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	21234^9067+9067^21234	84033	Hans Havermann	05/2017
4502	2^279095-109717	84016	Enzo Doria	04/2014
4503	14^73282-99	83991	Lelio R Paula	11/2015
4504	21457^8200+8200^21457	83979	Hans Havermann	06/2017
4505	89*10^83976-7	83978	Robert Price	03/2017
4506	2^278955+173	83974	Lelio R Paula	06/2012
4507	(7*2^278851+1)/39	83942	Lelio R Paula	12/2012
4508	(9913*2^278844-1)/40803	83940	Lelio R Paula	04/2015
4509	5^120076-14846	83930	Enzo Doria	02/2013
4510	(85*10^83921-1)/3	83923	Robert Price	07/2017
4511	(2^278770-3)/23	83917	Lelio R Paula	12/2012
4512	(10^83916+449)/9	83916	Serge Batalov	12/2014
4513	2^278715+99	83902	Lelio R Paula	06/2012
4514	40235!2-2^40235	83899	Robert Price	09/2015
4515	2^278698-171	83897	Lelio R Paula	06/2012
4516	6^107802+25	83887	Lelio R Paula	12/2015
4517	8*10^83880+39	83881	Robert Price	01/2017
4518	(58*10^83878+23)/9	83879	Robert Price	09/2015
4519	7^99244-90	83871	Lelio R Paula	10/2015
4520	2^278554+4257	83854	Lelio R Paula	08/2013
4521	2^278504-109619	83839	Enzo Doria	04/2014
4522	2^278499+1870433	83837	Enzo Doria	05/2016
4523	105^41475+104	83829	Norbert Schneider	11/2016
4524	15^71276-68	83828	Lelio R Paula	11/2015
4525	2^278464-216413	83827	Enzo Doria	04/2013
4526	2^278400+40755	83807	Lelio R Paula	08/2013
4527	(9*2^278381-1)/7	83802	Lelio R Paula	02/2014
4528	39^87813+6^87813+24^87813	83796	Mike Oakes	12/2010
4529	19551^19268+19268^19551	83773	Hans Havermann	05/2017
4530	20625^11522+11522^20625	83770	Hans Havermann	05/2017
4531	(87^43189+1)/88	83764	Paul Bourdelais	08/2017
4532	2^278235-49	83758	Lelio R Paula	06/2012
4533	23543^3610+3610^23543	83755	Hans Havermann	05/2017
4535	18^66711-91	83741	Lelio R Paula	11/2015
4534	4*10^83740-89	83741	Robert Price	08/2017
4536	(3*2^278172-1)/11	83738	Lelio R Paula	02/2014
4537	(15*29^57251+2561)/28	83724	Curtis Bright	05/2015
4538	4*7^99059-9	83716	Lelio R Paula	10/2014
4539	(2^278128-3)/126844724149	83714	Lelio R Paula	12/2012
4540	2^278077+1867211	83710	Enzo Doria	03/2016
4541	2^278059-27	83705	Lelio R Paula	06/2012
4542	214^35917+35917^214	83702	Norbert Schneider	12/2014
4543	(23*10^83693+7)/3	83694	Robert Price	10/2015
4544	85^43375-2	83689	Lelio R Paula	09/2013
4545	5*3^175360+4	83669	Lelio R Paula	07/2014
4546	(23^61441-1)/22	83665	Robert Price	01/2012
4547	20091^14596+14596^20091	83664	Hans Havermann	03/2017
4548	2^277907-110629	83659	Enzo Doria	05/2014
4549	19522^19283+19283^19522	83656	Hans Havermann	04/2017
4550	8*5^119664-3	83643	Lelio R Paula	10/2014
4551	8*3^175299-7	83640	Lelio R Paula	07/2014
4552	3^175250+22	83616	Robert Price	12/2013
4553	11^80285+30	83609	Lelio R Paula	10/2015
4554	26870^1293+1293^26870	83609	Hans Havermann	03/2017
4555	2^277691+1874423	83594	Enzo Doria	06/2016
4556	13^75022-60	83571	Lelio R Paula	11/2015
4557	14^72905-51	83559	Lelio R Paula	11/2015
4558	(17*2^277565-1)/543	83554	Lelio R Paula	02/2014
4559	5^119532-12	83550	Lelio R Paula	10/2015
4560	6^107358-16253	83541	Enzo Doria	02/2013
4561	2^277478-460211	83530	Enzo Doria	06/2015
4562	(22*10^83525-7)/3	83526	Erik Branger	09/2014
