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	436^40459+40459^436	106791	Norbert Schneider	03/2019
5252	(21^80761+1)/22	106783	Paul Bourdelais	03/2010
5253	(115*10^106772-7)/9	106774	Robert Price	02/2020
5254	2^354640-354640+1	106758	Robert Price	10/2014
5255	(2^354603+2606)/2	106746	Stefano Morozzi	09/2020
5256	2^354585+95	106741	Lelio R Paula	10/2011
5257	(206*10^106737+1)/9	106739	Robert Price	04/2022
5258	2^354553+189	106732	Lelio R Paula	10/2011
5259	(2^354546+1338)/2	106729	Stefano Morozzi	02/2021
5260	2^354514-109031	106720	Enzo Doria	04/2014
5261	2^354509-109465	106718	Enzo Doria	04/2014
5262	(15*2^354478-1)/26983	106706	Lelio R Paula	03/2014
5263	Phi(217618,10)/899798636917	106693	Makoto Kamada	06/2019
5264	15^90710+28	106684	Lelio R Paula	04/2017
5265	7^126237+34	106683	Lelio R Paula	03/2017
5266	2^354385-115315	106681	Enzo Doria	06/2015
5267	2^354327-19305	106664	Enzo Doria	06/2013
5268	(35*10^106649+1)/9	106650	Serge Batalov	11/2010
5269	10^106636+97	106637	Lelio R Paula	02/2017
5270	10^106636-22923	106636	Patrick De Geest	03/2017
5271	2^354220-57	106631	Lelio R Paula	10/2011
5272	(68*10^106628-329)/9	106629	Robert Price	03/2021
5273	(29*10^106620-77)/3	106621	Robert Price	02/2020
5274	(746*10^106618+1)/9	106620	Robert Price	03/2020
5275	2*10^106613+29	106614	Robert Price	02/2021
5276	2^354157-17041	106612	Enzo Doria	05/2013
5277	12^98778+73	106600	Lelio R Paula	02/2017
5278	33333^1576+1576^33333	106585	Hans Havermann	11/2020
5279	2^354064+1870651	106584	Enzo Doria	05/2016
5280	24568^21779+21779^24568	106577	Hans Havermann	11/2020
5281	2^353992-57	106563	Lelio R Paula	10/2011
5282	9*10^106559+59	106560	Robert Price	01/2020
5283	7*10^106553+27	106554	Robert Price	11/2020
5284	28847^4938+4938^28847	106548	Hans Havermann	10/2020
5285	NSW(139160)	106535	Robert Price	12/2018
5286	(7*10^106516+113)/3	106517	Robert Price	02/2018
5287	2^353832-1853849	106515	Enzo Doria	09/2015
5288	(7^126037-1)/6	106513	Paul Bourdelais	09/2008
5289	2^353794-18453	106503	Enzo Doria	05/2013
5290	(2^353761+2094)/2	106493	Stefano Morozzi	09/2020
5291	2^353728+7695	106483	Lelio R Paula	01/2017
5292	26476^10509+10509^26476	106475	Hans Havermann	10/2020
5293	2^353672-303	106466	Yves Minet	02/2012
5294	6^136811+101	106460	Lelio R Paula	02/2017
5295	2^353641+1871981	106457	Enzo Doria	05/2016
5296	(8*10^106454-29)/3	106455	Robert Price	07/2018
5297	27845^6654+6654^27845	106454	Hans Havermann	11/2020
5298	10^106449-700001	106449	Robert Price	08/2021
5299	25316^16017+16017^25316	106444	Hans Havermann	11/2020
5300	2^353553+54615	106431	Lelio R Paula	01/2017
5301	2^353544-18897	106428	Enzo Doria	05/2013
5302	28894^4823+4823^28894	106426	Hans Havermann	11/2020
5303	(19*10^106422+29)/3	106423	Robert Price	12/2021
5304	(694*10^106418+53)/9	106420	Robert Price	02/2022
5305	25696^13829+13829^25696	106402	Hans Havermann	11/2020
5306	6^136729-133	106396	Lelio R Paula	02/2017
5307	2^353418+1605	106390	Lelio R Paula	01/2017
5308	2^353387+65	106381	Lelio R Paula	10/2011
5309	2^353372+74311	106376	Enzo Doria	04/2016
5310	2^353344-3693	106368	Yves Minet	03/2017
5311	(772*10^106365-7)/9	106367	Robert Price	06/2022
5312	(56*10^106351+619)/9	106352	Robert Price	05/2021
