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 ?
5251	(10^86453-1)/9	86453	Lew Baxter	10/2000
5252	87^44563-86^44563	86431	Robert Price	05/2015
5253	6^111057+61	86420	Lelio R Paula	12/2015
5254	2^287057-109909	86413	Enzo Doria	04/2014
5255	5^123608+22	86399	Lelio R Paula	10/2015
5256	(31*10^86364-121)/9	86365	Robert Price	06/2016
5257	2^286859+71663	86354	Enzo Doria	04/2016
5258	2^286740+29835	86318	Lelio R Paula	10/2013
5259	2*10^86310+9^86310	86311	Mike Oakes	05/2011
5260	11^82878-1860	86309	Enzo Doria	12/2012
5261	2^286547+16095	86260	Lelio R Paula	10/2013
5262	(58*10^86242+329)/9	86243	Robert Price	11/2017
5263	2^286455-110427	86232	Enzo Doria	05/2014
5264	(37*10^86230+53)/9	86231	Robert Price	05/2015
5265	8*3^180700+5	86217	Lelio R Paula	08/2014
5266	3^180697-40	86215	Lelio R Paula	12/2015
5267	(13*2^286318-1)/13257	86188	Lelio R Paula	02/2014
5268	2^286165+77	86145	Lelio R Paula	08/2012
5269	9*2^286140+7	86138	Lelio R Paula	08/2014
5270	(29*2^286108-1)/2002367	86123	Lelio R Paula	02/2014
5271	10^86110+161113	86111	Patrick De Geest	07/2013
5272	10^86110-69	86110	Robert Price	05/2011
5273	2^286036-869688105	86106	Lelio R Paula	07/2016
5274	(77*10^86072+31)/9	86073	Robert Price	10/2015
5275	2^285923+345	86072	Lelio R Paula	09/2013
5276	13^77266-90	86070	Lelio R Paula	11/2015
5277	2^285910-458903	86068	Enzo Doria	04/2015
5278	2^285904-125	86066	Lelio R Paula	08/2012
5279	2^285836+65835	86046	Lelio R Paula	09/2013
5280	(2^285766+78557)/3	86024	Lelio R Paula	01/2013
5281	(5*10^86011-107)/3	86012	Robert Price	01/2017
5282	6^110522+163	86003	Lelio R Paula	12/2015
5283	41^53323-40^53323	85999	Robert Price	07/2012
5284	2^285678-109617	85998	Enzo Doria	04/2014
5285	6^110506-16673	85991	Enzo Doria	02/2013
5287	2^285569-741	85965	Lelio R Paula	09/2013
5286	(32*10^85964+31)/9	85965	Robert Price	05/2015
5288	133^40466+132	85944	Norbert Schneider	02/2019
5289	6*10^85910-7	85911	Dmitry Domanov	11/2010
5290	(412*10^85897-7)/9	85899	Robert Price	10/2017
5291	4*10^85881+63	85882	Robert Price	06/2016
5292	(10^85864+53)/9	85864	Robert Price	01/2015
5293	2^285230+345	85863	Lelio R Paula	09/2013
5294	(5*10^85855-473)/9	85855	Robert Price	12/2017
5295	2^285199+75683	85854	Enzo Doria	04/2016
5296	(76*10^85847-211)/9	85848	Robert Price	10/2017
5297	p(17832)#/2+512	85845	Robert Price	05/2017
5298	(16*10^85839+167)/3	85840	Robert Price	10/2017
5299	11^82426-1230	85838	Enzo Doria	11/2012
5300	2^285113-109881	85828	Enzo Doria	04/2014
5301	5^122746-92	85796	Lelio R Paula	10/2015
5302	2^285001-113461	85794	Enzo Doria	08/2014
5303	(11*10^85782-131)/3	85783	Robert Price	02/2017
5304	2^284913-110491	85768	Enzo Doria	05/2014
5305	6^110220+47	85768	Lelio R Paula	12/2015
5306	3*6^110202-5	85755	Lelio R Paula	10/2014
5307	(157^39047-1)/156	85742	Alexander Zhirkov	06/2016
5308	(3^179705+7)/250	85739	Lelio R Paula	12/2012
5309	2^284734-6555	85714	Lelio R Paula	09/2013
5310	(10^85712+53)/9	85712	Robert Price	01/2015
5311	3*10^85703+11	85704	Robert Price	11/2017
5312	(6883*2^284668-1)/3	85697	Lelio R Paula	04/2015
5313	20^65855+83	85680	Lelio R Paula	01/2016
