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 ?
6501	(8*10^69674-53)/9	69674	Robert Price	11/2014
6502	(44*10^69663-413)/9	69664	Robert Price	10/2017
6503	(77*10^69656-23)/9	69657	Robert Price	10/2015
6504	6^89509+131	69652	Lelio R Paula	09/2013
6505	(78557*2^231349+1)/35	69647	Lelio R Paula	06/2014
6506	(11*10^69645+19)/3	69646	Robert Price	03/2016
6507	11^66875-28	69644	Lelio R Paula	09/2013
6508	2^231347+71483	69643	Enzo Doria	04/2016
6509	(14^60763+3^60763)/17	69641	Robert Price	04/2013
6510	(4*10^69626+173)/3	69627	Robert Price	01/2017
6511	2^231289+255	69625	Lelio R Paula	04/2012
6512	2^231234-112913	69609	Enzo Doria	06/2014
6513	(265*10^69602-7)/3	69604	Robert Price	07/2016
6514	2^231182-112841	69593	Enzo Doria	06/2014
6515	(15*2^231129+1)/23	69577	Lelio R Paula	08/2012
6516	3^145806-28	69568	Lelio R Paula	09/2013
6517	(265*10^69554-7)/3	69556	Robert Price	07/2016
6518	2^231052-113159	69554	Enzo Doria	07/2014
6519	11^66784-8	69549	Lelio R Paula	09/2013
6520	Phi(104409,10)/2296999	69546	Maksym Voznyy	07/2015
6521	2^231016-110523	69543	Enzo Doria	05/2014
6522	2^231014+577294575	69543	Lelio R Paula	02/2016
6523	14^60658+67	69522	Lelio R Paula	09/2013
6524	5^99418+36	69491	Lelio R Paula	06/2013
6525	7^82203-30	69470	Lelio R Paula	09/2013
6526	(63^38609-1)/62	69469	Paul Bourdelais	08/2017
6527	5^99359-2^99360	69449	Mike Oakes	12/2010
6528	(29*2^230684+1)/1395	69442	Lelio R Paula	08/2012
6529	(19*10^69424+77)/3	69425	Robert Price	08/2016
6530	19^54287-96	69420	Lelio R Paula	09/2013
6531	2^230541+58905	69400	Lelio R Paula	04/2012
6532	2^230506+12705	69390	Lelio R Paula	02/2013
6533	8*6^89156-5	69378	Lelio R Paula	09/2014
6534	2^230438-111347	69369	Enzo Doria	05/2014
6535	2^230428-99	69366	Lelio R Paula	02/2012
6536	(62^38699+1)/63	69362	Paul Bourdelais	08/2017
6537	3*10^69354+17	69355	Robert Price	03/2017
6538	(493*10^69340-7)/9	69342	Robert Price	07/2016
6539	(41*10^69321+373)/9	69322	Robert Price	04/2017
6540	6^89072+53	69312	Lelio R Paula	09/2013
6541	155^31639+2	69300	Lelio R Paula	05/2013
6542	3*7^81965-4	69269	Lelio R Paula	09/2014
6543	(16*10^69265+41)/3	69266	Robert Price	10/2017
6544	(86*10^69260-77)/9	69261	Robert Price	05/2016
6545	9*5^99087+4	69260	Lelio R Paula	09/2014
6546	3^145145+2660	69252	Lelio R Paula	09/2013
6547	11^66492-1140	69245	Enzo Doria	11/2012
6548	5*3^145129-4	69245	Lelio R Paula	04/2014
6549	7*3^145126+8	69244	Lelio R Paula	04/2014
6550	11^66480-2370	69232	Enzo Doria	12/2012
6551	2^229962-65	69226	Lelio R Paula	02/2012
6552	2^229958-110733	69225	Enzo Doria	05/2014
6553	V(332407)	69225	Serge Batalov	03/2015
6554	6^88959+7	69224	Lelio R Paula	09/2013
6555	15^58855-94	69219	Lelio R Paula	09/2013
6556	(2^229838+47)/12081	69185	Lelio R Paula	04/2012
6557	3^144952+98	69160	Lelio R Paula	09/2013
6558	5^98941-72	69157	Lelio R Paula	06/2013
6559	(17*2^229604-1)/229	69117	Lelio R Paula	01/2014
6560	2^229585-1063	69112	Yves Minet	11/2012
6561	(13*2^229567-1)/19	69107	Lelio R Paula	01/2014
6562	(13*2^229393-1)/5	69055	Lelio R Paula	01/2014
6563	(53*10^69050-17)/9	69051	Robert Price	09/2015
