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	10^90807+7279	90808	Patrick De Geest	01/2019
4502	10^90800-6453	90800	Patrick De Geest	11/2018
4503	11^87187-1710	90796	Enzo Doria	12/2012
4504	5*10^90793+21	90794	Robert Price	01/2017
4505	(22*10^90792-13)/9	90793	Robert Price	03/2015
4506	2^301591-1615	90788	Lelio R Paula	02/2016
4507	(52^52901+1)/53	90777	Paul Bourdelais	08/2017
4508	2^301546-109037	90775	Enzo Doria	04/2014
4509	10^90772+4029	90773	Patrick De Geest	11/2018
4510	10^90770-431	90770	Patrick De Geest	11/2018
4511	14^79195-3	90768	Lelio R Paula	06/2016
4512	10^90766+877	90767	Patrick De Geest	11/2018
4513	2^301517-1861693	90766	Enzo Doria	11/2015
4514	10^90765-4797	90765	Patrick De Geest	11/2018
4515	10^90757+7573	90758	Patrick De Geest	11/2018
4516	10^90756-8727	90756	Patrick De Geest	11/2018
4517	10^90749+823	90750	Patrick De Geest	11/2018
4519	2^301460-173	90749	Lelio R Paula	11/2012
4518	10^90748+4213	90749	Patrick De Geest	11/2018
4520	10^90747-9279	90747	Patrick De Geest	11/2018
4521	(85*10^90745-103)/9	90746	Robert Price	10/2017
4522	10^90726+4077	90727	Patrick De Geest	11/2018
4523	10^90721+181	90722	Patrick De Geest	11/2018
4524	2^301312-89	90704	Lelio R Paula	11/2012
4525	10^90696+6349	90697	Patrick De Geest	11/2018
4526	2^301285-129	90696	Lelio R Paula	11/2012
4527	2^301282-109991	90695	Enzo Doria	04/2014
4528	10^90690+8877	90691	Patrick De Geest	11/2018
4529	10^90683-2577	90683	Patrick De Geest	11/2018
4530	2^301228-1854269	90679	Enzo Doria	09/2015
4531	(151*10^90669-1)/3	90671	Robert Price	04/2017
4532	(32*10^90669+13)/9	90670	Robert Price	04/2015
4533	10^90669+9793	90670	Patrick De Geest	11/2018
4534	10^90665-3087	90665	Patrick De Geest	11/2018
4535	10^90662-9519	90662	Patrick De Geest	11/2018
4536	10^90661+2373	90662	Patrick De Geest	11/2018
4537	3*5^129698+8	90656	Lelio R Paula	10/2014
4538	F(433781)	90655	Henri Lifchitz	09/2003
4539	19^70891+82	90653	Lelio R Paula	06/2016
4540	(29*2^301124-1)/13	90648	Lelio R Paula	02/2014
4541	10^90636-3101	90636	Patrick De Geest	11/2018
4542	7*3^189953-8	90632	Lelio R Paula	08/2014
4543	10^90626-1131	90626	Patrick De Geest	11/2018
4544	11^87022-1800	90625	Enzo Doria	12/2012
4545	10^90623+861	90624	Patrick De Geest	11/2018
4546	(2^301042+47)/12036969	90616	Lelio R Paula	06/2013
4547	2^301004-2786939	90612	Enzo Doria	03/2016
4548	10^90611-9737	90611	Patrick De Geest	11/2018
4549	10^90609+6823	90610	Patrick De Geest	11/2018
4550	2^300980-27	90605	Lelio R Paula	11/2012
4551	2*10^90597-7	90598	Dmitry Domanov	11/2010
4552	197^39485+2	90597	Lelio R Paula	06/2013
4553	7^107198+48	90593	Lelio R Paula	04/2016
4554	(86*10^90588+121)/9	90589	Robert Price	03/2017
4555	2^300923+53	90587	Lelio R Paula	11/2012
4556	2^300874+7	90573	Lelio R Paula	10/2012
4557	10^90567+9489	90568	Patrick De Geest	11/2018
4558	5^129568-56	90565	Lelio R Paula	04/2016
4559	2^300847-112831	90564	Enzo Doria	06/2014
4560	10^90562-2981	90562	Patrick De Geest	11/2018
4561	10^90549+3811	90550	Patrick De Geest	11/2018
4562	10^90532+8169	90533	Patrick De Geest	11/2018
4563	10^90531+9831	90532	Patrick De Geest	11/2018
