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 ?
8501	(266*10^64102-17)/3	64104	Robert Price	06/2016
8502	p(13679)#/2+64	64097	Robert Price	03/2017
8503	19^50119+94	64090	Lelio R Paula	08/2013
8504	2^212880-147	64084	Lelio R Paula	08/2011
8505	11^61523-4590	64070	Enzo Doria	01/2013
8506	5^91663+38	64070	Lelio R Paula	05/2013
8507	5^91650+52	64061	Lelio R Paula	05/2013
8508	2^212770+69	64051	Lelio R Paula	08/2011
8509	(3^134227+1)/4	64042	Paul Bourdelais	11/2007
8510	(2*10^64041-17)/3	64041	Robert Price	08/2014
8511	(15^54449+1)/16	64036	Paul Bourdelais	03/2010
8512	(29*10^64027+91)/3	64028	Robert Price	03/2016
8513	(lucasV(1,2,425405)+2)/(17*89)	64027	Mike Oakes	03/2017
8514	16878!+16878#-1	64022	D. Gazzoni Filho & Lucas Teixeira	05/2005
8515	15862^10863+10863^15862	64019	Hans Havermann	06/2019
8516	2^212663+53	64018	Lelio R Paula	08/2011
8517	(4*10^64014+197)/3	64015	Robert Price	03/2017
8518	85402!6-3	64014	Robert Price	08/2018
8519	(140^29819+1)/141	63994	Richard Fischer	05/2018
8520	15313^15094+15094^15313	63991	Hans Havermann	06/2019
8521	10^63986+63	63987	Robert Price	01/2011
8522	10^63986-31557	63986	Patrick De Geest	05/2013
8523	15699^11900+11900^15699	63983	Hans Havermann	07/2019
8524	31487!2-2^31487	63982	Robert Price	09/2015
8525	(21*2^212522-1)/1416323	63971	Lelio R Paula	01/2014
8526	5^91517+98	63968	Lelio R Paula	04/2013
8527	(19*10^63960-43)/3	63961	Robert Price	10/2017
8528	(62*10^63954-17)/9	63955	Robert Price	09/2015
8530	5^91493-4^91493	63951	Predrag Minovic	04/2004
8529	V(364793)	63951	Serge Batalov	03/2015
8531	19^50004+58	63943	Lelio R Paula	05/2013
8532	5*6^82172-7	63943	Lelio R Paula	09/2014
8533	(56*10^63942+223)/9	63943	Robert Price	07/2016
8534	19^50000-24	63938	Lelio R Paula	05/2013
8535	(23*2^212374-1)/27019	63928	Lelio R Paula	01/2014
8536	(9*2^212355-1)/761	63924	Lelio R Paula	01/2014
8538	2^212344-183	63922	Lelio R Paula	08/2011
8537	(58695*2^212336-1)/379	63922	Lelio R Paula	04/2015
8539	10^63916+79	63917	Robert Price	01/2011
8540	10^63916-76823	63916	Patrick De Geest	05/2013
8541	2^212295-25	63908	Lelio R Paula	08/2011
8542	2^212285-2383	63905	Yves Minet	10/2013
8543	267^26336+26336^267	63905	Norbert Schneider	09/2014
8544	(-lucasV(1,2,424552)-2)/1601	63899	Mike Oakes	03/2017
8546	19^49962+60	63890	Lelio R Paula	05/2013
8545	3^133906-113056	63890	Enzo Doria	07/2014
8547	7933^16384+7932^16384	63889	Richard Fischer	09/2019
8548	(lucasV(1,2,424451)+2)/3	63886	Mike Oakes	03/2017
8549	3*6^82092+5	63881	Lelio R Paula	09/2014
8550	15441^13706+13706^15441	63879	Hans Havermann	02/2017
8551	2^212154-776351	63865	Paul Bourdelais	03/2013
8552	35^41359+2	63862	Lelio R Paula	05/2013
8553	(61*10^63857-43)/9	63858	Robert Price	09/2015
8554	(2^212131-3)/485	63856	Lelio R Paula	04/2012
8555	2^212112-459995	63853	Enzo Doria	06/2015
8556	15^54290+58	63850	Lelio R Paula	05/2013
8557	3*2^212097-7	63849	Lelio R Paula	04/2014
8558	55^36683-54	63842	Norbert Schneider	08/2014
8559	(509203*2^212056-1)/3	63841	Lelio R Paula	04/2015
8560	(3^133805-7)/172	63839	Lelio R Paula	04/2012
8561	2^212049+149	63834	Lelio R Paula	08/2011
8562	5^91318-18	63829	Lelio R Paula	04/2013
