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 (> 30000)	Who ?	When ?
4501	5^119439-66	83485	Lelio R Paula	10/2015
4502	(14*10^83471-101)/3	83472	Robert Price	04/2017
4503	5*6^107263+7	83468	Lelio R Paula	10/2014
4504	(64*10^83461-1)/9	83462	Serge Batalov	11/2010
4505	17^67796-92	83420	Lelio R Paula	11/2015
4506	2^277106-110057	83418	Enzo Doria	04/2014
4507	6^107200-19	83418	Lelio R Paula	12/2015
4508	11^80096-1830	83412	Enzo Doria	12/2012
4509	3^174801+56	83402	Lelio R Paula	12/2015
4510	2^277033-111973	83396	Enzo Doria	05/2014
4511	20519^11572+11572^20519	83378	Hans Havermann	03/2017
4512	20850^9971+9971^20850	83374	Hans Havermann	03/2017
4513	6^107122-18863	83358	Enzo Doria	03/2013
4514	3^174697-34	83352	Robert Price	11/2013
4515	(9787*2^276855-1)/2345	83343	Lelio R Paula	04/2015
4516	2^276825+75227	83333	Enzo Doria	04/2016
4517	5^119214+84	83328	Lelio R Paula	10/2015
4518	2^276803-159	83327	Lelio R Paula	06/2012
4519	(3*2^276753-1)/25	83311	Lelio R Paula	02/2014
4520	114^40495+40495^114	83295	Norbert Schneider	12/2014
4521	39967!2+1024	83282	Robert Price	02/2015
4523	2^276641+57	83278	Lelio R Paula	06/2012
4522	35^53934-3414	83278	Enzo Doria	03/2013
4524	(2^276655+78557)/365425	83276	Lelio R Paula	12/2012
4525	2^276615-4035	83270	Lelio R Paula	08/2013
4526	2^276588+1155	83262	Lelio R Paula	08/2013
4528	2^276587-937	83261	Yves Minet	10/2009
4527	2^276584-113183	83261	Enzo Doria	07/2014
4529	(2^276592-1017)/13843739	83256	Lelio R Paula	12/2012
4530	2^276547-109591	83249	Enzo Doria	04/2014
4531	13^74733-32	83249	Lelio R Paula	11/2015
4532	2^276523-2587	83242	Yves Minet	07/2014
4533	18^66311-43	83239	Lelio R Paula	11/2015
4534	11^79919-1530	83228	Enzo Doria	12/2012
4535	2^276468-109745	83226	Enzo Doria	04/2014
4536	2^276462+5385	83224	Lelio R Paula	08/2013
4537	(9787*2^276422-1)/3	83215	Lelio R Paula	04/2015
4539	2^276391-15	83202	Lelio R Paula	06/2012
4538	(4*10^83201+173)/3	83202	Robert Price	01/2017
4540	2^276316-109655	83180	Enzo Doria	04/2014
4541	2^276305-112063	83177	Enzo Doria	06/2014
4542	(10^(241585+1)+5410^41585-1)/9	83171	Robert Price	04/2017
4543	74913!4-2	83161	Robert Price	07/2017
4544	2^276227-1837207	83153	Enzo Doria	05/2015
4545	(2^276227+3)/7	83152	Lelio R Paula	12/2012
4546	2^276184-63389	83140	Paul Bourdelais	02/2012
4547	2^276066-111603	83105	Enzo Doria	05/2014
4548	(2^276028-3)*6-7	83094	Gilbert Mozzo	09/2016
4549	(2^275897+9)/1153	83051	Lelio R Paula	12/2012
4550	2^275879-109807	83048	Enzo Doria	04/2014
4552	F(397379)	83047	Henri Lifchitz	08/2003
4551	U(397379)	83047	Serge Batalov	03/2015
4553	3^174040-14	83039	Robert Price	08/2013
4554	(86*10^83038-221)/9	83039	Robert Price	06/2017
4555	2^275841-6883	83037	Lelio R Paula	07/2011
4556	3^174002-140	83021	Lelio R Paula	12/2015
4557	6^106681+77	83014	Lelio R Paula	12/2015
4558	11^79701-3150	83001	Enzo Doria	12/2012
4559	(55459*2^275657+1)/21	82985	Lelio R Paula	06/2014
4560	2^275535-6855	82945	Lelio R Paula	08/2013
4562	3^173828-14	82938	Robert Price	08/2013
4561	2^275512-109677	82938	Enzo Doria	04/2014
4563	2^275446-110045	82918	Enzo Doria	04/2014