4563	(30^56543+1)/31	83520	Robert Price	07/2013
4564	2^277417-460783	83511	Paul Bourdelais	04/2013
4565	(22699*2^277387+1)/219	83504	Lelio R Paula	06/2014
4566	(31*2^277383-1)/247	83500	Lelio R Paula	02/2014
4567	21368^8085+8085^21368	83500	Hans Havermann	04/2017
4568	(9*2^277342+1)/13	83489	Lelio R Paula	12/2012
4569	5^119439-66	83485	Lelio R Paula	10/2015
4570	(14*10^83471-101)/3	83472	Robert Price	04/2017
4571	5*6^107263+7	83468	Lelio R Paula	10/2014
4572	(64*10^83461-1)/9	83462	Serge Batalov	11/2010
4573	17^67796-92	83420	Lelio R Paula	11/2015
4574	2^277106-110057	83418	Enzo Doria	04/2014
4575	6^107200-19	83418	Lelio R Paula	12/2015
4576	11^80096-1830	83412	Enzo Doria	12/2012
4577	3^174801+56	83402	Lelio R Paula	12/2015
4578	2^277033-111973	83396	Enzo Doria	05/2014
4579	20519^11572+11572^20519	83378	Hans Havermann	03/2017
4580	20850^9971+9971^20850	83374	Hans Havermann	03/2017
4581	6^107122-18863	83358	Enzo Doria	03/2013
4582	4*10^83354-89	83355	Robert Price	08/2017
4583	3^174697-34	83352	Robert Price	11/2013
4584	(9787*2^276855-1)/2345	83343	Lelio R Paula	04/2015
4585	2^276825+75227	83333	Enzo Doria	04/2016
4586	5^119214+84	83328	Lelio R Paula	10/2015
4587	2^276803-159	83327	Lelio R Paula	06/2012
4588	(3*2^276753-1)/25	83311	Lelio R Paula	02/2014
4589	114^40495+40495^114	83295	Norbert Schneider	12/2014
4590	39967!2+1024	83282	Robert Price	02/2015
4591	2^276641+57	83278	Lelio R Paula	06/2012
4592	35^53934-3414	83278	Enzo Doria	03/2013
4593	(2^276655+78557)/365425	83276	Lelio R Paula	12/2012
4594	2^276615-4035	83270	Lelio R Paula	08/2013
4595	2^276588+1155	83262	Lelio R Paula	08/2013
4597	2^276587-937	83261	Yves Minet	10/2009
4596	2^276584-113183	83261	Enzo Doria	07/2014
4598	(2^276592-1017)/13843739	83256	Lelio R Paula	12/2012
4599	2^276547-109591	83249	Enzo Doria	04/2014
4600	13^74733-32	83249	Lelio R Paula	11/2015
4601	2^276523-2587	83242	Yves Minet	07/2014
4602	18^66311-43	83239	Lelio R Paula	11/2015
4603	11^79919-1530	83228	Enzo Doria	12/2012
4604	2^276468-109745	83226	Enzo Doria	04/2014
4605	2^276462+5385	83224	Lelio R Paula	08/2013
4606	(9787*2^276422-1)/3	83215	Lelio R Paula	04/2015
4608	2^276391-15	83202	Lelio R Paula	06/2012
4607	(4*10^83201+173)/3	83202	Robert Price	01/2017
4609	2^276316-109655	83180	Enzo Doria	04/2014
4610	2^276305-112063	83177	Enzo Doria	06/2014
4611	(10^(241585+1)+5410^41585-1)/9	83171	Robert Price	04/2017
4612	74913!4-2	83161	Robert Price	07/2017
4613	2^276227-1837207	83153	Enzo Doria	05/2015
4614	(2^276227+3)/7	83152	Lelio R Paula	12/2012
4615	2^276184-63389	83140	Paul Bourdelais	02/2012
4616	2^276066-111603	83105	Enzo Doria	05/2014
4617	(2^276028-3)*6-7	83094	Gilbert Mozzo	09/2016
4618	(2^275897+9)/1153	83051	Lelio R Paula	12/2012
4619	2^275879-109807	83048	Enzo Doria	04/2014
4621	F(397379)	83047	Henri Lifchitz	08/2003
4620	U(397379)	83047	Serge Batalov	03/2015
4622	3^174040-14	83039	Robert Price	08/2013
4623	(86*10^83038-221)/9	83039	Robert Price	06/2017
4624	2^275841-6883	83037	Lelio R Paula	07/2011
4625	3^174002-140	83021	Lelio R Paula	12/2015
4626	6^106681+77	83014	Lelio R Paula	12/2015
