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 ?
4501	2^299639-187	90201	Lelio R Paula	10/2012
4502	10^90199-2891	90199	Patrick De Geest	09/2018
4503	2^299631+183	90198	Lelio R Paula	10/2012
4504	10^90196-9683	90196	Patrick De Geest	09/2018
4505	10^90193-9809	90193	Patrick De Geest	09/2018
4506	(21*2^299611-1)/29	90192	Lelio R Paula	02/2014
4507	2^299567+113	90179	Lelio R Paula	10/2012
4508	2^299550+189	90174	Lelio R Paula	10/2012
4509	10^90170-6749	90170	Patrick De Geest	09/2018
4510	(2^299535+3)/29	90168	Lelio R Paula	01/2013
4511	10^90160-5613	90160	Patrick De Geest	09/2018
4512	(97*10^90155-1)/3	90157	Serge Batalov	12/2014
4513	3^188938+8680	90147	Lelio R Paula	04/2016
4514	10^90146-2027	90146	Patrick De Geest	09/2018
4516	6^115840-55	90142	Lelio R Paula	05/2016
4515	(5*10^90142-473)/9	90142	Robert Price	12/2017
4517	8*7^106659+5	90139	Lelio R Paula	10/2014
4518	2^299406-16653	90131	Enzo Doria	05/2013
4520	208049#+(216091#)/(208049#)	90128	Makoto Morimoto	04/2016
4519	10^90128-8387	90128	Patrick De Geest	09/2018
4521	(F(5)^128941-F(4)^128941)/F(3)	90126	Wayne Halsdorf	03/2012
4522	6^115819-53	90125	Lelio R Paula	05/2016
4523	10^90123+6313	90124	Patrick De Geest	09/2018
4524	6^115816-16853	90123	Enzo Doria	02/2013
4525	6^115813-23	90121	Lelio R Paula	05/2016
4526	(22*10^90110+161)/3	90111	Robert Price	02/2017
4527	(2^299330-509203)/69	90106	Lelio R Paula	01/2013
4528	10^90105-767	90105	Patrick De Geest	09/2018
4529	10^90104-7703	90104	Patrick De Geest	09/2018
4530	10^90103+9159	90104	Patrick De Geest	09/2018
4531	10^90101-3207	90101	Patrick De Geest	09/2018
4532	(29*10^90096-17)/3	90097	Erik Branger	09/2014
4533	10^90089-3573	90089	Patrick De Geest	09/2018
4534	2^299247+1870529	90083	Enzo Doria	05/2016
4535	10^90079+1609	90080	Patrick De Geest	09/2018
4536	2^299229-2797783	90077	Enzo Doria	04/2016
4537	2^299220-16317	90075	Enzo Doria	04/2013
4538	11^86491-1350	90072	Enzo Doria	12/2012
4539	10^90071-1233	90071	Patrick De Geest	09/2018
4540	10^90069-7841	90069	Patrick De Geest	09/2018
4541	(31*10^90064-1)/3	90066	Robert Price	03/2017
4542	10^90060-839	90060	Patrick De Geest	09/2018
4543	10^90052+2361	90053	Patrick De Geest	09/2018
4544	10^90047+619	90048	Patrick De Geest	09/2018
4545	L(430949)/861899/1440387561539	90045	Serge Batalov	07/2017
4546	2^299112+73951	90042	Enzo Doria	04/2016
4547	8^99702+7^(99702-1)	90040	Robert Price	02/2016
4548	10^90038-9687	90038	Patrick De Geest	09/2018
4549	5*10^90033+3	90034	Dmitry Domanov	11/2010
4550	10^90030-1461	90030	Patrick De Geest	09/2018
4551	243^37738+37738^243	90029	Norbert Schneider	01/2015
4552	10^90025-8703	90025	Patrick De Geest	09/2018
4553	2^299048-113297	90023	Enzo Doria	07/2014
4554	10^90015+849	90016	Patrick De Geest	09/2018
4555	10^90010+6811	90011	Patrick De Geest	09/2018
4556	10^90010-183597	90010	Patrick De Geest	11/2018
4557	10^90009+58321	90010	Patrick De Geest	11/2018
4558	10^90008+847	90009	Patrick De Geest	09/2018
4559	10^90009-356013	90009	Patrick De Geest	11/2018
4561	3^188648+92	90008	Lelio R Paula	12/2015
4560	10^90008-706049	90008	Patrick De Geest	11/2018