4564	(2^275473+47)/29526097447	82916	Lelio R Paula	12/2012
4565	3^173755-14	82903	Robert Price	08/2013
4566	2^275363-112309	82893	Enzo Doria	06/2014
4567	61^46427-60	82888	Norbert Schneider	10/2014
4568	3*10^82880-7^82880	82881	Mike Oakes	02/2010
4570	2^275290+90195	82871	Lelio R Paula	07/2013
4569	(35*10^82870-71)/9	82871	Robert Price	05/2015
4571	2^275270-1859621	82865	Enzo Doria	03/2016
4572	2^275259+81	82862	Henri Lifchitz	01/2007
4573	7^98003+98003^7+1	82823	Robert Price	05/2014
4574	10^82790+126043	82791	Patrick De Geest	07/2013
4575	10^82790-47	82790	Robert Price	05/2011
4576	2^274985-112663	82779	Enzo Doria	06/2014
4577	2^274935+15015	82764	Lelio R Paula	07/2013
4578	(17*2^274922+1)/3	82761	Lelio R Paula	12/2012
4579	(43*10^82752-61)/9	82753	Robert Price	06/2015
4580	(3*2^274862+1)/1027	82740	Lelio R Paula	12/2012
4581	(31*2^274848-1)/4065	82736	Lelio R Paula	02/2014
4582	(4^137405+23)/3	82726	Robert Price	02/2017
4583	2^274791-110491	82721	Enzo Doria	05/2014
4584	(11*2^274776-1)/95	82715	Lelio R Paula	02/2014
4585	2^274704-111395	82695	Enzo Doria	05/2014
4586	2^274686-3911	82689	Yves Minet	04/2017
4587	(2^274663-1017)/48871318292279	82669	Lelio R Paula	12/2012
4588	(3^173263-5)/14498	82664	Lelio R Paula	12/2012
4589	2^274511-64875	82637	Lelio R Paula	08/2013
4590	12^76572-83	82636	Lelio R Paula	11/2015
4591	3^173191-2^173191	82634	Mike Oakes	02/2004
4592	14^72072-15	82604	Lelio R Paula	11/2015
4593	(55459*2^274339+1)/3	82589	Lelio R Paula	06/2014
4594	2^274351+123	82588	Lelio R Paula	06/2012
4595	(1017*2^274339-1)/3515	82584	Lelio R Paula	04/2015
4596	6^106086+113	82551	Lelio R Paula	12/2015
4597	2^274093-58695	82511	Lelio R Paula	07/2013
4598	7*10^82509-47	82510	Robert Price	02/2017
4599	2^274081-6555	82507	Lelio R Paula	07/2013
4601	2^274074-274074+1	82505	Robert Price	10/2014
4602	14^71985+47	82505	Lelio R Paula	11/2015
4600	5*10^82504+21	82505	Robert Price	01/2017
4603	6^106014-139	82495	Lelio R Paula	12/2015
4604	(2^274046+47)/753	82494	Lelio R Paula	12/2012
4605	2^274008-1838099	82485	Enzo Doria	05/2015
4606	2^273981-110029	82477	Enzo Doria	04/2014
4607	19^64490-30	82467	Lelio R Paula	12/2015
4609	2^273785+11715	82418	Lelio R Paula	07/2013
4608	8*10^82417+51	82418	Robert Price	05/2017
4610	11^79133-10	82409	Theodore Burton	11/2005
4611	91^42063+90	82404	Norbert Schneider	01/2016
4613	2^273662-63	82381	Lelio R Paula	06/2012
4612	2^273661+255	82381	Lelio R Paula	07/2013
4614	(62*10^82377-17)/9	82378	Robert Price	09/2015
4615	(11*10^82323+91)/3	82323	Robert Price	02/2017
4616	15^69984+32	82308	Lelio R Paula	11/2015
4617	9*6^105746+7	82288	Lelio R Paula	10/2014
4618	89^42211-88	82286	Norbert Schneider	01/2016
4619	gcd(V(1476435),5F(295287)(F(295287)+1)+1)	82281	Serge Batalov	04/2015
4620	2^273282-110241	82267	Enzo Doria	05/2014
4621	(13^73849+4^73849)/17	82263	Robert Price	05/2013
4623	10^82254+9^(82254+1)	82255	Robert Price	08/2016
4622	10^82254+457773	82255	Patrick De Geest	12/2016
4624	10^82254-99609	82254	Patrick De Geest	12/2016
4625	18^65524+13	82251	Lelio R Paula	11/2015
4626	2^273206-107	82244	Lelio R Paula	06/2012
