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 ?
5501	(134569^16384+1)/2	84033	Richard Fischer	06/2018
5502	2^279095-109717	84016	Enzo Doria	04/2014
5503	14^73282-99	83991	Lelio R Paula	11/2015
5504	21457^8200+8200^21457	83979	Hans Havermann	06/2017
5505	89*10^83976-7	83978	Robert Price	03/2017
5506	2^278955+173	83974	Lelio R Paula	06/2012
5507	(7*2^278851+1)/39	83942	Lelio R Paula	12/2012
5508	(9913*2^278844-1)/40803	83940	Lelio R Paula	04/2015
5509	5^120076-14846	83930	Enzo Doria	02/2013
5510	(85*10^83921-1)/3	83923	Robert Price	07/2017
5511	(2^278770-3)/23	83917	Lelio R Paula	12/2012
5512	(10^83916+449)/9	83916	Serge Batalov	12/2014
5513	2^278715+99	83902	Lelio R Paula	06/2012
5514	(132109^16384+1)/2	83902	Richard Fischer	05/2018
5515	40235!2-2^40235	83899	Robert Price	09/2015
5516	2^278698-171	83897	Lelio R Paula	06/2012
5517	(19*10^83894-43)/3	83895	Robert Price	10/2017
5518	6^107802+25	83887	Lelio R Paula	12/2015
5519	8*10^83880+39	83881	Robert Price	01/2017
5520	(58*10^83878+23)/9	83879	Robert Price	09/2015
5521	7^99244-90	83871	Lelio R Paula	10/2015
5522	2^278554+4257	83854	Lelio R Paula	08/2013
5523	2^278504-109619	83839	Enzo Doria	04/2014
5524	2^278499+1870433	83837	Enzo Doria	05/2016
5525	105^41475+104	83829	Norbert Schneider	11/2016
5526	15^71276-68	83828	Lelio R Paula	11/2015
5527	2^278464-216413	83827	Enzo Doria	04/2013
5528	(76*10^83816-211)/9	83817	Robert Price	10/2017
5529	(8*10^83811-101)/3	83812	Robert Price	10/2017
5530	2^278400+40755	83807	Lelio R Paula	08/2013
5531	(9*2^278381-1)/7	83802	Lelio R Paula	02/2014
5532	39^87813+6^87813+24^87813	83796	Mike Oakes	12/2010
5533	19551^19268+19268^19551	83773	Hans Havermann	05/2017
5534	20625^11522+11522^20625	83770	Hans Havermann	05/2017
5535	(44*10^83768-791)/9	83769	Robert Price	10/2017
5536	(87^43189+1)/88	83764	Paul Bourdelais	08/2017
5537	2^278235-49	83758	Lelio R Paula	06/2012
5538	23543^3610+3610^23543	83755	Hans Havermann	05/2017
5540	18^66711-91	83741	Lelio R Paula	11/2015
5539	4*10^83740-89	83741	Robert Price	08/2017
5541	(3*2^278172-1)/11	83738	Lelio R Paula	02/2014
5542	(15*29^57251+2561)/28	83724	Curtis Bright	05/2015
5543	4*7^99059-9	83716	Lelio R Paula	10/2014
5544	(2^278128-3)/126844724149	83714	Lelio R Paula	12/2012
5545	2^278077+1867211	83710	Enzo Doria	03/2016
5546	2^278059-27	83705	Lelio R Paula	06/2012
5547	214^35917+35917^214	83702	Norbert Schneider	12/2014
5548	(23*10^83693+7)/3	83694	Robert Price	10/2015
5549	85^43375-2	83689	Lelio R Paula	09/2013
5550	5*3^175360+4	83669	Lelio R Paula	07/2014
5551	(23^61441-1)/22	83665	Robert Price	01/2012
5552	20091^14596+14596^20091	83664	Hans Havermann	03/2017
5553	2^277907-110629	83659	Enzo Doria	05/2014
5554	19522^19283+19283^19522	83656	Hans Havermann	04/2017
5555	8*5^119664-3	83643	Lelio R Paula	10/2014
5556	8*3^175299-7	83640	Lelio R Paula	07/2014
5557	(26*10^83638-413)/9	83639	Robert Price	10/2017
5558	3^175250+22	83616	Robert Price	12/2013
5560	11^80285+30	83609	Lelio R Paula	10/2015
5559	26870^1293+1293^26870	83609	Hans Havermann	03/2017
5561	2^277691+1874423	83594	Enzo Doria	06/2016
