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	26167^5794+5794^26167	98466	Hans Havermann	01/2020
5252	(6883*2^327047-1)/77	98453	Lelio R Paula	05/2015
5253	(71*10^98446+1)/9	98447	Serge Batalov	11/2010
5254	13^88363+94	98432	Lelio R Paula	08/2016
5255	48^58543-47^58543	98425	Jean-Louis Charton	11/2005
5256	6^126481+41	98422	Lelio R Paula	08/2016
5257	78*10^98413-7	98415	Robert Price	05/2017
5258	22634^22263+22263^22634	98404	Hans Havermann	07/2020
5259	7^116416+46	98383	Lelio R Paula	08/2016
5260	7^116407-24	98376	Lelio R Paula	07/2016
5261	439^37228+37228^439	98374	Norbert Schneider	08/2018
5262	2^326782-1860671	98372	Enzo Doria	03/2016
5263	17^79948+58	98372	Lelio R Paula	08/2016
5264	22499^22602-22602^22499	98368	Norbert Schneider	08/2020
5265	3^206143-98	98356	Lelio R Paula	08/2016
5266	8*5^140705+7	98350	Lelio R Paula	11/2014
5267	(2^326632+1662)/2	98326	Stefano Morozzi	09/2020
5268	2^326585+11	98312	Lelio R Paula	12/2012
5269	2^326582-459161	98311	Enzo Doria	05/2015
5271	(2^326548+9)/5	98301	Lelio R Paula	10/2013
5270	(2^326549+18)/10	98301	Stefano Morozzi	03/2020
5272	2^326538+71659	98298	Enzo Doria	04/2016
5273	(2^326520+2082)/2	98293	Stefano Morozzi	09/2020
5274	(2^326521+1002)/2	98293	Stefano Morozzi	09/2020
5275	15^83575-58	98292	Lelio R Paula	08/2016
5276	10^98288+3	98289	Robert Price	03/2011
5277	10^98288-117017	98288	Patrick De Geest	11/2011
5278	(44*10^98284-719)/9	98285	Robert Price	12/2017
5279	23466^15419+15419^23466	98277	Hans Havermann	02/2020
5280	2^326421-2797573	98263	Enzo Doria	04/2016
5281	2^326401+16095	98257	Lelio R Paula	07/2016
5282	7^116240-116240^7	98235	Norbert Schneider	05/2017
5283	17^79826-78	98222	Lelio R Paula	08/2016
5284	2^326268-809	98217	Yves Minet	04/2011
5285	22659^21590+21590^22659	98210	Hans Havermann	10/2019
5286	22268^22587-22587^22268	98202	Norbert Schneider	08/2020
5287	(418*10^98199+23)/9	98201	Robert Price	08/2017
5288	12*10^98198-7	98200	Robert Price	11/2017
5289	15^83496-76	98199	Lelio R Paula	08/2016
5290	(10223*2^326179+1)/6125	98190	Lelio R Paula	07/2014
5291	9*5^140471-4	98186	Lelio R Paula	11/2014
5292	22774^20455+20455^22774	98175	Hans Havermann	07/2020
5293	2^326069-2383	98157	Yves Minet	10/2013
5294	2^325973+1185	98128	Lelio R Paula	07/2016
5295	(25*2^325949-1)/17	98121	Lelio R Paula	02/2014
5296	2^325945-1847269	98120	Enzo Doria	07/2015
5297	8*10^98111-67	98112	Robert Price	10/2017
5298	(2^325902+1138)/2	98106	Stefano Morozzi	09/2020
5299	2^325866+15	98096	Lelio R Paula	12/2012
5300	22591^21952+21952^22591	98079	Hans Havermann	02/2020
5301	2^325765+1974305	98066	Enzo Doria	06/2016
5302	2^325733-58695	98056	Lelio R Paula	07/2016
5303	2^325717-3645	98051	Lelio R Paula	07/2016
5304	(2^325704+718)/2	98047	Stefano Morozzi	09/2020
5305	23968^12293+12293^23968	98021	Hans Havermann	11/2019
5306	(23*2^325583-1)/21	98011	Lelio R Paula	02/2014
5307	(7*10^98007-13)/3	98008	Robert Price	06/2016
5308	(2^325544+1110)/2	97999	Stefano Morozzi	09/2020
5309	2^325512-459959	97989	Enzo Doria	05/2015
5310	(2^325492+682)/2	97983	Stefano Morozzi	09/2020
5311	(3^205354-8)/17	97978	Lelio R Paula	09/2013
5312	2^325433+76817	97966	Enzo Doria	05/2016