6564	(43*10^69048+47)/9	69049	Robert Price	12/2017
6565	2^229305-1868533	69028	Enzo Doria	04/2016
6566	2^229297+1385	69026	Lelio R Paula	04/2012
6567	18^54986-2441	69023	Enzo Doria	03/2013
6568	(34*10^69021-7)/9/3/67	69020	Makoto Morimoto	04/2016
6569	5^98736-14636	69014	Enzo Doria	02/2013
6570	(13^61949-5^61949)/8	69007	Robert Price	03/2013
6571	(2^229227+5)/611	69002	Lelio R Paula	04/2012
6572	2^229216-113279	69001	Enzo Doria	07/2014
6573	10^68994+51913	68995	Patrick De Geest	03/2016
6575	10^68994-10^5814-1	68994	Serge Batalov	01/2011
6574	10^68994-82947	68994	Patrick De Geest	03/2016
6576	(17*2^229136-1)/2381	68975	Lelio R Paula	01/2014
6577	2^229113+107	68970	Lelio R Paula	02/2012
6578	11^66202-4410	68943	Enzo Doria	01/2013
6579	12^63883+5	68942	Lelio R Paula	07/2013
6580	(9913*2^229002-1)/399903	68935	Lelio R Paula	04/2015
6581	2^228962-111581	68925	Enzo Doria	05/2014
6582	2^228944+81	68920	Henri Lifchitz	01/2007
6583	11^66174-54	68914	Lelio R Paula	09/2013
6584	2^228913-111265	68910	Enzo Doria	05/2014
6585	2^228902+73519	68907	Enzo Doria	04/2016
6586	(47*2^228884+1)/63	68901	Lelio R Paula	04/2015
6587	2^228821+76427	68882	Enzo Doria	05/2016
6588	3^144340+50	68868	Lelio R Paula	09/2013
6589	2^228758-112967	68864	Enzo Doria	06/2014
6590	2^228743-111379	68859	Enzo Doria	05/2014
6591	2^228741-110911	68858	Enzo Doria	05/2014
6593	lucasU(1926,1,20964)-lucasU(1926,1,20963)	68857	Mike Oakes	05/2009
6592	3*5^98511-8	68857	Lelio R Paula	09/2014
6594	2^228717+467	68851	Lelio R Paula	02/2011
6595	Phi(153218,10)/2211855049/23592660859/497714117291	68849	Maksym Voznyy	10/2011
6596	(509203*2^228665-1)/35	68840	Lelio R Paula	04/2015
6597	8^76213-7^76213	68828	Ananda Tallur & Jean-Louis Charton	11/2003
6598	11^66074-1050	68809	Enzo Doria	11/2012
6599	(68*10^68798-11)/3	68800	Robert Price	10/2017
6600	2^228484+181	68781	Lelio R Paula	02/2012
6601	2^228479-58695	68780	Lelio R Paula	04/2012
6602	2^228465-15853	68775	Enzo Doria	04/2013
6603	11^66040-5400	68774	Enzo Doria	01/2013
6604	(13*2^228441-1)/575	68766	Lelio R Paula	01/2014
6605	(17*2^228393+1)/295	68752	Lelio R Paula	08/2012
6606	2*10^68744+41	68745	Robert Price	01/2017
6607	11^66011-150	68744	Enzo Doria	08/2012
6608	(13*2^228304-1)/81	68726	Lelio R Paula	01/2014
6609	2^228295-111079	68724	Enzo Doria	05/2014
6611	(3^144039+7)/22	68723	Lelio R Paula	04/2012
6610	(8*10^68722+49)/3	68723	Robert Price	03/2016
6612	(35*10^68718+1)/9	68719	Serge Batalov	11/2010
6613	2^228271-228271	68717	Henri Lifchitz	11/2004
6614	2^228257+82875	68713	Lelio R Paula	02/2013
6615	3^144013+40	68712	Lelio R Paula	09/2013
6616	13^61671-86	68699	Lelio R Paula	09/2013
6617	(46*10^68698+683)/9	68699	Robert Price	12/2017
6618	17^55828-72	68694	Lelio R Paula	09/2013
6619	6^88259+61	68679	Lelio R Paula	09/2013
6620	18^54699-5	68663	Lelio R Paula	09/2013
6621	33^45216+2	68662	Lelio R Paula	05/2013
6623	(2^228073-5)/3	68657	Lelio R Paula	04/2012
6622	(2^(6*38012+1)-5)/3	68657	Kevin Acres	11/2013
6624	2^228055-111607	68652	Enzo Doria	05/2014
6625	2^228054-114761	68652	Enzo Doria	05/2015