5562	13^75022-60	83571	Lelio R Paula	11/2015
5563	14^72905-51	83559	Lelio R Paula	11/2015
5564	(17*2^277565-1)/543	83554	Lelio R Paula	02/2014
5565	5^119532-12	83550	Lelio R Paula	10/2015
5566	6^107358-16253	83541	Enzo Doria	02/2013
5567	2^277478-460211	83530	Enzo Doria	06/2015
5568	(22*10^83525-7)/3	83526	Erik Branger	09/2014
5569	(30^56543+1)/31	83520	Robert Price	07/2013
5570	2^277417-460783	83511	Paul Bourdelais	04/2013
5571	(22699*2^277387+1)/219	83504	Lelio R Paula	06/2014
5572	(31*2^277383-1)/247	83500	Lelio R Paula	02/2014
5573	21368^8085+8085^21368	83500	Hans Havermann	04/2017
5574	(9*2^277342+1)/13	83489	Lelio R Paula	12/2012
5575	5^119439-66	83485	Lelio R Paula	10/2015
5576	(14*10^83471-101)/3	83472	Robert Price	04/2017
5577	5*6^107263+7	83468	Lelio R Paula	10/2014
5578	(64*10^83461-1)/9	83462	Serge Batalov	11/2010
5579	2^277244-175709	83459	Hans Havermann	10/2018
5580	17^67796-92	83420	Lelio R Paula	11/2015
5581	2^277106-110057	83418	Enzo Doria	04/2014
5582	6^107200-19	83418	Lelio R Paula	12/2015
5583	11^80096-1830	83412	Enzo Doria	12/2012
5584	3^174801+56	83402	Lelio R Paula	12/2015
5585	2^277033-111973	83396	Enzo Doria	05/2014
5586	120^40105-119	83386	Norbert Schneider	09/2018
5587	20519^11572+11572^20519	83378	Hans Havermann	03/2017
5588	20850^9971+9971^20850	83374	Hans Havermann	03/2017
5589	6^107122-18863	83358	Enzo Doria	03/2013
5590	4*10^83354-89	83355	Robert Price	08/2017
5591	3^174697-34	83352	Robert Price	11/2013
5592	(9787*2^276855-1)/2345	83343	Lelio R Paula	04/2015
5593	2^276825+75227	83333	Enzo Doria	04/2016
5594	5^119214+84	83328	Lelio R Paula	10/2015
5595	2^276803-159	83327	Lelio R Paula	06/2012
5596	(3*2^276753-1)/25	83311	Lelio R Paula	02/2014
5597	114^40495+40495^114	83295	Norbert Schneider	12/2014
5598	39967!2+1024	83282	Robert Price	02/2015
5599	2^276641+57	83278	Lelio R Paula	06/2012
5600	35^53934-3414	83278	Enzo Doria	03/2013
5601	(2^276655+78557)/365425	83276	Lelio R Paula	12/2012
5602	2^276615-4035	83270	Lelio R Paula	08/2013
5603	2^276588+1155	83262	Lelio R Paula	08/2013
5605	2^276587-937	83261	Yves Minet	10/2009
5604	2^276584-113183	83261	Enzo Doria	07/2014
5606	(2^276592-1017)/13843739	83256	Lelio R Paula	12/2012
5607	2^276547-109591	83249	Enzo Doria	04/2014
5608	13^74733-32	83249	Lelio R Paula	11/2015
5609	2^276523-2587	83242	Yves Minet	07/2014
5610	18^66311-43	83239	Lelio R Paula	11/2015
5611	11^79919-1530	83228	Enzo Doria	12/2012
5612	2^276468-109745	83226	Enzo Doria	04/2014
5613	2^276462+5385	83224	Lelio R Paula	08/2013
5614	(9787*2^276422-1)/3	83215	Lelio R Paula	04/2015
5615	2^276391-15	83202	Lelio R Paula	06/2012
5616	(4*10^83201+173)/3	83202	Robert Price	01/2017
5617	2^276316-109655	83180	Enzo Doria	04/2014
5618	2^276305-112063	83177	Enzo Doria	06/2014
5619	(10^(241585+1)+5410^41585-1)/9	83171	Robert Price	04/2017
5620	74913!4-2	83161	Robert Price	07/2017
5621	2^276227-1837207	83153	Enzo Doria	05/2015
5622	(2^276227+3)/7	83152	Lelio R Paula	12/2012
5623	2^276184-63389	83140	Paul Bourdelais	02/2012
5624	2^276066-111603	83105	Enzo Doria	05/2014
5625	(2^276028-3)*6-7	83094	Gilbert Mozzo	09/2016