5314	2^353277-20089	106347	Enzo Doria	06/2013
5313	2^353275+72173	106347	Enzo Doria	04/2016
5315	2^353268-17705	106345	Enzo Doria	05/2013
5316	2^353267-19857	106344	Enzo Doria	06/2013
5317	(46*10^106343+143)/9	106344	Robert Price	01/2019
5318	(2^353189+3054)/2	106321	Stefano Morozzi	09/2020
5319	35087^1072+1072^35087	106321	Hans Havermann	10/2020
5320	(2^353184+1290)/2	106319	Stefano Morozzi	01/2021
5321	26985^8684+8684^26985	106287	Hans Havermann	10/2020
5322	(2^353051+606)/2	106279	Stefano Morozzi	09/2020
5324	222748^3+3^222748	106278	Anatoly F. Selevich	12/2010
5323	(46*10^106277+107)/9	106278	Robert Price	06/2022
5325	(9179*2^353019-1)/9	106273	Lelio R Paula	05/2015
5326	2^353025+72257	106272	Enzo Doria	04/2016
5329	2^352932-20345	106244	Enzo Doria	06/2013
5327	(2^353011-3)/745325861246794515484535	106244	Lelio R Paula	12/2013
5328	25628^13983+13983^25628	106244	Hans Havermann	10/2020
5330	2^352883-187	106229	Lelio R Paula	10/2011
5331	20^81649-19^81649	106228	Jean-Louis Charton	03/2011
5332	(55*10^106222+377)/9	106223	Robert Price	02/2019
5333	2^352814-131	106208	Lelio R Paula	10/2011
5334	2^352752+73951	106189	Enzo Doria	04/2016
5335	6^136434+5	106167	Lelio R Paula	11/2014
5336	25296^15737+15737^25296	106166	Hans Havermann	09/2020
5337	8*10^106157-13	106158	Robert Price	08/2019
5338	7*5^151872-8	106155	Lelio R Paula	11/2014
5339	105^52520-2	106153	Lelio R Paula	10/2017
5340	(23*10^106152-29)/3	106153	Robert Price	03/2022
5341	2^352601-1604809	106144	Enzo Doria	05/2015
5342	12^98353-43	106141	Lelio R Paula	02/2017
5343	2^352585-18901	106139	Enzo Doria	05/2013
5344	26363^10614+10614^26363	106135	Hans Havermann	09/2020
5345	(2^352554-3)/193	106128	Lelio R Paula	12/2013
5346	2^352540+15015	106126	Lelio R Paula	01/2017
5347	25068^17119+17119^25068	106125	Hans Havermann	09/2020
5348	2^352524-3149	106121	Yves Minet	10/2014
5349	(7*10^106119-67)/3	106120	Robert Price	10/2021
5350	2^352486-1858781	106109	Enzo Doria	04/2016
5351	2^352444+12705	106097	Lelio R Paula	01/2017
5352	28561^5182+5182^28561	106090	Hans Havermann	10/2020
5353	(182*10^106083+43)/9	106085	Robert Price	02/2020
5354	(266*10^106066+1)/3	106068	Robert Price	04/2020
5355	2^352228-18953	106032	Enzo Doria	05/2013
5356	(2^352223+1118)/2	106030	Stefano Morozzi	09/2020
5357	(2^352212+2250)/2	106027	Stefano Morozzi	01/2021
5358	(2^352136+2638)/2	106004	Stefano Morozzi	09/2020
5359	2^352107+1872533	105995	Enzo Doria	05/2016
5360	(2^352096+2086)/2	105992	Stefano Morozzi	09/2020
5361	2^352066-2591	105983	Yves Minet	07/2014
5362	2^352030+715	105972	Lelio R Paula	10/2011
5363	9*6^136176-5	105967	Lelio R Paula	11/2014
5364	17099*2^351991+58329	105965	Paul Vanderveen	12/2017
5365	28582^5097+5097^28582	105963	Hans Havermann	09/2020
5366	155^48377+2	105962	Lelio R Paula	08/2013
5367	(23*10^105944-119)/3	105945	Robert Price	07/2021
5368	2^351865+1869707	105922	Enzo Doria	05/2016
5369	24974^17427+17427^24974	105921	Hans Havermann	09/2020
5370	25163^16194+16194^25163	105920	Hans Havermann	09/2020
5371	2^351831+23	105912	Lelio R Paula	10/2011
5372	(2^351818+3798)/2	105908	Stefano Morozzi	02/2021
5373	9*2^351784-5	105899	Lelio R Paula	09/2014
5374	(2^351776+2766)/2	105895	Stefano Morozzi	01/2021