5313	5*10^97963+81	97964	Robert Price	08/2017
5314	2^325390-109061	97953	Enzo Doria	04/2014
5315	13^87921+24	97940	Lelio R Paula	08/2016
5316	961^32831-960^32831	97926	Jean-Louis Charton	02/2011
5317	22600^21499+21499^22600	97913	Hans Havermann	05/2020
5318	2^325215+12909	97900	Lelio R Paula	07/2016
5319	22619^21286+21286^22619	97898	Hans Havermann	04/2020
5320	(85*10^97876-49)/9	97877	Robert Price	12/2020
5321	7*10^97874-69	97875	Robert Price	01/2017
5323	(17^79537+5^79537)/22	97865	Robert Price	06/2013
5322	15^83212+22	97865	Lelio R Paula	08/2016
5324	2^325087-109057	97861	Enzo Doria	04/2014
5325	2^325074+1870657	97858	Enzo Doria	05/2016
5327	2^325066-2111	97855	Yves Minet	08/2013
5326	CopelandErdos(97855)	97855	Eric W. Weisstein	10/2015
5328	26660^4677+4677^26660	97842	Hans Havermann	12/2019
5329	18^77944-89	97841	Lelio R Paula	07/2016
5330	119^47136+118	97833	Norbert Schneider	09/2018
5331	6^125720-17663	97830	Enzo Doria	02/2013
5332	2^324972-2069	97827	Yves Minet	05/2013
5333	2^324958-4691	97823	Yves Minet	05/2019
5334	2^324944-2788319	97818	Enzo Doria	03/2016
5335	22845^19112+19112^22845	97807	Hans Havermann	10/2019
5336	(2^324898+1270)/2	97804	Stefano Morozzi	09/2020
5338	4*10^97799-9	97800	Erik Branger	11/2013
5337	2^324882+577294575	97800	Lelio R Paula	09/2016
5339	2^324863-1867921	97794	Enzo Doria	04/2016
5340	6^125662-18473	97785	Enzo Doria	03/2013
5341	12^90604+11	97779	Lelio R Paula	07/2016
5342	5^139830+24	97737	Lelio R Paula	04/2016
5343	(2^324672+1198)/2	97736	Stefano Morozzi	09/2020
5344	2^324612+1155	97718	Lelio R Paula	07/2016
5345	(2^324597+3542)/2	97714	Stefano Morozzi	09/2020
5346	19^76404-44	97702	Lelio R Paula	07/2016
5347	2^324505-2983	97686	Yves Minet	04/2011
5348	(144^45259+1)/145	97684	Paul Bourdelais	08/2019
5349	(31*2^324496-1)/45	97683	Lelio R Paula	02/2014
5350	6^125488-17843	97649	Enzo Doria	02/2013
5351	(2^324350+3198)/2	97639	Stefano Morozzi	09/2020
5352	7^115515-2	97622	Lelio R Paula	09/2013
5353	(89^50069-1)/88	97603	Paul Bourdelais	08/2017
5354	6^125418-5	97595	Lelio R Paula	11/2014
5355	(2^324193+3522)/2	97592	Stefano Morozzi	09/2020
5356	(2^324172+666)/2	97586	Stefano Morozzi	09/2020
5357	2^324076+1155	97557	Lelio R Paula	07/2016
5358	(2^324074+9)/13	97555	Lelio R Paula	10/2013
5359	(55459*2^323993+1)/21	97536	Lelio R Paula	07/2014
5360	13^87557-12^87557	97534	Jean-Louis Charton	12/2008
5361	2^323946+73939	97518	Enzo Doria	04/2016
5362	2^323937+1866947	97515	Enzo Doria	03/2016
5364	6^125290-18533	97495	Enzo Doria	03/2013
5363	(2^323870+1650)/2	97495	Stefano Morozzi	09/2020
5365	2^323845+101	97488	Lelio R Paula	12/2012
5366	18^77662+65	97487	Lelio R Paula	07/2016
5367	22634^20265+20265^22634	97479	Hans Havermann	04/2020
5368	2^323772+76771	97466	Enzo Doria	05/2016
5369	2^323765-112213	97463	Enzo Doria	06/2014
5370	22730^19389+19389^22730	97457	Hans Havermann	02/2020
5371	2^323720-6555	97450	Lelio R Paula	07/2016
5372	2^323694-1860401	97442	Enzo Doria	03/2016
5373	20^74886+3	97429	Lelio R Paula	06/2016
5374	24476^9561+9561^24476	97427	Hans Havermann	01/2020
5375	(2^323623+1766)/2	97420	Stefano Morozzi	09/2020
5377	3*10^97399+73	97400	Robert Price	04/2016
5376	7^115252-50	97400	Lelio R Paula	07/2016
