106084+40	89652	Lelio R Paula	10/2015
5242	(86*10^89640-311)/9	89641	Robert Price	10/2017
5243	3*10^89608-59	89609	Robert Price	10/2017
5244	3^187780-11038	89594	Enzo Doria	05/2014
5245	(13*2^297560-1)/49151787	89568	Lelio R Paula	02/2014
5246	5^128141-36	89567	Lelio R Paula	10/2015
5247	4*7^105951+9	89540	Lelio R Paula	10/2014
5248	(7*10^89539-439)/9	89539	Robert Price	09/2017
5249	2^297397+177257	89526	Enzo Doria	05/2016
5250	(5*10^89510+79)/3	89511	Robert Price	11/2017

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Probable Primes Top 10000

(255312 PRPs in the top)