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	(7*2^300406-1)/3	90432	Lelio R Paula	02/2014
5002	10^90430+3339	90431	Patrick De Geest	11/2018
5003	10^90430-63477	90430	Patrick De Geest	07/2019
5004	10^90414+229593	90415	Patrick De Geest	07/2019
5005	10^90414-1547	90414	Patrick De Geest	11/2018
5006	10^90404+47041	90405	Patrick De Geest	07/2019
5007	10^90404-6429	90404	Patrick De Geest	11/2018
5008	10^90401+2077	90402	Patrick De Geest	11/2018
5009	10^90401-368637	90401	Patrick De Geest	07/2019
5010	4*5^129332+3	90400	Lelio R Paula	10/2014
5011	10^90397+19783	90398	Patrick De Geest	07/2019
5012	10^90397-323	90397	Patrick De Geest	11/2018
5013	2^300249-16245	90384	Enzo Doria	04/2013
5014	(7*10^90371-313)/9	90371	Robert Price	11/2016
5015	10^90363+58677	90364	Patrick De Geest	07/2019
5016	10^90363-3557	90363	Patrick De Geest	11/2018
5017	10^90358+104641	90359	Patrick De Geest	07/2019
5020	2*6^116118+7	90358	Lelio R Paula	10/2014
5019	10^90358-4979	90358	Patrick De Geest	11/2018
5018	10^90357+112837	90358	Patrick De Geest	07/2019
5021	10^90357-189593	90357	Patrick De Geest	07/2019
5022	10^90356+53113	90357	Patrick De Geest	07/2019
5023	10^90356-7197	90356	Patrick De Geest	11/2018
5024	10^90353+603211	90354	Patrick De Geest	07/2019
5025	10^90353-1089	90353	Patrick De Geest	11/2018
5026	(24737*2^300101+1)/25	90343	Lelio R Paula	06/2014
5027	4*10^90334-21	90335	Robert Price	04/2016
5028	10^90322+137691	90323	Patrick De Geest	07/2019
5029	10^90322-9551	90322	Patrick De Geest	11/2018
5030	10^90316+9991	90317	Patrick De Geest	11/2018
5031	10^90316-45627	90316	Patrick De Geest	07/2019
5032	10^90315+32889	90316	Patrick De Geest	07/2019
5034	2^300019-110335	90315	Enzo Doria	05/2014
5033	10^90315-8561	90315	Patrick De Geest	11/2018
5035	FAB2(300001,5032)	90310	Robert Price	05/2019
5036	FAB2(300001,29405)	90310	Robert Price	05/2019
5037	2^299949-1005	90294	Lelio R Paula	11/2013
5038	10^90279+62457	90280	Patrick De Geest	07/2019
5039	10^90279-1551	90279	Patrick De Geest	09/2018
5040	2^299868-109613	90270	Enzo Doria	04/2014
5041	10^90259+359299	90260	Patrick De Geest	07/2019
5042	10^90259-9443	90259	Patrick De Geest	09/2018
5043	10^90252+102873	90253	Patrick De Geest	07/2019
5044	10^90252-8103	90252	Patrick De Geest	09/2018
5045	5*2^299799-3	90250	Lelio R Paula	08/2014
5046	13^81008-2	90239	Lelio R Paula	09/2013
5047	64^49957-63^49957	90232	Robert Price	07/2013
5048	10^90227+56281	90228	Patrick De Geest	06/2016
5051	2^299725+315	90227	Lelio R Paula	11/2013
5049	10^90227-1000000001	90227	Robert Price	05/2016
5050	10^90227-68763	90227	Patrick De Geest	06/2016
5052	5^129082+48	90225	Lelio R Paula	03/2016
5053	2^299699+195	90219	Lelio R Paula	10/2012
5054	(55*10^90211-1)/9	90212	Ray Chandler	02/2012
5055	10^90209+8971	90210	Patrick De Geest	09/2018
5056	10^90209-724797	90209	Patrick De Geest	07/2019
5057	10^90208+189531	90209	Patrick De Geest	07/2019
5058	10^90208-2247	90208	Patrick De Geest	09/2018
5059	116^43693-115	90203	Norbert Schneider	08/2018
5060	10^90202+3553	90203	Patrick De Geest	09/2018
5062	3^189053+280	90202	Lelio R Paula	04/2016
5061	10^90202-67793	90202	Patrick De Geest	07/2019