5314	6^110105+53	85679	Lelio R Paula	12/2015
5315	(10^85666-97)/3	85666	Robert Kinser	10/2017
5317	2^284567-7605	85664	Lelio R Paula	09/2013
5316	9*5^122555-2	85664	Lelio R Paula	10/2014
5318	5^122554-14	85662	Lelio R Paula	10/2015
5319	9*5^122543+4	85655	Lelio R Paula	10/2014
5320	3^179489-2^(179489-1)	85639	Robert Price	01/2016
5321	2^284429+177	85622	Lelio R Paula	08/2012
5322	2*3^179452+5	85621	Lelio R Paula	07/2014
5323	(19^66919+3^66919)/22	85572	Robert Price	07/2013
5324	66^47023-65	85561	Norbert Schneider	11/2014
5325	6^109943+13	85553	Lelio R Paula	12/2015
5326	2^284183-4747	85548	Yves Minet	05/2019
5327	(2^284167-509203)/34564775	85536	Lelio R Paula	01/2013
5328	2^284133-3	85533	M. Frind & P. Underwood	07/2002
5329	2^284113+315	85527	Lelio R Paula	09/2013
5330	(28*10^85500+149)/3	85501	Robert Price	10/2017
5331	(16*10^85495-19)/3	85496	Robert Price	03/2016
5332	2^284004+177	85494	Lelio R Paula	08/2012
5333	(16*10^85473-91)/3	85474	Robert Price	06/2016
5334	3^179120+22	85462	Robert Price	12/2013
5335	2^283872-2792249	85454	Enzo Doria	03/2016
5336	(29*10^85438+259)/9	85439	Robert Price	04/2017
5337	2^283817+82875	85438	Lelio R Paula	09/2013
5338	(2^283815-5)/201	85435	Lelio R Paula	01/2013
5339	2^283796-125	85432	Lelio R Paula	08/2012
5340	(29*2^283784-1)/13	85428	Lelio R Paula	02/2014
5341	15^72592-28	85375	Lelio R Paula	11/2015
5342	2^283604-58695	85374	Lelio R Paula	09/2013
5343	(44*10^85370-503)/9	85371	Robert Price	10/2017
5344	496^31671+31671^496	85369	Norbert Schneider	07/2017
5345	(15*2^283583-1)/103051	85364	Lelio R Paula	02/2014
5346	15^72572+92	85352	Lelio R Paula	11/2015
5347	2^283473-1615	85334	Lelio R Paula	09/2013
5348	2^283466-15	85332	Lelio R Paula	08/2012
5349	11^81916-7020	85307	Enzo Doria	02/2013
5350	6^109626-7	85306	Lelio R Paula	11/2014
5351	2^283374-110327	85305	Enzo Doria	05/2014
5352	33*10^85297+7	85299	Robert Price	07/2016
5353	18^67933+41	85275	Lelio R Paula	11/2015
5354	2^283271-109341	85274	Enzo Doria	04/2014
5355	(25*10^85249-73)/3	85250	Robert Price	09/2016
5356	2*5^121959+3	85246	Lelio R Paula	10/2014
5357	19834^19834+8947	85235	Henri Lifchitz	11/2004
5358	2^283140+1915	85234	Lelio R Paula	09/2013
5359	3*10^85227-97	85228	Robert Price	08/2017
5360	(16*10^85221-31)/3	85222	Robert Price	03/2016
5361	2^283083+1869383	85217	Enzo Doria	05/2016
5362	(24737*2^283051+1)/17	85211	Lelio R Paula	06/2014
5363	(2^283032+78557)/3	85201	Lelio R Paula	01/2013
5364	2^283026-109893	85200	Enzo Doria	04/2014
5365	(2^283012+78557)/129	85193	Lelio R Paula	01/2013
5366	(10^(242589+1)+7210^42589-1)/9	85179	Robert Price	09/2017
5367	2^282860-109727	85150	Enzo Doria	04/2014
5368	2^282819+1869413	85138	Enzo Doria	05/2016
5369	3^178428+2	85132	Ray Chandler	07/2011
5370	(22699*2^282742+1)/73	85117	Lelio R Paula	06/2014
5371	(16^70687+5^70687)/21	85115	Robert Price	07/2013
5372	(3^178352-2)/7	85095	Lelio R Paula	12/2012
5373	11^81699-2790	85081	Enzo Doria	12/2012
5374	2^282612-95	85075	Lelio R Paula	08/2012
5375	2^282609-4069	85074	Yves Minet	02/2018
5376	75^45366-2	85065	Lelio R Paula	08/2013
5377	2^282511+69	85045	Lelio R Paula	08/2012
