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	8*6^121849-7	94818	Lelio R Paula	10/2014
5252	(85*10^94802+473)/9	94803	Robert Price	03/2017
5253	21767^21852-21852^21767	94790	Norbert Schneider	06/2020
5254	2^314870-108761	94786	Enzo Doria	03/2014
5255	5*2^314841-3	94778	Lelio R Paula	08/2014
5256	(2^314842+550)/2	94777	Stefano Morozzi	09/2020
5257	(2^314787+2630)/2	94761	Stefano Morozzi	09/2020
5258	6^121772+113	94758	Lelio R Paula	05/2016
5259	(2^314740+3642)/2	94746	Stefano Morozzi	09/2020
5260	6^121756-16253	94745	Enzo Doria	02/2013
5261	2^314718-112793	94740	Enzo Doria	06/2014
5262	2^314697-1847293	94734	Enzo Doria	07/2015
5263	22836^14065+14065^22836	94727	Hans Havermann	09/2020
5265	2^314548-249	94689	Yves Minet	02/2012
5264	5^135469+42	94689	Lelio R Paula	04/2016
5266	gcd(V(1137755),5F(227551)(F(227551)-1)+1)	94676	Serge Batalov	04/2015
5267	25773^4712+4712^25773	94670	Hans Havermann	08/2020
5268	(2^314485+3614)/2	94670	Stefano Morozzi	09/2020
5269	(2*10^94604+547)/9	94604	Robert Price	10/2017
5270	(2^314164+2562)/2	94573	Stefano Morozzi	09/2020
5271	3*2^314152+5	94570	Lelio R Paula	08/2014
5272	2*6^121530-5	94570	Lelio R Paula	10/2014
5273	7*10^94563+87	94564	Robert Price	11/2016
5274	2^314114-109677	94558	Enzo Doria	04/2014
5275	(218389#+240867)/(311811)	94557	Makoto Morimoto	10/2017
5276	2^314059+76583	94542	Enzo Doria	05/2016
5277	2^314041-4035	94536	Lelio R Paula	03/2016
5278	(2^314028+3102)/2	94532	Stefano Morozzi	09/2020
5279	(2^314012+618)/2	94527	Stefano Morozzi	09/2020
5280	(7*2^314003-11)/15	94524	Renaud Lifchitz	03/2011
5281	11^90760-4710	94517	Enzo Doria	01/2013
5282	21675^21796+21796^21675	94507	Norbert Schneider	04/2020
5283	(7*2^313926-1)/148821	94497	Lelio R Paula	02/2014
5284	94*10^94493-3	94495	Robert Price	11/2016
5285	(1000547^15749+1)/1000548	94492	Faysal YAtim	12/2008
5286	(2^313859+2706)/2	94481	Stefano Morozzi	09/2020
5287	(F(375345)^2+L(375345)^2)/4	94477	Henri Lifchitz	10/2017
5288	7^111792-32	94476	Lelio R Paula	04/2016
5289	(202*10^94441-1)/3	94443	Robert Price	05/2020
5290	11^90680-5850	94434	Enzo Doria	01/2013
5291	(752^32833-1)/751	94432	Michael Stocker	05/2020
5292	2^313675-110125	94426	Enzo Doria	04/2014
5293	(2999*29^64556-2427)/4	94410	Curtis Bright	05/2015
5294	2^313609-112225	94406	Enzo Doria	06/2014
5295	2^313584+72901	94399	Enzo Doria	04/2016
5296	(2^313562+730)/2	94392	Stefano Morozzi	09/2020
5297	2^313510-112865	94376	Enzo Doria	06/2014
5298	7*10^94373+87	94374	Robert Price	11/2016
5299	(9^98897+8^98897)/17	94371	Robert Price	12/2012
5300	2^313453-114703	94359	Enzo Doria	04/2015
5301	8*10^94357-51	94358	Robert Price	10/2017
5302	25903^4392+4392^25903	94356	Hans Havermann	09/2020
5303	31706^945+945^31706	94340	Hans Havermann	09/2020
5304	(379*10^94337-1)/9	94339	Robert Price	08/2017
5305	2^313344-313344+1	94326	Robert Price	10/2014
5306	(2^313313+3662)/2	94317	Stefano Morozzi	09/2020
5307	20^72481-49	94300	Lelio R Paula	05/2016
5308	44725!2+128	94289	Robert Price	03/2015
5309	4*10^94286+9	94287	Robert Price	05/2015
5310	17^76621+24	94279	Lelio R Paula	07/2016
5311	26274^3875+3875^26274	94279	Hans Havermann	09/2020
5312	2^313156-112859	94270	Enzo Doria	06/2014
