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	(29*10^70194-11)/9	70195	Robert Price	04/2015
6502	3^147109+196	70189	Lelio R Paula	05/2014
6503	(34*10^70191-7)/9/3/40583/573047	70181	Makoto Morimoto	05/2016
6504	9^73538+8^(73538+1)	70174	Robert Price	06/2016
6505	2*5^100391+7	70171	Lelio R Paula	10/2014
6506	99^35156-2	70159	Lelio R Paula	08/2013
6507	(68*10^70148+7)/3	70150	Robert Price	03/2016
6508	11^67360-6030	70149	Enzo Doria	01/2013
6509	(35*10^70130-377)/9	70131	Robert Price	12/2017
6510	49391!3+3^49391	70128	Robert Price	09/2015
6511	(229*10^70122-1)/3	70124	Robert Price	12/2016
6512	7^82975-92	70123	Lelio R Paula	07/2014
6513	65^38670+58	70106	Lelio R Paula	01/2016
6514	105^34684+34684^105	70103	Serge Batalov	05/2014
6515	134^32955-133	70099	Norbert Schneider	03/2015
6517	2^232836-227903	70091	Enzo Doria	12/2012
6516	2^232837-1859173	70091	Enzo Doria	03/2016
6518	3*2^232820+5	70087	Lelio R Paula	04/2014
6520	2^232799+90195	70080	Lelio R Paula	02/2013
6519	2^232799-112237	70080	Enzo Doria	06/2014
6521	2^232759+262145	70068	Lelio R Paula	04/2012
6522	3*2^232750+7	70066	Lelio R Paula	04/2014
6523	12^64918-11	70059	Lelio R Paula	01/2015
6524	7^82899-12	70058	Lelio R Paula	09/2013
6525	(22*10^70051-13)/9	70052	Robert Price	03/2015
6526	(2^232685-7)/2514625	70039	Lelio R Paula	04/2012
6527	18^55786-5363	70027	Enzo Doria	03/2013
6528	(2^(77537*3+1)+243)/7	70023	Kevin Acres	11/2013
6529	2^232602+169	70021	Lelio R Paula	02/2012
6530	(137^32768+29^32768)/2	70016	Jeppe Stig Nielsen	04/2018
6531	2^232580+72133	70014	Enzo Doria	04/2016
6532	4*6^89958-7	70002	Lelio R Paula	09/2014
6533	10^70000+80487	70001	Milton L. Brown	05/2006
6534	10^69999+134857	70000	Patrick De Geest	02/2007
6539	10^70000-9273	70000	Patrick De Geest	08/2009
6535	(79*10^69999-7)/9	70000	Robert Price	01/2015
6536	((2^43112609)/10^38420)%10^70000	70000	Michael Vang	10/2016
6537	(2^756839/10^36014)%10^70000	70000	Michael Vang	12/2016
6538	(2^74207281/10^32641)%10^70000	70000	Michael Vang	12/2016
6540	10^69999-88251	69999	Patrick De Geest	08/2009
6541	2^232507+1089	69992	Lelio R Paula	04/2012
6542	(17*2^232445+1)/5	69974	Lelio R Paula	08/2012
6543	(529^25693+1)/530	69972	Richard Fischer	12/2017
6544	7^82778+48	69956	Lelio R Paula	09/2013
6545	7*2^232381+3	69955	Lelio R Paula	04/2014
6546	2^232362-110541	69948	Enzo Doria	05/2014
6547	2^232326-112391	69938	Enzo Doria	06/2014
6548	3^146575+236	69935	Lelio R Paula	09/2013
6549	30^47341-29	69929	Norbert Schneider	02/2014
6550	5^100040-68	69925	Lelio R Paula	09/2013
6551	(35*10^69866-593)/9	69867	Robert Price	08/2017
6552	2^232045-17295	69853	Lelio R Paula	04/2012
6553	(2^231987+78557)/95	69834	Lelio R Paula	05/2012
6554	2^231955+74243	69826	Yves Minet	03/2011
6555	2^231946-15873	69823	Enzo Doria	04/2013
6556	18^55618+95	69816	Lelio R Paula	09/2013
6557	6^89712+5^(89712-1)	69810	Robert Price	02/2016
6558	2^231870+135	69800	Lelio R Paula	02/2012
6559	(23*2^231827-1)/4179	69785	Lelio R Paula	01/2014
6560	2^231778+54615	69773	Lelio R Paula	04/2012
6561	(19*2^231780+1)/235	69772	Lelio R Paula	08/2012