4627	2^273193-459145	82240	Enzo Doria	05/2015
4629	2^273126+36937	82220	Yves Minet	06/2010
4628	39505!2+128	82220	Robert Price	03/2015
4630	2^273053-112111	82198	Enzo Doria	06/2014
4631	2^273016+1185	82187	Lelio R Paula	07/2013
4632	(2^273008+3)/7	82183	Lelio R Paula	12/2012
4633	5^117554-15386	82167	Enzo Doria	02/2013
4634	2^272907-111439	82154	Enzo Doria	05/2014
4635	(67607*2^272901+1)/50790115	82149	Lelio R Paula	06/2014
4636	2^272875-69	82144	Lelio R Paula	06/2012
4637	7^97197+4	82141	Robert Price	01/2014
4638	(4*6^105554+1)/5	82137	Serge Batalov	10/2014
4639	6^105531-109	82120	Lelio R Paula	12/2015
4640	2^272766-65	82111	Lelio R Paula	06/2012
4641	19^64205-78	82103	Lelio R Paula	12/2015
4642	2^272702+1869979	82092	Enzo Doria	05/2016
4643	(29*2^272687-1)/9	82088	Lelio R Paula	02/2014
4644	(5*10^82085-119)/3	82086	Robert Price	04/2016
4645	2^272660-110049	82079	Enzo Doria	04/2014
4646	6^105474+67	82075	Lelio R Paula	12/2015
4647	2^272637+82875	82072	Lelio R Paula	07/2013
4648	2^272587-31	82057	Lelio R Paula	06/2012
4649	8*5^117368+9	82038	Lelio R Paula	10/2014
4650	(101525^16384+1)/131074	82023	Lelio R Paula	11/2011
4651	4*5^117343-7	82020	Lelio R Paula	10/2014
4652	(265*10^81990+17)/3	81992	Robert Price	05/2016
4653	3^171843+10	81990	Robert Price	10/2013
4654	(7*10^81985+107)/3	81986	Robert Price	02/2017
4655	(3*2^272356+1)/177163	81983	Lelio R Paula	12/2012
4656	2^272296-111149	81970	Enzo Doria	05/2014
4657	(9*2^272243-1)/7	81954	Lelio R Paula	02/2014
4658	2^272177-111223	81934	Enzo Doria	05/2014
4659	(151009^15817+1)/151010	81912	Faysal YAtim	06/2017
4660	(16*10^81896-19)/3	81897	Robert Price	03/2016
4661	(2^271922+78557)/63	81855	Lelio R Paula	12/2012
4662	(10^81848+77)/3	81848	Robert Price	01/2017
4663	(24737*2^271883+1)/3757	81846	Lelio R Paula	06/2014
4664	10^81778+39	81779	Robert Price	03/2011
4665	10^81778-171999	81778	Patrick De Geest	07/2013
4666	(14*10^81767-11)/3	81768	Erik Branger	09/2014
4667	2^271541+1868417	81742	Enzo Doria	04/2016
4668	(2^271549-1)/238749682487	81734	Jens K. Andersen	02/2009
4669	2^271484-167	81725	Lelio R Paula	06/2012
4670	2^271382+12909	81695	Lelio R Paula	07/2013
4671	49^48334+48	81694	Norbert Schneider	07/2014
4672	7^96668+48	81694	Lelio R Paula	10/2015
4673	11^78435-1410	81682	Enzo Doria	12/2012
4674	5*10^81653+9	81654	Dmitry Domanov	11/2010
4675	(2^271211-1)/613961495159	81631	Jens K. Andersen	02/2009
4676	3^171068+52	81621	Lelio R Paula	12/2015
4677	2^271115-110407	81614	Enzo Doria	05/2014
4678	2^271111-110635	81613	Enzo Doria	05/2014
4679	2^271098-111	81609	Lelio R Paula	06/2012
4680	(77*10^81606+13)/9	81607	Robert Price	10/2015
4681	2^271064-2790209	81599	Enzo Doria	03/2016
4682	(13*2^271053-1)/3095	81593	Lelio R Paula	02/2014
4683	2^271040-57	81592	Lelio R Paula	06/2012
4684	(14*10^81585+73)/3	81586	Robert Price	04/2016
4685	127^38779+126	81584	Norbert Schneider	02/2015
4686	18^64966-43	81551	Lelio R Paula	11/2015
4687	(2^270840+47)/591	81529	Lelio R Paula	12/2012
4688	20^62654+87	81515	Lelio R Paula	01/2016
4689	(19*10^81488+191)/3	81489	Robert Price	01/2017
4690	8*10^81487+21	81488	Robert Price	02/2017