5313	6^121130-59	94258	Lelio R Paula	05/2016
5314	3^197542+28	94252	Robert Price	11/2013
5315	(2^313076+3550)/2	94245	Stefano Morozzi	09/2020
5316	(3^197521+2)/51655	94237	Lelio R Paula	04/2013
5317	2^313045-5955	94236	Lelio R Paula	03/2016
5318	22099^18358+18358^22099	94227	Hans Havermann	08/2020
5319	(67*10^94212+23)/9	94213	Ray Chandler	02/2011
5320	2^312909-1865203	94195	Enzo Doria	03/2016
5321	25013^5830+5830^25013	94191	Hans Havermann	09/2020
5322	2^312848-149	94177	Lelio R Paula	11/2012
5323	4^156403-77597	94164	Mike Oakes	04/2011
5324	18^75004-85	94151	Lelio R Paula	06/2016
5325	19^73622-48	94145	Lelio R Paula	06/2016
5326	(11^90397-3^90397)/8	94138	Robert Price	04/2011
5327	(3^197287+5)/16	94129	Lelio R Paula	04/2013
5328	24220^7691+7691^24220	94119	Hans Havermann	09/2020
5329	12^87212-37	94118	Lelio R Paula	06/2016
5330	11^90376+76	94117	Lelio R Paula	05/2016
5331	(6^120946-11)/5	94114	Paul Bourdelais	11/2011
5332	(2^312622+534)/2	94109	Stefano Morozzi	09/2020
5333	(10^94096+191)/3	94096	Robert Price	11/2017
5334	23794^9005+9005^23794	94093	Hans Havermann	09/2020
5335	2^312562-112685	94091	Enzo Doria	06/2014
5336	137^44026-2	94072	Lelio R Paula	10/2017
5337	s(164441)	94052	Robert Price	05/2020
5338	2^312404-869688105	94043	Lelio R Paula	09/2016
5339	2^312387+2793533	94038	Enzo Doria	03/2016
5341	10^94016+91	94017	Robert Price	04/2011
5340	(15*2^312325-1)/7201	94017	Lelio R Paula	02/2014
5342	10^94016-188963	94016	Patrick De Geest	08/2013
5343	(17*2^312315-1)/45	94016	Lelio R Paula	02/2014
5344	23866^8691+8691^23866	94010	Hans Havermann	08/2020
5345	6^120802+7661	94003	Mike Oakes	04/2011
5346	(67607*2^312254+1)/177	94001	Lelio R Paula	06/2014
5347	(2^312245+702)/2	93995	Stefano Morozzi	09/2020
5348	(11*2^312207+1)/19	93984	Lelio R Paula	09/2013
5349	2^312201+51	93982	Lelio R Paula	11/2012
5350	(4*6^120749+1)/5	93961	Serge Batalov	10/2014
5351	3^196892+58	93942	Lelio R Paula	05/2016
5352	2^312060+18915	93940	Lelio R Paula	03/2016
5353	42^57867-41	93933	Norbert Schneider	08/2018
5354	2^311992-16209	93919	Enzo Doria	04/2013
5355	(85^48677+1)/86	93917	Paul Bourdelais	08/2017
5356	2^311965-39	93911	Lelio R Paula	11/2012
5357	2^311920-111689	93898	Enzo Doria	05/2014
5358	130^44414+129	93889	Norbert Schneider	01/2019
5359	(2^311892+2730)/2	93889	Stefano Morozzi	09/2020
5360	7*10^93887-47	93888	Robert Price	02/2017
5361	(2^311778+1530)/2	93855	Stefano Morozzi	09/2020
5362	12^86965-13	93851	Lelio R Paula	06/2016
5363	24862^5953+5953^24862	93848	Hans Havermann	09/2020
5364	22299^16148+16148^22299	93837	Hans Havermann	08/2020
5365	2^311705+16095	93833	Lelio R Paula	03/2016
5366	(2^311701+3002)/2	93832	Stefano Morozzi	09/2020
5368	2^311665-81	93821	Lelio R Paula	11/2012
5367	(2^311665+2654)/2	93821	Stefano Morozzi	09/2020
5369	(2^311648+3058)/2	93816	Stefano Morozzi	09/2020
5370	730^32761+32761^730	93806	Norbert Schneider	09/2017
5371	11^90073+92	93802	Lelio R Paula	05/2016
5372	6*10^93792+41	93793	Robert Price	01/2017
5373	10^93790+64611	93791	Patrick De Geest	04/2020
5376	(2^311580+7)/591329	93790	Lelio R Paula	06/2013
5374	10^93790-123456789	93790	Robert Price	02/2020
5375	10^93790-157517	93790	Patrick De Geest	04/2020