5063	2^299639-187	90201	Lelio R Paula	10/2012
5064	10^90199+254031	90200	Patrick De Geest	07/2019
5065	10^90199-2891	90199	Patrick De Geest	09/2018
5066	2^299631+183	90198	Lelio R Paula	10/2012
5067	10^90196+187539	90197	Patrick De Geest	07/2019
5068	10^90196-9683	90196	Patrick De Geest	09/2018
5069	10^90193+104973	90194	Patrick De Geest	07/2019
5070	10^90193-9809	90193	Patrick De Geest	09/2018
5071	(21*2^299611-1)/29	90192	Lelio R Paula	02/2014
5072	2^299567+113	90179	Lelio R Paula	10/2012
5073	2^299550+189	90174	Lelio R Paula	10/2012
5074	10^90170+376063	90171	Patrick De Geest	07/2019
5075	10^90170-6749	90170	Patrick De Geest	09/2018
5076	(2^299535+3)/29	90168	Lelio R Paula	01/2013
5077	10^90160+271947	90161	Patrick De Geest	07/2019
5078	10^90160-5613	90160	Patrick De Geest	09/2018
5079	(97*10^90155-1)/3	90157	Serge Batalov	12/2014
5080	3^188938+8680	90147	Lelio R Paula	04/2016
5081	10^90146+160209	90147	Patrick De Geest	07/2019
5082	10^90146-2027	90146	Patrick De Geest	09/2018
5083	6^115840-55	90142	Lelio R Paula	05/2016
5084	(5*10^90142-473)/9	90142	Robert Price	12/2017
5085	8*7^106659+5	90139	Lelio R Paula	10/2014
5086	2^299406-16653	90131	Enzo Doria	05/2013
5087	10^90128+288673	90129	Patrick De Geest	07/2019
5088	208049#+(216091#)/(208049#)	90128	Makoto Morimoto	04/2016
5089	10^90128-8387	90128	Patrick De Geest	09/2018
5090	(F(5)^128941-F(4)^128941)/F(3)	90126	Wayne Halsdorf	03/2012
5091	6^115819-53	90125	Lelio R Paula	05/2016
5092	10^90123+6313	90124	Patrick De Geest	09/2018
5094	6^115816-16853	90123	Enzo Doria	02/2013
5093	10^90123-22617	90123	Patrick De Geest	07/2019
5095	6^115813-23	90121	Lelio R Paula	05/2016
5096	(22*10^90110+161)/3	90111	Robert Price	02/2017
5098	(2^299330-509203)/69	90106	Lelio R Paula	01/2013
5097	10^90105+915759	90106	Patrick De Geest	07/2019
5100	10^90105-767	90105	Patrick De Geest	09/2018
5099	10^90104+48189	90105	Patrick De Geest	07/2019
5101	10^90104-7703	90104	Patrick De Geest	09/2018
5102	10^90103+9159	90104	Patrick De Geest	09/2018
5103	10^90103-208457	90103	Patrick De Geest	07/2019
5104	10^90102+73011	90103	Patrick De Geest	07/2019
5105	10^90102-602433	90102	Patrick De Geest	07/2019
5106	10^90101+1225537	90102	Patrick De Geest	07/2019
5107	10^90101-3207	90101	Patrick De Geest	09/2018
5108	(29*10^90096-17)/3	90097	Erik Branger	09/2014
5109	10^90089+143181	90090	Patrick De Geest	07/2019
5110	10^90089-3573	90089	Patrick De Geest	09/2018
5111	2^299247+1870529	90083	Enzo Doria	05/2016
5112	10^90079+1609	90080	Patrick De Geest	09/2018
5113	10^90079-230043	90079	Patrick De Geest	07/2019
5114	2^299229-2797783	90077	Enzo Doria	04/2016
5115	2^299220-16317	90075	Enzo Doria	04/2013
5116	11^86491-1350	90072	Enzo Doria	12/2012
5117	10^90071+52333	90072	Patrick De Geest	07/2019
5118	10^90071-1233	90071	Patrick De Geest	09/2018
5119	10^90069+158527	90070	Patrick De Geest	07/2019
5120	10^90069-7841	90069	Patrick De Geest	09/2018
5121	(31*10^90064-1)/3	90066	Robert Price	03/2017
5122	10^90060+149431	90061	Patrick De Geest	07/2019
5123	10^90060-839	90060	Patrick De Geest	09/2018
5124	10^90052+2361	90053	Patrick De Geest	09/2018
