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	(41*10^97085+373)/9	97086	Robert Price	04/2017
5002	2^322413+77	97056	Lelio R Paula	12/2012
5003	2^322406+177	97054	Lelio R Paula	12/2012
5004	(14*10^97044+31)/9	97045	Robert Price	02/2015
5005	2^322302+255255	97023	Lelio R Paula	07/2016
5006	2^322196-113093	96991	Enzo Doria	07/2014
5007	(2^322169+2690)/2	96983	Stefano Morozzi	09/2020
5008	23109^15668+15668^23109	96943	Hans Havermann	07/2020
5009	2^322000-1861469	96932	Enzo Doria	03/2016
5010	2^321971-112747	96923	Enzo Doria	06/2014
5011	23754^12023+12023^23754	96917	Hans Havermann	07/2020
5012	11^93062-92	96915	Lelio R Paula	06/2016
5013	(2^321922+2214)/2	96908	Stefano Morozzi	09/2020
5014	(2^321900+2086)/2	96902	Stefano Morozzi	09/2020
5015	(11*2^321841-7)/15	96884	Renaud Lifchitz	03/2011
5016	3^203051+34	96880	Lelio R Paula	05/2016
5017	2*10^96867-51	96868	Robert Price	11/2017
5018	(2^321779+2618)/2	96865	Stefano Morozzi	09/2020
5019	(64*10^96863-1)/27	96864	Serge Batalov	05/2010
5020	2^321716-2786939	96847	Enzo Doria	03/2016
5021	22496^20181+20181^22496	96844	Hans Havermann	03/2020
5022	2^321701-113053	96842	Enzo Doria	07/2014
5023	2^321700-28635	96842	Lelio R Paula	06/2016
5024	(5*2^321691-1)/27	96838	Lelio R Paula	02/2014
5025	6^124433-124433	96828	Robert Price	01/2014
5026	2^321631+69	96821	Lelio R Paula	12/2012
5027	(13*2^321606+1)/119	96813	Lelio R Paula	11/2013
5028	(46*10^96798-1)/9	96799	Serge Batalov	10/2014
5029	(59*10^96798+31)/9	96799	Robert Price	09/2015
5030	(2^321536+2062)/2	96792	Stefano Morozzi	09/2020
5031	223319#+231223	96790	Makoto Morimoto	02/2016
5032	2^321519-28635	96787	Lelio R Paula	06/2016
5033	2^321487-1867237	96778	Enzo Doria	03/2016
5034	2^321461-63	96770	Lelio R Paula	12/2012
5035	2^321439+123	96763	Lelio R Paula	12/2012
5036	2^321434+709	96762	Lelio R Paula	02/2013
5037	(2^321415+554)/2	96756	Stefano Morozzi	09/2020
5038	14^84413+89	96749	Lelio R Paula	07/2016
5039	(28*10^96743+71)/9	96744	Serge Batalov	12/2008
5040	13^86847+96	96743	Lelio R Paula	06/2016
5041	9*2^321336-7	96733	Lelio R Paula	08/2014
5042	(209*10^96722-17)/3	96724	Robert Price	05/2017
5043	2^321237-4615	96702	Yves Minet	05/2019
5044	2^321187-1159	96687	Yves Minet	11/2012
5045	2^321182-1850081	96686	Enzo Doria	08/2015
5046	23359^13768+13768^23359	96680	Hans Havermann	06/2020
5047	2^321116-112829	96666	Enzo Doria	06/2014
5048	2^321108-109499	96664	Enzo Doria	04/2014
5050	2^321098+2793859	96661	Enzo Doria	03/2016
5049	(2^321100+1170)/2	96661	Stefano Morozzi	09/2020
5051	2^321057+4097	96648	Lelio R Paula	06/2016
5053	(4435*29^66081-4)/7	96640	Curtis Bright	05/2015
5052	22743^17750+17750^22743	96640	Hans Havermann	04/2020
5054	22882^16679+16679^22882	96612	Hans Havermann	02/2020
5055	23452^13163+13163^23452	96608	Hans Havermann	02/2020
5056	(2^320863+666)/2	96590	Stefano Morozzi	09/2020
5057	p(19849)#/2-64	96581	Robert Price	04/2017
5059	2^320817+189	96576	Lelio R Paula	12/2012
5058	2^320816-4685	96576	Yves Minet	05/2019
5060	(361*10^96567-163)/9	96569	Robert Price	10/2017
5061	2^320788-110327	96567	Enzo Doria	05/2014
5062	2^320764+793	96560	Lelio R Paula	02/2013
5063	(9179*2^320652-1)/221	96528	Lelio R Paula	05/2015
