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 ?
6501	10^72730+224011	72731	Patrick De Geest	05/2013
6502	10^72730-99	72730	Robert Price	05/2011
6503	3*10^72723+67	72724	Robert Price	11/2017
6504	(11^69833+3^69833)/14	72723	Robert Price	03/2013
6505	(10^72723-79)/3	72723	Robert Price	10/2017
6506	(88*10^72711-43)/9	72712	Robert Price	11/2015
6507	3^152379+280	72704	Lelio R Paula	01/2015
6508	(25*10^72703-241)/9	72704	Robert Price	01/2017
6509	(47*10^72696+133)/9	72697	Robert Price	04/2017
6510	17^59077-90	72692	Lelio R Paula	01/2015
6511	65^40096+58	72691	Lelio R Paula	01/2016
6512	(29*2^241446-1)/245	72682	Lelio R Paula	01/2014
6514	11^69783-38400000	72672	Enzo Doria	01/2013
6513	2^241409-112903	72672	Enzo Doria	06/2014
6515	(3^152287+1)/4	72659	Paul Bourdelais	04/2008
6516	3^152249-56	72642	Lelio R Paula	01/2015
6517	10^72631+37	72632	Robert Price	01/2011
6518	10^72631-8813	72631	Patrick De Geest	05/2013
6519	(19*2^241254+1)/101	72624	Lelio R Paula	08/2012
6520	(9^76103+8^76103)/17	72620	Robert Price	12/2012
6521	2^241220-112337	72615	Enzo Doria	06/2014
6522	(82*10^72612+449)/9	72613	Robert Price	02/2017
6523	2^241169-15793	72600	Enzo Doria	04/2013
6524	9*10^72595+11	72596	Robert Kinser	01/2017
6525	(25*2^241048+1)/89	72563	Lelio R Paula	08/2012
6526	(22*10^72560+17)/3	72561	Robert Price	09/2015
6527	2^241032-23	72558	Lelio R Paula	02/2012
6528	34485*10^72550+2^241004-3	72555	Gilbert Mozzo	12/2012
6529	2^241004-3	72550	M. Frind & P. Underwood	07/2002
6530	97*10^72522-3	72524	Robert Price	01/2017
6531	(68*10^72516+7)/3	72518	Robert Price	03/2016
6532	(78557*2^240844+1)/63	72505	Lelio R Paula	06/2014
6533	67^39701-66	72497	Norbert Schneider	11/2014
6534	(185*10^72484+7)/3	72486	Robert Price	02/2017
6536	(293*27^50631-1736)/13	72473	Curtis Bright	05/2015
6535	103^36005-102	72473	Norbert Schneider	10/2016
6537	15^61616+88	72467	Lelio R Paula	01/2015
6538	45^43831+2	72462	Lelio R Paula	05/2013
6539	2^240692-492389	72456	Paul Bourdelais	03/2013
6540	(646*10^72446-7)/9	72448	Robert Price	07/2016
6541	9*6^93083+7	72434	Lelio R Paula	10/2014
6542	2^240617-3645	72433	Lelio R Paula	05/2013
6543	11^69531-24000	72410	Enzo Doria	12/2012
6544	(22699*2^240396+1)/55	72370	Lelio R Paula	06/2014
6545	6^92995+13	72365	Lelio R Paula	01/2015
6546	(11*10^72362-149)/3	72363	Robert Price	01/2017
6547	(2^240381+3)/51655	72358	Lelio R Paula	05/2012
6548	6^92974-55	72348	Lelio R Paula	01/2015
6549	2^240295+11	72337	Lelio R Paula	02/2012
6550	(14*10^72326-53)/3	72327	Robert Price	12/2016
6551	15^61493-46	72322	Lelio R Paula	01/2015
6552	lucasU(46,1,43497)-lucasU(46,1,43496)	72315	Mike Oakes	04/2009
6553	5*10^72302+9	72303	Dmitry Domanov	11/2010
6554	(9787*2^240179-1)/265	72303	Lelio R Paula	04/2015
6555	11^69419-3120	72293	Enzo Doria	12/2012
6556	4*10^72274-83	72275	Robert Price	10/2017
6557	10^72267+33	72268	Robert Price	01/2011
6558	10^72267-553947	72267	Patrick De Geest	05/2013
6559	11^69389-1380	72262	Enzo Doria	12/2012
6560	(16^60013-5^60013)/11	72262	Robert Price	07/2013
6561	7^85507-30	72262	Lelio R Paula	08/2014
6562	(19*2^240026-1)/15	72256	Lelio R Paula	02/2014