5125	10^90052-90929	90052	Patrick De Geest	07/2019
5126	10^90047+619	90048	Patrick De Geest	09/2018
5127	10^90047-151071	90047	Patrick De Geest	07/2019
5128	L(430949)/861899/1440387561539	90045	Serge Batalov	07/2017
5129	2^299112+73951	90042	Enzo Doria	04/2016
5130	8^99702+7^(99702-1)	90040	Robert Price	02/2016
5131	10^90038+157803	90039	Patrick De Geest	07/2019
5132	10^90038-9687	90038	Patrick De Geest	09/2018
5133	5*10^90033+3	90034	Dmitry Domanov	11/2010
5134	10^90030+225813	90031	Patrick De Geest	07/2019
5135	10^90030-1461	90030	Patrick De Geest	09/2018
5136	243^37738+37738^243	90029	Norbert Schneider	01/2015
5137	10^90025+70569	90026	Patrick De Geest	07/2019
5138	10^90025-8703	90025	Patrick De Geest	09/2018
5139	2^299048-113297	90023	Enzo Doria	07/2014
5140	10^90015+849	90016	Patrick De Geest	09/2018
5141	10^90015-228387	90015	Patrick De Geest	07/2019
5142	10^90010+6811	90011	Patrick De Geest	09/2018
5143	10^90010-183597	90010	Patrick De Geest	11/2018
5144	10^90009+58321	90010	Patrick De Geest	11/2018
5145	10^90008+847	90009	Patrick De Geest	09/2018
5146	10^90009-356013	90009	Patrick De Geest	11/2018
5148	3^188648+92	90008	Lelio R Paula	12/2015
5147	10^90008-706049	90008	Patrick De Geest	11/2018
5149	5*2^298991+7	90006	Lelio R Paula	08/2014
5150	(25*2^298997+1)/3267	90005	Lelio R Paula	01/2013
5151	10^90000+8869	90001	Patrick De Geest	12/2009
5153	10^89999+82939	90000	Dirk Augustin	04/2007
5152	10^90000-140343	90000	Patrick De Geest	12/2009
5154	10^89999-194891	89999	Patrick De Geest	11/2009
5155	19^70365-78	89980	Lelio R Paula	12/2015
5156	NaturalLogarithmOf2(89973)	89973	Eric W. Weisstein	10/2015
5157	2^298852-64875	89964	Lelio R Paula	11/2013
5158	18^71659+37	89952	Lelio R Paula	12/2015
5159	(2908*29^61501-3)/7	89942	Curtis Bright	05/2015
5160	17^73067+20	89906	Lelio R Paula	11/2015
5161	2^298637-99	89899	Lelio R Paula	10/2012
5162	9^94188+38^94188-24^94188-3*2^94188	89879	Mike Oakes	01/2011
5163	9*10^89858+19	89859	Robert Price	05/2016
5164	2^298501+1870067	89858	Enzo Doria	05/2016
5165	11^86280-98	89852	Lelio R Paula	11/2015
5166	2^298473-110059	89850	Enzo Doria	04/2014
5167	19^70263-32	89850	Lelio R Paula	12/2015
5168	(299*10^89836-17)/3	89838	Robert Price	01/2017
5169	3^188286+14	89836	Robert Price	09/2013
5170	gcd(V(1091095),5F(218219)(F(218219)+1)+1)	89822	Serge Batalov	04/2015
5171	2^298367+58905	89818	Lelio R Paula	11/2013
5172	2^298319-109657	89803	Enzo Doria	04/2014
5173	8*10^89800+81	89801	Robert Price	05/2017
5174	18^71505-91	89759	Lelio R Paula	12/2015
5175	(7^106187+1)/8	89738	Paul Bourdelais	04/2008
5176	2^298079-109531	89731	Enzo Doria	04/2014
5177	117^43380+116	89718	Norbert Schneider	08/2018
5178	(22699*2^298016+1)/385	89714	Lelio R Paula	06/2014
5179	156(10^(422427)-1)/101-1	89709	Robert Price	05/2014
5180	2^298003-66945	89708	Lelio R Paula	11/2013
5181	(23*10^89705-83)/3	89706	Robert Price	09/2017
5182	17^72900-54	89700	Lelio R Paula	11/2015
5183	3*2^297956+5	89695	Lelio R Paula	08/2014
5184	20^68938-11	89691	Lelio R Paula	01/2016
5185	89*10^89687-7	89689	Robert Price	03/2017
5186	(297847^16384+1)/2	89686	Richard Fischer	08/2019
5187	2^297923+77783	89684	Enzo Doria	05/2016