6626	2^228041+1185	68648	Lelio R Paula	04/2012
6627	2^228040-1037	68647	Yves Minet	11/2012
6628	2*F(328450)-1	68642	Henri Lifchitz	12/2009
6629	5^98201-34	68640	Lelio R Paula	06/2013
6630	9^71910+38^71910-24^71910-3*2^71910	68620	Mike Oakes	12/2010
6631	7*2^227780-3	68570	Lelio R Paula	04/2014
6632	2^227733-121	68555	Lelio R Paula	02/2012
6633	2^227702-16967	68546	Enzo Doria	05/2013
6634	2^227689-111655	68542	Enzo Doria	05/2014
6635	gcd(V(823915),5F(164783)(F(164783)-1)+1)	68536	Serge Batalov	04/2015
6636	5^98051+2	68535	Ray Chandler	07/2011
6637	5*10^68524+51	68525	Robert Price	01/2017
6638	(11*10^68520-149)/3	68521	Robert Price	01/2017
6639	19^53573-78	68507	Lelio R Paula	09/2013
6640	(68*10^68504+13)/9	68505	Ray Chandler	10/2010
6641	9*5^98003+4	68503	Lelio R Paula	09/2014
6642	2^227528+51	68493	Lelio R Paula	02/2012
6643	3^143497+8	68466	Lelio R Paula	04/2012
6644	2^227430-95	68464	Lelio R Paula	02/2012
6645	(8*10^68455+13)/3	68456	Robert Price	11/2017
6646	3*5^97934-2	68454	Lelio R Paula	09/2014
6647	20^52613+77	68452	Lelio R Paula	09/2013
6648	2^227371+32769	68446	Lelio R Paula	04/2012
6649	(3^143465+4)/21270420067	68440	Lelio R Paula	04/2012
6650	CopelandErdos(68433)	68433	Eric W. Weisstein	08/2013
6651	2^227323+75431	68432	Enzo Doria	04/2016
6652	2^227314-1965	68429	Lelio R Paula	04/2012
6653	2^227303-110617	68426	Enzo Doria	05/2014
6654	7^80963+66	68422	Lelio R Paula	07/2013
6655	2^227290+73849	68422	Enzo Doria	04/2016
6656	(14^59693-1)/13	68415	Paul Bourdelais	06/2008
6657	2^227256-2786249	68411	Enzo Doria	03/2016
6659	8*10^68400-7	68401	Dmitry Domanov	11/2010
6658	(15*2^227228-1)/583	68401	Lelio R Paula	01/2014
6660	2^227210+1869169	68398	Enzo Doria	05/2016
6661	2^227159-1838635	68382	Enzo Doria	05/2015
6662	44*10^68368+3	68370	Robert Price	08/2017
6663	2^227115-7807	68369	Lelio R Paula	10/2009
6664	2^227078-47355	68358	Lelio R Paula	04/2012
6665	(2^227063-1017)/349	68351	Lelio R Paula	04/2012
6666	2^227057+148091	68351	Lelio R Paula	04/2012
6667	2^227046+187	68348	Lelio R Paula	02/2012
6668	9*10^68331+59	68332	Robert Price	10/2017
6669	11^65608-720	68324	Enzo Doria	11/2012
6670	(32*10^68320+319)/9	68321	Robert Price	10/2017
6671	33408!2-2^33408-1	68315	Joe McLean	05/2017
6672	2^226894-123	68302	Lelio R Paula	02/2012
6673	10^68297+141559	68298	Patrick De Geest	05/2013
6674	10^68297-93	68297	Robert Price	05/2011
6675	680^24107-679^24107	68284	Jean-Louis Charton	07/2010
6676	12^63267+59	68277	Lelio R Paula	07/2013
6677	2^226785-1159	68270	Yves Minet	11/2012
6678	7^80769+90	68258	Lelio R Paula	07/2013
6679	(88*10^68256-1)/3	68258	Robert Price	10/2017
6680	2^226741+66587	68256	Yves Minet	10/2010
6681	2^226720-112403	68250	Enzo Doria	06/2014
6682	(78557*2^226694+1)/3	68247	Lelio R Paula	06/2014
6683	(83*10^68231+7)/9	68232	Robert Price	10/2015
6684	65^37636+16	68231	Lelio R Paula	01/2016
6685	5^97615-4^(97615+1)	68230	Robert Price	04/2016
6686	12^63200-43	68205	Lelio R Paula	07/2013
6687	-330*Bern(21940)/223790620733	68201	Serge Batalov	04/2015
6688	3^142925+8680	68193	Lelio R Paula	06/2013
6689	3*2^226512-7	68188	Lelio R Paula	04/2014
