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	2^294492-65	88651	Lelio R Paula	10/2012
5252	20^68120-53	88627	Lelio R Paula	01/2016
5253	122^42477-121	88623	Norbert Schneider	10/2018
5254	2^294391-113257	88621	Enzo Doria	07/2014
5255	5^126784-15476	88619	Enzo Doria	02/2013
5256	2^294327+9	88602	Lelio R Paula	10/2012
5257	2^294320+18915	88600	Lelio R Paula	10/2013
5258	(98*10^88595-89)/99	88595	Ray Chandler	07/2011
5259	(17*2^294262-1)/13	88582	Lelio R Paula	02/2014
5260	(2*10^88545+7)/9	88545	Erik Branger	03/2011
5261	2^294137-133	88545	Lelio R Paula	10/2012
5262	(2^294092-1017)/1171	88528	Lelio R Paula	01/2013
5263	4^147036+147036^4+1	88525	Robert Price	04/2014
5264	(14^77213-5^77213)/9	88496	Robert Price	04/2013
5265	2^293965+2793377	88493	Enzo Doria	03/2016
5266	11^84971-150	88489	Enzo Doria	08/2012
5267	48^52626-47	88478	Norbert Schneider	08/2018
5268	(2^293956-1017)/39851376696677	88476	Lelio R Paula	01/2013
5269	11^84958-2190	88475	Enzo Doria	12/2012
5270	2^293880-111347	88467	Enzo Doria	05/2014
5271	(106*10^88459-1)/3	88461	Serge Batalov	12/2014
5272	10^88457+278733	88458	Patrick De Geest	07/2017
5273	10^88457-401	88457	Robert Price	06/2017
5274	11^84908-1680	88423	Enzo Doria	12/2012
5275	2^293679-112075	88407	Enzo Doria	06/2014
5276	6^113608-65	88405	Lelio R Paula	12/2015
5277	2^293624+82875	88390	Lelio R Paula	10/2013
5278	2^293612-112337	88387	Enzo Doria	06/2014
5279	758^30693+30693^758	88386	Norbert Schneider	05/2017
5280	gcd(V(1062695),5F(212539)(F(212539)-1)+1)	88383	Serge Batalov	04/2015
5281	5*10^88377+77	88378	Robert Price	06/2016
5282	(5*2^293526+1)/303	88359	Lelio R Paula	01/2013
5283	2^293461-2785843	88341	Enzo Doria	03/2016
5284	2^293416-1037	88328	Yves Minet	11/2012
5285	(2^293384-7)/3	88317	Lelio R Paula	01/2013
5286	(3^185092-5)/4	88311	Lelio R Paula	01/2013
5287	(5*10^88303-173)/3	88304	Robert Price	11/2017
5288	14^77039-57	88297	Lelio R Paula	11/2015
5289	3*10^88293-59	88294	Robert Price	10/2017
5290	5^126303+42	88283	Lelio R Paula	10/2015
5292	19^69025-18	88266	Theodore Burton	01/2006
5291	140^41128+139	88266	Norbert Schneider	04/2019
5293	5*10^88261-3	88262	Dmitry Domanov	11/2010
5294	8^97731-7^(97731-1)	88260	Robert Price	04/2016
5295	5*10^88254+59	88255	Robert Price	09/2016
5296	4*3^184968-7	88253	Lelio R Paula	08/2014
5297	7^104426+88	88251	Lelio R Paula	10/2015
5298	2^293142+99	88245	Lelio R Paula	10/2012
5299	11^84736-2130	88244	Enzo Doria	12/2012
5300	(10^110315+1)/(10^22063+1)/5824812682167648578460281641	88225	Makoto Kamada	04/2019
5301	2^293068-89	88223	Lelio R Paula	10/2012
5302	2^293014-109655	88207	Enzo Doria	04/2014
5303	8*7^104371-3	88205	Lelio R Paula	10/2014
5304	2^292995-2145	88201	Lelio R Paula	10/2013
5305	5*10^88182+77	88183	Robert Price	06/2016
5307	2^292929+43877	88181	Donovan Johnson	04/2005
5306	6^113321+131	88181	Lelio R Paula	12/2015
5308	2^292904-583949	88173	Paul Bourdelais	04/2013
5309	2^292894-111851	88170	Enzo Doria	05/2014
5310	2^292872-2797349	88164	Enzo Doria	03/2016
5311	2^292860-109685	88160	Enzo Doria	04/2014
5312	9*6^113288-5	88157	Lelio R Paula	10/2014
5313	(2*10^88112-23)/3	88112	Robert Price	09/2017
