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 ?
7501	((2^43112609)/10^38420)%10^70000	70000	Michael Vang	10/2016
7502	(2^756839/10^36014)%10^70000	70000	Michael Vang	12/2016
7503	(2^74207281/10^32641)%10^70000	70000	Michael Vang	12/2016
7504	10^69999-88251	69999	Patrick De Geest	08/2009
7505	2^232507+1089	69992	Lelio R Paula	04/2012
7506	(17*2^232445+1)/5	69974	Lelio R Paula	08/2012
7507	(529^25693+1)/530	69972	Richard Fischer	12/2017
7508	7^82778+48	69956	Lelio R Paula	09/2013
7510	7*2^232381+3	69955	Lelio R Paula	04/2014
7509	19305^4204+4204^19305	69955	Hans Havermann	10/2019
7511	2^232362-110541	69948	Enzo Doria	05/2014
7512	19442^3957+3957^19442	69940	Hans Havermann	09/2019
7513	2^232326-112391	69938	Enzo Doria	06/2014
7514	3^146575+236	69935	Lelio R Paula	09/2013
7515	30^47341-29	69929	Norbert Schneider	02/2014
7516	5^100040-68	69925	Lelio R Paula	09/2013
7517	9946^17491+17491^9946	69923	Norbert Schneider	07/2019
7518	(35*10^69866-593)/9	69867	Robert Price	08/2017
7519	2^232045-17295	69853	Lelio R Paula	04/2012
7520	(2^231987+78557)/95	69834	Lelio R Paula	05/2012
7521	2^231955+74243	69826	Yves Minet	03/2011
7522	2^231946-15873	69823	Enzo Doria	04/2013
7523	18^55618+95	69816	Lelio R Paula	09/2013
7524	6^89712+5^(89712-1)	69810	Robert Price	02/2016
7525	2^231870+135	69800	Lelio R Paula	02/2012
7526	(23*2^231827-1)/4179	69785	Lelio R Paula	01/2014
7527	2^231778+54615	69773	Lelio R Paula	04/2012
7528	(19*2^231780+1)/235	69772	Lelio R Paula	08/2012
7529	14^60866+27	69761	Lelio R Paula	09/2013
7530	13^62619-44	69755	Lelio R Paula	09/2013
7531	(2^231715-509203)/35	69752	Lelio R Paula	05/2012
7532	2^231711-110467	69752	Enzo Doria	05/2014
7533	(19^54547+18^54547)/37	69751	Robert Price	08/2013
7534	(23*2^231697-1)/45	69748	Lelio R Paula	01/2014
7535	2^231696-1861499	69748	Enzo Doria	03/2016
7536	2^231684-147	69744	Lelio R Paula	02/2012
7537	(23*2^231686-1)/1183	69743	Lelio R Paula	01/2014
7538	2^231591-477397	69716	Paul Bourdelais	03/2013
7539	16916^13209+13209^16916	69709	Hans Havermann	09/2019
7540	16568^16095+16095^16568	69697	Hans Havermann	09/2019
7541	11^66916-420	69686	Enzo Doria	08/2012
7542	5^99680-13706	69674	Enzo Doria	02/2013
7543	(8*10^69674-53)/9	69674	Robert Price	11/2014
7544	(44*10^69663-413)/9	69664	Robert Price	10/2017
7545	18950^4743+4743^18950	69662	Hans Havermann	10/2019
7546	(77*10^69656-23)/9	69657	Robert Price	10/2015
7547	6^89509+131	69652	Lelio R Paula	09/2013
7548	(78557*2^231349+1)/35	69647	Lelio R Paula	06/2014
7549	(11*10^69645+19)/3	69646	Robert Price	03/2016
7550	11^66875-28	69644	Lelio R Paula	09/2013
7551	2^231347+71483	69643	Enzo Doria	04/2016
7552	(14^60763+3^60763)/17	69641	Robert Price	04/2013
7553	(4*10^69626+173)/3	69627	Robert Price	01/2017
7554	2^231289+255	69625	Lelio R Paula	04/2012
7555	19794^3287+3287^19794	69612	Hans Havermann	09/2019
7556	2^231234-112913	69609	Enzo Doria	06/2014
7557	(265*10^69602-7)/3	69604	Robert Price	07/2016
7558	2^231182-112841	69593	Enzo Doria	06/2014
7559	(15*2^231129+1)/23	69577	Lelio R Paula	08/2012
7560	3^145806-28	69568	Lelio R Paula	09/2013
7561	(265*10^69554-7)/3	69556	Robert Price	07/2016