5378	224737#+393581	97389	Nicolas PALAU	12/2016
5379	(2^323468+3186)/2	97374	Stefano Morozzi	09/2020
5380	(2^323456+538)/2	97370	Stefano Morozzi	09/2020
5381	23277^15236+15236^23277	97365	Hans Havermann	07/2020
5383	(26*10^97353+31)/3	97354	Robert Price	07/2016
5382	(2^323403+3510)/2	97354	Stefano Morozzi	09/2020
5384	23756^12519+12519^23756	97342	Hans Havermann	07/2020
5385	23991^11402+11402^23991	97332	Hans Havermann	07/2020
5386	61^54517-60^54517	97331	Jean-Louis Charton	09/2005
5387	(38*10^97329+187)/9	97330	Robert Price	11/2017
5388	86455!4+8	97319	Robert Price	09/2019
5389	22591^20310+20310^22591	97316	Hans Havermann	06/2020
5390	25101^7520+7520^25101	97297	Hans Havermann	05/2020
5391	p(19982)#/2-1024	97293	Robert Price	09/2017
5392	6^125021-85	97286	Lelio R Paula	08/2016
5393	2^323164-47355	97283	Lelio R Paula	07/2016
5394	(3^203902+4)/36051015157	97276	Lelio R Paula	09/2013
5395	2^323054-6555	97249	Lelio R Paula	07/2016
5396	22822^18247+18247^22822	97249	Hans Havermann	02/2020
5397	9*10^97247-29	97248	Robert Price	05/2017
5398	24382^9735+9735^24382	97244	Hans Havermann	02/2020
5399	(31*10^97242+41)/9	97243	Robert Price	04/2015
5400	GoldenRatioPrime[97241]	97241	Eric W. Weisstein	06/2009
5401	12^90098-41	97233	Lelio R Paula	07/2016
5402	2^322928-216929	97212	Enzo Doria	05/2014
5403	(7*2^322896-1)/57	97201	Lelio R Paula	02/2014
5404	(2^322897+5)/3146107489	97193	Lelio R Paula	10/2013
5405	(2^322789+2214)/2	97169	Stefano Morozzi	09/2020
5406	2^322725+75761	97150	Enzo Doria	04/2016
5407	(13*2^322686+1)/119	97138	Lelio R Paula	11/2013
5408	22402^21639+21639^22402	97118	Hans Havermann	07/2020
5409	23399^14128+14128^23399	97108	Hans Havermann	06/2020
5410	(2^322525+2606)/2	97090	Stefano Morozzi	09/2020
5411	(41*10^97085+373)/9	97086	Robert Price	04/2017
5412	2^322413+77	97056	Lelio R Paula	12/2012
5413	2^322406+177	97054	Lelio R Paula	12/2012
5414	(14*10^97044+31)/9	97045	Robert Price	02/2015
5415	2^322302+255255	97023	Lelio R Paula	07/2016
5416	2^322196-113093	96991	Enzo Doria	07/2014
5417	(2^322169+2690)/2	96983	Stefano Morozzi	09/2020
5418	23109^15668+15668^23109	96943	Hans Havermann	07/2020
5419	2^322000-1861469	96932	Enzo Doria	03/2016
5420	2^321971-112747	96923	Enzo Doria	06/2014
5421	23754^12023+12023^23754	96917	Hans Havermann	07/2020
5422	11^93062-92	96915	Lelio R Paula	06/2016
5423	(2^321922+2214)/2	96908	Stefano Morozzi	09/2020
5424	(2^321900+2086)/2	96902	Stefano Morozzi	09/2020
5425	(11*2^321841-7)/15	96884	Renaud Lifchitz	03/2011
5426	3^203051+34	96880	Lelio R Paula	05/2016
5427	2*10^96867-51	96868	Robert Price	11/2017
5428	(2^321779+2618)/2	96865	Stefano Morozzi	09/2020
5429	(64*10^96863-1)/27	96864	Serge Batalov	05/2010
5430	2^321716-2786939	96847	Enzo Doria	03/2016
5431	22496^20181+20181^22496	96844	Hans Havermann	03/2020
5432	2^321701-113053	96842	Enzo Doria	07/2014
5433	2^321700-28635	96842	Lelio R Paula	06/2016
5434	(5*2^321691-1)/27	96838	Lelio R Paula	02/2014
5435	6^124433-124433	96828	Robert Price	01/2014
5436	2^321631+69	96821	Lelio R Paula	12/2012
5437	(13*2^321606+1)/119	96813	Lelio R Paula	11/2013
5438	(46*10^96798-1)/9	96799	Serge Batalov	10/2014