5378	69^46249+2	85045	Lelio R Paula	06/2013
5379	3^178226+10	85036	Robert Price	10/2013
5380	(182*10^85017+43)/9	85019	Robert Price	11/2017
5381	(14*10^85010+73)/3	85011	Robert Price	04/2016
5382	9*2^282338-7	84994	Lelio R Paula	08/2014
5383	(9913*2^282330-1)/1578003	84988	Lelio R Paula	04/2015
5384	2^282203+5	84952	Lelio R Paula	08/2012
5385	2^282184+13	84946	Lelio R Paula	08/2012
5386	11^81568-2400	84945	Enzo Doria	12/2012
5387	11^81562-2340	84939	Enzo Doria	12/2012
5388	(41*10^84927+31)/9	84928	Robert Price	05/2015
5389	(2*10^84904-17)/3	84904	Robert Price	08/2014
5390	(4^141017+23)/3	84901	Robert Price	02/2017
5391	6^109100-18653	84897	Enzo Doria	03/2013
5392	2^281973+1025	84883	Lelio R Paula	09/2013
5393	2^281951-109651	84876	Enzo Doria	04/2014
5394	11^81491-5430	84865	Enzo Doria	01/2013
5395	((1+sqrt(3)+sqrt(2))^79357-1)((1+sqrt(3)-sqrt(2))^79357-1)((1-sqrt(3)+sqrt(2))^79357-1)*((1-sqrt(3	84849	Mike Oakes	04/2009
5396	2^281825-1861483	84838	Enzo Doria	03/2016
5397	2^281809-97305	84833	Lelio R Paula	09/2013
5398	2^281780-114893	84825	Enzo Doria	05/2015
5399	3^177719+64	84794	Lelio R Paula	12/2015
5401	2^281675-199	84793	Lelio R Paula	08/2012
5400	2^281673-111223	84793	Enzo Doria	05/2014
5402	(4*10^84779+149)/9	84779	Robert Price	03/2017
5403	129^40167-128	84777	Norbert Schneider	01/2019
5404	(72*10^84772-27)/9	84773	Ray Chandler	01/2011
5405	11^81398-630	84768	Enzo Doria	11/2012
5406	(25*2^281577-1)/23	84764	Lelio R Paula	02/2014
5407	2^281500-455	84740	Yves Minet	03/2012
5408	10^84725+1145141919	84726	Marisa Kirisame	03/2015
5409	10^84725+142041	84726	Patrick De Geest	10/2015
5410	10^84725-138677	84725	Patrick De Geest	02/2016
5411	76^45044+75	84720	Norbert Schneider	02/2015
5412	54^48897-53	84709	Norbert Schneider	08/2014
5413	(9913*2^281377-1)/65	84706	Lelio R Paula	04/2015
5414	Phi(171124,10)/29946701/7761329021/58560344041	84700	Maksym Voznyy	11/2015
5415	2^281337-111223	84691	Enzo Doria	05/2014
5416	2^281308+54615	84683	Lelio R Paula	09/2013
5417	7*5^121144-6	84677	Lelio R Paula	10/2014
5418	(2^281252+47)/3	84665	Lelio R Paula	01/2013
5419	11^81297-3150	84663	Enzo Doria	12/2012
5420	2^281208-303	84653	Yves Minet	02/2012
5421	197^36892-2	84648	Lelio R Paula	10/2017
5422	(21*2^281187+1)/2483	84644	Lelio R Paula	01/2013
5423	11^81247-84	84611	Lelio R Paula	10/2015
5424	17^68747-64	84590	Lelio R Paula	11/2015
5425	5^121018-15596	84588	Enzo Doria	02/2013
5426	6^108702+7	84587	Lelio R Paula	11/2014
5427	10^84582+100677	84583	Patrick De Geest	05/2016
5428	10^84582-8001	84582	Robert Price	03/2016
5429	3*5^121004-8	84579	Lelio R Paula	10/2014
5430	5^120996-84	84573	Lelio R Paula	10/2015
5431	(10223*2^280881+1)/68419	84553	Lelio R Paula	06/2014
5432	2^280852+97681	84545	Yves Minet	08/2004
5433	2^280848-1203	84544	Lelio R Paula	09/2013
5434	5^120946-24	84538	Lelio R Paula	10/2015
5435	2^280810-2111	84533	Yves Minet	08/2013
5436	11^81161-5160	84521	Enzo Doria	01/2013
5437	2^280737-93	84511	Lelio R Paula	08/2012
5438	2^280698+315	84499	Lelio R Paula	09/2013
5439	3^177099-340	84498	Lelio R Paula	12/2015
5440	(5*10^84469-107)/3	84470	Robert Price	01/2017