6690	14^59484+57	68177	Lelio R Paula	08/2013
6691	11^65438-2190	68147	Enzo Doria	12/2012
6692	91^34784-2	68144	Lelio R Paula	09/2013
6693	(2^226336-3)*6-7	68135	Gilbert Mozzo	06/2016
6694	(22*10^68133-37)/3	68134	Robert Price	05/2017
6695	5^97476+36	68133	Lelio R Paula	06/2013
6696	3*5^97474-2	68132	Lelio R Paula	09/2014
6697	12^63130+49	68129	Lelio R Paula	07/2013
6698	2^226281+5385	68118	Lelio R Paula	04/2012
6699	2^226257-3049	68111	Yves Minet	10/2014
6700	(28*10^68107-43)/3	68108	Robert Price	04/2016
6701	2^226243-2587	68106	Yves Minet	07/2014
6702	20^52346-11	68104	Lelio R Paula	09/2013
6703	2^226205-99	68095	Lelio R Paula	02/2012
6704	2^226187-49	68090	Lelio R Paula	02/2012
6705	3^142708+76	68090	Lelio R Paula	06/2013
6706	7*10^68088-89	68089	Robert Price	01/2017
6707	2^226154+71839	68080	Enzo Doria	04/2016
6708	(10^68078+59)/3	68078	Serge Batalov	12/2014
6710	14^59387+69	68066	Lelio R Paula	08/2013
6709	2^226108-113429	68066	Enzo Doria	07/2014
6711	(62*10^68059-197)/9	68060	Robert Price	10/2017
6712	(24^49307-1)/23	68053	Robert Price	04/2012
6713	15^57859-28	68048	Lelio R Paula	08/2013
6714	(509203*2^226003-1)/13	68039	Lelio R Paula	04/2015
6715	2^226015-111361	68038	Enzo Doria	05/2014
6716	(10^(234016+1)+7210^34016-1)/9	68033	Robert Price	09/2017
6717	4*10^68020+91	68021	Robert Price	11/2017
6718	156(10^(417000)-1)/101-1	68001	Robert Price	05/2014
6719	2^225878-1017	67997	Lelio R Paula	04/2012
6720	38^75289+5^75289-34^75289+3*2^75289	67994	Mike Oakes	11/2010
6721	3*2^225865+5	67993	Lelio R Paula	04/2014
6723	11^65284-5820	67987	Enzo Doria	01/2013
6722	19^53166+70	67987	Lelio R Paula	08/2013
6724	2^225837+75407	67984	Enzo Doria	04/2016
6725	3^142464-112654	67973	Enzo Doria	06/2014
6726	2^225777+95	67966	Lelio R Paula	02/2012
6727	(2^225641-1017)/138815	67920	Lelio R Paula	04/2012
6728	2^225609-18445	67916	Enzo Doria	05/2013
6729	2^225542-177	67895	Lelio R Paula	02/2012
6730	2^225536-29	67894	Henri Lifchitz	05/2005
6731	11^65190-3390	67889	Enzo Doria	12/2012
6732	3^142249-2^(142249-1)	67871	Robert Price	01/2016
6733	11^65168-4830	67866	Enzo Doria	01/2013
6734	10^67863+58627	67864	Patrick De Geest	01/2016
6735	10^67863-11	67863	Robert Price	05/2011
6736	(1!)^2+(2!)^2+(3!)^2+...+(9566!)^2	67856	T. D. Noe	02/2006
6737	(19*2^225357-1)/11	67840	Lelio R Paula	01/2014
6738	9*6^87164-7	67828	Lelio R Paula	09/2014
6739	131^32034+130	67825	Norbert Schneider	03/2015
6740	(29*2^225314+1)/10881	67824	Lelio R Paula	08/2012
6741	(134*10^67816+7)/3	67818	Robert Price	02/2017
6742	2^225261+855	67811	Lelio R Paula	04/2012
6743	(29*2^225252-1)/2933	67806	Lelio R Paula	01/2014
6744	(4*10^67796+23)/9	67796	Robert Price	11/2014
6745	(23*2^225177+1)/31	67785	Lelio R Paula	08/2012
6746	(4*10^67784+149)/9	67784	Robert Price	03/2017
6747	2^225120+151	67768	Lelio R Paula	02/2012
6748	(44^41233+1)/45	67763	Robert Price	11/2013
6749	8*10^67742+9	67743	Dmitry Domanov	11/2010
6750	2^224977+1089	67725	Lelio R Paula	04/2012

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PRP Records

Probable Primes Top 10000

(205869 PRPs in the top)