5314	(73*10^88105+17)/9	88106	Robert Price	10/2015
5315	11^84588+78	88090	Lelio R Paula	11/2015
5316	(265*10^88077+11)/3	88079	Robert Price	03/2017
5317	91^44959-90^44959	88077	Robert Price	07/2015
5318	6^113177-5^113177	88069	Jean-Louis Charton	01/2009
5319	(10^88020+101)/3	88020	Robert Price	04/2016
5320	52^51285-51	88006	Norbert Schneider	09/2018
5321	(10^(243982+1)-610^43982-1)/3	87965	Robert Price	02/2016
5322	(424*10^87930-1)/9	87932	Robert Price	11/2017
5323	p(18225)#/2+128	87929	Robert Price	04/2017
5324	4*6^112977+7	87914	Lelio R Paula	10/2014
5325	14^76677+69	87882	Lelio R Paula	11/2015
5326	(22*10^87863-1)/3	87864	Robert Price	12/2014
5327	2^291822-2797811	87848	Enzo Doria	04/2016
5328	2^291716-111389	87816	Enzo Doria	05/2014
5329	(782*10^87809-71)/9	87811	Robert Price	06/2017
5330	3^184039+1820	87809	Lelio R Paula	12/2015
5331	12^81356+41	87798	Lelio R Paula	11/2015
5332	6^112792-18983	87770	Enzo Doria	03/2013
5333	3*6^112787-5	87766	Lelio R Paula	10/2014
5334	7^103848+82	87762	Lelio R Paula	10/2015
5335	(19*2^291534-1)/178696395	87754	Lelio R Paula	02/2014
5336	(3^183915+5)/128	87748	Lelio R Paula	01/2013
5337	19^68619+24	87747	Lelio R Paula	12/2015
5339	2^291480+1185	87745	Lelio R Paula	10/2013
5338	2^291482+1867369	87745	Enzo Doria	03/2016
5340	2^291467-937	87741	Yves Minet	05/2013
5341	(25*10^87726+161)/3	87727	Robert Price	01/2017
5342	11^84239-2850	87726	Enzo Doria	12/2012
5343	10^87720+215541	87721	Patrick De Geest	01/2011
5344	10^87720-3	87720	Markus Tervooren	07/2010
5345	(5*10^87712-473)/9	87712	Robert Price	12/2017
5346	(2^291357+5)/6847	87704	Lelio R Paula	01/2013
5347	93^44541-2	87679	Lelio R Paula	09/2013
5348	2^291261-109561	87679	Enzo Doria	04/2014
5349	(4*10^87669+149)/9	87669	Robert Price	03/2017
5350	2^291217+4257	87666	Lelio R Paula	10/2013
5351	2*12^81214-5^81214	87645	Mike Oakes	12/2010
5352	(5*10^87622-473)/9	87622	Robert Price	12/2017
5353	12^81188+85	87617	Lelio R Paula	11/2015
5354	(21*2^290980-1)/5	87595	Lelio R Paula	02/2014
5355	2^290958+127	87588	Lelio R Paula	09/2012
5356	2^290923-67	87577	Lelio R Paula	09/2012
5357	3*10^87573-97	87574	Robert Price	08/2017
5358	(13*10^87565+11)/3	87566	Robert Price	05/2015
5359	(2^290857-7)/55	87555	Lelio R Paula	01/2013
5360	2^290802+82875	87541	Lelio R Paula	10/2013
5361	(509203*2^290792-1)/7560987	87536	Lelio R Paula	04/2015
5362	3^183441+236	87524	Lelio R Paula	12/2015
5363	2^290618-33	87485	Lelio R Paula	09/2012
5364	(184*10^87473-1)/3	87475	Robert Price	02/2017
5365	2^290534-115151	87460	Enzo Doria	06/2015
5366	2^290512-109757	87453	Enzo Doria	04/2014
5367	(32*10^87448-41)/9	87449	Robert Price	05/2015
5368	(2^290491+9)/3179	87444	Lelio R Paula	01/2013
5369	(25*2^290489-1)/51809	87443	Lelio R Paula	02/2014
5370	2^290426+82875	87427	Lelio R Paula	11/2013
5371	3*2^290415-7	87425	Lelio R Paula	08/2014
5373	10^87408+57	87409	Robert Price	03/2011
5372	2^290366+74779	87409	Enzo Doria	04/2016
5374	10^87408-123569	87408	Patrick De Geest	07/2013
5375	2^290265+58905	87379	Lelio R Paula	10/2013
5376	7^103391+16	87376	Lelio R Paula	10/2015