5377	12^86900-77	93781	Lelio R Paula	06/2016
5378	2^311508-109769	93774	Enzo Doria	04/2014
5379	2^311486-1859621	93767	Enzo Doria	03/2016
5380	Phi(93811,10)/968129521/2109997013/3280113810431/639637782545831	93765	Kurt Beschorner	04/2015
5381	(10^93811-1)/(996812952121099970133280113810431639637782545831)	93765	Gord Palameta	10/2018
5382	2^311471+311469	93763	Renaud Lifchitz	01/2003
5383	(88*10^93760-1)/3	93762	Robert Price	10/2017
5384	2^311426+79459	93749	Enzo Doria	06/2016
5385	21537^21634+21634^21537	93745	Norbert Schneider	04/2020
5386	(2^311360+3078)/2	93729	Stefano Morozzi	09/2020
5387	(2^311341+2186)/2	93723	Stefano Morozzi	09/2020
5388	(2^311313+774)/2	93715	Stefano Morozzi	09/2020
5390	2^311294+5775	93709	Lelio R Paula	03/2016
5389	25155^5312+5312^25155	93709	Hans Havermann	09/2020
5391	2^311252-1017	93697	Lelio R Paula	03/2016
5392	2^311247-112041	93695	Enzo Doria	06/2014
5393	7*10^93692-83	93693	Robert Price	09/2017
5394	2^311205-109645	93683	Enzo Doria	04/2014
5395	5^134027-84	93681	Lelio R Paula	04/2016
5396	(2^311148-1017)/557	93663	Lelio R Paula	06/2013
5397	(2^311027-2^155514+1)/5	93628		11/2006
5398	26748^3161+3161^26748	93614	Hans Havermann	08/2020
5399	3^196192-28	93608	Robert Price	12/2013
5400	216091#+261433	93606	Makoto Morimoto	12/2015
5401	5^133917+68	93604	Lelio R Paula	04/2016
5402	2^310924-1709	93598	Yves Minet	03/2013
5403	24555^6476+6476^24555	93587	Hans Havermann	08/2020
5404	(2^310867+734)/2	93580	Stefano Morozzi	09/2020
5405	(266*10^93577-11)/3	93579	Robert Price	09/2016
5406	(16*10^93577+161)/3	93578	Robert Price	05/2016
5407	3^196113-56	93570	Lelio R Paula	04/2016
5408	2^310806-110345	93562	Enzo Doria	05/2014
5409	3^196093+86	93561	Lelio R Paula	04/2016
5410	2^310780-2327	93555	Yves Minet	10/2013
5411	30^63332+41	93550	Lelio R Paula	08/2012
5412	(21181*2^310707+1)/21	93536	Lelio R Paula	06/2014
5413	8*5^133807+7	93528	Lelio R Paula	10/2014
5414	2^310686+8193	93526	Lelio R Paula	03/2016
5415	22681^13282+13282^22681	93520	Hans Havermann	09/2020
5416	2^310646+63	93514	Lelio R Paula	11/2012
5417	(77*10^93508+31)/9	93509	Robert Price	10/2015
5418	(1000907^15583+1)/1000908	93499	Faysal YAtim	04/2009
5419	(2*10^93497+7)/9	93497	Erik Branger	03/2011
5420	3^195958-112852	93496	Enzo Doria	07/2014
5421	2^310583+16385	93495	Lelio R Paula	03/2016
5422	(9913*2^310557-1)/35	93490	Lelio R Paula	04/2015
5423	9*7^110614+2	93481	Lelio R Paula	11/2014
5424	(19*10^93467+83)/3	93468	Robert Price	08/2020
5425	2^310469-8295	93461	Lelio R Paula	03/2016
5426	2^310459-1159	93458	Yves Minet	11/2012
5427	6^120075-95	93437	Lelio R Paula	05/2016
5428	(2^310362+1758)/2	93428	Stefano Morozzi	09/2020
5429	148^43041-147	93411	Norbert Schneider	05/2019
5430	2^310289+98327	93407	Yves Minet	11/2010
5431	21769^19510+19510^21769	93395	Hans Havermann	08/2020
5432	2^310217-113143	93385	Enzo Doria	07/2014
5433	7^110494-68	93379	Lelio R Paula	04/2016
5434	2^310184-113093	93375	Enzo Doria	07/2014
5435	2^310180-110417	93374	Enzo Doria	05/2014
5436	gcd(V(1124905),5F(224981)(F(224981)-1)+1)	93372	Serge Batalov	04/2015
5437	(2^310173+3150)/2	93372	Stefano Morozzi	09/2020
5438	3^195669+68	93358	Lelio R Paula	04/2016