5064	23288^13947+13947^23288	96517	Hans Havermann	07/2020
5065	2^320616-78795	96516	Lelio R Paula	03/2016
5066	2^320612-461939	96514	Enzo Doria	07/2015
5067	10^96504+987654321	96505	Robert Price	12/2019
5068	10^96504+71887	96505	Patrick De Geest	02/2020
5069	22654^18195+18195^22654	96505	Hans Havermann	07/2020
5070	10^96504-139277	96504	Patrick De Geest	02/2020
5071	5*2^320431+7	96461	Lelio R Paula	08/2014
5072	19^75431-90	96458	Lelio R Paula	06/2016
5073	(2^320370+3)/67	96440	Lelio R Paula	10/2013
5074	2^320309+1871477	96423	Enzo Doria	05/2016
5075	tau(809^6028)	96410	Nik Lygeros / Olivier Rozier / LR team	10/2013
5076	(21*2^320252-1)/1895	96404	Lelio R Paula	02/2014
5077	2^320232-173	96400	Lelio R Paula	12/2012
5078	175^42975-2	96395	Lelio R Paula	10/2017
5079	(2^320170+2718)/2	96381	Stefano Morozzi	09/2020
5080	10^96377+199911	96378	Patrick De Geest	12/2016
5081	10^96377-20001	96377	Robert Price	11/2016
5082	2^320124-2790449	96367	Enzo Doria	03/2016
5083	22488^19255+19255^22488	96351	Hans Havermann	11/2019
5084	23248^13939+13939^23248	96346	Hans Havermann	11/2019
5086	2^320043-108775	96343	Enzo Doria	04/2014
5085	24989^7168+7168^24989	96343	Hans Havermann	11/2019
5087	10^96338+424939	96339	Patrick De Geest	03/2016
5088	10^96338-9281	96338	Robert Price	09/2015
5089	(3*2^320008+1)/7	96332	Lelio R Paula	09/2013
5090	25699^5596+5596^25699	96317	Hans Havermann	07/2020
5091	26502^4297+4297^26502	96287	Hans Havermann	07/2020
5092	2^319838+4257	96281	Lelio R Paula	03/2016
5093	2^319830-16995	96279	Lelio R Paula	03/2016
5094	6^123713+143	96268	Lelio R Paula	05/2016
5095	(28*10^96265-97)/3	96266	Robert Price	07/2016
5096	103^47825-102	96264	Norbert Schneider	10/2016
5097	(2^319777+2082)/2	96263	Stefano Morozzi	09/2020
5098	(2^319771+3686)/2	96261	Stefano Morozzi	09/2020
5099	2^319713-81	96244	Lelio R Paula	11/2012
5100	(55459*2^319706+1)/20167	96242	Lelio R Paula	07/2014
5101	22834^16393+16393^22834	96238	Hans Havermann	05/2020
5102	12^89153-43	96213	Lelio R Paula	06/2016
5104	(2*10^96195-59)/3	96195	Robert Price	05/2017
5103	9*10^96194-77	96195	Robert Price	08/2020
5105	2^319545+147	96193	Lelio R Paula	11/2012
5106	23357^13128+13128^23357	96189	Hans Havermann	02/2020
5107	25952^5073+5073^25952	96160	Hans Havermann	12/2019
5108	(50^56597+1)/51	96155	Robert Price	03/2014
5109	22313^20374+20374^22313	96149	Hans Havermann	12/2019
5110	22279^20668+20668^22279	96141	Hans Havermann	11/2019
5111	(41*10^96137-59)/9	96138	Robert Price	10/2017
5112	2^319353-110343	96135	Enzo Doria	05/2014
5113	11^92309-42	96130	Lelio R Paula	05/2016
5114	14^83869-13^83869	96125	Jean-Louis Charton	01/2009
5115	(7*10^96112+143)/3	96113	Robert Price	04/2016
5116	26731^3940+3940^26731	96112	Hans Havermann	07/2020
5117	22640^17583+17583^22640	96109	Hans Havermann	07/2020
5118	2^319237+65835	96100	Lelio R Paula	03/2016
5119	2^319194-1841	96087	Yves Minet	03/2013
5120	23949^10280+10280^23949	96084	Hans Havermann	07/2020
5121	20^73847-31	96078	Lelio R Paula	05/2016
5122	50^56543-49	96065	Norbert Schneider	09/2018
5123	2^319107-109555	96061	Enzo Doria	04/2014
5124	(3*2^319114-1)/2627	96060	Lelio R Paula	02/2014
5125	2^319098-112157	96059	Enzo Doria	06/2014