5377	(115*10^87368-7)/9	87370	Robert Price	11/2017
5378	(92^44491-1)/91	87369	Paul Bourdelais	08/2017
5379	8*7^103379+3	87367	Lelio R Paula	10/2014
5380	(2^290226+7)/71	87365	Lelio R Paula	01/2013
5381	13^78407-30	87341	Lelio R Paula	11/2015
5382	4*10^87337-99	87338	Robert Price	12/2016
5383	7*10^87319+39	87320	Robert Price	07/2016
5384	3*5^124921+2	87317	Lelio R Paula	10/2014
5385	3^182984+88	87306	Lelio R Paula	12/2015
5386	(10^87323-1)/(9*33909262597306826117)	87303	Alfred Reich	02/2019
5387	4*10^87287-99	87288	Robert Price	12/2016
5388	11^83813-1860	87283	Enzo Doria	12/2012
5389	734^30453+30453^734	87270	Norbert Schneider	04/2017
5390	12^80855+29	87258	Lelio R Paula	11/2015
5391	3*6^112119-5	87247	Lelio R Paula	10/2014
5392	12^80806+79	87205	Lelio R Paula	11/2015
5393	91382^9+9^91382	87201	Andrey Kulsha	11/2004
5394	(21181*2^289657+1)/81	87198	Lelio R Paula	06/2014
5395	6^112054-47	87195	Lelio R Paula	12/2015
5396	(55459*2^289632+1)/55	87191	Lelio R Paula	06/2014
5397	15^74131-68	87185	Lelio R Paula	11/2015
5398	2^289583-741	87174	Lelio R Paula	10/2013
5399	7^103146+12	87169	Lelio R Paula	10/2015
5400	5*2^289556-3	87166	Lelio R Paula	08/2014
5401	2^289543-112735	87162	Enzo Doria	06/2014
5402	8*3^182655-7	87150	Lelio R Paula	08/2014
5403	2*10^87144+81	87145	Robert Price	01/2017
5404	7^103106+2*3^103106	87135	Mike Oakes	08/2010
5405	8*3^182614+7	87130	Lelio R Paula	08/2014
5406	(2^289368-509203)/9	87108	Lelio R Paula	01/2013
5407	3^182566+14	87107	Robert Price	09/2013
5408	(3^182385-5)/2	87020	Lelio R Paula	01/2013
5409	11^83534-8	86992	Lelio R Paula	11/2015
5410	4^144479-14267	86986	Mike Oakes	03/2011
5411	(145*10^86982-1)/9	86984	Serge Batalov	12/2014
5412	(151*10^86963-1)/3	86965	Robert Price	04/2017
5413	15^73940-58	86961	Lelio R Paula	11/2015
5414	2^288761-113143	86926	Enzo Doria	07/2014
5415	2^288747+3083	86922	Yves Minet	03/2011
5416	30^58842+29	86917	Norbert Schneider	03/2017
5417	(10^86906-13)/3	86906	Robert Price	02/2017
5418	2^288692-110027	86905	Enzo Doria	04/2014
5419	(2^288682+7)/259895449	86894	Lelio R Paula	01/2013
5420	(2^288636+47)/1293	86885	Lelio R Paula	01/2013
5421	3^182089-34	86879	Robert Price	11/2013
5422	2^288543-109801	86861	Enzo Doria	04/2014
5423	60^48847-59	86858	Norbert Schneider	10/2014
5424	2^288470-64875	86839	Lelio R Paula	10/2013
5425	10^86816+32997	86817	Patrick De Geest	07/2013
5426	10^86816-99	86816	Robert Price	05/2011
5427	(89*10^86802-539)/9	86803	Robert Price	11/2017
5428	41487!2+256	86786	Robert Price	01/2015
5429	(5*2^288301-1)/999	86785	Lelio R Paula	02/2014
5430	2^288243+76043	86770	Enzo Doria	04/2016
5431	(29*2^288232+1)/15	86767	Lelio R Paula	01/2013
5432	9*6^111495+5	86761	Lelio R Paula	10/2014
5433	(5*2^288202+1)/81	86757	Lelio R Paula	01/2013
5434	9*7^102654-2	86754	Lelio R Paula	10/2014
5435	2^288122-112841	86734	Enzo Doria	06/2014
5436	5^124062-68	86716	Lelio R Paula	10/2015
5437	(2^288007-3)/125	86697	Lelio R Paula	01/2013
5438	379*10^86691+9	86694	Arkadiusz Wesolowski	10/2011
5439	7^102555+48	86670	Lelio R Paula	10/2015
5440	2^287902-4961	86668	Yves Minet	05/2019
5441	77779!4+2	86660	Robert Price	08/2017