8563	18468^2857+2857^18468	63824	Hans Havermann	03/2017
8564	(2^212024-5)/1111	63823	Lelio R Paula	04/2012
8565	2^211961+12915	63807	Lelio R Paula	02/2013
8566	13046^15503-15503^13046	63803	Norbert Schneider	09/2019
8568	(3^133707-7)/5780	63791	Lelio R Paula	04/2012
8567	(44*10^63790-161)/9	63791	Robert Price	11/2017
8569	747^22198+22198^747	63782	Norbert Schneider	07/2016
8571	2^211800-17169	63759	Enzo Doria	05/2013
8570	(85*10^63757-1)/3	63759	Robert Price	07/2017
8572	85089!6-8	63757	Robert Price	08/2018
8573	(14*10^63747-11)/3	63748	Erik Branger	09/2014
8574	91*19^49848+6	63746	Curtis Bright	05/2015
8575	18855^2402+2402^18855	63741	Hans Havermann	03/2017
8576	(142*10^63734-7)/9	63736	Robert Price	02/2017
8577	2^211699-111	63728	Lelio R Paula	08/2011
8578	11^61192-5550	63725	Enzo Doria	01/2013
8579	(11*10^63718+7)/9	63719	Serge Batalov	06/2011
8580	6^81872-13	63709	Lelio R Paula	04/2013
8581	3^133522+98	63707	Lelio R Paula	05/2013
8583	2^211607-61	63701	Lelio R Paula	08/2011
8582	5^91135+8	63701	Lelio R Paula	04/2013
8584	11^61157-270	63689	Enzo Doria	07/2012
8585	10^63685+1145141919	63686	Marisa Kirisame	03/2015
8586	10^63685+103837	63686	Patrick De Geest	03/2016
8587	10^63685-130797	63685	Patrick De Geest	03/2016
8588	2^211547+1155*211547	63682	Henri Lifchitz	02/2005
8589	2^211543+45	63681	Lelio R Paula	08/2011
8590	2^211534+43	63679	Lelio R Paula	08/2011
8591	11^61140-60	63671	Enzo Doria	07/2012
8592	2^211491-112321	63666	Enzo Doria	06/2014
8593	19085^2164+2164^19085	63654	Hans Havermann	03/2017
8594	(2^211430-5)/859	63644	Lelio R Paula	04/2012
8595	2^211401-91	63639	Lelio R Paula	08/2011
8596	(6883*2^211378-1)/69	63634	Lelio R Paula	04/2015
8597	(F(152232)^3-F(152231)^3)/F(152230)	63629	Wayne Halsdorf	03/2012
8598	(29*2^211384-1)/50122621	63627	Lelio R Paula	01/2014
8599	2^211333+15015	63618	Lelio R Paula	01/2013
8600	33^41889-32	63610	Norbert Schneider	03/2014
8601	13^57093+18	63599	Lelio R Paula	05/2013
8602	(5*2^211219-1)/9	63583	Lelio R Paula	01/2014
8603	(107*10^63576-17)/9	63578	Robert Price	02/2017
8604	23^46687-1020	63575	Enzo Doria	08/2012
8605	(67607*2^211188+1)/5234319	63573	Lelio R Paula	06/2014
8606	(3^133243+7)/10726	63570	Lelio R Paula	04/2012
8607	(7*2^211181+1)/2745	63570	Lelio R Paula	06/2012
8608	(20^48859-1)/19	63566	Paul Bourdelais	03/2010
8609	2*3^133227+5	63566	Lelio R Paula	04/2014
8610	2^211155+113	63564	Lelio R Paula	08/2011
8611	2^211134+345	63558	Lelio R Paula	09/2011
8612	2^211121+16385	63554	Lelio R Paula	09/2011
8613	16996^5483+5483^16996	63549	Hans Havermann	02/2017
8614	(2^211079+9)/364283	63536	Lelio R Paula	03/2012
8615	3*10^63522+13	63523	Robert Price	08/2017
8616	15852^10157+10157^15852	63516	Hans Havermann	02/2017
8617	2^210948-15873	63502	Enzo Doria	04/2013
8618	7^75136+6	63498	Lelio R Paula	04/2013
8619	2^210928+12915	63496	Lelio R Paula	02/2013
8620	7*10^63493+39	63494	Robert Price	07/2016
8621	2^210909+135	63490	Lelio R Paula	08/2011
8622	(3*2^210832+1)/7	63467	Lelio R Paula	07/2012
8623	8*7^75098-3	63467	Lelio R Paula	09/2014
8624	17683^3882+3882^17683	63466	Hans Havermann	03/2017
8626	Pell-LucasQ(165799)/2	63464	Eric W. Weisstein	11/2006
