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	(3*29^72089-1075)/4	105423	Curtis Bright	05/2015
5252	(2^350187+2658)/2	105417	Stefano Morozzi	09/2020
5253	2^350139-109009	105403	Enzo Doria	04/2014
5254	(2^350129+3026)/2	105400	Stefano Morozzi	09/2020
5255	(2^350097+2070)/2	105390	Stefano Morozzi	09/2020
5256	3*5^150763+4	105380	Lelio R Paula	11/2014
5257	12^97643+91	105375	Lelio R Paula	02/2017
5258	6*5^150744-7	105367	Lelio R Paula	11/2014
5259	(2^350018+2074)/2	105366	Stefano Morozzi	09/2020
5260	4*10^105364-39	105365	Robert Price	09/2020
5262	2^349996-112169	105360	Enzo Doria	06/2014
5261	(2^349997+3702)/2	105360	Stefano Morozzi	09/2020
5263	(418*10^105343+23)/9	105345	Robert Price	02/2020
5264	25490^13563+13563^25490	105334	Hans Havermann	10/2020
5265	11^101142-1080	105329	Enzo Doria	12/2012
5266	(68*10^105320-41)/9	105321	Robert Price	10/2013
5267	24800^17649+17649^24800	105319	Hans Havermann	09/2020
5268	3^220712-9934	105307	Enzo Doria	05/2014
5269	7*10^105296+9	105297	Robert Price	09/2015
5270	89*10^105284-7	105286	Robert Price	04/2020
5271	2^349739+1873373	105282	Enzo Doria	06/2016
5272	7^124574+24	105278	Lelio R Paula	11/2016
5273	2^349708-20957	105273	Enzo Doria	06/2013
5274	34115^1218+1218^34115	105267	Hans Havermann	09/2020
5275	2^349649-20469	105255	Enzo Doria	06/2013
5276	2^349607-20109	105243	Enzo Doria	06/2013
5277	(85*10^105242+473)/9	105243	Robert Price	01/2020
5278	2^349594-19085	105239	Enzo Doria	05/2013
5279	2^349530+1874479	105220	Enzo Doria	06/2016
5280	(3^220528+8)/8081	105215	Lelio R Paula	12/2013
5281	(106*10^105199+17)/3	105201	Robert Price	04/2021
5282	(2^349452+3570)/2	105196	Stefano Morozzi	09/2020
5283	3^220464-112852	105189	Enzo Doria	07/2014
5284	2^349419-17349	105186	Enzo Doria	05/2013
5285	2^349400-2579	105180	Yves Minet	07/2014
5286	8*5^150471+3	105176	Lelio R Paula	11/2014
5287	(2^349359+2298)/2	105168	Stefano Morozzi	02/2021
5288	655^37342+37342^655	105165	Norbert Schneider	08/2018
5289	13^94403+94	105160	Lelio R Paula	12/2016
5290	2^349301-112309	105151	Enzo Doria	06/2014
5291	30291^2960+2960^30291	105149	Hans Havermann	09/2020
5292	27350^6981+6981^27350	105132	Hans Havermann	09/2020
5294	9*2^349220+5	105127	Lelio R Paula	09/2014
5293	(2^349225+3122)/2	105127	Stefano Morozzi	09/2020
5295	7*3^220317+8	105119	Lelio R Paula	09/2014
5296	7^124386+88	105119	Lelio R Paula	11/2016
5297	(2^349197+570)/2	105119	Stefano Morozzi	09/2020
5298	2^349171-19657	105111	Enzo Doria	06/2013
5299	(2^349115+590)/2	105094	Stefano Morozzi	09/2020
5300	(2^(6*58185+1)-5)/3	105093	Kevin Acres	11/2013
5301	(2^349111-5)/3	105093	Lelio R Paula	12/2013
5302	675^37142+37142^675	105087	Norbert Schneider	08/2018
5303	2^348981-2797573	105054	Enzo Doria	04/2016
5304	2^348869-6555	105021	Lelio R Paula	01/2017
5305	5^150217+78	104998	Lelio R Paula	11/2016
5306	(88*10^104989-1)/3	104991	Robert Price	04/2020
5307	(28*10^104972+149)/3	104973	Robert Price	12/2019
5308	24927^16262+16262^24927	104972	Hans Havermann	10/2020
5309	2^348703-113005	104971	Enzo Doria	06/2014
5310	(191*10^104956-17)/3	104958	Robert Price	11/2021
5312	2^348612-809	104943	Yves Minet	05/2013
5311	(73*10^104942-1)/9	104943	Robert Price	01/2015
5313	2^348583-350407	104934	Enzo Doria	06/2015