6563	(3^151426-2)/661337	72243	Lelio R Paula	06/2012
6564	gcd(V(1296375),5F(259275)(F(259275)-1)+1)	72227	Serge Batalov	04/2015
6565	2^239863-112267	72206	Enzo Doria	06/2014
6566	2^239853-114853	72203	Enzo Doria	05/2015
6567	(4*10^72174+149)/9	72174	Robert Price	03/2017
6569	(2^239671+9)/296131	72143	Lelio R Paula	05/2012
6568	2^239651-110665	72143	Enzo Doria	05/2014
6570	(29*2^239650-1)/3305	72140	Lelio R Paula	01/2014
6571	241^30280+30280^241	72128	Norbert Schneider	11/2014
6572	(68*10^72120-23)/9	72121	Robert Price	10/2015
6573	(9^75571+8^75571)/17	72112	Robert Price	12/2012
6574	(15*2^239530-1)/173	72105	Lelio R Paula	01/2014
6575	2^239513-112519	72101	Enzo Doria	06/2014
6576	(10^72097+149)/3	72097	Serge Batalov	12/2014
6577	2^239442-6555	72080	Lelio R Paula	05/2012
6578	2*5^103106+3	72069	Lelio R Paula	10/2014
6579	2^239402-197	72068	Lelio R Paula	02/2012
6580	2^239356-111875	72054	Enzo Doria	05/2014
6581	(38*10^72050-119)/9	72051	Robert Price	11/2016
6582	2^239339+15015	72049	Lelio R Paula	01/2013
6583	159^32728+2	72048	Lelio R Paula	05/2013
6584	15^61259-38	72047	Lelio R Paula	01/2015
6585	92^36683-91^36683	72038	Robert Price	08/2015
6586	2^239280+54615	72031	Lelio R Paula	05/2012
6587	(47*2^239267+1)/77	72027	Lelio R Paula	04/2015
6588	(85*10^72025-1)/3	72027	Robert Price	07/2017
6589	2^239236-97305	72018	Lelio R Paula	05/2012
6590	144^33361-143	72006	Norbert Schneider	11/2018
6591	2^239169+59	71998	Lelio R Paula	02/2012
6592	lucasU(2010,1,21796)-lucasU(2010,1,21795)	71994	Mike Oakes	05/2009
6593	(15*2^239171-1)/106301	71994	Lelio R Paula	01/2014
6594	(29^49211-1)/28	71965	Robert Price	04/2012
6595	(299*10^71963+1)/3	71965	Robert Price	11/2017
6597	L(344293)	71953	Renaud Lifchitz	09/2003
6596	V(344293)	71953	Serge Batalov	03/2015
6598	6*10^71951+7	71952	Dmitry Domanov	11/2010
6599	3^150798+40	71949	Lelio R Paula	01/2015
6600	2^238961+95	71935	Lelio R Paula	02/2012
6601	2^238936-407	71927	Yves Minet	02/2012
6602	2^238923-28635	71923	Lelio R Paula	05/2012
6603	10^71910+25119	71911	Patrick De Geest	05/2016
6604	10^71910-801	71910	Robert Price	04/2016
6605	2^238845-112651	71900	Enzo Doria	06/2014
6606	2^238792-111245	71884	Enzo Doria	05/2014
6607	6*7^85059+5	71884	Lelio R Paula	10/2014
6608	2^238752-110589	71872	Enzo Doria	05/2014
6609	12^66581+7	71853	Lelio R Paula	07/2014
6610	(7*2^238691+1)/41229	71850	Lelio R Paula	06/2012
6611	4*3^150568-5	71840	Lelio R Paula	04/2014
6612	6^92301+67	71825	Lelio R Paula	01/2015
6613	2^238568+98765331	71817	Jason Earls	01/2009
6614	2^238541-112723	71808	Enzo Doria	06/2014
6615	2^238529-15949	71805	Enzo Doria	04/2013
6616	9*5^102721-8	71800	Lelio R Paula	10/2014
6617	2^238494-165	71794	Lelio R Paula	02/2012
6618	2^238389-110905	71763	Enzo Doria	05/2014
6619	(145*10^71760-1)/9	71762	Serge Batalov	12/2014
6620	7^84913+5062	71760	Mike Oakes	02/2010
6621	(F(11446)^31-F(11445)^31)/F(11444)	71753	Wayne Halsdorf	03/2012
6622	2^238268-97305	71726	Lelio R Paula	05/2012
6623	gcd(V(1330365),5F(266073)(F(266073)-1)+1)	71724	Serge Batalov	04/2015
6624	2^238235-113247	71716	Enzo Doria	07/2014
6625	2*12^66450-5^66450	71712	Mike Oakes	11/2010