5126	15^81673+94	96055	Lelio R Paula	07/2016
5127	2^319074+1871749	96051	Enzo Doria	05/2016
5128	25670^5517+5517^25670	96050	Hans Havermann	06/2020
5129	2^319007-112111	96031	Enzo Doria	06/2014
5130	2^318946-1421	96013	Yves Minet	01/2013
5131	22830^16003+16003^22830	95982	Hans Havermann	02/2020
5132	2^318834-110411	95979	Enzo Doria	05/2014
5133	2^318831-1965	95978	Lelio R Paula	03/2016
5134	(5*10^95976+7)/3	95977	Erik Branger	03/2014
5135	22871^15696+15696^22871	95962	Hans Havermann	01/2020
5136	23167^13860+13860^23167	95953	Hans Havermann	01/2020
5137	5*3^201089-8	95945	Lelio R Paula	08/2014
5138	2^318711-139	95942	Lelio R Paula	11/2012
5139	2^318635-1167	95919	Lelio R Paula	03/2016
5140	15^81555+16	95917	Lelio R Paula	07/2016
5141	(37*10^95895+377)/9	95896	Robert Price	10/2017
5142	(22699*2^318527+1)/21	95890	Lelio R Paula	07/2014
5143	2^318496-97305	95877	Lelio R Paula	03/2016
5144	22129^21496+21496^22129	95871	Hans Havermann	07/2020
5146	2^318466+15015	95868	Lelio R Paula	03/2016
5145	24847^7216+7216^24847	95868	Hans Havermann	07/2020
5147	23706^11065+11065^23706	95866	Hans Havermann	07/2020
5148	6^123187-173129	95859	Mike Oakes	04/2011
5149	2^318423-487	95855	Yves Minet	03/2012
5150	(2^318359+678)/2	95836	Stefano Morozzi	09/2020
5151	(10223*2^318350+1)/1563	95834	Lelio R Paula	07/2014
5152	(2^318267+2550)/2	95808	Stefano Morozzi	09/2020
5153	45369!2+1024	95787	Robert Price	02/2015
5154	3^200758-86	95786	Lelio R Paula	05/2016
5155	(2^318271+1)/(346031404238891654090604244843)	95781	Gord Palameta	12/2018
5156	(2^318171+2030)/2	95779	Stefano Morozzi	09/2020
5157	3*10^95776-59	95777	Robert Price	10/2017
5158	193^41901-2	95768	Lelio R Paula	10/2017
5159	(2^318124+2502)/2	95765	Stefano Morozzi	09/2020
5160	4*10^95752-71	95753	Robert Price	11/2017
5161	23640^11197+11197^23640	95721	Hans Havermann	12/2019
5162	((10^47850-1)10000/9+6421)10^47850+(10^47850-1)/9	95704	Hans Havermann	05/2019
5163	(509203*2^317881-1)/52805	95693	Lelio R Paula	04/2015
5164	(2^317853+1086)/2	95683	Stefano Morozzi	09/2020
5165	4*10^95672+91	95673	Robert Price	11/2017
5166	6*10^95665+43	95666	Robert Price	07/2020
5167	(11*10^95641-113)/3	95642	Robert Price	01/2017
5168	(13*10^95588+11)/3	95589	Robert Price	05/2015
5169	Phi(191188,10)/191189	95587	Maksym Voznyy	11/2015
5170	3^200325+70	95580	Lelio R Paula	05/2016
5171	(25*10^95574-7)/9	95575	Robert Price	12/2014
5172	(2^317485-3)/21313	95569	Lelio R Paula	06/2013
5173	2^317464+31	95567	Lelio R Paula	11/2012
5174	(2^317451+2114)/2	95562	Stefano Morozzi	09/2020
5175	7^113073+82	95558	Lelio R Paula	04/2016
5176	2^317251+465	95503	Lelio R Paula	03/2016
5177	19^74684+58	95503	Lelio R Paula	06/2016
5178	(2^317250-7)/339	95500	Lelio R Paula	07/2013
5179	6^122718-79	95494	Lelio R Paula	05/2016
5180	22168^20291+20291^22168	95485	Hans Havermann	10/2019
5181	2^317141-110491	95469	Enzo Doria	05/2014
5182	(2^317097+3014)/2	95456	Stefano Morozzi	09/2020
5183	2^317094+76309	95455	Enzo Doria	05/2016
5184	2^317085+95	95453	Lelio R Paula	11/2012
5185	(17*10^95451-377)/9	95452	Robert Price	11/2017
5186	2^317057-109551	95444	Enzo Doria	04/2014
5187	3^200026+28	95437	Lelio R Paula	05/2016
5188	2^317024+93	95434	Donovan Johnson	06/2008