5314	2^348531-949	104919	Yves Minet	05/2012
5315	20^80636-59	104910	Lelio R Paula	12/2016
5316	8*10^104893-13	104894	Robert Price	08/2019
5318	2^348437+35	104890	Lelio R Paula	09/2011
5317	25208^14487+14487^25208	104890	Hans Havermann	09/2020
5319	2^348348+135	104864	Lelio R Paula	09/2011
5320	(29*10^104858+349)/9	104859	Robert Price	06/2021
5321	6*10^104852-31	104853	Robert Price	07/2020
5323	(2^348284+9)/25	104843	Lelio R Paula	12/2013
5322	75^55914-74	104843	Norbert Schneider	01/2015
5324	2^348268+255255	104840	Lelio R Paula	01/2017
5325	35540^891+891^35540	104839	Hans Havermann	09/2020
5326	5^149985-52	104836	Lelio R Paula	11/2016
5327	2^348224-20249	104826	Enzo Doria	06/2013
5328	(2^348217+2522)/2	104824	Stefano Morozzi	09/2020
5329	2^348212-20105	104823	Enzo Doria	06/2013
5330	24647^17898+17898^24647	104819	Hans Havermann	10/2020
5331	20^80562+19	104814	Lelio R Paula	12/2016
5332	2*10^104811-87	104812	Robert Price	04/2018
5333	2^348149-20053	104804	Enzo Doria	06/2013
5334	2^348095-171	104788	Lelio R Paula	09/2011
5335	25383^13412+13412^25383	104769	Hans Havermann	09/2020
5336	2^348003-20377	104760	Enzo Doria	06/2013
5337	2^347994-741	104757	Lelio R Paula	12/2016
5338	(2^347993+2234)/2	104757	Stefano Morozzi	01/2021
5339	(2^347990+790)/2	104756	Stefano Morozzi	09/2020
5340	25137^14702+14702^25137	104756	Hans Havermann	09/2020
5341	(13*2^347972-1)/282309	104746	Lelio R Paula	03/2014
5342	2^347910-109937	104732	Enzo Doria	04/2014
5343	(88*10^104709-637)/9	104710	Robert Price	11/2020
5344	(13*10^104702+71)/3	104703	Robert Price	06/2021
5345	5^149794+28	104702	Lelio R Paula	11/2016
5346	105^51800-2	104698	Lelio R Paula	10/2017
5347	(16^86939+3^86939)/19	104684	Robert Price	06/2013
5348	(15^89009-1)/14	104682	Paul Bourdelais	03/2010
5349	2^347731-18609	104678	Enzo Doria	05/2013
5350	4*6^134519+7	104677	Lelio R Paula	11/2014
5351	(34*10^104672-259)/9	104673	Robert Price	12/2021
5352	25321^13588+13588^25321	104656	Hans Havermann	09/2020
5353	2^347612-18545	104642	Enzo Doria	05/2013
5356	6^134465+95	104635	Lelio R Paula	11/2016
5354	(2^347588+3718)/2	104635	Stefano Morozzi	09/2020
5355	(166*10^104633-7)/3	104635	Robert Price	11/2020
5357	2^347517-17301	104614	Enzo Doria	05/2013
5358	(2^347493+3186)/2	104606	Stefano Morozzi	09/2020
5359	(2^347490+2574)/2	104605	Stefano Morozzi	09/2020
5360	3^219222-310	104596	Lelio R Paula	11/2016
5361	25993^10554+10554^25993	104581	Hans Havermann	09/2020
5362	(15*2^347399-1)/13	104578	Lelio R Paula	03/2014
5363	2^347372-17853	104570	Enzo Doria	05/2013
5364	2^347314+99	104552	Lelio R Paula	09/2011
5365	2^347300-22233	104548	Enzo Doria	06/2013
5366	2^347287-19845	104544	Enzo Doria	06/2013
5367	(31*2^347254-1)/891	104533	Lelio R Paula	03/2014
5368	5F(250091)(F(250091)-1)+1	104532	Serge Batalov	04/2015
5369	7*2^347239-3	104531	Lelio R Paula	09/2014
5370	(3^219098-8)/514147439969	104525	Lelio R Paula	12/2013
5371	5*3^219047+8	104513	Lelio R Paula	09/2014
5372	2^347148-109073	104502	Enzo Doria	04/2014
5373	2^347129-20145	104497	Enzo Doria	06/2013
5374	4*10^104461-57	104462	Robert Price	10/2018
5375	(2^346989+590)/2	104454	Stefano Morozzi	09/2020
5376	2^346923-19585	104435	Enzo Doria	05/2013
5377	(11*2^346864-1)/175	104416	Lelio R Paula	03/2014
