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 ?
7501	2^212112-459995	63853	Enzo Doria	06/2015
7502	15^54290+58	63850	Lelio R Paula	05/2013
7503	3*2^212097-7	63849	Lelio R Paula	04/2014
7504	55^36683-54	63842	Norbert Schneider	08/2014
7505	(509203*2^212056-1)/3	63841	Lelio R Paula	04/2015
7506	(3^133805-7)/172	63839	Lelio R Paula	04/2012
7507	2^212049+149	63834	Lelio R Paula	08/2011
7508	5^91318-18	63829	Lelio R Paula	04/2013
7509	18468^2857+2857^18468	63824	Hans Havermann	03/2017
7510	(2^212024-5)/1111	63823	Lelio R Paula	04/2012
7511	2^211961+12915	63807	Lelio R Paula	02/2013
7513	(3^133707-7)/5780	63791	Lelio R Paula	04/2012
7512	(44*10^63790-161)/9	63791	Robert Price	11/2017
7514	747^22198+22198^747	63782	Norbert Schneider	07/2016
7515	2^211800-17169	63759	Enzo Doria	05/2013
7516	(85*10^63757-1)/3	63759	Robert Price	07/2017
7517	85089!6-8	63757	Robert Price	08/2018
7518	(14*10^63747-11)/3	63748	Erik Branger	09/2014
7519	91*19^49848+6	63746	Curtis Bright	05/2015
7520	18855^2402+2402^18855	63741	Hans Havermann	03/2017
7521	(142*10^63734-7)/9	63736	Robert Price	02/2017
7522	2^211699-111	63728	Lelio R Paula	08/2011
7523	11^61192-5550	63725	Enzo Doria	01/2013
7524	(11*10^63718+7)/9	63719	Serge Batalov	06/2011
7525	6^81872-13	63709	Lelio R Paula	04/2013
7526	3^133522+98	63707	Lelio R Paula	05/2013
7528	2^211607-61	63701	Lelio R Paula	08/2011
7527	5^91135+8	63701	Lelio R Paula	04/2013
7529	11^61157-270	63689	Enzo Doria	07/2012
7531	10^63685+1145141919	63686	Marisa Kirisame	03/2015
7530	10^63685+103837	63686	Patrick De Geest	03/2016
7532	10^63685-130797	63685	Patrick De Geest	03/2016
7533	2^211547+1155*211547	63682	Henri Lifchitz	02/2005
7534	2^211543+45	63681	Lelio R Paula	08/2011
7535	2^211534+43	63679	Lelio R Paula	08/2011
7536	11^61140-60	63671	Enzo Doria	07/2012
7537	2^211491-112321	63666	Enzo Doria	06/2014
7538	19085^2164+2164^19085	63654	Hans Havermann	03/2017
7539	(2^211430-5)/859	63644	Lelio R Paula	04/2012
7540	2^211401-91	63639	Lelio R Paula	08/2011
7541	(6883*2^211378-1)/69	63634	Lelio R Paula	04/2015
7542	(F(152232)^3-F(152231)^3)/F(152230)	63629	Wayne Halsdorf	03/2012
7543	(29*2^211384-1)/50122621	63627	Lelio R Paula	01/2014
7544	2^211333+15015	63618	Lelio R Paula	01/2013
7545	33^41889-32	63610	Norbert Schneider	03/2014
7546	13^57093+18	63599	Lelio R Paula	05/2013
7547	(5*2^211219-1)/9	63583	Lelio R Paula	01/2014
7548	(107*10^63576-17)/9	63578	Robert Price	02/2017
7549	23^46687-1020	63575	Enzo Doria	08/2012
7550	(67607*2^211188+1)/5234319	63573	Lelio R Paula	06/2014
7551	(3^133243+7)/10726	63570	Lelio R Paula	04/2012
7552	(7*2^211181+1)/2745	63570	Lelio R Paula	06/2012
7554	(20^48859-1)/19	63566	Paul Bourdelais	03/2010
7553	2*3^133227+5	63566	Lelio R Paula	04/2014
7555	2^211155+113	63564	Lelio R Paula	08/2011
7556	2^211134+345	63558	Lelio R Paula	09/2011
7557	2^211121+16385	63554	Lelio R Paula	09/2011
7558	16996^5483+5483^16996	63549	Hans Havermann	02/2017
7559	(2^211079+9)/364283	63536	Lelio R Paula	03/2012
7560	3*10^63522+13	63523	Robert Price	08/2017
7561	15852^10157+10157^15852	63516	Hans Havermann	02/2017
7562	2^210948-15873	63502	Enzo Doria	04/2013