7562	2^231052-113159	69554	Enzo Doria	07/2014
7563	(10^9+1)(10^129+1)(10^831+1)*(10^107199+1)/1001/(10^387+1)/(10^2493+1)/(10^35733+1)	69552	Makoto Kamada	03/2019
7564	11^66784-8	69549	Lelio R Paula	09/2013
7565	Phi(104409,10)/2296999	69546	Maksym Voznyy	07/2015
7566	2^231016-110523	69543	Enzo Doria	05/2014
7567	2^231014+577294575	69543	Lelio R Paula	02/2016
7568	14^60658+67	69522	Lelio R Paula	09/2013
7569	5^99418+36	69491	Lelio R Paula	06/2013
7570	7^82203-30	69470	Lelio R Paula	09/2013
7571	(63^38609-1)/62	69469	Paul Bourdelais	08/2017
7572	5^99359-2^99360	69449	Mike Oakes	12/2010
7573	(29*2^230684+1)/1395	69442	Lelio R Paula	08/2012
7574	17692^8411+8411^17692	69439	Hans Havermann	09/2019
7575	(19*10^69424+77)/3	69425	Robert Price	08/2016
7576	19^54287-96	69420	Lelio R Paula	09/2013
7577	20739^2222+2222^20739	69409	Hans Havermann	09/2019
7578	2^230541+58905	69400	Lelio R Paula	04/2012
7579	2^230506+12705	69390	Lelio R Paula	02/2013
7580	8*6^89156-5	69378	Lelio R Paula	09/2014
7581	2^230438-111347	69369	Enzo Doria	05/2014
7582	2^230428-99	69366	Lelio R Paula	02/2012
7583	(62^38699+1)/63	69362	Paul Bourdelais	08/2017
7584	3*10^69354+17	69355	Robert Price	03/2017
7585	(493*10^69340-7)/9	69342	Robert Price	07/2016
7586	(41*10^69321+373)/9	69322	Robert Price	04/2017
7587	6^89072+53	69312	Lelio R Paula	09/2013
7588	155^31639+2	69300	Lelio R Paula	05/2013
7589	3*7^81965-4	69269	Lelio R Paula	09/2014
7590	(16*10^69265+41)/3	69266	Robert Price	10/2017
7591	(86*10^69260-77)/9	69261	Robert Price	05/2016
7592	9*5^99087+4	69260	Lelio R Paula	09/2014
7593	3^145145+2660	69252	Lelio R Paula	09/2013
7594	11^66492-1140	69245	Enzo Doria	11/2012
7595	5*3^145129-4	69245	Lelio R Paula	04/2014
7596	7*3^145126+8	69244	Lelio R Paula	04/2014
7597	11^66480-2370	69232	Enzo Doria	12/2012
7598	2^229962-65	69226	Lelio R Paula	02/2012
7599	2^229958-110733	69225	Enzo Doria	05/2014
7600	V(332407)	69225	Serge Batalov	03/2015
7601	6^88959+7	69224	Lelio R Paula	09/2013
7602	15^58855-94	69219	Lelio R Paula	09/2013
7603	159773#-p(159773)	69212	Henri Lifchitz	12/2018
7604	20223^2638+2638^20223	69189	Hans Havermann	09/2019
7605	(2^229838+47)/12081	69185	Lelio R Paula	04/2012
7606	3^144952+98	69160	Lelio R Paula	09/2013
7607	5^98941-72	69157	Lelio R Paula	06/2013
7608	63329!4+256	69147	Robert Price	09/2019
7609	16422^16229+16229^16422	69142	Hans Havermann	09/2019
7610	(17*2^229604-1)/229	69117	Lelio R Paula	01/2014
7611	2^229585-1063	69112	Yves Minet	11/2012
7612	(13*2^229567-1)/19	69107	Lelio R Paula	01/2014
7613	(13*2^229393-1)/5	69055	Lelio R Paula	01/2014
7614	(53*10^69050-17)/9	69051	Robert Price	09/2015
7615	(43*10^69048+47)/9	69049	Robert Price	12/2017
7616	2^229305-1868533	69028	Enzo Doria	04/2016
7617	2^229297+1385	69026	Lelio R Paula	04/2012
7618	18^54986-2441	69023	Enzo Doria	03/2013
7619	(34*10^69021-7)/9/3/67	69020	Makoto Morimoto	04/2016
7620	5^98736-14636	69014	Enzo Doria	02/2013
7621	(13^61949-5^61949)/8	69007	Robert Price	03/2013
7622	(2^229227+5)/611	69002	Lelio R Paula	04/2012
7623	2^229216-113279	69001	Enzo Doria	07/2014
7624	10^68994+51913	68995	Patrick De Geest	03/2016
7626	10^68994-10^5814-1	68994	Serge Batalov	01/2011