5378	2^346854+346854^2+1	104414	Robert Price	06/2014
5379	2^346834+11715	104408	Lelio R Paula	04/2015
5380	24276^19961+19961^24276	104392	Hans Havermann	09/2020
5381	79^55009+78	104387	Norbert Schneider	02/2015
5382	3^218744+58	104368	Lelio R Paula	11/2016
5383	9*10^104361+89	104362	Robert Price	11/2019
5384	25048^14665+14665^25048	104358	Hans Havermann	09/2020
5385	2^346649+65	104352	Lelio R Paula	09/2011
5386	2^346638-17265	104349	Enzo Doria	05/2013
5387	(2^346606+2082)/2	104339	Stefano Morozzi	09/2020
5388	(2^346607+2070)/2	104339	Stefano Morozzi	09/2020
5389	(2^346582+3202)/2	104332	Stefano Morozzi	09/2020
5390	26092^9967+9967^26092	104331	Hans Havermann	09/2020
5391	5*10^104326+77	104327	Robert Price	12/2018
5392	(2^346564+2026)/2	104326	Stefano Morozzi	09/2020
5394	2^346527-111817	104316	Enzo Doria	05/2014
5393	6^134055+101	104316	Lelio R Paula	11/2016
5395	92105!4+8	104312	Robert Price	09/2019
5396	6^134013+163	104283	Lelio R Paula	11/2016
5397	(2^346318+862)/2	104252	Stefano Morozzi	02/2021
5399	18^83049-89	104250	Lelio R Paula	01/2017
5398	(2^346311+606)/2	104250	Stefano Morozzi	09/2020
5400	(166*10^104230+11)/3	104232	Robert Price	03/2021
5401	2^346213+484049	104221	Enzo Doria	04/2017
5402	18^83021-91	104214	Lelio R Paula	01/2017
5403	10^104212+128779	104213	Patrick De Geest	05/2016
5404	10^104212+237447	104213	Patrick De Geest	05/2016
5405	10^104212+242139	104213	Patrick De Geest	05/2016
5406	10^104212+269199	104213	Patrick De Geest	05/2016
5407	24254^19803+19803^24254	104213	Hans Havermann	09/2020
5408	(10^104212-71)/1	104212	Serge Batalov	12/2014
5409	23678^23821-23821^23678	104202	Norbert Schneider	01/2020
5410	2^346078+7695	104180	Lelio R Paula	12/2016
5411	2^346055-19537	104173	Enzo Doria	05/2013
5412	(3*2^346057+1)/77	104173	Lelio R Paula	12/2013
5413	2^346037-20125	104168	Enzo Doria	06/2013
5414	(34*10^104168-7)/9/13/551179	104162	Makoto Morimoto	05/2016
5415	6^133854-17993	104159	Enzo Doria	03/2013
5416	2^345990+1874239	104154	Enzo Doria	06/2016
5417	2^345988-20373	104153	Enzo Doria	06/2013
5418	(2^345965+2214)/2	104146	Stefano Morozzi	09/2020
5419	(26*10^104132-503)/9	104133	Robert Price	07/2018
5420	3*5^148968+8	104125	Lelio R Paula	11/2014
5421	(7*10^104113+53)/3	104114	Robert Price	05/2018
5422	p(21253)#/2+8	104113	Robert Price	01/2017
5423	33582^1259+1259^33582	104106	Hans Havermann	09/2020
5424	32958^1441+1441^32958	104104	Hans Havermann	09/2020
5425	29127^3748+3748^29127	104095	Hans Havermann	09/2020
5426	322^41507+41507^322	104094	Norbert Schneider	12/2014
5427	6^133768-17423	104092	Enzo Doria	03/2013
5428	2^345786-19557	104092	Enzo Doria	05/2013
5430	171^46606-2	104072	Lelio R Paula	10/2017
5429	(29*10^104071+91)/3	104072	Robert Price	04/2020
5431	2^345704-149	104068	Lelio R Paula	09/2011
5432	25821^10712+10712^25821	104056	Hans Havermann	09/2020
5433	(2^345662+2038)/2	104055	Stefano Morozzi	09/2020
5434	6^133704-17273	104042	Enzo Doria	02/2013
5435	(3*2^345590-1)/23	104033	Lelio R Paula	03/2014
5436	(19*2^345590+1)/33859	104030	Lelio R Paula	12/2013
5437	2^345547+11	104021	Lelio R Paula	09/2011
5438	(19*10^104014-49)/3	104015	Robert Price	05/2019
5439	(2^345519+1794)/2	104012	Stefano Morozzi	01/2021
5440	2^345504+723	104008	Lelio R Paula	09/2011