4564	2^300718+255255	90526	Lelio R Paula	02/2016
4565	10^90516-6783	90516	Patrick De Geest	11/2018
4566	10^90511-6977	90511	Patrick De Geest	11/2018
4567	2^300637+95	90501	Lelio R Paula	11/2012
4568	7^107087-24	90500	Lelio R Paula	04/2016
4569	10^90499-5823	90499	Patrick De Geest	11/2018
4571	(10^90499+3^90499)/13	90498	Robert Price	01/2013
4570	13^81241+90	90498	Lelio R Paula	06/2016
4572	10^90480+5131	90481	Patrick De Geest	11/2018
4573	6^116273-85	90478	Lelio R Paula	05/2016
4574	10^90473+3139	90474	Patrick De Geest	11/2018
4575	10^90470+2319	90471	Patrick De Geest	11/2018
4576	6^116256-17573	90465	Enzo Doria	02/2013
4577	2^300502+54615	90461	Lelio R Paula	02/2016
4578	(13*2^300487+1)/45	90456	Lelio R Paula	09/2013
4579	10^90453-3969	90453	Patrick De Geest	11/2018
4580	10^90440+1359	90441	Patrick De Geest	11/2018
4581	(3^189545-8)/5	90436	Lelio R Paula	01/2013
4582	(7*2^300406-1)/3	90432	Lelio R Paula	02/2014
4583	10^90430+3339	90431	Patrick De Geest	11/2018
4584	10^90414-1547	90414	Patrick De Geest	11/2018
4585	10^90404-6429	90404	Patrick De Geest	11/2018
4586	10^90401+2077	90402	Patrick De Geest	11/2018
4587	4*5^129332+3	90400	Lelio R Paula	10/2014
4588	10^90397-323	90397	Patrick De Geest	11/2018
4589	2^300249-16245	90384	Enzo Doria	04/2013
4590	(7*10^90371-313)/9	90371	Robert Price	11/2016
4591	10^90363-3557	90363	Patrick De Geest	11/2018
4593	2*6^116118+7	90358	Lelio R Paula	10/2014
4592	10^90358-4979	90358	Patrick De Geest	11/2018
4594	10^90356-7197	90356	Patrick De Geest	11/2018
4595	10^90353-1089	90353	Patrick De Geest	11/2018
4596	(24737*2^300101+1)/25	90343	Lelio R Paula	06/2014
4597	4*10^90334-21	90335	Robert Price	04/2016
4598	10^90322-9551	90322	Patrick De Geest	11/2018
4599	10^90316+9991	90317	Patrick De Geest	11/2018
4601	2^300019-110335	90315	Enzo Doria	05/2014
4600	10^90315-8561	90315	Patrick De Geest	11/2018
4602	2^299949-1005	90294	Lelio R Paula	11/2013
4603	10^90279-1551	90279	Patrick De Geest	09/2018
4604	2^299868-109613	90270	Enzo Doria	04/2014
4605	10^90259-9443	90259	Patrick De Geest	09/2018
4606	10^90252-8103	90252	Patrick De Geest	09/2018
4607	5*2^299799-3	90250	Lelio R Paula	08/2014
4608	13^81008-2	90239	Lelio R Paula	09/2013
4609	64^49957-63^49957	90232	Robert Price	07/2013
4610	10^90227+56281	90228	Patrick De Geest	06/2016
4613	2^299725+315	90227	Lelio R Paula	11/2013
4611	10^90227-1000000001	90227	Robert Price	05/2016
4612	10^90227-68763	90227	Patrick De Geest	06/2016
4614	5^129082+48	90225	Lelio R Paula	03/2016
4615	2^299699+195	90219	Lelio R Paula	10/2012
4616	(55*10^90211-1)/9	90212	Ray Chandler	02/2012
4617	10^90209+8971	90210	Patrick De Geest	09/2018
4618	10^90208-2247	90208	Patrick De Geest	09/2018
4619	116^43693-115	90203	Norbert Schneider	08/2018
4620	10^90202+3553	90203	Patrick De Geest	09/2018
4621	3^189053+280	90202	Lelio R Paula	04/2016
4622	2^299639-187	90201	Lelio R Paula	10/2012
4623	10^90199-2891	90199	Patrick De Geest	09/2018
4624	2^299631+183	90198	Lelio R Paula	10/2012
4625	10^90196-9683	90196	Patrick De Geest	09/2018
4626	10^90193-9809	90193	Patrick De Geest	09/2018
4627	(21*2^299611-1)/29	90192	Lelio R Paula	02/2014