7625	10^68994-82947	68994	Patrick De Geest	03/2016
7627	(17*2^229136-1)/2381	68975	Lelio R Paula	01/2014
7628	2^229113+107	68970	Lelio R Paula	02/2012
7629	16877^12198+12198^16877	68965	Hans Havermann	09/2019
7630	11^66202-4410	68943	Enzo Doria	01/2013
7631	12^63883+5	68942	Lelio R Paula	07/2013
7632	(9913*2^229002-1)/399903	68935	Lelio R Paula	04/2015
7633	2^228962-111581	68925	Enzo Doria	05/2014
7634	2^228944+81	68920	Henri Lifchitz	01/2007
7635	11^66174-54	68914	Lelio R Paula	09/2013
7636	16756^12959+12959^16756	68911	Hans Havermann	09/2019
7637	2^228913-111265	68910	Enzo Doria	05/2014
7638	18917^4392+4392^18917	68909	Hans Havermann	09/2019
7639	2^228902+73519	68907	Enzo Doria	04/2016
7640	(47*2^228884+1)/63	68901	Lelio R Paula	04/2015
7641	16542^14591+14591^16542	68883	Hans Havermann	09/2019
7642	2^228821+76427	68882	Enzo Doria	05/2016
7643	3^144340+50	68868	Lelio R Paula	09/2013
7644	2^228758-112967	68864	Enzo Doria	06/2014
7645	2^228743-111379	68859	Enzo Doria	05/2014
7646	2^228741-110911	68858	Enzo Doria	05/2014
7648	lucasU(1926,1,20964)-lucasU(1926,1,20963)	68857	Mike Oakes	05/2009
7647	3*5^98511-8	68857	Lelio R Paula	09/2014
7649	2^228717+467	68851	Lelio R Paula	02/2011
7650	Phi(153218,10)/2211855049/23592660859/497714117291	68849	Maksym Voznyy	10/2011
7651	(509203*2^228665-1)/35	68840	Lelio R Paula	04/2015
7652	8^76213-7^76213	68828	Ananda Tallur & Jean-Louis Charton	11/2003
7653	11^66074-1050	68809	Enzo Doria	11/2012
7654	(68*10^68798-11)/3	68800	Robert Price	10/2017
7655	2^228484+181	68781	Lelio R Paula	02/2012
7656	2^228479-58695	68780	Lelio R Paula	04/2012
7657	2^228465-15853	68775	Enzo Doria	04/2013
7658	11^66040-5400	68774	Enzo Doria	01/2013
7659	(13*2^228441-1)/575	68766	Lelio R Paula	01/2014
7660	(17*2^228393+1)/295	68752	Lelio R Paula	08/2012
7661	17859^7072+7072^17859	68749	Hans Havermann	09/2019
7662	2*10^68744+41	68745	Robert Price	01/2017
7663	11^66011-150	68744	Enzo Doria	08/2012
7664	(13*2^228304-1)/81	68726	Lelio R Paula	01/2014
7665	2^228295-111079	68724	Enzo Doria	05/2014
7667	(3^144039+7)/22	68723	Lelio R Paula	04/2012
7666	(8*10^68722+49)/3	68723	Robert Price	03/2016
7668	(35*10^68718+1)/9	68719	Serge Batalov	11/2010
7669	2^228271-228271	68717	Henri Lifchitz	11/2004
7670	2^228257+82875	68713	Lelio R Paula	02/2013
7671	3^144013+40	68712	Lelio R Paula	09/2013
7672	13^61671-86	68699	Lelio R Paula	09/2013
7673	(46*10^68698+683)/9	68699	Robert Price	12/2017
7674	17^55828-72	68694	Lelio R Paula	09/2013
7675	18675^4762+4762^18675	68683	Hans Havermann	09/2019
7676	6^88259+61	68679	Lelio R Paula	09/2013
7677	18^54699-5	68663	Lelio R Paula	09/2013
7678	33^45216+2	68662	Lelio R Paula	05/2013
7680	(2^228073-5)/3	68657	Lelio R Paula	04/2012
7679	(2^(6*38012+1)-5)/3	68657	Kevin Acres	11/2013
7681	2^228055-111607	68652	Enzo Doria	05/2014
7682	2^228054-114761	68652	Enzo Doria	05/2015
7683	2^228041+1185	68648	Lelio R Paula	04/2012
7684	2^228040-1037	68647	Yves Minet	11/2012
7685	2*F(328450)-1	68642	Henri Lifchitz	12/2009
7686	5^98201-34	68640	Lelio R Paula	06/2013
7687	9^71910+38^71910-24^71910-3*2^71910	68620	Mike Oakes	12/2010
7688	18177^5948+5948^18177	68607	Hans Havermann	09/2019