5441	(3^177002+7)/6696022272161744	84436	Lelio R Paula	12/2012
5442	(2^280500-1017)/823	84436	Lelio R Paula	01/2013
5443	14^73660-5	84424	Lelio R Paula	11/2015
5444	(19*10^84409-61)/3	84410	Robert Price	04/2017
5445	2^280388+117	84406	Lelio R Paula	08/2012
5446	2^280389-566533	84406	Paul Bourdelais	03/2013
5447	(141584^16384+1)/65537	84390	Syoichiro Yamada	06/2008
5448	119^40652+118	84376	Norbert Schneider	09/2018
5449	2^280240-173	84361	Lelio R Paula	08/2012
5450	(184*10^84348-1)/3	84350	Robert Price	02/2017
5451	4*10^84346+93	84347	Robert Price	01/2017
5452	7*2^280156-5	84337	Lelio R Paula	08/2014
5453	8*7^99782-3	84327	Lelio R Paula	10/2014
5454	2^280116+133	84324	Lelio R Paula	08/2012
5455	2^280118+54615	84324	Lelio R Paula	09/2013
5456	(509203*2^280090-1)/3	84321	Lelio R Paula	04/2015
5457	6^108354+47	84316	Lelio R Paula	12/2015
5458	10^84305+141963	84306	Patrick De Geest	07/2013
5459	10^84305-57	84305	Robert Price	05/2011
5460	9^88339+38^88339-24^88339-3*2^88339	84297	Mike Oakes	01/2011
5461	3^176648-112804	84283	Enzo Doria	06/2014
5462	6^108310+115	84282	Lelio R Paula	12/2015
5463	(11*2^279968-1)/5	84280	Lelio R Paula	02/2014
5464	6^108288-16643	84265	Enzo Doria	02/2013
5465	2^279917-58695	84264	Lelio R Paula	08/2013
5466	65^46477+36	84259	Lelio R Paula	01/2016
5467	2^279866-1907	84249	Yves Minet	05/2013
5468	(3^176580-5)/28076	84246	Lelio R Paula	12/2012
5469	(p(17530)#+4)/2	84246	Robert Price	09/2017
5470	(2*10^84239+1)/3	84239	Serge Batalov	07/2009
5472	18^67103-41	84233	Lelio R Paula	11/2015
5471	20^64743-43	84233	Lelio R Paula	01/2016
5473	143^39070+39070^143	84209	Serge Batalov	05/2014
5474	11^80857-5400	84204	Enzo Doria	01/2013
5475	(13*10^84179+161)/3	84180	Robert Price	04/2017
5476	2^279634-110405	84179	Enzo Doria	05/2014
5477	(74*10^84170+313)/9	84171	Robert Price	11/2017
5478	2^279582-1017	84163	Lelio R Paula	08/2013
5479	(22*10^84159-19)/3	84160	Robert Price	02/2017
5480	p(17513)#/2+512	84156	Robert Price	05/2017
5481	(19*10^84144-43)/3	84145	Robert Price	10/2017
5482	(9*2^279507-1)/137	84139	Lelio R Paula	02/2014
5483	11^80792-810	84137	Enzo Doria	11/2012
5484	(97*10^84134-1)/3	84136	Serge Batalov	12/2014
5485	p(17507)#/2+32	84125	Robert Price	12/2016
5486	21485^8224+8224^21485	84116	Hans Havermann	04/2017
5487	3^176294-340	84114	Lelio R Paula	12/2015
5488	(3^176287+4)/2191	84107	Lelio R Paula	12/2012
5489	2^279388-719	84105	Yves Minet	05/2012
5490	(22699*2^279378+1)/221	84104	Lelio R Paula	06/2014
5491	2^279332-110447	84088	Enzo Doria	05/2014
5492	2^279320+7	84084	Lelio R Paula	06/2012
5493	127^39966-2	84081	Lelio R Paula	10/2017
5494	(11*2^279240-1)/95	84059	Lelio R Paula	02/2014
5495	2^279218-111347	84053	Enzo Doria	05/2014
5496	35^54435+2	84052	Lelio R Paula	05/2013
5497	(31*2^279191-1)/12511523	84040	Lelio R Paula	02/2014
5498	20996^10059+10059^20996	84038	Hans Havermann	05/2017
5499	97*10^84033-3	84035	Robert Price	01/2017
5500	21234^9067+9067^21234	84033	Hans Havermann	05/2017

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PRP Records

Probable Primes Top 10000

(252932 PRPs in the top)