4628	2^299567+113	90179	Lelio R Paula	10/2012
4629	2^299550+189	90174	Lelio R Paula	10/2012
4630	10^90170-6749	90170	Patrick De Geest	09/2018
4631	(2^299535+3)/29	90168	Lelio R Paula	01/2013
4632	10^90160-5613	90160	Patrick De Geest	09/2018
4633	(97*10^90155-1)/3	90157	Serge Batalov	12/2014
4634	3^188938+8680	90147	Lelio R Paula	04/2016
4635	10^90146-2027	90146	Patrick De Geest	09/2018
4637	6^115840-55	90142	Lelio R Paula	05/2016
4636	(5*10^90142-473)/9	90142	Robert Price	12/2017
4638	8*7^106659+5	90139	Lelio R Paula	10/2014
4639	2^299406-16653	90131	Enzo Doria	05/2013
4641	208049#+(216091#)/(208049#)	90128	Makoto Morimoto	04/2016
4640	10^90128-8387	90128	Patrick De Geest	09/2018
4642	(F(5)^128941-F(4)^128941)/F(3)	90126	Wayne Halsdorf	03/2012
4643	6^115819-53	90125	Lelio R Paula	05/2016
4644	10^90123+6313	90124	Patrick De Geest	09/2018
4645	6^115816-16853	90123	Enzo Doria	02/2013
4646	6^115813-23	90121	Lelio R Paula	05/2016
4647	(22*10^90110+161)/3	90111	Robert Price	02/2017
4648	(2^299330-509203)/69	90106	Lelio R Paula	01/2013
4649	10^90105-767	90105	Patrick De Geest	09/2018
4650	10^90104-7703	90104	Patrick De Geest	09/2018
4651	10^90103+9159	90104	Patrick De Geest	09/2018
4652	10^90101-3207	90101	Patrick De Geest	09/2018
4653	(29*10^90096-17)/3	90097	Erik Branger	09/2014
4654	10^90089-3573	90089	Patrick De Geest	09/2018
4655	2^299247+1870529	90083	Enzo Doria	05/2016
4656	10^90079+1609	90080	Patrick De Geest	09/2018
4657	2^299229-2797783	90077	Enzo Doria	04/2016
4658	2^299220-16317	90075	Enzo Doria	04/2013
4659	11^86491-1350	90072	Enzo Doria	12/2012
4660	10^90071-1233	90071	Patrick De Geest	09/2018
4661	10^90069-7841	90069	Patrick De Geest	09/2018
4662	(31*10^90064-1)/3	90066	Robert Price	03/2017
4663	10^90060-839	90060	Patrick De Geest	09/2018
4664	10^90052+2361	90053	Patrick De Geest	09/2018
4665	10^90047+619	90048	Patrick De Geest	09/2018
4666	L(430949)/861899/1440387561539	90045	Serge Batalov	07/2017
4667	2^299112+73951	90042	Enzo Doria	04/2016
4668	8^99702+7^(99702-1)	90040	Robert Price	02/2016
4669	10^90038-9687	90038	Patrick De Geest	09/2018
4670	5*10^90033+3	90034	Dmitry Domanov	11/2010
4671	10^90030-1461	90030	Patrick De Geest	09/2018
4672	243^37738+37738^243	90029	Norbert Schneider	01/2015
4673	10^90025-8703	90025	Patrick De Geest	09/2018
4674	2^299048-113297	90023	Enzo Doria	07/2014
4675	10^90015+849	90016	Patrick De Geest	09/2018
4676	10^90010+6811	90011	Patrick De Geest	09/2018
4677	10^90010-183597	90010	Patrick De Geest	11/2018
4678	10^90009+58321	90010	Patrick De Geest	11/2018
4679	10^90008+847	90009	Patrick De Geest	09/2018
4680	10^90009-356013	90009	Patrick De Geest	11/2018
4682	3^188648+92	90008	Lelio R Paula	12/2015
4681	10^90008-706049	90008	Patrick De Geest	11/2018
4683	5*2^298991+7	90006	Lelio R Paula	08/2014
4684	(25*2^298997+1)/3267	90005	Lelio R Paula	01/2013
4685	10^90000+8869	90001	Patrick De Geest	12/2009
4687	10^89999+82939	90000	Dirk Augustin	04/2007
4686	10^90000-140343	90000	Patrick De Geest	12/2009
4688	10^89999-194891	89999	Patrick De Geest	11/2009
4689	19^70365-78	89980	Lelio R Paula	12/2015