6562	14^60866+27	69761	Lelio R Paula	09/2013
6563	13^62619-44	69755	Lelio R Paula	09/2013
6564	(2^231715-509203)/35	69752	Lelio R Paula	05/2012
6565	2^231711-110467	69752	Enzo Doria	05/2014
6566	(19^54547+18^54547)/37	69751	Robert Price	08/2013
6567	(23*2^231697-1)/45	69748	Lelio R Paula	01/2014
6568	2^231696-1861499	69748	Enzo Doria	03/2016
6569	2^231684-147	69744	Lelio R Paula	02/2012
6570	(23*2^231686-1)/1183	69743	Lelio R Paula	01/2014
6571	2^231591-477397	69716	Paul Bourdelais	03/2013
6572	11^66916-420	69686	Enzo Doria	08/2012
6573	5^99680-13706	69674	Enzo Doria	02/2013
6574	(8*10^69674-53)/9	69674	Robert Price	11/2014
6575	(44*10^69663-413)/9	69664	Robert Price	10/2017
6576	(77*10^69656-23)/9	69657	Robert Price	10/2015
6577	6^89509+131	69652	Lelio R Paula	09/2013
6578	(78557*2^231349+1)/35	69647	Lelio R Paula	06/2014
6579	(11*10^69645+19)/3	69646	Robert Price	03/2016
6580	11^66875-28	69644	Lelio R Paula	09/2013
6581	2^231347+71483	69643	Enzo Doria	04/2016
6582	(14^60763+3^60763)/17	69641	Robert Price	04/2013
6583	(4*10^69626+173)/3	69627	Robert Price	01/2017
6584	2^231289+255	69625	Lelio R Paula	04/2012
6585	2^231234-112913	69609	Enzo Doria	06/2014
6586	(265*10^69602-7)/3	69604	Robert Price	07/2016
6587	2^231182-112841	69593	Enzo Doria	06/2014
6588	(15*2^231129+1)/23	69577	Lelio R Paula	08/2012
6589	3^145806-28	69568	Lelio R Paula	09/2013
6590	(265*10^69554-7)/3	69556	Robert Price	07/2016
6591	2^231052-113159	69554	Enzo Doria	07/2014
6592	11^66784-8	69549	Lelio R Paula	09/2013
6593	Phi(104409,10)/2296999	69546	Maksym Voznyy	07/2015
6594	2^231016-110523	69543	Enzo Doria	05/2014
6595	2^231014+577294575	69543	Lelio R Paula	02/2016
6596	14^60658+67	69522	Lelio R Paula	09/2013
6597	5^99418+36	69491	Lelio R Paula	06/2013
6598	7^82203-30	69470	Lelio R Paula	09/2013
6599	(63^38609-1)/62	69469	Paul Bourdelais	08/2017
6600	5^99359-2^99360	69449	Mike Oakes	12/2010
6601	(29*2^230684+1)/1395	69442	Lelio R Paula	08/2012
6602	(19*10^69424+77)/3	69425	Robert Price	08/2016
6603	19^54287-96	69420	Lelio R Paula	09/2013
6604	2^230541+58905	69400	Lelio R Paula	04/2012
6605	2^230506+12705	69390	Lelio R Paula	02/2013
6606	8*6^89156-5	69378	Lelio R Paula	09/2014
6607	2^230438-111347	69369	Enzo Doria	05/2014
6608	2^230428-99	69366	Lelio R Paula	02/2012
6609	(62^38699+1)/63	69362	Paul Bourdelais	08/2017
6610	3*10^69354+17	69355	Robert Price	03/2017
6611	(493*10^69340-7)/9	69342	Robert Price	07/2016
6612	(41*10^69321+373)/9	69322	Robert Price	04/2017
6613	6^89072+53	69312	Lelio R Paula	09/2013
6614	155^31639+2	69300	Lelio R Paula	05/2013
6615	3*7^81965-4	69269	Lelio R Paula	09/2014
6616	(16*10^69265+41)/3	69266	Robert Price	10/2017
6617	(86*10^69260-77)/9	69261	Robert Price	05/2016
6618	9*5^99087+4	69260	Lelio R Paula	09/2014
6619	3^145145+2660	69252	Lelio R Paula	09/2013
6620	11^66492-1140	69245	Enzo Doria	11/2012
6621	5*3^145129-4	69245	Lelio R Paula	04/2014
6622	7*3^145126+8	69244	Lelio R Paula	04/2014
6623	11^66480-2370	69232	Enzo Doria	12/2012
6624	2^229962-65	69226	Lelio R Paula	02/2012
6625	2^229958-110733	69225	Enzo Doria	05/2014
6626	V(332407)	69225	Serge Batalov	03/2015