6626	(2^238213+lucasV(1,2,238213)+1)/4	71709	Mike Oakes	11/2016
6627	2^238199-111817	71706	Enzo Doria	05/2014
6628	lucasU(46,1,43125)+lucasU(46,1,43124)	71696	Mike Oakes	04/2009
6629	2^238144+98765331	71689	Jason Earls	01/2009
6630	18^57102-4265	71679	Enzo Doria	03/2013
6631	(73*10^71670-1)/9	71671	Robert Price	01/2015
6632	2^238081+1155*238081	71670	Henri Lifchitz	02/2005
6633	2^238067-111925	71666	Enzo Doria	05/2014
6634	36^46030+35	71637	Norbert Schneider	04/2014
6635	(74*10^71621+313)/9	71622	Robert Price	11/2017
6636	2^237905-91	71617	Lelio R Paula	02/2012
6637	(31*2^237902-1)/123	71616	Lelio R Paula	01/2014
6638	(15185*2^237866-1)/43967	71605	Lelio R Paula	04/2015
6639	(24737*2^237841+1)/25	71601	Lelio R Paula	06/2014
6640	2^237846+1299	71599	Lelio R Paula	05/2012
6641	6^92004+199801	71594	Mike Oakes	02/2011
6642	159^32516+2	71581	Lelio R Paula	05/2013
6643	2^237781+855	71580	Lelio R Paula	05/2012
6644	2^237720-4079	71561	Yves Minet	06/2011
6645	2^237698-110945	71555	Enzo Doria	05/2014
6646	2^237695-113239	71554	Enzo Doria	07/2014
6647	8*5^102362-9	71549	Lelio R Paula	10/2014
6648	(4*10^71546-31)/9	71546	Erik Branger	05/2011
6649	2^237650+37	71540	Lelio R Paula	02/2012
6650	18^56977-4391	71522	Enzo Doria	03/2013
6651	(22699*2^237565+1)/4136637	71512	Lelio R Paula	06/2014
6652	((1+sqrt(7)+sqrt(6))^48479-1)((1+sqrt(7)-sqrt(6))^48479-1)((1-sqrt(7)+sqrt(6))^48479-1)*((1-sqrt(7	71512	Mike Oakes	05/2009
6653	(26*10^71503+7)/3	71504	Erik Branger	11/2013
6654	(4*10^71498+173)/3	71499	Robert Price	01/2017
6655	3^149848+110	71496	Lelio R Paula	11/2014
6656	2^237498+513	71495	Lelio R Paula	05/2012
6657	2^237485+107	71491	Lelio R Paula	02/2012
6658	(2^237465+9)/2419	71481	Lelio R Paula	05/2012
6659	2^237439-112237	71477	Enzo Doria	06/2014
6660	2^237407-9787	71467	Lelio R Paula	11/2009
6661	2^237383+72953	71460	Enzo Doria	04/2016
6662	82^37337-81^37337	71457	Robert Price	01/2015
6663	(1017*2^237313-1)/19	71441	Lelio R Paula	04/2015
6664	2^237311+191	71438	Lelio R Paula	02/2012
6665	2^237280-59	71429	Lelio R Paula	02/2012
6666	11^68564-98	71403	Lelio R Paula	01/2015
6667	2^237173+74801	71397	Enzo Doria	04/2016
6668	15^60697+56	71386	Lelio R Paula	01/2015
6669	2^237118+177	71380	Lelio R Paula	02/2012
6670	2^237110+69	71378	Lelio R Paula	02/2012
6671	15^60690-58	71377	Lelio R Paula	01/2015
6672	(5*2^237125-1)/599851191	71374	Lelio R Paula	01/2014
6673	(3^149567+2)/539	71359	Lelio R Paula	06/2012
6674	(5*10^71357-143)/3	71358	Robert Price	04/2016
6675	2^237039-114621	71356	Enzo Doria	05/2015
6676	12^66116-37	71352	Lelio R Paula	02/2015
6677	(3^149497+2^149497)/5	71328	Jean-Louis Charton	10/2010
6678	2^236941-66945	71327	Lelio R Paula	05/2012
6679	2^236911-1147	71318	Yves Minet	10/2009
6680	65^39337+42	71315	Lelio R Paula	01/2016
6681	6*10^71299+7	71300	Dmitry Domanov	11/2010
6682	(25*2^236843+1)/3753	71295	Lelio R Paula	06/2012
6683	10^71291+15187	71292	Patrick De Geest	03/2016
6685	10^71291-5587309119	71291	Robert Price	03/2015
6684	10^71291-273581	71291	Patrick De Geest	03/2016
6686	-numer(bernoulli(22808)/22808)	71290	T. D. Noe	09/2005
6687	15105^17054+17054^15105	71271	Norbert Schneider	08/2018