5442	2^287809-111355	86640	Enzo Doria	05/2014
5443	(47*2^287795+1)/7	86636	Lelio R Paula	04/2015
5444	9*7^102504+8	86627	Lelio R Paula	10/2014
5445	3^181551+32	86622	Robert Price	11/2013
5446	2^287735-521347	86617	Paul Bourdelais	05/2013
5447	(1017*2^287600-1)/91	86578	Lelio R Paula	04/2015
5448	2^287540-112967	86559	Enzo Doria	06/2014
5449	3^181407+20	86554	Robert Price	10/2013
5450	(13*10^86546+83)/3	86547	Robert Price	09/2016
5451	2^287482-4715	86541	Yves Minet	05/2019
5452	3^181378-2^(181378-1)	86540	Robert Price	01/2016
5453	83^45080-2	86513	Lelio R Paula	08/2013
5454	(78557*2^287351+1)/611	86504	Lelio R Paula	06/2014
5455	25*29^59147+20936	86498	Curtis Bright	05/2015
5456	2^287298+1871359	86486	Enzo Doria	05/2016
5457	118^41740-117	86481	Norbert Schneider	08/2018
5458	3*10^86478+89	86479	Robert Price	03/2017
5459	2^287272-79049	86478	Paul Bourdelais	02/2012
5460	9067052((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
5461	8118242((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
5462	7790642((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
5463	7683852((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
5464	7008912((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
5465	6523202((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
5466	3779202((10^86453-1)/9)+1	86458	Danilo Nitsche	01/2016
5467	2550602((10^86453-1)/9)+1	86458	Danilo Nitsche	01/2016
5468	1871112((10^86453-1)/9)+1	86458	Danilo Nitsche	01/2016
5469	(10^86453-1)/9	86453	Lew Baxter	10/2000
5470	87^44563-86^44563	86431	Robert Price	05/2015
5471	6^111057+61	86420	Lelio R Paula	12/2015
5472	2^287057-109909	86413	Enzo Doria	04/2014
5473	5^123608+22	86399	Lelio R Paula	10/2015
5474	(31*10^86364-121)/9	86365	Robert Price	06/2016
5475	2^286859+71663	86354	Enzo Doria	04/2016
5476	2^286740+29835	86318	Lelio R Paula	10/2013
5477	2*10^86310+9^86310	86311	Mike Oakes	05/2011
5478	11^82878-1860	86309	Enzo Doria	12/2012
5479	2^286547+16095	86260	Lelio R Paula	10/2013
5480	(58*10^86242+329)/9	86243	Robert Price	11/2017
5481	2^286455-110427	86232	Enzo Doria	05/2014
5482	(37*10^86230+53)/9	86231	Robert Price	05/2015
5483	8*3^180700+5	86217	Lelio R Paula	08/2014
5484	3^180697-40	86215	Lelio R Paula	12/2015
5485	(13*2^286318-1)/13257	86188	Lelio R Paula	02/2014
5486	2^286165+77	86145	Lelio R Paula	08/2012
5487	9*2^286140+7	86138	Lelio R Paula	08/2014
5488	(29*2^286108-1)/2002367	86123	Lelio R Paula	02/2014
5489	10^86110+161113	86111	Patrick De Geest	07/2013
5490	10^86110-69	86110	Robert Price	05/2011
5491	2^286036-869688105	86106	Lelio R Paula	07/2016
5492	(77*10^86072+31)/9	86073	Robert Price	10/2015
5493	2^285923+345	86072	Lelio R Paula	09/2013
5494	13^77266-90	86070	Lelio R Paula	11/2015
5495	2^285910-458903	86068	Enzo Doria	04/2015
5496	2^285904-125	86066	Lelio R Paula	08/2012
5497	2^285836+65835	86046	Lelio R Paula	09/2013
5498	(2^285766+78557)/3	86024	Lelio R Paula	01/2013
5499	(5*10^86011-107)/3	86012	Robert Price	01/2017
5500	6^110522+163	86003	Lelio R Paula	12/2015

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PRP Records

Probable Primes Top 10000

(253476 PRPs in the top)