5375	(85*10^105881+203)/9	105882	Robert Price	09/2020
5376	2^351671-112387	105864	Enzo Doria	06/2014
5377	2^351669-109501	105863	Enzo Doria	04/2014
5378	2^351644+74731	105856	Enzo Doria	04/2016
5379	13^95025-42	105853	Lelio R Paula	12/2016
5380	2^351599+15015	105842	Lelio R Paula	01/2017
5381	19^82763+90	105834	Lelio R Paula	01/2017
5382	(205*10^105831-1)/3	105833	Robert Price	11/2021
5383	26050^11551+11551^26050	105832	Hans Havermann	09/2020
5384	(9179*2^351540-1)/221	105826	Lelio R Paula	05/2015
5385	20^81329-51	105812	Lelio R Paula	01/2017
5386	(5*10^105811+211)/9	105811	Robert Price	02/2018
5387	2^351483+28425	105807	Lelio R Paula	01/2017
5388	25231^15610+15610^25231	105804	Hans Havermann	09/2020
5389	15^89960+86	105802	Lelio R Paula	02/2017
5390	2^351460-17289	105801	Enzo Doria	05/2013
5391	19^82735+22	105798	Lelio R Paula	01/2017
5392	2^351435-109077	105793	Enzo Doria	04/2014
5393	2^351393+1089	105780	Lelio R Paula	01/2017
5394	2^351364+72631	105772	Enzo Doria	04/2016
5395	(2^351333+3626)/2	105762	Stefano Morozzi	09/2020
5396	26818^8783+8783^26818	105761	Hans Havermann	09/2020
5399	2^351305+1872467	105754	Enzo Doria	05/2016
5398	3^221649+16	105754	Lelio R Paula	11/2016
5397	32511^1790+1790^32511	105754	Hans Havermann	09/2020
5400	8*3^221637-5	105749	Lelio R Paula	09/2014
5401	2^351279-2780449	105746	Enzo Doria	03/2016
5402	(2^351263+3198)/2	105741	Stefano Morozzi	09/2020
5403	15^89903-26	105735	Lelio R Paula	02/2017
5405	2^351213-73	105726	Lelio R Paula	10/2011
5404	(2^351214+1210)/2	105726	Stefano Morozzi	09/2020
5406	2^351192-4589	105720	Yves Minet	07/2011
5407	20^81250-33	105709	Lelio R Paula	12/2016
5408	(2^351133+3530)/2	105702	Stefano Morozzi	09/2020
5409	(2^351103+534)/2	105693	Stefano Morozzi	09/2020
5410	2^351076-113159	105685	Enzo Doria	07/2014
5411	93^53688-2	105684	Lelio R Paula	09/2013
5412	2^351060-4559	105680	Yves Minet	07/2011
5413	((10^52836-1)10000/9+5927)10^52836+(10^52836-1)/9	105676	Hans Havermann	08/2019
5414	11^101473-750	105674	Enzo Doria	11/2012
5415	3*5^151181-8	105672	Lelio R Paula	11/2014
5416	15^89831-34	105650	Lelio R Paula	02/2017
5418	11^101448-360	105648	Enzo Doria	08/2012
5417	3*7^125011+4	105648	Lelio R Paula	11/2014
5419	2^350943-113269	105645	Enzo Doria	07/2014
5420	2*10^105636-91	105637	Robert Price	04/2020
5421	24231^22880+22880^24231	105634	Hans Havermann	09/2020
5422	35296^983+983^35296	105626	Hans Havermann	09/2020
5423	2^350868-19725	105622	Enzo Doria	06/2013
5424	2^350858-59291	105619	Enzo Doria	10/2015
5425	2^350851+135	105617	Lelio R Paula	10/2011
5426	2^350841-741	105614	Lelio R Paula	01/2017
5427	3*10^105582+77	105583	Robert Price	09/2018
5428	24915^17284+17284^24915	105581	Hans Havermann	09/2020
5429	(5*10^105576-53)/3	105577	Robert Price	09/2020
5430	8*10^105571+3	105572	Robert Price	08/2015
5431	2^350674-78557	105564	Jorge Menendez	03/2018
5432	2*5^151026-3	105563	Lelio R Paula	11/2014
5433	(2^350702+5)/34264674063	105562	Lelio R Paula	12/2013
5434	6^135647-5^135647	105554	Jean-Louis Charton	02/2009
5435	3^221211+236	105545	Lelio R Paula	11/2016
5436	(32*10^105530-77)/9	105531	Robert Price	06/2018
5437	10^105515+33	105516	Lelio R Paula	11/2016
5438	24644^19125+19125^24644	105516	Hans Havermann	10/2020