6627	6^88959+7	69224	Lelio R Paula	09/2013
6628	15^58855-94	69219	Lelio R Paula	09/2013
6629	(2^229838+47)/12081	69185	Lelio R Paula	04/2012
6630	3^144952+98	69160	Lelio R Paula	09/2013
6631	5^98941-72	69157	Lelio R Paula	06/2013
6632	(17*2^229604-1)/229	69117	Lelio R Paula	01/2014
6633	2^229585-1063	69112	Yves Minet	11/2012
6634	(13*2^229567-1)/19	69107	Lelio R Paula	01/2014
6635	(13*2^229393-1)/5	69055	Lelio R Paula	01/2014
6636	(53*10^69050-17)/9	69051	Robert Price	09/2015
6637	(43*10^69048+47)/9	69049	Robert Price	12/2017
6638	2^229305-1868533	69028	Enzo Doria	04/2016
6639	2^229297+1385	69026	Lelio R Paula	04/2012
6640	18^54986-2441	69023	Enzo Doria	03/2013
6641	(34*10^69021-7)/9/3/67	69020	Makoto Morimoto	04/2016
6642	5^98736-14636	69014	Enzo Doria	02/2013
6643	(13^61949-5^61949)/8	69007	Robert Price	03/2013
6644	(2^229227+5)/611	69002	Lelio R Paula	04/2012
6645	2^229216-113279	69001	Enzo Doria	07/2014
6646	10^68994+51913	68995	Patrick De Geest	03/2016
6648	10^68994-10^5814-1	68994	Serge Batalov	01/2011
6647	10^68994-82947	68994	Patrick De Geest	03/2016
6649	(17*2^229136-1)/2381	68975	Lelio R Paula	01/2014
6650	2^229113+107	68970	Lelio R Paula	02/2012
6651	11^66202-4410	68943	Enzo Doria	01/2013
6652	12^63883+5	68942	Lelio R Paula	07/2013
6653	(9913*2^229002-1)/399903	68935	Lelio R Paula	04/2015
6654	2^228962-111581	68925	Enzo Doria	05/2014
6655	2^228944+81	68920	Henri Lifchitz	01/2007
6656	11^66174-54	68914	Lelio R Paula	09/2013
6657	2^228913-111265	68910	Enzo Doria	05/2014
6658	2^228902+73519	68907	Enzo Doria	04/2016
6659	(47*2^228884+1)/63	68901	Lelio R Paula	04/2015
6660	2^228821+76427	68882	Enzo Doria	05/2016
6661	3^144340+50	68868	Lelio R Paula	09/2013
6662	2^228758-112967	68864	Enzo Doria	06/2014
6663	2^228743-111379	68859	Enzo Doria	05/2014
6664	2^228741-110911	68858	Enzo Doria	05/2014
6666	lucasU(1926,1,20964)-lucasU(1926,1,20963)	68857	Mike Oakes	05/2009
6665	3*5^98511-8	68857	Lelio R Paula	09/2014
6667	2^228717+467	68851	Lelio R Paula	02/2011
6668	Phi(153218,10)/2211855049/23592660859/497714117291	68849	Maksym Voznyy	10/2011
6669	(509203*2^228665-1)/35	68840	Lelio R Paula	04/2015
6670	8^76213-7^76213	68828	Ananda Tallur & Jean-Louis Charton	11/2003
6671	11^66074-1050	68809	Enzo Doria	11/2012
6672	(68*10^68798-11)/3	68800	Robert Price	10/2017
6673	2^228484+181	68781	Lelio R Paula	02/2012
6674	2^228479-58695	68780	Lelio R Paula	04/2012
6675	2^228465-15853	68775	Enzo Doria	04/2013
6676	11^66040-5400	68774	Enzo Doria	01/2013
6677	(13*2^228441-1)/575	68766	Lelio R Paula	01/2014
6678	(17*2^228393+1)/295	68752	Lelio R Paula	08/2012
6679	2*10^68744+41	68745	Robert Price	01/2017
6680	11^66011-150	68744	Enzo Doria	08/2012
6681	(13*2^228304-1)/81	68726	Lelio R Paula	01/2014
6682	2^228295-111079	68724	Enzo Doria	05/2014
6684	(3^144039+7)/22	68723	Lelio R Paula	04/2012
6683	(8*10^68722+49)/3	68723	Robert Price	03/2016
6685	(35*10^68718+1)/9	68719	Serge Batalov	11/2010
6686	2^228271-228271	68717	Henri Lifchitz	11/2004
6687	2^228257+82875	68713	Lelio R Paula	02/2013
6688	3^144013+40	68712	Lelio R Paula	09/2013