4562	5*2^298991+7	90006	Lelio R Paula	08/2014
4563	(25*2^298997+1)/3267	90005	Lelio R Paula	01/2013
4564	10^90000+8869	90001	Patrick De Geest	12/2009
4566	10^89999+82939	90000	Dirk Augustin	04/2007
4565	10^90000-140343	90000	Patrick De Geest	12/2009
4567	10^89999-194891	89999	Patrick De Geest	11/2009
4568	19^70365-78	89980	Lelio R Paula	12/2015
4569	NaturalLogarithmOf2(89973)	89973	Eric W. Weisstein	10/2015
4570	2^298852-64875	89964	Lelio R Paula	11/2013
4571	18^71659+37	89952	Lelio R Paula	12/2015
4572	(2908*29^61501-3)/7	89942	Curtis Bright	05/2015
4573	17^73067+20	89906	Lelio R Paula	11/2015
4574	2^298637-99	89899	Lelio R Paula	10/2012
4575	9^94188+38^94188-24^94188-3*2^94188	89879	Mike Oakes	01/2011
4576	9*10^89858+19	89859	Robert Price	05/2016
4577	2^298501+1870067	89858	Enzo Doria	05/2016
4578	11^86280-98	89852	Lelio R Paula	11/2015
4579	2^298473-110059	89850	Enzo Doria	04/2014
4580	19^70263-32	89850	Lelio R Paula	12/2015
4581	(299*10^89836-17)/3	89838	Robert Price	01/2017
4582	3^188286+14	89836	Robert Price	09/2013
4583	gcd(V(1091095),5F(218219)(F(218219)+1)+1)	89822	Serge Batalov	04/2015
4584	2^298367+58905	89818	Lelio R Paula	11/2013
4585	2^298319-109657	89803	Enzo Doria	04/2014
4586	8*10^89800+81	89801	Robert Price	05/2017
4587	18^71505-91	89759	Lelio R Paula	12/2015
4588	(7^106187+1)/8	89738	Paul Bourdelais	04/2008
4589	2^298079-109531	89731	Enzo Doria	04/2014
4590	117^43380+116	89718	Norbert Schneider	08/2018
4591	(22699*2^298016+1)/385	89714	Lelio R Paula	06/2014
4592	156(10^(422427)-1)/101-1	89709	Robert Price	05/2014
4593	2^298003-66945	89708	Lelio R Paula	11/2013
4594	(23*10^89705-83)/3	89706	Robert Price	09/2017
4595	17^72900-54	89700	Lelio R Paula	11/2015
4596	3*2^297956+5	89695	Lelio R Paula	08/2014
4597	20^68938-11	89691	Lelio R Paula	01/2016
4598	89*10^89687-7	89689	Robert Price	03/2017
4599	2^297923+77783	89684	Enzo Doria	05/2016
4600	11^86107-24576000	89672	Enzo Doria	02/2013
4601	2^297878-111911	89671	Enzo Doria	05/2014
4602	7^106084+40	89652	Lelio R Paula	10/2015
4603	(86*10^89640-311)/9	89641	Robert Price	10/2017
4604	3*10^89608-59	89609	Robert Price	10/2017
4605	3^187780-11038	89594	Enzo Doria	05/2014
4606	(13*2^297560-1)/49151787	89568	Lelio R Paula	02/2014
4607	5^128141-36	89567	Lelio R Paula	10/2015
4608	4*7^105951+9	89540	Lelio R Paula	10/2014
4609	(7*10^89539-439)/9	89539	Robert Price	09/2017
4610	2^297397+177257	89526	Enzo Doria	05/2016
4611	2^297346-16241	89511	Enzo Doria	04/2013
4612	(5*10^89510+79)/3	89511	Robert Price	11/2017
4614	4^148663-3^148663	89505	Jean-Louis Charton	11/2005
4613	2^297328-869688105	89505	Lelio R Paula	07/2016
4615	2^297325-459043	89504	Enzo Doria	05/2015
4616	2^297310-112391	89500	Enzo Doria	06/2014
4617	2^297296-112157	89496	Enzo Doria	06/2014
4618	57^50966-2	89490	Lelio R Paula	08/2013
4619	(266*10^89482+1)/3	89484	Robert Price	02/2016
4620	(14*10^89480-101)/3	89481	Robert Price	04/2017
4621	2^297122+99	89443	Lelio R Paula	10/2012
4622	(3^187435-5)/1286	89427	Lelio R Paula	01/2013
4623	(25*10^89413+161)/3	89414	Robert Price	01/2017
4624	2^296990+1870699	89403	Enzo Doria	05/2016