5189	2^316999+1605	95427	Lelio R Paula	03/2016
5190	(2^317000+3210)/2	95427	Stefano Morozzi	09/2020
5191	2^316995-110427	95426	Enzo Doria	05/2014
5192	22300^18987+18987^22300	95410	Hans Havermann	06/2020
5194	2^316937+177	95408	Lelio R Paula	11/2012
5193	4*10^95407+91	95408	Robert Price	11/2017
5195	2^316908+1915	95399	Lelio R Paula	03/2016
5196	2^316894+99	95395	Lelio R Paula	11/2012
5197	(2^316887+2546)/2	95393	Stefano Morozzi	09/2020
5198	2*10^95374-21	95375	Robert Price	09/2020
5199	6^122547+11	95361	Lelio R Paula	05/2016
5200	2^316771+82875	95358	Lelio R Paula	03/2016
5201	(2^316765+3102)/2	95356	Stefano Morozzi	09/2020
5202	(23*10^95326+1)/3	95327	Serge Batalov	05/2009
5203	1*10^95326+57	95327	Robert Price	03/2011
5204	10^95326-393687	95326	Patrick De Geest	09/2013
5205	(3^199803+4)/479539	95325	Lelio R Paula	04/2013
5206	2^316654-109481	95323	Enzo Doria	04/2014
5207	8*10^95316+51	95317	Robert Price	05/2017
5208	(50^56099+43^56099)/93	95309	Serge Batalov	12/2016
5209	(23*2^316559+1)/3925	95292	Lelio R Paula	09/2013
5211	(71*10^95277-539)/9	95278	Robert Price	11/2017
5210	23422^11691+11691^23422	95278	Hans Havermann	10/2019
5212	19^74503-56	95271	Lelio R Paula	06/2016
5213	11^91475-4380	95262	Enzo Doria	01/2013
5214	(62*10^95251-611)/9	95252	Robert Price	05/2017
5215	(2^316321-509203)/69377	95218	Lelio R Paula	06/2013
5216	26541^3868+3868^26541	95216	Hans Havermann	07/2020
5217	(79*10^95214-43)/9	95215	Erik Branger	11/2013
5218	(9*2^316233-1)/1751	95194	Lelio R Paula	02/2014
5219	5*2^316213+9	95191	Lelio R Paula	08/2014
5220	2*10^95188-91	95189	Robert Price	04/2020
5221	2^316205-1848163	95188	Enzo Doria	07/2015
5222	2^316185-2787913	95182	Enzo Doria	04/2016
5223	(2^316174+3538)/2	95178	Stefano Morozzi	09/2020
5224	(9787*2^316142-1)/3	95172	Lelio R Paula	04/2015
5225	2^316140-5	95168	Henri Lifchitz	02/2006
5226	(15185*2^316117-1)/3	95165	Lelio R Paula	04/2015
5227	(34*10^95153-7)/9/19/19157	95149	Makoto Morimoto	05/2016
5228	2^316069+76817	95147	Enzo Doria	05/2016
5229	(199*10^95134-7)/3	95136	Robert Price	02/2017
5230	2^316027-97305	95134	Lelio R Paula	03/2016
5231	2^316006-2798051	95128	Enzo Doria	04/2016
5232	24994^6397+6397^24994	95127	Hans Havermann	02/2020
5233	2^315921-2797603	95102	Enzo Doria	04/2016
5234	2*10^95095+63	95096	Robert Price	10/2017
5235	2^315857+1299	95083	Lelio R Paula	03/2016
5236	(2^315858+2598)/2	95083	Stefano Morozzi	09/2020
5237	14^82955-43	95078	Lelio R Paula	06/2016
5238	(2*10^95072-17)/3	95072	Robert Price	08/2014
5239	(2^315779+1610)/2	95059	Stefano Morozzi	09/2020
5240	21938^21513+21513^21938	95051	Hans Havermann	09/2020
5241	2^315727+65	95044	Lelio R Paula	11/2012
5242	2^315725+1885757	95043	Enzo Doria	03/2017
5243	23277^12058+12058^23277	95000	Hans Havermann	09/2020
5244	1*10^94983+21	94984	Robert Price	03/2011
5245	10^94983-717	94983	Patrick De Geest	08/2013
5246	17^77187-82	94975	Lelio R Paula	07/2016
5247	3*10^94964+37	94965	Robert Price	10/2017
5248	(2^315481-1017)/20627285	94962	Lelio R Paula	06/2013
5249	2^315423-110329	94952	Enzo Doria	05/2014
5250	11^91169-7230	94943	Enzo Doria	02/2013

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Probable Primes Top 10000

(271023 PRPs in the top)