8625	2^210820-16905	63464	Enzo Doria	05/2013
8627	5^90795-36	63463	Lelio R Paula	04/2013
8628	84731!6-48	63463	Robert Price	08/2018
8629	2^210816-13197	63462	Enzo Doria	10/2012
8630	2^210750+133	63443	Lelio R Paula	08/2011
8631	291^25742+25742^291	63426	Norbert Schneider	09/2014
8632	(3^132908+8)/279859	63408	Lelio R Paula	04/2012
8633	6^81480-139	63404	Lelio R Paula	04/2013
8634	2^210576-173	63390	Lelio R Paula	08/2011
8635	18^50497+55	63388	Lelio R Paula	05/2013
8636	2^210545+11	63381	Lelio R Paula	08/2011
8637	2^210543+63	63380	Lelio R Paula	08/2011
8638	155^28929-154	63365	Norbert Schneider	12/2018
8639	83^33016+82	63361	Norbert Schneider	04/2015
8640	2^210464+98765331	63356	Jason Earls	12/2008
8641	7*10^63351+9	63352	Dmitry Domanov	11/2010
8642	58483!4+4	63351	Robert Price	09/2019
8643	p(13534)#/2+512	63348	Robert Price	05/2017
8644	1741^19546+19546^1741	63345	Serge Batalov	05/2014
8645	10^63336+19819	63337	Patrick De Geest	12/2013
8646	10^63336-122883	63336	Patrick De Geest	12/2013
8647	(19^49523-2^49523)/17	63327	Robert Price	09/2013
8648	(2^210378+47)/95516931	63323	Lelio R Paula	03/2012
8649	31191!2+256	63316	Robert Price	01/2015
8650	16458^7031+7031^16458	63315	Hans Havermann	01/2017
8651	(lucasV(1,2,420636)-2)/(731^2210319)	63303	Mike Oakes	03/2017
8652	156^28864+155	63303	Norbert Schneider	12/2018
8653	(2^210283+7)/1691145	63296	Lelio R Paula	03/2012
8654	2^210217+1299	63282	Lelio R Paula	09/2011
8655	(2^210221-3)/269	63281	Lelio R Paula	04/2012
8656	Phi(193404,10)/386809/8122969	63268	Maksym Voznyy	10/2011
8657	96^31913-95	63261	Norbert Schneider	04/2016
8658	3^132572+280	63253	Lelio R Paula	04/2013
8659	3^132570-2^(132570-1)	63252	Robert Price	01/2016
8660	11^60734-4920	63248	Enzo Doria	01/2013
8662	2^210061+21	63235	Donovan Johnson	06/2006
8661	18^50375+95	63235	Lelio R Paula	05/2013
8663	85^32773-2	63233	Lelio R Paula	08/2013
8664	(-lucasV(1,2,420115)-2)/(3*5^3)	63232	Mike Oakes	02/2017
8665	(2^210054-1017)/671	63230	Lelio R Paula	04/2012
8666	3*2^210022+5	63224	Lelio R Paula	04/2014
8667	15^53756+32	63222	Lelio R Paula	05/2013
8668	17^51380+22	63221	Lelio R Paula	05/2013
8669	(lucasV(1,2,420045)+2)/257	63221	Mike Oakes	02/2017
8670	43^38700+42	63216	Norbert Schneider	06/2014
8671	5^90431-96	63209	Lelio R Paula	04/2013
8672	(172*10^63202-1)/9	63204	Serge Batalov	12/2014
8673	(43*10^63200+83)/9	63201	Robert Price	08/2017
8674	2^209914-16005	63191	Enzo Doria	04/2013
8675	3*6^81190-5	63179	Lelio R Paula	09/2014
8676	2^209820+4257	63163	Lelio R Paula	10/2011
8677	99^31648+2	63158	Lelio R Paula	05/2013
8678	16976^5253+5253^16976	63158	Hans Havermann	01/2017
8679	2^209790+67	63154	Lelio R Paula	08/2011
8680	145878#-p(145878)	63152	Henri Lifchitz	12/2018
8681	2^209759+90195	63144	Lelio R Paula	02/2013
8682	145823#+211507	63142	Arkadiusz Wesolowski	03/2013
8683	2^209707+513	63129	Lelio R Paula	10/2011
8684	(3^132314-8)/17	63129	Lelio R Paula	04/2012
8685	(2*10^63117+7)/9	63117	Erik Branger	03/2011
8686	9*2^209654-7	63114	Lelio R Paula	04/2014
8687	84304!6-9	63112	Robert Price	08/2018
8688	11^60598-14	63107	Lelio R Paula	05/2013
8689	15103^15078+15078^15103	63106	Hans Havermann	01/2017