6688	(2^236738+9)/13	71265	Lelio R Paula	05/2012
6689	5^101949+42	71260	Lelio R Paula	07/2014
6690	5*10^71237+9	71238	Dmitry Domanov	11/2010
6691	2^236634-16025	71234	Enzo Doria	04/2013
6692	71^38478+70	71233	Norbert Schneider	12/2014
6693	9*7^84280+8	71226	Lelio R Paula	10/2014
6694	(10^71223+59)/3	71223	Serge Batalov	12/2014
6695	(15185*2^236569-1)/453	71216	Lelio R Paula	04/2015
6696	51829#+(216091#)/(51829#)	71208	Makoto Morimoto	03/2016
6697	2^236528-173	71203	Lelio R Paula	02/2012
6698	3*2^236511-5	71198	Lelio R Paula	04/2014
6699	2^236477-99	71187	Lelio R Paula	02/2012
6700	11^68356-2130	71186	Enzo Doria	12/2012
6701	15128^17031+17031^15128	71186	Norbert Schneider	08/2018
6702	11^68355-3120	71185	Enzo Doria	12/2012
6703	36^45737-35^45737	71181	Robert Price	10/2012
6704	(3^149183-lucasV(1,3,149183)+1)/3	71178	Paul Vanderveen	12/2017
6705	2^236432+25	71174	Lelio R Paula	02/2012
6706	5^101818-12806	71168	Enzo Doria	02/2013
6707	(7*10^71166-457)/9	71166	Robert Price	09/2017
6708	65^39253+62	71163	Lelio R Paula	01/2016
6709	39^44718+38	71150	Norbert Schneider	05/2014
6710	2^236296-407	71133	Yves Minet	02/2012
6711	2^236286-117	71130	Lelio R Paula	02/2012
6712	2^236257-111193	71121	Enzo Doria	05/2014
6713	7^84149-36	71115	Lelio R Paula	08/2014
6714	164176#-p(164176)	71108	Henri Lifchitz	12/2018
6715	2^236209-112123	71106	Enzo Doria	06/2014
6716	18^56644-4985	71104	Enzo Doria	03/2013
6717	(46*10^71077+521)/9	71078	Robert Price	08/2017
6718	21^53753+2	71074	Ray Chandler	08/2011
6719	(86*10^71068-311)/9	71069	Robert Price	10/2017
6720	2^236081-110923	71068	Enzo Doria	05/2014
6721	(293*27^49642-1736)/13	71058	Curtis Bright	05/2015
6722	65^39192+22	71052	Lelio R Paula	01/2016
6723	(439#+1)^397-439#^397	71038	Mike Oakes	11/2010
6724	7^84050-2	71031	Lelio R Paula	09/2013
6725	20^54558-23	70982	Lelio R Paula	01/2015
6726	2^235793-112555	70981	Enzo Doria	06/2014
6727	49936!3-3^49936	70981	Robert Price	08/2015
6728	2^235787-78795	70979	Lelio R Paula	05/2012
6729	Perrin(581132)	70970	Eric W. Weisstein	02/2011
6730	14^61913-97	70961	Lelio R Paula	01/2015
6732	2^235720+16321	70959	Yves Minet	03/2010
6731	2^235718+16095	70959	Lelio R Paula	05/2012
6733	163841#+349933	70957	Nicolas PALAU	11/2016
6734	2^235710+7	70956	Lelio R Paula	02/2012
6735	(175^31627+1)/176	70939	Eric Chen	10/2017
6736	2^235635-112087	70934	Enzo Doria	06/2014
6737	153^32467+152	70931	Norbert Schneider	11/2018
6739	2^235575-1965	70916	Lelio R Paula	05/2012
6738	6^91133+101	70916	Lelio R Paula	01/2015
6740	(21181*2^235505+1)/3	70898	Lelio R Paula	06/2014
6741	(14*10^70896+211)/9	70897	Robert Price	11/2017
6742	5^101425+84	70894	Lelio R Paula	07/2014
6743	177^31536+2	70893	Lelio R Paula	05/2013
6744	43*71^38292+4	70891	Serge Batalov	03/2016
6745	(29*2^235506-1)/112029785	70888	Lelio R Paula	01/2014
6746	11^68045-1530	70862	Enzo Doria	12/2012
6747	5*10^70858+21	70859	Robert Price	01/2017
6749	2^235326+3	70841	Donovan Johnson	02/2006
6748	34523!2+4	70841	Robert Price	02/2015
6750	(31*2^235307+1)/3	70836	Lelio R Paula	06/2012

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Probable Primes Top 10000

(252402 PRPs in the top)