4690	NaturalLogarithmOf2(89973)	89973	Eric W. Weisstein	10/2015
4691	2^298852-64875	89964	Lelio R Paula	11/2013
4692	18^71659+37	89952	Lelio R Paula	12/2015
4693	(2908*29^61501-3)/7	89942	Curtis Bright	05/2015
4694	17^73067+20	89906	Lelio R Paula	11/2015
4695	2^298637-99	89899	Lelio R Paula	10/2012
4696	9^94188+38^94188-24^94188-3*2^94188	89879	Mike Oakes	01/2011
4697	9*10^89858+19	89859	Robert Price	05/2016
4698	2^298501+1870067	89858	Enzo Doria	05/2016
4699	11^86280-98	89852	Lelio R Paula	11/2015
4700	2^298473-110059	89850	Enzo Doria	04/2014
4701	19^70263-32	89850	Lelio R Paula	12/2015
4702	(299*10^89836-17)/3	89838	Robert Price	01/2017
4703	3^188286+14	89836	Robert Price	09/2013
4704	gcd(V(1091095),5F(218219)(F(218219)+1)+1)	89822	Serge Batalov	04/2015
4705	2^298367+58905	89818	Lelio R Paula	11/2013
4706	2^298319-109657	89803	Enzo Doria	04/2014
4707	8*10^89800+81	89801	Robert Price	05/2017
4708	18^71505-91	89759	Lelio R Paula	12/2015
4709	(7^106187+1)/8	89738	Paul Bourdelais	04/2008
4710	2^298079-109531	89731	Enzo Doria	04/2014
4711	117^43380+116	89718	Norbert Schneider	08/2018
4712	(22699*2^298016+1)/385	89714	Lelio R Paula	06/2014
4713	156(10^(422427)-1)/101-1	89709	Robert Price	05/2014
4714	2^298003-66945	89708	Lelio R Paula	11/2013
4715	(23*10^89705-83)/3	89706	Robert Price	09/2017
4716	17^72900-54	89700	Lelio R Paula	11/2015
4717	3*2^297956+5	89695	Lelio R Paula	08/2014
4718	20^68938-11	89691	Lelio R Paula	01/2016
4719	89*10^89687-7	89689	Robert Price	03/2017
4720	2^297923+77783	89684	Enzo Doria	05/2016
4721	11^86107-24576000	89672	Enzo Doria	02/2013
4722	2^297878-111911	89671	Enzo Doria	05/2014
4723	7^106084+40	89652	Lelio R Paula	10/2015
4724	(86*10^89640-311)/9	89641	Robert Price	10/2017
4725	3*10^89608-59	89609	Robert Price	10/2017
4726	3^187780-11038	89594	Enzo Doria	05/2014
4727	(13*2^297560-1)/49151787	89568	Lelio R Paula	02/2014
4728	5^128141-36	89567	Lelio R Paula	10/2015
4729	4*7^105951+9	89540	Lelio R Paula	10/2014
4730	(7*10^89539-439)/9	89539	Robert Price	09/2017
4731	2^297397+177257	89526	Enzo Doria	05/2016
4732	2^297346-16241	89511	Enzo Doria	04/2013
4733	(5*10^89510+79)/3	89511	Robert Price	11/2017
4735	4^148663-3^148663	89505	Jean-Louis Charton	11/2005
4734	2^297328-869688105	89505	Lelio R Paula	07/2016
4736	2^297325-459043	89504	Enzo Doria	05/2015
4737	2^297310-112391	89500	Enzo Doria	06/2014
4738	2^297296-112157	89496	Enzo Doria	06/2014
4739	57^50966-2	89490	Lelio R Paula	08/2013
4740	(266*10^89482+1)/3	89484	Robert Price	02/2016
4741	(14*10^89480-101)/3	89481	Robert Price	04/2017
4742	2^297122+99	89443	Lelio R Paula	10/2012
4743	(3^187435-5)/1286	89427	Lelio R Paula	01/2013
4744	(25*10^89413+161)/3	89414	Robert Price	01/2017
4745	2^296990+1870699	89403	Enzo Doria	05/2016
4746	2^296972-1017	89398	Lelio R Paula	11/2013
4747	(7*10^89383+167)/3	89384	Robert Kinser	10/2017
4748	(85*10^89375-31)/9	89376	Robert Price	11/2015
4749	9*2^296870+7	89368	Lelio R Paula	08/2014
4750	100^44683-99^44683	89366	Robert Price	07/2013

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Probable Primes Top 10000

(252538 PRPs in the top)