5439	(59*10^96798+31)/9	96799	Robert Price	09/2015
5440	(2^321536+2062)/2	96792	Stefano Morozzi	09/2020
5441	223319#+231223	96790	Makoto Morimoto	02/2016
5442	2^321519-28635	96787	Lelio R Paula	06/2016
5443	2^321487-1867237	96778	Enzo Doria	03/2016
5444	2^321461-63	96770	Lelio R Paula	12/2012
5445	2^321439+123	96763	Lelio R Paula	12/2012
5446	2^321434+709	96762	Lelio R Paula	02/2013
5447	(2^321415+554)/2	96756	Stefano Morozzi	09/2020
5448	14^84413+89	96749	Lelio R Paula	07/2016
5449	(28*10^96743+71)/9	96744	Serge Batalov	12/2008
5450	13^86847+96	96743	Lelio R Paula	06/2016
5451	9*2^321336-7	96733	Lelio R Paula	08/2014
5452	(209*10^96722-17)/3	96724	Robert Price	05/2017
5453	2^321237-4615	96702	Yves Minet	05/2019
5454	2^321187-1159	96687	Yves Minet	11/2012
5455	2^321182-1850081	96686	Enzo Doria	08/2015
5456	23359^13768+13768^23359	96680	Hans Havermann	06/2020
5457	2^321116-112829	96666	Enzo Doria	06/2014
5458	2^321108-109499	96664	Enzo Doria	04/2014
5459	2^321098+2793859	96661	Enzo Doria	03/2016
5460	(2^321100+1170)/2	96661	Stefano Morozzi	09/2020
5461	2^321057+4097	96648	Lelio R Paula	06/2016
5463	(4435*29^66081-4)/7	96640	Curtis Bright	05/2015
5462	22743^17750+17750^22743	96640	Hans Havermann	04/2020
5464	22882^16679+16679^22882	96612	Hans Havermann	02/2020
5465	23452^13163+13163^23452	96608	Hans Havermann	02/2020
5466	(2^320863+666)/2	96590	Stefano Morozzi	09/2020
5467	p(19849)#/2-64	96581	Robert Price	04/2017
5469	2^320817+189	96576	Lelio R Paula	12/2012
5468	2^320816-4685	96576	Yves Minet	05/2019
5470	(361*10^96567-163)/9	96569	Robert Price	10/2017
5471	2^320788-110327	96567	Enzo Doria	05/2014
5472	2^320764+793	96560	Lelio R Paula	02/2013
5473	(9179*2^320652-1)/221	96528	Lelio R Paula	05/2015
5474	23288^13947+13947^23288	96517	Hans Havermann	07/2020
5475	2^320616-78795	96516	Lelio R Paula	03/2016
5476	2^320612-461939	96514	Enzo Doria	07/2015
5477	10^96504+987654321	96505	Robert Price	12/2019
5478	10^96504+71887	96505	Patrick De Geest	02/2020
5479	22654^18195+18195^22654	96505	Hans Havermann	07/2020
5480	10^96504-139277	96504	Patrick De Geest	02/2020
5481	5*2^320431+7	96461	Lelio R Paula	08/2014
5482	19^75431-90	96458	Lelio R Paula	06/2016
5483	(2^320370+3)/67	96440	Lelio R Paula	10/2013
5484	2^320309+1871477	96423	Enzo Doria	05/2016
5485	tau(809^6028)	96410	Nik Lygeros / Olivier Rozier / LR team	10/2013
5486	(21*2^320252-1)/1895	96404	Lelio R Paula	02/2014
5487	2^320232-173	96400	Lelio R Paula	12/2012
5488	175^42975-2	96395	Lelio R Paula	10/2017
5489	(2^320170+2718)/2	96381	Stefano Morozzi	09/2020
5490	10^96377+199911	96378	Patrick De Geest	12/2016
5491	10^96377-20001	96377	Robert Price	11/2016
5492	2^320124-2790449	96367	Enzo Doria	03/2016
5493	22488^19255+19255^22488	96351	Hans Havermann	11/2019
5494	23248^13939+13939^23248	96346	Hans Havermann	11/2019
5496	2^320043-108775	96343	Enzo Doria	04/2014
5495	24989^7168+7168^24989	96343	Hans Havermann	11/2019
5497	10^96338+424939	96339	Patrick De Geest	03/2016
5498	10^96338-9281	96338	Robert Price	09/2015
5499	(3*2^320008+1)/7	96332	Lelio R Paula	09/2013
5500	25699^5596+5596^25699	96317	Hans Havermann	07/2020

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