7563	7^75136+6	63498	Lelio R Paula	04/2013
7564	2^210928+12915	63496	Lelio R Paula	02/2013
7565	7*10^63493+39	63494	Robert Price	07/2016
7566	2^210909+135	63490	Lelio R Paula	08/2011
7567	(3*2^210832+1)/7	63467	Lelio R Paula	07/2012
7568	8*7^75098-3	63467	Lelio R Paula	09/2014
7569	17683^3882+3882^17683	63466	Hans Havermann	03/2017
7571	Pell-LucasQ(165799)/2	63464	Eric W. Weisstein	11/2006
7570	2^210820-16905	63464	Enzo Doria	05/2013
7572	5^90795-36	63463	Lelio R Paula	04/2013
7573	84731!6-48	63463	Robert Price	08/2018
7574	2^210816-13197	63462	Enzo Doria	10/2012
7575	2^210750+133	63443	Lelio R Paula	08/2011
7576	291^25742+25742^291	63426	Norbert Schneider	09/2014
7577	(3^132908+8)/279859	63408	Lelio R Paula	04/2012
7578	6^81480-139	63404	Lelio R Paula	04/2013
7579	2^210576-173	63390	Lelio R Paula	08/2011
7580	18^50497+55	63388	Lelio R Paula	05/2013
7581	2^210545+11	63381	Lelio R Paula	08/2011
7582	2^210543+63	63380	Lelio R Paula	08/2011
7583	83^33016+82	63361	Norbert Schneider	04/2015
7584	2^210464+98765331	63356	Jason Earls	12/2008
7585	7*10^63351+9	63352	Dmitry Domanov	11/2010
7586	p(13534)#/2+512	63348	Robert Price	05/2017
7587	1741^19546+19546^1741	63345	Serge Batalov	05/2014
7588	10^63336+19819	63337	Patrick De Geest	12/2013
7589	10^63336-122883	63336	Patrick De Geest	12/2013
7590	(19^49523-2^49523)/17	63327	Robert Price	09/2013
7591	(2^210378+47)/95516931	63323	Lelio R Paula	03/2012
7592	31191!2+256	63316	Robert Price	01/2015
7593	16458^7031+7031^16458	63315	Hans Havermann	01/2017
7594	(lucasV(1,2,420636)-2)/(731^2210319)	63303	Mike Oakes	03/2017
7595	(2^210283+7)/1691145	63296	Lelio R Paula	03/2012
7596	2^210217+1299	63282	Lelio R Paula	09/2011
7597	(2^210221-3)/269	63281	Lelio R Paula	04/2012
7598	Phi(193404,10)/386809/8122969	63268	Maksym Voznyy	10/2011
7599	96^31913-95	63261	Norbert Schneider	04/2016
7600	3^132572+280	63253	Lelio R Paula	04/2013
7601	3^132570-2^(132570-1)	63252	Robert Price	01/2016
7602	11^60734-4920	63248	Enzo Doria	01/2013
7604	2^210061+21	63235	Donovan Johnson	06/2006
7603	18^50375+95	63235	Lelio R Paula	05/2013
7605	85^32773-2	63233	Lelio R Paula	08/2013
7606	(-lucasV(1,2,420115)-2)/(3*5^3)	63232	Mike Oakes	02/2017
7607	(2^210054-1017)/671	63230	Lelio R Paula	04/2012
7608	3*2^210022+5	63224	Lelio R Paula	04/2014
7609	15^53756+32	63222	Lelio R Paula	05/2013
7610	17^51380+22	63221	Lelio R Paula	05/2013
7611	(lucasV(1,2,420045)+2)/257	63221	Mike Oakes	02/2017
7612	43^38700+42	63216	Norbert Schneider	06/2014
7613	5^90431-96	63209	Lelio R Paula	04/2013
7614	(172*10^63202-1)/9	63204	Serge Batalov	12/2014
7615	(43*10^63200+83)/9	63201	Robert Price	08/2017
7616	2^209914-16005	63191	Enzo Doria	04/2013
7617	3*6^81190-5	63179	Lelio R Paula	09/2014
7618	2^209820+4257	63163	Lelio R Paula	10/2011
7619	99^31648+2	63158	Lelio R Paula	05/2013
7620	16976^5253+5253^16976	63158	Hans Havermann	01/2017
7621	2^209790+67	63154	Lelio R Paula	08/2011
7622	2^209759+90195	63144	Lelio R Paula	02/2013
7623	145823#+211507	63142	Arkadiusz Wesolowski	03/2013
7624	2^209707+513	63129	Lelio R Paula	10/2011
7625	(3^132314-8)/17	63129	Lelio R Paula	04/2012