5188	11^86107-24576000	89672	Enzo Doria	02/2013
5189	2^297878-111911	89671	Enzo Doria	05/2014
5190	7^106084+40	89652	Lelio R Paula	10/2015
5191	(86*10^89640-311)/9	89641	Robert Price	10/2017
5192	3*10^89608-59	89609	Robert Price	10/2017
5193	3^187780-11038	89594	Enzo Doria	05/2014
5194	(13*2^297560-1)/49151787	89568	Lelio R Paula	02/2014
5195	5^128141-36	89567	Lelio R Paula	10/2015
5196	4*7^105951+9	89540	Lelio R Paula	10/2014
5197	(7*10^89539-439)/9	89539	Robert Price	09/2017
5198	2^297397+177257	89526	Enzo Doria	05/2016
5200	2^297346-16241	89511	Enzo Doria	04/2013
5199	(5*10^89510+79)/3	89511	Robert Price	11/2017
5201	4^148663-3^148663	89505	Jean-Louis Charton	11/2005
5202	2^297328-869688105	89505	Lelio R Paula	07/2016
5203	2^297325-459043	89504	Enzo Doria	05/2015
5204	2^297310-112391	89500	Enzo Doria	06/2014
5205	2^297296-112157	89496	Enzo Doria	06/2014
5206	57^50966-2	89490	Lelio R Paula	08/2013
5207	(266*10^89482+1)/3	89484	Robert Price	02/2016
5208	(14*10^89480-101)/3	89481	Robert Price	04/2017
5209	2^297122+99	89443	Lelio R Paula	10/2012
5210	(3^187435-5)/1286	89427	Lelio R Paula	01/2013
5211	(25*10^89413+161)/3	89414	Robert Price	01/2017
5212	2^296990+1870699	89403	Enzo Doria	05/2016
5213	2^296972-1017	89398	Lelio R Paula	11/2013
5214	(7*10^89383+167)/3	89384	Robert Kinser	10/2017
5215	(85*10^89375-31)/9	89376	Robert Price	11/2015
5216	9*2^296870+7	89368	Lelio R Paula	08/2014
5217	100^44683-99^44683	89366	Robert Price	07/2013
5218	2^296810+76519	89349	Enzo Doria	05/2016
5219	8^98928+7^(98928+1)	89341	Robert Price	06/2016
5220	(3^187247+4)/1027	89337	Lelio R Paula	01/2013
5221	(3^187235-2)/2045	89331	Lelio R Paula	01/2013
5222	2^296736-432149	89327	Paul Bourdelais	05/2013
5223	2^296737-112519	89327	Enzo Doria	06/2014
5224	2^296718-3645	89322	Lelio R Paula	11/2013
5225	2^296681-16221	89310	Enzo Doria	04/2013
5226	2^296669-16513	89307	Enzo Doria	04/2013
5227	2^296619-16357	89292	Enzo Doria	04/2013
5228	2^296614-110051	89290	Enzo Doria	04/2014
5229	(3^187138+8)/83147	89283	Lelio R Paula	01/2013
5230	(2*10^89279+457)/9	89279	Robert Price	01/2017
5231	15^75907-28	89274	Lelio R Paula	11/2015
5232	2^296547-37	89270	Yves Minet	01/2012
5233	2^296485+191	89251	Lelio R Paula	10/2012
5234	2^296467-75	89246	Lelio R Paula	10/2012
5235	2^296416-109535	89231	Enzo Doria	04/2014
5236	(23*2^296406+1)/3	89228	Lelio R Paula	01/2013
5237	66^49037-65	89225	Norbert Schneider	11/2014
5238	2^296377-16245	89219	Enzo Doria	04/2013
5239	2^296372-64875	89217	Lelio R Paula	11/2013
5240	5*6^114648-7	89215	Lelio R Paula	10/2014
5241	3*10^89206+13	89207	Robert Price	08/2017
5242	7*3^186960-4	89204	Lelio R Paula	08/2014
5243	2^296290-112133	89193	Enzo Doria	06/2014
5244	6^114620-17003	89192	Enzo Doria	02/2013
5245	(4*10^89189+41)/9	89189	Robert Price	11/2014
5246	2^296261-161181	89184	Enzo Doria	04/2013
5247	(19*2^296269-1)/530623	89182	Lelio R Paula	02/2014
5248	3^186903-10	89176	Robert Price	09/2013
5249	7*10^89169-3	89170	Dmitry Domanov	11/2010
5250	(2^296221-1017)/35	89170	Lelio R Paula	01/2013

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Probable Primes Top 10000

(255169 PRPs in the top)