8690	15346^12941+12941^15346	63103	Hans Havermann	01/2017
8692	3^132253+76	63101	Lelio R Paula	04/2013
8691	(56*10^63100+403)/9	63101	Robert Price	10/2017
8693	17549^3936+3936^17549	63090	Hans Havermann	01/2017
8694	(55459*2^209553+1)/423	63084	Lelio R Paula	06/2014
8695	(331^25033-1)/330	63077	Eric Chen	09/2017
8697	20^48480+31	63074	Lelio R Paula	06/2013
8696	(26*10^63073-23)/3	63074	Robert Price	08/2016
8698	2^209499+76253	63066	Enzo Doria	04/2016
8699	11^60546-11340	63053	Enzo Doria	12/2012
8700	2^209426+57889	63044	Yves Minet	02/2010
8701	(22699*2^209405+1)/21	63041	Lelio R Paula	06/2014
8702	5^90189+54	63040	Lelio R Paula	04/2013
8703	(22*10^63034-73)/3	63035	Robert Price	09/2017
8704	(314021^11467+1)/314022	63029	Faysal YAtim	05/2008
8705	V(301486)	63007	Henri Lifchitz	05/2003
8706	(31*2^209298+1)/95	63005	Lelio R Paula	08/2012
8707	(27*2^209245+1)/5	62990	Lelio R Paula	08/2012
8708	6^80946-5^(80946-1)	62989	Robert Price	05/2016
8709	467^23596+23596^467	62986	Norbert Schneider	08/2016
8710	(7*2^209212-1)/3	62980	Lelio R Paula	01/2014
8711	(27*2^209206-1)/11	62978	Lelio R Paula	01/2014
8712	1456^19909+19909^1456	62976	Serge Batalov	05/2014
8713	(5^90107-1)/(4*2162569)	62976	Gord Palameta	07/2019
8714	(3^131964-5)/185212396	62955	Lelio R Paula	04/2012
8715	35^40772-1466	62955	Enzo Doria	03/2013
8716	5^90064-13706	62953	Enzo Doria	02/2013
8717	(22*10^62926+257)/9	62927	Robert Price	11/2017
8718	(13*10^62914+401)/9	62915	Robert Price	10/2017
8719	2^208993+107	62914	Lelio R Paula	08/2011
8720	2^208993+77	62914	Lelio R Paula	08/2011
8721	189^27636-2	62913	Lelio R Paula	10/2017
8722	(2^208948-7)/261	62898	Lelio R Paula	03/2012
8723	15804^9545+9545^15804	62897	Hans Havermann	06/2019
8724	(151*10^62879-1)/3	62881	Robert Price	04/2017
8725	15^53464-82	62879	Lelio R Paula	05/2013
8726	11018^15555-15555^11018	62875	Norbert Schneider	11/2019
8727	2^208843-112921	62869	Enzo Doria	06/2014
8728	2^208779+81	62849	Henri Lifchitz	01/2007
8729	159^28548+158	62846	Norbert Schneider	12/2018
8730	(21181*2^208780+1)/8993838841	62844	Lelio R Paula	06/2014
8731	(73*10^62824+17)/9	62825	Robert Price	10/2015
8732	3^131670-82	62823	Lelio R Paula	04/2013
8733	19^49128-90	62823	Lelio R Paula	05/2013
8734	17687^3562+3562^17687	62819	Hans Havermann	06/2019
8735	11^60314-4410	62811	Enzo Doria	01/2013
8736	(17*2^208614-1)/53	62799	Lelio R Paula	01/2014
8737	2^208594+93	62794	Donovan Johnson	06/2008
8738	(-lucasV(1,2,417184)+2)/(3*104297)	62788	Mike Oakes	02/2017
8739	(2^208534+7)/9059	62772	Lelio R Paula	03/2012
8741	(13^56333+1)/14	62751	Paul Bourdelais	03/2010
8740	10^62750+57	62751	Robert Price	01/2011
8742	10^62750-267429	62750	Patrick De Geest	01/2013
8743	2^208427-69	62743	Lelio R Paula	08/2011
8744	2^208421-111775	62741	Enzo Doria	05/2014
8745	2^208404-112079	62736	Enzo Doria	06/2014
8746	15242^13041+13041^15242	62726	Hans Havermann	06/2019
8747	2^208343-2221	62718	Yves Minet	08/2013
8748	2^208335+513	62716	Lelio R Paula	10/2011
8749	(2^208328+47)/3	62713	Lelio R Paula	03/2012
8750	11^60220-2040	62713	Enzo Doria	12/2012

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Probable Primes Top 10000

(255244 PRPs in the top)