5626	2^275926-4691	83063	Yves Minet	05/2019
5627	(2^275897+9)/1153	83051	Lelio R Paula	12/2012
5628	2^275879-109807	83048	Enzo Doria	04/2014
5630	F(397379)	83047	Henri Lifchitz	08/2003
5629	U(397379)	83047	Serge Batalov	03/2015
5632	3^174040-14	83039	Robert Price	08/2013
5631	(86*10^83038-221)/9	83039	Robert Price	06/2017
5633	2^275841-6883	83037	Lelio R Paula	07/2011
5634	3^174002-140	83021	Lelio R Paula	12/2015
5635	6^106681+77	83014	Lelio R Paula	12/2015
5636	187^36539-2	83011	Lelio R Paula	10/2017
5637	11^79701-3150	83001	Enzo Doria	12/2012
5638	(55459*2^275657+1)/21	82985	Lelio R Paula	06/2014
5639	(7*10^82960-457)/9	82960	Robert Price	09/2017
5640	2^275535-6855	82945	Lelio R Paula	08/2013
5641	3^173828-14	82938	Robert Price	08/2013
5642	2^275512-109677	82938	Enzo Doria	04/2014
5643	2^275446-110045	82918	Enzo Doria	04/2014
5644	(2^275473+47)/29526097447	82916	Lelio R Paula	12/2012
5645	3^173755-14	82903	Robert Price	08/2013
5646	(182*10^82898+43)/9	82900	Robert Price	11/2017
5647	2^275363-112309	82893	Enzo Doria	06/2014
5648	61^46427-60	82888	Norbert Schneider	10/2014
5649	3*10^82880-7^82880	82881	Mike Oakes	02/2010
5651	2^275290+90195	82871	Lelio R Paula	07/2013
5650	(35*10^82870-71)/9	82871	Robert Price	05/2015
5652	2^275270-1859621	82865	Enzo Doria	03/2016
5653	2^275259+81	82862	Henri Lifchitz	01/2007
5654	(113703^16384+1)/2	82834	Richard Fischer	04/2018
5655	7^98003+98003^7+1	82823	Robert Price	05/2014
5656	10^82790+126043	82791	Patrick De Geest	07/2013
5657	10^82790-47	82790	Robert Price	05/2011
5658	2^274985-112663	82779	Enzo Doria	06/2014
5659	2^274935+15015	82764	Lelio R Paula	07/2013
5660	(17*2^274922+1)/3	82761	Lelio R Paula	12/2012
5661	(43*10^82752-61)/9	82753	Robert Price	06/2015
5662	(3*2^274862+1)/1027	82740	Lelio R Paula	12/2012
5663	(31*2^274848-1)/4065	82736	Lelio R Paula	02/2014
5664	(4^137405+23)/3	82726	Robert Price	02/2017
5665	2^274791-110491	82721	Enzo Doria	05/2014
5666	(11*2^274776-1)/95	82715	Lelio R Paula	02/2014
5667	(47*10^82706-119)/9	82707	Robert Price	09/2017
5668	2^274704-111395	82695	Enzo Doria	05/2014
5669	2^274686-3911	82689	Yves Minet	04/2017
5670	(2^274663-1017)/48871318292279	82669	Lelio R Paula	12/2012
5671	(3^173263-5)/14498	82664	Lelio R Paula	12/2012
5672	2^274511-64875	82637	Lelio R Paula	08/2013
5673	12^76572-83	82636	Lelio R Paula	11/2015
5674	3^173191-2^173191	82634	Mike Oakes	02/2004
5675	14^72072-15	82604	Lelio R Paula	11/2015
5676	(55459*2^274339+1)/3	82589	Lelio R Paula	06/2014
5677	2^274351+123	82588	Lelio R Paula	06/2012
5678	(1017*2^274339-1)/3515	82584	Lelio R Paula	04/2015
5679	6^106086+113	82551	Lelio R Paula	12/2015
5680	(17*10^82540-377)/9	82541	Robert Price	11/2017
5681	2^274093-58695	82511	Lelio R Paula	07/2013
5682	7*10^82509-47	82510	Robert Price	02/2017
5683	2^274081-6555	82507	Lelio R Paula	07/2013
5684	2^274074-274074+1	82505	Robert Price	10/2014
5685	14^71985+47	82505	Lelio R Paula	11/2015
5686	5*10^82504+21	82505	Robert Price	01/2017
5687	6^106014-139	82495	Lelio R Paula	12/2015
5688	(2^274046+47)/753	82494	Lelio R Paula	12/2012
5689	2^274008-1838099	82485	Enzo Doria	05/2015