6689	13^61671-86	68699	Lelio R Paula	09/2013
6690	(46*10^68698+683)/9	68699	Robert Price	12/2017
6691	17^55828-72	68694	Lelio R Paula	09/2013
6692	6^88259+61	68679	Lelio R Paula	09/2013
6693	18^54699-5	68663	Lelio R Paula	09/2013
6694	33^45216+2	68662	Lelio R Paula	05/2013
6696	(2^228073-5)/3	68657	Lelio R Paula	04/2012
6695	(2^(6*38012+1)-5)/3	68657	Kevin Acres	11/2013
6697	2^228055-111607	68652	Enzo Doria	05/2014
6698	2^228054-114761	68652	Enzo Doria	05/2015
6699	2^228041+1185	68648	Lelio R Paula	04/2012
6700	2^228040-1037	68647	Yves Minet	11/2012
6701	2*F(328450)-1	68642	Henri Lifchitz	12/2009
6702	5^98201-34	68640	Lelio R Paula	06/2013
6703	9^71910+38^71910-24^71910-3*2^71910	68620	Mike Oakes	12/2010
6704	7*2^227780-3	68570	Lelio R Paula	04/2014
6705	2^227733-121	68555	Lelio R Paula	02/2012
6706	2^227702-16967	68546	Enzo Doria	05/2013
6707	2^227689-111655	68542	Enzo Doria	05/2014
6708	gcd(V(823915),5F(164783)(F(164783)-1)+1)	68536	Serge Batalov	04/2015
6709	5^98051+2	68535	Ray Chandler	07/2011
6710	5*10^68524+51	68525	Robert Price	01/2017
6711	(11*10^68520-149)/3	68521	Robert Price	01/2017
6712	19^53573-78	68507	Lelio R Paula	09/2013
6713	(68*10^68504+13)/9	68505	Ray Chandler	10/2010
6714	9*5^98003+4	68503	Lelio R Paula	09/2014
6715	2^227528+51	68493	Lelio R Paula	02/2012
6716	3^143497+8	68466	Lelio R Paula	04/2012
6717	2^227430-95	68464	Lelio R Paula	02/2012
6718	(8*10^68455+13)/3	68456	Robert Price	11/2017
6719	3*5^97934-2	68454	Lelio R Paula	09/2014
6720	20^52613+77	68452	Lelio R Paula	09/2013
6721	2^227371+32769	68446	Lelio R Paula	04/2012
6722	(3^143465+4)/21270420067	68440	Lelio R Paula	04/2012
6723	CopelandErdos(68433)	68433	Eric W. Weisstein	08/2013
6724	2^227323+75431	68432	Enzo Doria	04/2016
6725	2^227314-1965	68429	Lelio R Paula	04/2012
6726	2^227303-110617	68426	Enzo Doria	05/2014
6727	7^80963+66	68422	Lelio R Paula	07/2013
6728	2^227290+73849	68422	Enzo Doria	04/2016
6729	(14^59693-1)/13	68415	Paul Bourdelais	06/2008
6730	2^227256-2786249	68411	Enzo Doria	03/2016
6732	8*10^68400-7	68401	Dmitry Domanov	11/2010
6731	(15*2^227228-1)/583	68401	Lelio R Paula	01/2014
6733	2^227210+1869169	68398	Enzo Doria	05/2016
6734	2^227159-1838635	68382	Enzo Doria	05/2015
6735	44*10^68368+3	68370	Robert Price	08/2017
6736	2^227115-7807	68369	Lelio R Paula	10/2009
6737	2^227078-47355	68358	Lelio R Paula	04/2012
6738	(2^227063-1017)/349	68351	Lelio R Paula	04/2012
6739	2^227057+148091	68351	Lelio R Paula	04/2012
6740	2^227046+187	68348	Lelio R Paula	02/2012
6741	9*10^68331+59	68332	Robert Price	10/2017
6742	11^65608-720	68324	Enzo Doria	11/2012
6743	(32*10^68320+319)/9	68321	Robert Price	10/2017
6744	33408!2-2^33408-1	68315	Joe McLean	05/2017
6745	2^226894-123	68302	Lelio R Paula	02/2012
6746	10^68297+141559	68298	Patrick De Geest	05/2013
6747	10^68297-93	68297	Robert Price	05/2011
6748	680^24107-679^24107	68284	Jean-Louis Charton	07/2010
6749	12^63267+59	68277	Lelio R Paula	07/2013
6750	2^226785-1159	68270	Yves Minet	11/2012

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Probable Primes Top 10000

(212140 PRPs in the top)