5441	2^345498-20037	104006	Enzo Doria	06/2013
5442	18^82854-37	104005	Lelio R Paula	01/2017
5443	(2^345497+2070)/2	104005	Stefano Morozzi	09/2020
5444	2^345486-109065	104002	Enzo Doria	04/2014
5445	2^345487-1851507	104002	Enzo Doria	08/2015
5446	2^345476+777	103999	Lelio R Paula	09/2011
5447	(2^345477+1554)/2	103999	Stefano Morozzi	09/2020
5448	4*10^103981-83	103982	Robert Price	10/2018
5449	(2^345327+3206)/2	103954	Stefano Morozzi	09/2020
5450	(5*2^345321-1)/3	103953	Lelio R Paula	03/2014
5451	(2^345267-9)/539049127	103927	Lelio R Paula	12/2013
5452	(19*10^103907+77)/3	103908	Robert Price	05/2019
5453	(78557*2^345163+1)/78589	103905	Lelio R Paula	07/2014
5454	2^345106-112181	103888	Enzo Doria	06/2014
5455	(2^345105+1326)/2	103887	Stefano Morozzi	02/2021
5456	2^345079+99	103880	Lelio R Paula	09/2011
5457	(2^345034+1198)/2	103866	Stefano Morozzi	09/2020
5458	11^99736-1500	103865	Enzo Doria	12/2012
5459	(2^345010+2082)/2	103859	Stefano Morozzi	09/2020
5460	23263^23784-23784^23263	103857	Norbert Schneider	01/2020
5461	3*10^103844+31	103845	Robert Price	06/2021
5462	23927^21814+21814^23927	103813	Hans Havermann	09/2020
5463	2^344842-20157	103808	Enzo Doria	06/2013
5464	(47*2^344822+1)/1071	103801	Lelio R Paula	05/2015
5465	2^344802-20765	103796	Enzo Doria	06/2013
5466	2^344794-3821	103794	Yves Minet	05/2011
5467	2^344782-109103	103790	Enzo Doria	04/2014
5468	3^217521-112292	103784	Enzo Doria	06/2014
5469	2^344759-3505	103783	Lelio R Paula	11/2016
5470	2^344735-147	103776	Lelio R Paula	09/2011
5471	L(496533)-p(496533)	103770	Robert Price	02/2018
5472	2*10^103749-69	103750	Robert Price	03/2018
5473	(55459*2^344617+1)/3	103745	Lelio R Paula	07/2014
5474	2^344607-108891	103738	Enzo Doria	03/2014
5475	(2^344608+3798)/2	103738	Stefano Morozzi	02/2021
5476	(148*10^103718-1)/3	103720	Robert Price	03/2020
5477	2^344541-19561	103718	Enzo Doria	05/2013
5478	(1017*2^344529-1)/569	103714	Lelio R Paula	05/2015
5479	(2^344503+1758)/2	103706	Stefano Morozzi	09/2020
5480	(4*10^103703-1)/3	103704	Serge Batalov	08/2009
5481	2^344444-455	103688	Yves Minet	03/2012
5482	(4*10^103678-43)/3	103679	Robert Price	01/2022
5483	(1353^238539617^9)/10^307661	103673	Hans Havermann	06/2017
5484	(2^344367+2738)/2	103665	Stefano Morozzi	01/2021
5486	2^344317-109933	103650	Enzo Doria	04/2014
5485	26055^9508+9508^26055	103650	Hans Havermann	09/2020
5487	2^344309-1852033	103648	Enzo Doria	08/2015
5488	25729^10672+10672^25729	103643	Hans Havermann	09/2020
5489	(2^344289+1166)/2	103642	Stefano Morozzi	09/2020
5490	3*10^103637+61	103638	Robert Price	09/2020
5491	(2^344246+1614)/2	103629	Stefano Morozzi	09/2020
5492	2^344213-21253	103619	Enzo Doria	06/2013
5493	2^344196-465	103614	Lelio R Paula	11/2016
5494	2^344187-20001	103611	Enzo Doria	06/2013
5495	(117191#+(355573#)/(117191#))/(200233679)	103602	Makoto Morimoto	10/2017
5496	20^79621-19^79621	103590	Jean-Louis Charton	03/2011
5497	Phi(155391,10)/1243129	103586	Maksym Voznyy	09/2015
5498	2^344085-20365	103580	Enzo Doria	06/2013
5499	5^148169+54	103566	Lelio R Paula	11/2016
5500	2^344017-108795	103560	Enzo Doria	03/2014

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Probable Primes Top 10000

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