5690	2^273981-110029	82477	Enzo Doria	04/2014
5691	19^64490-30	82467	Lelio R Paula	12/2015
5693	2^273785+11715	82418	Lelio R Paula	07/2013
5692	8*10^82417+51	82418	Robert Price	05/2017
5694	11^79133-10	82409	Theodore Burton	11/2005
5695	91^42063+90	82404	Norbert Schneider	01/2016
5697	2^273662-63	82381	Lelio R Paula	06/2012
5696	2^273661+255	82381	Lelio R Paula	07/2013
5698	(62*10^82377-17)/9	82378	Robert Price	09/2015
5699	2^273608+524287	82365	Paul Underwood	08/2018
5700	8*10^82360-51	82361	Robert Price	10/2017
5701	(79*10^82347-1)/3	82349	Robert Price	11/2017
5702	(11*10^82323+91)/3	82323	Robert Price	02/2017
5703	(189977#+19081)/(19081*17260483)	82317	Makoto Morimoto	10/2017
5704	(189977#+196924)/(271354128874441)	82316	Makoto Morimoto	10/2017
5705	15^69984+32	82308	Lelio R Paula	11/2015
5706	9*6^105746+7	82288	Lelio R Paula	10/2014
5707	89^42211-88	82286	Norbert Schneider	01/2016
5708	gcd(V(1476435),5F(295287)(F(295287)+1)+1)	82281	Serge Batalov	04/2015
5709	(19*10^82270-43)/3	82271	Robert Price	10/2017
5710	2^273282-110241	82267	Enzo Doria	05/2014
5711	(13^73849+4^73849)/17	82263	Robert Price	05/2013
5712	10^82254+9^(82254+1)	82255	Robert Price	08/2016
5713	10^82254+457773	82255	Patrick De Geest	12/2016
5714	10^82254-99609	82254	Patrick De Geest	12/2016
5715	(754*10^82250-7)/9	82252	Robert Price	11/2017
5716	18^65524+13	82251	Lelio R Paula	11/2015
5717	2^273206-107	82244	Lelio R Paula	06/2012
5718	2^273193-459145	82240	Enzo Doria	05/2015
5720	2^273126+36937	82220	Yves Minet	06/2010
5719	39505!2+128	82220	Robert Price	03/2015
5721	2^273053-112111	82198	Enzo Doria	06/2014
5722	2^273016+1185	82187	Lelio R Paula	07/2013
5723	(2^273008+3)/7	82183	Lelio R Paula	12/2012
5724	5^117554-15386	82167	Enzo Doria	02/2013
5725	(38*10^82161+403)/9	82162	Robert Price	11/2017
5726	2^272907-111439	82154	Enzo Doria	05/2014
5727	(67607*2^272901+1)/50790115	82149	Lelio R Paula	06/2014
5728	2^272875-69	82144	Lelio R Paula	06/2012
5729	7^97197+4	82141	Robert Price	01/2014
5730	(4*6^105554+1)/5	82137	Serge Batalov	10/2014
5731	2^272826-4433	82129	Yves Minet	03/2019
5732	6^105531-109	82120	Lelio R Paula	12/2015
5733	2^272766-65	82111	Lelio R Paula	06/2012
5734	19^64205-78	82103	Lelio R Paula	12/2015
5735	2^272702+1869979	82092	Enzo Doria	05/2016
5736	(29*2^272687-1)/9	82088	Lelio R Paula	02/2014
5737	(5*10^82085-119)/3	82086	Robert Price	04/2016
5738	2^272660-110049	82079	Enzo Doria	04/2014
5739	6^105474+67	82075	Lelio R Paula	12/2015
5740	2^272637+82875	82072	Lelio R Paula	07/2013
5741	2^272587-31	82057	Lelio R Paula	06/2012
5742	(41*10^82044-59)/9	82045	Robert Price	10/2017
5743	8*5^117368+9	82038	Lelio R Paula	10/2014
5744	(101525^16384+1)/131074	82023	Lelio R Paula	11/2011
5745	4*5^117343-7	82020	Lelio R Paula	10/2014
5746	(265*10^81990+17)/3	81992	Robert Price	05/2016
5747	3^171843+10	81990	Robert Price	10/2013
5748	(7*10^81985+107)/3	81986	Robert Price	02/2017
5749	(3*2^272356+1)/177163	81983	Lelio R Paula	12/2012
5750	2^272296-111149	81970	Enzo Doria	05/2014

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Probable Primes Top 10000

(252932 PRPs in the top)