4625	2^296972-1017	89398	Lelio R Paula	11/2013
4626	(7*10^89383+167)/3	89384	Robert Kinser	10/2017
4627	(85*10^89375-31)/9	89376	Robert Price	11/2015
4628	9*2^296870+7	89368	Lelio R Paula	08/2014
4629	100^44683-99^44683	89366	Robert Price	07/2013
4630	2^296810+76519	89349	Enzo Doria	05/2016
4631	8^98928+7^(98928+1)	89341	Robert Price	06/2016
4632	(3^187247+4)/1027	89337	Lelio R Paula	01/2013
4633	(3^187235-2)/2045	89331	Lelio R Paula	01/2013
4635	2^296736-432149	89327	Paul Bourdelais	05/2013
4634	2^296737-112519	89327	Enzo Doria	06/2014
4636	2^296718-3645	89322	Lelio R Paula	11/2013
4637	2^296681-16221	89310	Enzo Doria	04/2013
4638	2^296669-16513	89307	Enzo Doria	04/2013
4639	2^296619-16357	89292	Enzo Doria	04/2013
4640	2^296614-110051	89290	Enzo Doria	04/2014
4641	(3^187138+8)/83147	89283	Lelio R Paula	01/2013
4642	(2*10^89279+457)/9	89279	Robert Price	01/2017
4643	15^75907-28	89274	Lelio R Paula	11/2015
4644	2^296547-37	89270	Yves Minet	01/2012
4645	2^296485+191	89251	Lelio R Paula	10/2012
4646	2^296467-75	89246	Lelio R Paula	10/2012
4647	2^296416-109535	89231	Enzo Doria	04/2014
4648	(23*2^296406+1)/3	89228	Lelio R Paula	01/2013
4649	66^49037-65	89225	Norbert Schneider	11/2014
4650	2^296377-16245	89219	Enzo Doria	04/2013
4651	2^296372-64875	89217	Lelio R Paula	11/2013
4652	5*6^114648-7	89215	Lelio R Paula	10/2014
4653	3*10^89206+13	89207	Robert Price	08/2017
4654	7*3^186960-4	89204	Lelio R Paula	08/2014
4655	2^296290-112133	89193	Enzo Doria	06/2014
4656	6^114620-17003	89192	Enzo Doria	02/2013
4657	(4*10^89189+41)/9	89189	Robert Price	11/2014
4658	2^296261-161181	89184	Enzo Doria	04/2013
4659	(19*2^296269-1)/530623	89182	Lelio R Paula	02/2014
4660	3^186903-10	89176	Robert Price	09/2013
4661	7*10^89169-3	89170	Dmitry Domanov	11/2010
4663	(2^296221-1017)/35	89170	Lelio R Paula	01/2013
4662	(43*10^89169+47)/9	89170	Robert Price	12/2017
4664	(10^89160+29)/3	89160	Serge Batalov	12/2014
4665	(28*10^89141-97)/3	89142	Robert Price	07/2016
4666	2^296116-734639	89140	Paul Bourdelais	04/2013
4667	6^114544-133	89133	Lelio R Paula	12/2015
4668	2^296076-113297	89128	Enzo Doria	07/2014
4669	(11*2^296060-1)/215	89122	Lelio R Paula	02/2014
4670	5*10^89118+81	89119	Robert Price	08/2017
4671	2^296037-1411	89117	Yves Minet	01/2013
4672	2^296020-2604809	89111	Enzo Doria	05/2015
4673	2^296016+81	89110	Henri Lifchitz	02/2007
4674	2^296010-11	89108	Lelio R Paula	10/2012
4675	2^295998-111911	89105	Enzo Doria	05/2014
4676	(2^296014+47)/93991149	89102	Lelio R Paula	01/2013
4677	2^295939-16621	89087	Enzo Doria	04/2013
4678	2^295934-109691	89086	Enzo Doria	04/2014
4679	(185*10^89063+7)/3	89065	Robert Price	02/2017
4680	2^295831+143	89055	Lelio R Paula	10/2012
4681	31^59713-30	89054	Theodore Burton	02/2007
4682	(7*2^295834-1)/27663	89052	Lelio R Paula	02/2014
4683	123^42608+2	89047	Lelio R Paula	05/2013
4684	6^114433-114433^6	89047	Norbert Schneider	04/2017
4685	2^295800-459659	89045	Enzo Doria	05/2015
4686	(52*10^89037-1)/3	89039	Robert Price	02/2017
4687	(6^114398-11)/5	89019	Paul Bourdelais	11/2011
4688	11^85470-5850	89008	Enzo Doria	02/2013