7626	(2*10^63117+7)/9	63117	Erik Branger	03/2011
7627	9*2^209654-7	63114	Lelio R Paula	04/2014
7628	84304!6-9	63112	Robert Price	08/2018
7629	11^60598-14	63107	Lelio R Paula	05/2013
7630	15103^15078+15078^15103	63106	Hans Havermann	01/2017
7631	15346^12941+12941^15346	63103	Hans Havermann	01/2017
7632	3^132253+76	63101	Lelio R Paula	04/2013
7633	(56*10^63100+403)/9	63101	Robert Price	10/2017
7634	17549^3936+3936^17549	63090	Hans Havermann	01/2017
7635	(55459*2^209553+1)/423	63084	Lelio R Paula	06/2014
7636	(331^25033-1)/330	63077	Eric Chen	09/2017
7637	20^48480+31	63074	Lelio R Paula	06/2013
7638	(26*10^63073-23)/3	63074	Robert Price	08/2016
7639	2^209499+76253	63066	Enzo Doria	04/2016
7640	11^60546-11340	63053	Enzo Doria	12/2012
7641	2^209426+57889	63044	Yves Minet	02/2010
7642	(22699*2^209405+1)/21	63041	Lelio R Paula	06/2014
7643	5^90189+54	63040	Lelio R Paula	04/2013
7644	(22*10^63034-73)/3	63035	Robert Price	09/2017
7645	(314021^11467+1)/314022	63029	Faysal YAtim	05/2008
7646	V(301486)	63007	Henri Lifchitz	05/2003
7647	(31*2^209298+1)/95	63005	Lelio R Paula	08/2012
7648	(27*2^209245+1)/5	62990	Lelio R Paula	08/2012
7649	6^80946-5^(80946-1)	62989	Robert Price	05/2016
7650	467^23596+23596^467	62986	Norbert Schneider	08/2016
7651	(7*2^209212-1)/3	62980	Lelio R Paula	01/2014
7652	(27*2^209206-1)/11	62978	Lelio R Paula	01/2014
7653	1456^19909+19909^1456	62976	Serge Batalov	05/2014
7654	(3^131964-5)/185212396	62955	Lelio R Paula	04/2012
7655	35^40772-1466	62955	Enzo Doria	03/2013
7656	5^90064-13706	62953	Enzo Doria	02/2013
7657	(22*10^62926+257)/9	62927	Robert Price	11/2017
7658	(13*10^62914+401)/9	62915	Robert Price	10/2017
7659	2^208993+107	62914	Lelio R Paula	08/2011
7660	2^208993+77	62914	Lelio R Paula	08/2011
7661	189^27636-2	62913	Lelio R Paula	10/2017
7662	(2^208948-7)/261	62898	Lelio R Paula	03/2012
7663	(151*10^62879-1)/3	62881	Robert Price	04/2017
7664	15^53464-82	62879	Lelio R Paula	05/2013
7665	2^208843-112921	62869	Enzo Doria	06/2014
7666	2^208779+81	62849	Henri Lifchitz	01/2007
7667	(21181*2^208780+1)/8993838841	62844	Lelio R Paula	06/2014
7668	(73*10^62824+17)/9	62825	Robert Price	10/2015
7669	3^131670-82	62823	Lelio R Paula	04/2013
7670	19^49128-90	62823	Lelio R Paula	05/2013
7671	11^60314-4410	62811	Enzo Doria	01/2013
7672	(17*2^208614-1)/53	62799	Lelio R Paula	01/2014
7673	2^208594+93	62794	Donovan Johnson	06/2008
7674	(-lucasV(1,2,417184)+2)/(3*104297)	62788	Mike Oakes	02/2017
7675	(2^208534+7)/9059	62772	Lelio R Paula	03/2012
7677	(13^56333+1)/14	62751	Paul Bourdelais	03/2010
7676	10^62750+57	62751	Robert Price	01/2011
7678	10^62750-267429	62750	Patrick De Geest	01/2013
7679	2^208427-69	62743	Lelio R Paula	08/2011
7680	2^208421-111775	62741	Enzo Doria	05/2014
7681	2^208404-112079	62736	Enzo Doria	06/2014
7682	2^208343-2221	62718	Yves Minet	08/2013
7683	2^208335+513	62716	Lelio R Paula	10/2011
7685	(2^208328+47)/3	62713	Lelio R Paula	03/2012
7684	11^60220-2040	62713	Enzo Doria	12/2012
7686	2^208292+81	62703	Henri Lifchitz	10/2005
7687	15013^15012-15012	62698	Henri Lifchitz	10/2014
7688	2^208271-112747	62696	Enzo Doria	06/2014
7689	11^60202-4380	62694	Enzo Doria	01/2013