5439	10^105515-41033	105515	Patrick De Geest	12/2016
5440	(29*2^350473-1)/267927	105499	Lelio R Paula	03/2014
5441	2^350455-430567	105498	Harrison Mesh	06/2022
5442	17^85732-72	105489	Lelio R Paula	01/2017
5443	(2^350399+3618)/2	105481	Stefano Morozzi	09/2020
5444	(2^350379+1010)/2	105475	Stefano Morozzi	09/2020
5445	25233^15118+15118^25233	105462	Hans Havermann	09/2020
5446	26261^10366+10366^26261	105454	Hans Havermann	09/2020
5447	2^350307-110329	105453	Enzo Doria	05/2014
5448	2^350253-20365	105437	Enzo Doria	06/2013
5449	(3*29^72089-1075)/4	105423	Curtis Bright	05/2015
5450	(2^350187+2658)/2	105417	Stefano Morozzi	09/2020
5451	4*10^105415-69	105416	Robert Price	01/2022
5452	(22*10^105407+179)/3	105408	Robert Price	02/2022
5453	2^350139-109009	105403	Enzo Doria	04/2014
5454	(2^350129+3026)/2	105400	Stefano Morozzi	09/2020
5455	(2^350097+2070)/2	105390	Stefano Morozzi	09/2020
5456	3*5^150763+4	105380	Lelio R Paula	11/2014
5457	12^97643+91	105375	Lelio R Paula	02/2017
5458	6*5^150744-7	105367	Lelio R Paula	11/2014
5459	(2^350018+2074)/2	105366	Stefano Morozzi	09/2020
5460	4*10^105364-39	105365	Robert Price	09/2020
5462	2^349996-112169	105360	Enzo Doria	06/2014
5461	(2^349997+3702)/2	105360	Stefano Morozzi	09/2020
5463	(418*10^105343+23)/9	105345	Robert Price	02/2020
5464	25490^13563+13563^25490	105334	Hans Havermann	10/2020
5465	11^101142-1080	105329	Enzo Doria	12/2012
5466	(68*10^105320-41)/9	105321	Robert Price	10/2013
5467	24800^17649+17649^24800	105319	Hans Havermann	09/2020
5468	3^220712-9934	105307	Enzo Doria	05/2014
5469	7*10^105296+9	105297	Robert Price	09/2015
5470	89*10^105284-7	105286	Robert Price	04/2020
5471	2^349739+1873373	105282	Enzo Doria	06/2016
5472	7^124574+24	105278	Lelio R Paula	11/2016
5473	2^349708-20957	105273	Enzo Doria	06/2013
5474	34115^1218+1218^34115	105267	Hans Havermann	09/2020
5475	2^349649-20469	105255	Enzo Doria	06/2013
5476	2^349607-20109	105243	Enzo Doria	06/2013
5477	(85*10^105242+473)/9	105243	Robert Price	01/2020
5478	2^349594-19085	105239	Enzo Doria	05/2013
5479	2^349530+1874479	105220	Enzo Doria	06/2016
5480	(3^220528+8)/8081	105215	Lelio R Paula	12/2013
5481	(106*10^105199+17)/3	105201	Robert Price	04/2021
5482	(2^349452+3570)/2	105196	Stefano Morozzi	09/2020
5483	3^220464-112852	105189	Enzo Doria	07/2014
5484	2^349419-17349	105186	Enzo Doria	05/2013
5485	2^349400-2579	105180	Yves Minet	07/2014
5486	8*5^150471+3	105176	Lelio R Paula	11/2014
5487	(2^349359+2298)/2	105168	Stefano Morozzi	02/2021
5488	655^37342+37342^655	105165	Norbert Schneider	08/2018
5489	13^94403+94	105160	Lelio R Paula	12/2016
5490	2^349301-112309	105151	Enzo Doria	06/2014
5491	30291^2960+2960^30291	105149	Hans Havermann	09/2020
5492	27350^6981+6981^27350	105132	Hans Havermann	09/2020
5494	9*2^349220+5	105127	Lelio R Paula	09/2014
5493	(2^349225+3122)/2	105127	Stefano Morozzi	09/2020
5495	7*3^220317+8	105119	Lelio R Paula	09/2014
5496	7^124386+88	105119	Lelio R Paula	11/2016
5497	(2^349197+570)/2	105119	Stefano Morozzi	09/2020
5498	2^349171-19657	105111	Enzo Doria	06/2013
5499	(2^349115+590)/2	105094	Stefano Morozzi	09/2020
5500	(2^(6*58185+1)-5)/3	105093	Kevin Acres	11/2013

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