7689	7*2^227780-3	68570	Lelio R Paula	04/2014
7690	15327^16382-16382^15327	68567	Norbert Schneider	11/2018
7691	2^227733-121	68555	Lelio R Paula	02/2012
7692	16460^14607+14607^16460	68549	Hans Havermann	09/2019
7693	2^227702-16967	68546	Enzo Doria	05/2013
7694	2^227689-111655	68542	Enzo Doria	05/2014
7695	gcd(V(823915),5F(164783)(F(164783)-1)+1)	68536	Serge Batalov	04/2015
7696	5^98051+2	68535	Ray Chandler	07/2011
7697	5*10^68524+51	68525	Robert Price	01/2017
7698	(11*10^68520-149)/3	68521	Robert Price	01/2017
7699	16624^13235+13235^16624	68520	Hans Havermann	09/2019
7700	16359^15430+15430^16359	68518	Hans Havermann	08/2019
7701	19^53573-78	68507	Lelio R Paula	09/2013
7702	(68*10^68504+13)/9	68505	Ray Chandler	10/2010
7703	9*5^98003+4	68503	Lelio R Paula	09/2014
7704	21121^1750+1750^21121	68497	Hans Havermann	10/2019
7705	2^227528+51	68493	Lelio R Paula	02/2012
7706	(146*28^47316+1)/3	68476	Karsten Bonath	06/2018
7707	3^143497+8	68466	Lelio R Paula	04/2012
7708	2^227430-95	68464	Lelio R Paula	02/2012
7709	(8*10^68455+13)/3	68456	Robert Price	11/2017
7710	3*5^97934-2	68454	Lelio R Paula	09/2014
7711	20^52613+77	68452	Lelio R Paula	09/2013
7712	2^227371+32769	68446	Lelio R Paula	04/2012
7713	(3^143465+4)/21270420067	68440	Lelio R Paula	04/2012
7714	CopelandErdos(68433)	68433	Eric W. Weisstein	08/2013
7715	2^227323+75431	68432	Enzo Doria	04/2016
7716	2^227314-1965	68429	Lelio R Paula	04/2012
7717	2^227303-110617	68426	Enzo Doria	05/2014
7719	7^80963+66	68422	Lelio R Paula	07/2013
7718	2^227290+73849	68422	Enzo Doria	04/2016
7720	(14^59693-1)/13	68415	Paul Bourdelais	06/2008
7721	2^227256-2786249	68411	Enzo Doria	03/2016
7723	8*10^68400-7	68401	Dmitry Domanov	11/2010
7722	(15*2^227228-1)/583	68401	Lelio R Paula	01/2014
7724	2^227210+1869169	68398	Enzo Doria	05/2016
7725	2^227159-1838635	68382	Enzo Doria	05/2015
7726	44*10^68368+3	68370	Robert Price	08/2017
7727	2^227115-7807	68369	Lelio R Paula	10/2009
7728	18469^5032+5032^18469	68368	Hans Havermann	08/2019
7729	2^227078-47355	68358	Lelio R Paula	04/2012
7730	16927^10920+10920^16927	68355	Hans Havermann	10/2019
7731	(2^227063-1017)/349	68351	Lelio R Paula	04/2012
7732	2^227057+148091	68351	Lelio R Paula	04/2012
7733	2^227046+187	68348	Lelio R Paula	02/2012
7734	2^227009-4693	68337	Yves Minet	05/2019
7735	9*10^68331+59	68332	Robert Price	10/2017
7736	11^65608-720	68324	Enzo Doria	11/2012
7737	(32*10^68320+319)/9	68321	Robert Price	10/2017
7738	33408!2-2^33408-1	68315	Joe McLean	05/2017
7739	2^226894-123	68302	Lelio R Paula	02/2012
7740	10^68297+141559	68298	Patrick De Geest	05/2013
7741	10^68297-93	68297	Robert Price	05/2011
7742	680^24107-679^24107	68284	Jean-Louis Charton	07/2010
7743	12^63267+59	68277	Lelio R Paula	07/2013
7744	2^226785-1159	68270	Yves Minet	11/2012
7745	7^80769+90	68258	Lelio R Paula	07/2013
7746	(88*10^68256-1)/3	68258	Robert Price	10/2017
7747	2^226741+66587	68256	Yves Minet	10/2010
7748	2^226720-112403	68250	Enzo Doria	06/2014
7749	(78557*2^226694+1)/3	68247	Lelio R Paula	06/2014
7750	(83*10^68231+7)/9	68232	Robert Price	10/2015

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Probable Primes Top 10000

(255169 PRPs in the top)