7690	(3^131403-4)/157	62693	Lelio R Paula	04/2012
7691	2^208127-126667	62653	Paul Bourdelais	01/2012
7692	71^33843+2	62653	Lelio R Paula	05/2013
7693	(3^131325+7)/1066850	62652	Lelio R Paula	04/2012
7695	2^208019+119	62620	Lelio R Paula	08/2011
7694	(-lucasV(1,2,416078)+2)/(11*190717)	62620	Mike Oakes	02/2017
7696	11^60126-11370	62615	Enzo Doria	12/2012
7697	2^207976-2489	62608	Yves Minet	07/2014
7698	(22699*2^207945+1)/281709	62597	Lelio R Paula	06/2014
7699	4*21^47335+205	62588	Curtis Bright	05/2015
7700	15^53210+8	62580	Lelio R Paula	05/2013
7701	2^207865+29	62574	Henri Lifchitz	08/2005
7702	15^53199-38	62567	Lelio R Paula	05/2013
7703	(F(24947)^13-F(24946)^13)/F(24945)	62560	Wayne Halsdorf	03/2012
7704	2^207782+58905	62549	Lelio R Paula	10/2011
7705	(2^207748-3)/8437	62535	Lelio R Paula	03/2012
7706	(2^207711+5)/13	62527	Lelio R Paula	03/2012
7707	(268*10^62523-1)/3	62525	Robert Price	10/2017
7708	10^62523+63	62524	Robert Price	01/2011
7709	10^62523-292373	62523	Patrick De Geest	01/2013
7711	2^207691+1155*207691	62522	Henri Lifchitz	02/2005
7710	(lucasV(1,2,415410)+2)/(17*653)	62522	Mike Oakes	02/2017
7712	2^207626-112157	62502	Enzo Doria	06/2014
7713	3^130987+52	62497	Lelio R Paula	04/2013
7714	8*6^80299-7	62486	Lelio R Paula	09/2014
7715	11^59997-2670	62481	Enzo Doria	12/2012
7716	93^31740+2	62480	Lelio R Paula	05/2013
7717	(10^62451+119)/3	62451	Serge Batalov	12/2014
7718	(2^207443+47)/7645	62443	Lelio R Paula	03/2012
7719	2^207364+115	62423	Lelio R Paula	08/2011
7720	3^130815-46	62415	Lelio R Paula	04/2013
7721	(F(182)^1657-F(181)^1657)/F(180)	62409	Wayne Halsdorf	03/2012
7722	20^47968-9483	62408	Enzo Doria	03/2013
7723	(10^62402+101)/3	62402	Robert Price	04/2016
7724	(13*2^207264-1)/3	62394	Lelio R Paula	01/2014
7725	(79*10^62387-61)/9	62388	Robert Price	10/2015
7726	5^89244+3*2^89244	62379	Mike Oakes	02/2010
7727	6^80160-13	62377	Lelio R Paula	04/2013
7728	(7*10^62362+53)/3	62363	Robert Price	10/2017
7729	(1000121^10391+1)/1000122	62341	Faysal YAtim	07/2008
7730	(17*10^62328-11)/3	62329	Robert Price	07/2015
7731	2^207023+11715	62321	Lelio R Paula	09/2011
7732	(265*10^62298+11)/3	62300	Robert Price	03/2017
7733	2^206947-69	62298	Lelio R Paula	08/2011
7734	2^206938+29835	62295	Lelio R Paula	02/2013
7735	2^206911-726877	62287	Paul Bourdelais	03/2013
7736	(6883*2^206884-1)/3	62282	Lelio R Paula	04/2015
7737	2^206892-112817	62281	Enzo Doria	06/2014
7738	(7*10^62278+113)/3	62279	Robert Price	10/2017
7739	3^130523+46	62276	Lelio R Paula	04/2013
7740	2^206872-113453	62275	Enzo Doria	07/2014
7741	2^206840-93	62266	Lelio R Paula	08/2011
7742	(1017*2^206815-1)/635	62258	Lelio R Paula	04/2015
7743	96^31406+95	62256	Norbert Schneider	03/2016
7744	(2^206824+7)/646213	62255	Lelio R Paula	03/2012
7745	2^206765-941683	62243	Paul Bourdelais	11/2012
7746	(6^79987-1)/5	62242	Paul Bourdelais	11/2007
7747	2^206755-1579	62240	Yves Minet	03/2013
7748	11^59764-5820	62238	Enzo Doria	01/2013
7749	5*10^62233+3	62234	Dmitry Domanov	11/2010
7750	8*3^130421+7	62228	Lelio R Paula	04/2014

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Probable Primes Top 10000

(218736 PRPs in the top)