4691	(73*10^81485+107)/9	81486	Robert Price	08/2016
4692	536^29847+29847^536	81458	Norbert Schneider	03/2017
4693	8*7^96378+9	81450	Lelio R Paula	10/2014
4694	2^270546-110345	81443	Enzo Doria	05/2014
4695	13^73105-60	81435	Lelio R Paula	11/2015
4696	44^49524+43	81391	Norbert Schneider	06/2014
4697	(3*2^270368-1)/13	81389	Lelio R Paula	02/2014
4698	(10^81363+719)/9	81363	Serge Batalov	12/2014
4699	(10^81353+449)/9	81353	Serge Batalov	12/2014
4700	14^70978-89	81350	Lelio R Paula	11/2015
4701	11^78108-2040	81342	Enzo Doria	12/2012
4702	3^170400-58	81302	Lelio R Paula	12/2015
4703	10^81297+36991	81298	Patrick De Geest	06/2013
4704	10^81297-57	81297	Robert Price	05/2011
4705	2^270055-113047	81295	Enzo Doria	07/2014
4706	18^64759-55	81291	Lelio R Paula	11/2015
4707	(2^269987+1)/3	81274	H.&R. Lifchitz	10/2000
4708	(31^54493-1)/30	81268	Alexander Zhirkov	10/2010
4709	(2^270059-1)/540119/6481417/7124976157756725967	81265	Dario Alpern	09/2014
4710	(2^269816+7)/424901	81218	Lelio R Paula	12/2012
4711	(23*10^81214+1)/3	81215	Serge Batalov	06/2009
4712	(17*2^269720+1)/303	81193	Lelio R Paula	07/2012
4713	56^46441-55^46441	81188	Robert Price	10/2013
4715	2^269664+177	81177	Lelio R Paula	06/2012
4714	(13*2^269665-1)/185	81177	Lelio R Paula	02/2014
4716	2^269539-112249	81140	Enzo Doria	06/2014
4717	((2170026-3)3^(170026-1)+1)/4	81128	Robert Price	01/2015
4718	(2^269495-5)/9	81126	Lelio R Paula	12/2012
4719	2^269490-3623	81125	Yves Minet	10/2009
4720	(55459*2^269444+1)/35	81114	Lelio R Paula	06/2014
4721	(2^269417+78557)/5257	81099	Lelio R Paula	12/2012
4722	4*5^116011-7	81089	Lelio R Paula	10/2014
4723	7*10^81058+79	81059	Robert Price	02/2017
4724	2^269236-109907	81049	Enzo Doria	04/2014
4725	(8*10^81029-11)/3	81030	Erik Branger	03/2014
4726	3*10^81021+7	81022	Erik Branger	11/2013
4727	6^104115+103	81018	Lelio R Paula	12/2015
4728	2^269120+1869151	81014	Enzo Doria	05/2016
4729	5^115901+12	81012	Lelio R Paula	10/2015
4730	(2^269083-9)/320369	80997	Lelio R Paula	12/2012
4731	17^65810-20	80976	Lelio R Paula	11/2015
4732	20^62236-23	80971	Lelio R Paula	01/2016
4733	2^268974-112181	80970	Enzo Doria	06/2014
4735	L(387433)	80969	Renaud Lifchitz	11/2003
4734	V(387433)	80969	Serge Batalov	03/2015
4736	(2^268955-509203)/5	80963	Lelio R Paula	12/2012
4737	(87398^16384+1)/65537	80957	Lelio R Paula	11/2011
4738	329^32160+32160^329	80954	Norbert Schneider	11/2014
4739	2^268859-159	80935	Lelio R Paula	05/2012
4740	(2^268841-lucasV(1,2,268841)+1)/2	80929	Mike Oakes	11/2016
4741	2^268827+5775	80925	Lelio R Paula	07/2013
4742	2^268824-110255	80925	Enzo Doria	05/2014
4743	2^268798-1868321	80917	Enzo Doria	04/2016
4744	2^268753-114621	80903	Enzo Doria	05/2015
4745	2^268743+1605	80900	Lelio R Paula	07/2013
4746	6^103954-139	80892	Lelio R Paula	12/2015
4747	10^80883+49	80884	Robert Price	03/2011
4748	10^80883-80327	80883	Patrick De Geest	07/2013
4749	6^103937+121	80879	Lelio R Paula	12/2015
4750	(26*10^80875-119)/3	80876	Robert Price	07/2016

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Probable Primes Top 10000

(177649 PRPs in the top)