5439	10^93356+91	93357	Robert Price	04/2011
5440	10^93356-28313	93356	Patrick De Geest	08/2013
5441	(85*10^93346+23)/9	93347	Robert Price	11/2015
5442	(3^195648-5)/3158276	93342	Lelio R Paula	04/2013
5443	3^195556+8680	93304	Lelio R Paula	04/2016
5444	2^309942-109991	93302	Enzo Doria	04/2014
5445	2^309926-1867301	93298	Enzo Doria	03/2016
5446	2^309924+85951	93297	Yves Minet	03/2011
5447	2^309896-4229	93288	Yves Minet	08/2018
5448	(86*10^93263-77)/9	93264	Robert Price	05/2016
5449	6^119836-125	93251	Lelio R Paula	05/2016
5450	(77*10^93249-257)/9	93250	Robert Price	10/2017
5451	21822^18749+18749^21822	93245	Hans Havermann	09/2020
5452	3^195430-2	93244	Theodore Burton	02/2007
5453	(13*10^93236+47)/3	93237	Robert Price	01/2017
5454	(67*10^93226-7)/3	93228	Robert Price	10/2017
5455	(86*10^93217-221)/9	93218	Robert Price	06/2017
5456	2^309637-16329	93211	Enzo Doria	04/2013
5457	(41*10^93207+49)/9	93208	Robert Price	04/2016
5458	14^81312-57	93194	Lelio R Paula	06/2016
5459	41^57783-40	93192	Theodore Burton	02/2007
5460	3*10^93179-97	93180	Robert Price	08/2017
5461	5*7^110252-4	93175	Lelio R Paula	11/2014
5462	22022^16959+16959^22022	93140	Hans Havermann	08/2020
5463	83061!4-512	93137	Robert Price	11/2019
5464	25169^5016+5016^25169	93135	Hans Havermann	08/2020
5465	2^309380-27	93133	Lelio R Paula	11/2012
5466	25653^4268+4268^25653	93127	Hans Havermann	08/2020
5467	(2^309334+2710)/2	93119	Stefano Morozzi	09/2020
5468	23*10^93116-7	93118	Robert Price	03/2016
5469	(2^309270+3214)/2	93100	Stefano Morozzi	09/2020
5470	(29*10^93082+1)/3	93083	Robert Price	11/2015
5471	(2^309198+3738)/2	93078	Stefano Morozzi	09/2020
5472	(58*10^93062-13)/9	93063	Robert Price	09/2015
5473	2^309131+1869383	93058	Enzo Doria	05/2016
5474	(2^309114+3610)/2	93053	Stefano Morozzi	09/2020
5475	2^309066-93	93039	Lelio R Paula	11/2012
5476	2^309063-113269	93038	Enzo Doria	07/2014
5477	3^194965+16	93022	Robert Price	10/2013
5478	2^308979+1869143	93012	Enzo Doria	05/2016
5479	5^133064+54	93008	Lelio R Paula	04/2016
5480	(2^308905-509203)/119	92988	Lelio R Paula	06/2013
5481	(94*10^92981-49)/99	92981	Ray Chandler	07/2011
5482	(2*10^92976-17)/3	92976	Robert Price	08/2014
5483	24783^5642+5642^24783	92972	Hans Havermann	08/2020
5484	2^308809+37967	92961	Phil Moore	03/2008
5485	(3^194825+5)/11656	92952	Lelio R Paula	04/2013
5486	(2^308679+5)/1573	92919	Lelio R Paula	06/2013
5487	2^308650+513	92913	Lelio R Paula	02/2016
5488	5*7^109936+6	92908	Lelio R Paula	10/2014
5489	2*10^92897+89	92898	Robert Price	07/2016
5490	(2^308585+3182)/2	92894	Stefano Morozzi	09/2020
5491	12^86073-29	92889	Lelio R Paula	06/2016
5492	2^308566-117	92888	Lelio R Paula	11/2012
5493	(17*10^92869-11)/3	92870	Robert Price	07/2015
5494	2^308459+75431	92856	Enzo Doria	04/2016
5495	2^308426-1866377	92846	Enzo Doria	03/2016
5496	24810^5521+5521^24810	92840	Hans Havermann	09/2020
5497	(96^46831-1)/95	92830	Paul Bourdelais	09/2017
5498	2^308349-112111	92823	Enzo Doria	06/2014
5499	9*10^92821+19	92822	Robert Price	05/2016
5500	2^308337-75	92819	Lelio R Paula	11/2012

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Probable Primes Top 10000

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