4689	(27*2^295634+1)/4687	88993	Lelio R Paula	01/2013
4690	(p(18424)#-4)/2	88985	Robert Price	09/2017
4691	2^295564-189	88974	Lelio R Paula	10/2012
4692	2^295557+73097	88972	Enzo Doria	04/2016
4693	11^85433-5760	88970	Enzo Doria	01/2013
4694	6*10^88938-91	88939	Robert Price	11/2017
4695	15^75619-88	88935	Lelio R Paula	11/2015
4696	2^295385-85	88920	Lelio R Paula	10/2012
4697	2^295385-16333	88920	Enzo Doria	04/2013
4698	2^295309+59	88897	Lelio R Paula	10/2012
4699	2^295288-109799	88891	Enzo Doria	04/2014
4700	10^88888+170373	88889	Stefano Morozzi	07/2018
4701	10^88888+271399	88889	Stefano Morozzi	07/2018
4702	10^88888+375397	88889	Stefano Morozzi	07/2018
4703	10^88888+548823	88889	Stefano Morozzi	07/2018
4704	10^88888+820861	88889	Stefano Morozzi	07/2018
4705	10^88888+1206349	88889	Stefano Morozzi	07/2018
4706	10^88888+1292047	88889	Stefano Morozzi	07/2018
4707	10^88888+1456029	88889	Stefano Morozzi	07/2018
4708	10^88888-490287	88888	Patrick De Geest	09/2018
4709	2^295245+65	88878	Lelio R Paula	10/2012
4710	Padovan(727734)	88874	Eric W. Weisstein	04/2011
4711	18^70793-17	88865	Lelio R Paula	11/2015
4712	6^114196-17573	88862	Enzo Doria	02/2013
4713	302^35829+35829^302	88857	Norbert Schneider	12/2014
4714	3^186223+16	88851	Robert Price	10/2013
4715	3*2^295139+7	88847	Lelio R Paula	08/2014
4716	3^186212-113008	88846	Enzo Doria	07/2014
4717	87^45803-86	88836	Norbert Schneider	11/2015
4718	2^295094-110273	88833	Enzo Doria	05/2014
4719	2^295080+1869151	88828	Enzo Doria	05/2016
4720	2^295027-113407	88812	Enzo Doria	07/2014
4721	(2*10^88808-71)/3	88808	Robert Price	01/2017
4722	13^79722-80	88806	Lelio R Paula	11/2015
4723	3^186103+104	88794	Lelio R Paula	12/2015
4724	(3*2^294971+1)/25565	88792	Lelio R Paula	01/2013
4725	2^294937-115003	88785	Enzo Doria	06/2015
4726	2^294868-109709	88765	Enzo Doria	04/2014
4727	2^294864-2985	88763	Yves Minet	09/2014
4728	(17*10^88761-41)/3	88762	Robert Price	09/2017
4729	2^294754+15015	88730	Lelio R Paula	10/2013
4730	(3^185951-7)/20	88720	Lelio R Paula	01/2013
4731	(2^294661+5)/443693383	88694	Lelio R Paula	01/2013
4732	(10^88680+11)/3	88680	Robert Price	11/2014
4733	2*7^104928-9	88675	Lelio R Paula	10/2014
4734	11^85150+12	88675	Lelio R Paula	11/2015
4735	8*6^113951+5	88673	Lelio R Paula	10/2014
4737	6^113940-18563	88663	Enzo Doria	03/2013
4736	38^56123-56123^38	88663	Norbert Schneider	02/2017
4738	2^294492-65	88651	Lelio R Paula	10/2012
4739	20^68120-53	88627	Lelio R Paula	01/2016
4740	122^42477-121	88623	Norbert Schneider	10/2018
4741	2^294391-113257	88621	Enzo Doria	07/2014
4742	5^126784-15476	88619	Enzo Doria	02/2013
4743	2^294327+9	88602	Lelio R Paula	10/2012
4744	2^294320+18915	88600	Lelio R Paula	10/2013
4745	(98*10^88595-89)/99	88595	Ray Chandler	07/2011
4746	(17*2^294262-1)/13	88582	Lelio R Paula	02/2014
4747	(2*10^88545+7)/9	88545	Erik Branger	03/2011
4748	2^294137-133	88545	Lelio R Paula	10/2012
4749	(2^294092-1017)/1171	88528	Lelio R Paula	01/2013
4750	4^147036+147036^4+1	88525	Robert Price	04/2014

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PRP Records

Probable Primes Top 10000

(252402 PRPs in the top)