4627	11^79701-3150	83001	Enzo Doria	12/2012
4628	(55459*2^275657+1)/21	82985	Lelio R Paula	06/2014
4629	2^275535-6855	82945	Lelio R Paula	08/2013
4631	3^173828-14	82938	Robert Price	08/2013
4630	2^275512-109677	82938	Enzo Doria	04/2014
4632	2^275446-110045	82918	Enzo Doria	04/2014
4633	(2^275473+47)/29526097447	82916	Lelio R Paula	12/2012
4634	3^173755-14	82903	Robert Price	08/2013
4635	2^275363-112309	82893	Enzo Doria	06/2014
4636	61^46427-60	82888	Norbert Schneider	10/2014
4637	3*10^82880-7^82880	82881	Mike Oakes	02/2010
4639	2^275290+90195	82871	Lelio R Paula	07/2013
4638	(35*10^82870-71)/9	82871	Robert Price	05/2015
4640	2^275270-1859621	82865	Enzo Doria	03/2016
4641	2^275259+81	82862	Henri Lifchitz	01/2007
4642	7^98003+98003^7+1	82823	Robert Price	05/2014
4643	10^82790+126043	82791	Patrick De Geest	07/2013
4644	10^82790-47	82790	Robert Price	05/2011
4645	2^274985-112663	82779	Enzo Doria	06/2014
4646	2^274935+15015	82764	Lelio R Paula	07/2013
4647	(17*2^274922+1)/3	82761	Lelio R Paula	12/2012
4648	(43*10^82752-61)/9	82753	Robert Price	06/2015
4649	(3*2^274862+1)/1027	82740	Lelio R Paula	12/2012
4650	(31*2^274848-1)/4065	82736	Lelio R Paula	02/2014
4651	(4^137405+23)/3	82726	Robert Price	02/2017
4652	2^274791-110491	82721	Enzo Doria	05/2014
4653	(11*2^274776-1)/95	82715	Lelio R Paula	02/2014
4654	(47*10^82706-119)/9	82707	Robert Price	09/2017
4655	2^274704-111395	82695	Enzo Doria	05/2014
4656	2^274686-3911	82689	Yves Minet	04/2017
4657	(2^274663-1017)/48871318292279	82669	Lelio R Paula	12/2012
4658	(3^173263-5)/14498	82664	Lelio R Paula	12/2012
4659	2^274511-64875	82637	Lelio R Paula	08/2013
4660	12^76572-83	82636	Lelio R Paula	11/2015
4661	3^173191-2^173191	82634	Mike Oakes	02/2004
4662	14^72072-15	82604	Lelio R Paula	11/2015
4663	(55459*2^274339+1)/3	82589	Lelio R Paula	06/2014
4664	2^274351+123	82588	Lelio R Paula	06/2012
4665	(1017*2^274339-1)/3515	82584	Lelio R Paula	04/2015
4666	6^106086+113	82551	Lelio R Paula	12/2015
4667	2^274093-58695	82511	Lelio R Paula	07/2013
4668	7*10^82509-47	82510	Robert Price	02/2017
4669	2^274081-6555	82507	Lelio R Paula	07/2013
4671	2^274074-274074+1	82505	Robert Price	10/2014
4672	14^71985+47	82505	Lelio R Paula	11/2015
4670	5*10^82504+21	82505	Robert Price	01/2017
4673	6^106014-139	82495	Lelio R Paula	12/2015
4674	(2^274046+47)/753	82494	Lelio R Paula	12/2012
4675	2^274008-1838099	82485	Enzo Doria	05/2015
4676	2^273981-110029	82477	Enzo Doria	04/2014
4677	19^64490-30	82467	Lelio R Paula	12/2015
4679	2^273785+11715	82418	Lelio R Paula	07/2013
4678	8*10^82417+51	82418	Robert Price	05/2017
4680	11^79133-10	82409	Theodore Burton	11/2005
4681	91^42063+90	82404	Norbert Schneider	01/2016
4683	2^273662-63	82381	Lelio R Paula	06/2012
4682	2^273661+255	82381	Lelio R Paula	07/2013
4684	(62*10^82377-17)/9	82378	Robert Price	09/2015
4685	(11*10^82323+91)/3	82323	Robert Price	02/2017
4686	15^69984+32	82308	Lelio R Paula	11/2015
4687	9*6^105746+7	82288	Lelio R Paula	10/2014
4688	89^42211-88	82286	Norbert Schneider	01/2016
4689	gcd(V(1476435),5F(295287)(F(295287)+1)+1)	82281	Serge Batalov	04/2015
4690	2^273282-110241	82267	Enzo Doria	05/2014
4691	(13^73849+4^73849)/17	82263	Robert Price	05/2013
4693	10^82254+9^(82254+1)	82255	Robert Price	08/2016
4692	10^82254+457773	82255	Patrick De Geest	12/2016
4694	10^82254-99609	82254	Patrick De Geest	12/2016
4695	18^65524+13	82251	Lelio R Paula	11/2015
4696	2^273206-107	82244	Lelio R Paula	06/2012
4697	2^273193-459145	82240	Enzo Doria	05/2015
4699	2^273126+36937	82220	Yves Minet	06/2010
4698	39505!2+128	82220	Robert Price	03/2015
4700	2^273053-112111	82198	Enzo Doria	06/2014
4701	2^273016+1185	82187	Lelio R Paula	07/2013
4702	(2^273008+3)/7	82183	Lelio R Paula	12/2012
4703	5^117554-15386	82167	Enzo Doria	02/2013
4704	2^272907-111439	82154	Enzo Doria	05/2014
4705	(67607*2^272901+1)/50790115	82149	Lelio R Paula	06/2014
4706	2^272875-69	82144	Lelio R Paula	06/2012
4707	7^97197+4	82141	Robert Price	01/2014
4708	(4*6^105554+1)/5	82137	Serge Batalov	10/2014
4709	6^105531-109	82120	Lelio R Paula	12/2015
4710	2^272766-65	82111	Lelio R Paula	06/2012
4711	19^64205-78	82103	Lelio R Paula	12/2015
4712	2^272702+1869979	82092	Enzo Doria	05/2016
4713	(29*2^272687-1)/9	82088	Lelio R Paula	02/2014
4714	(5*10^82085-119)/3	82086	Robert Price	04/2016
4715	2^272660-110049	82079	Enzo Doria	04/2014
4716	6^105474+67	82075	Lelio R Paula	12/2015
4717	2^272637+82875	82072	Lelio R Paula	07/2013
4718	2^272587-31	82057	Lelio R Paula	06/2012
4719	8*5^117368+9	82038	Lelio R Paula	10/2014
4720	(101525^16384+1)/131074	82023	Lelio R Paula	11/2011
4721	4*5^117343-7	82020	Lelio R Paula	10/2014
4722	(265*10^81990+17)/3	81992	Robert Price	05/2016
4723	3^171843+10	81990	Robert Price	10/2013
4724	(7*10^81985+107)/3	81986	Robert Price	02/2017
4725	(3*2^272356+1)/177163	81983	Lelio R Paula	12/2012
4726	2^272296-111149	81970	Enzo Doria	05/2014
4727	(9*2^272243-1)/7	81954	Lelio R Paula	02/2014
4728	2^272177-111223	81934	Enzo Doria	05/2014
4729	(151009^15817+1)/151010	81912	Faysal YAtim	06/2017
4730	(16*10^81896-19)/3	81897	Robert Price	03/2016
4731	(2^271922+78557)/63	81855	Lelio R Paula	12/2012
4732	(10^81848+77)/3	81848	Robert Price	01/2017
4733	(24737*2^271883+1)/3757	81846	Lelio R Paula	06/2014
4734	10^81778+39	81779	Robert Price	03/2011
4735	10^81778-171999	81778	Patrick De Geest	07/2013
4736	(14*10^81767-11)/3	81768	Erik Branger	09/2014
4737	2^271541+1868417	81742	Enzo Doria	04/2016
4738	(2^271549-1)/238749682487	81734	Jens K. Andersen	02/2009
4739	2^271484-167	81725	Lelio R Paula	06/2012
4740	2^271382+12909	81695	Lelio R Paula	07/2013
4741	49^48334+48	81694	Norbert Schneider	07/2014
4742	7^96668+48	81694	Lelio R Paula	10/2015
4743	11^78435-1410	81682	Enzo Doria	12/2012
4744	5*10^81653+9	81654	Dmitry Domanov	11/2010
4745	(2^271211-1)/613961495159	81631	Jens K. Andersen	02/2009
4746	3^171068+52	81621	Lelio R Paula	12/2015
4747	2^271115-110407	81614	Enzo Doria	05/2014
4748	2^271111-110635	81613	Enzo Doria	05/2014
4749	2^271098-111	81609	Lelio R Paula	06/2012
4750	(77*10^81606+13)/9	81607	Robert Price	10/2015

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Probable Primes Top 10000

(181746 PRPs in the top)