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	(2^232653+1494)/2	70036	Stefano Morozzi	01/2020
8502	18^55786-5363	70027	Enzo Doria	03/2013
8503	(2^(77537*3+1)+243)/7	70023	Kevin Acres	11/2013
8504	2^232602+169	70021	Lelio R Paula	02/2012
8505	(137^32768+29^32768)/2	70016	Jeppe Stig Nielsen	04/2018
8506	2^232580+72133	70014	Enzo Doria	04/2016
8507	4*6^89958-7	70002	Lelio R Paula	09/2014
8508	10^70000+80487	70001	Milton L. Brown	05/2006
8509	10^69999+134857	70000	Patrick De Geest	02/2007
8510	10^70000-9273	70000	Patrick De Geest	08/2009
8511	(79*10^69999-7)/9	70000	Robert Price	01/2015
8512	((2^43112609)/10^38420)%10^70000	70000	Michael Vang	10/2016
8513	(2^756839/10^36014)%10^70000	70000	Michael Vang	12/2016
8514	(2^74207281/10^32641)%10^70000	70000	Michael Vang	12/2016
8515	10^69999-88251	69999	Patrick De Geest	08/2009
8516	2^232507+1089	69992	Lelio R Paula	04/2012
8517	(2^232506+498)/2	69991	Stefano Morozzi	01/2020
8518	(17*2^232445+1)/5	69974	Lelio R Paula	08/2012
8519	(529^25693+1)/530	69972	Richard Fischer	12/2017
8520	(2^232416+498)/2	69964	Stefano Morozzi	01/2020
8521	(2^232410+2794)/2	69963	Stefano Morozzi	01/2020
8522	7^82778+48	69956	Lelio R Paula	09/2013
8524	7*2^232381+3	69955	Lelio R Paula	04/2014
8523	19305^4204+4204^19305	69955	Hans Havermann	10/2019
8525	2^232362-110541	69948	Enzo Doria	05/2014
8526	19442^3957+3957^19442	69940	Hans Havermann	09/2019
8527	2^232326-112391	69938	Enzo Doria	06/2014
8528	3^146575+236	69935	Lelio R Paula	09/2013
8529	30^47341-29	69929	Norbert Schneider	02/2014
8530	(2^232294+1218)/2	69928	Stefano Morozzi	01/2020
8531	5^100040-68	69925	Lelio R Paula	09/2013
8532	9946^17491+17491^9946	69923	Norbert Schneider	07/2019
8533	16351^16592-16592^16351	69912	Norbert Schneider	11/2019
8534	(2^232139+3746)/2	69881	Stefano Morozzi	01/2020
8535	(2^232132+2566)/2	69879	Stefano Morozzi	01/2020
8536	(35*10^69866-593)/9	69867	Robert Price	08/2017
8537	2^232045-17295	69853	Lelio R Paula	04/2012
8538	(2^231987+78557)/95	69834	Lelio R Paula	05/2012
8539	2^231955+74243	69826	Yves Minet	03/2011
8540	(2^231949+3290)/2	69824	Stefano Morozzi	01/2020
8541	2^231946-15873	69823	Enzo Doria	04/2013
8542	18^55618+95	69816	Lelio R Paula	09/2013
8543	6^89712+5^(89712-1)	69810	Robert Price	02/2016
8544	(2^231876+670)/2	69802	Stefano Morozzi	01/2020
8545	2^231870+135	69800	Lelio R Paula	02/2012
8546	(23*2^231827-1)/4179	69785	Lelio R Paula	01/2014
8547	2^231778+54615	69773	Lelio R Paula	04/2012
8548	(19*2^231780+1)/235	69772	Lelio R Paula	08/2012
8549	(2^231775+2430)/2	69771	Stefano Morozzi	01/2020
8550	14^60866+27	69761	Lelio R Paula	09/2013
8551	13^62619-44	69755	Lelio R Paula	09/2013
8552	(2^231715-509203)/35	69752	Lelio R Paula	05/2012
8553	2^231711-110467	69752	Enzo Doria	05/2014
8555	(19^54547+18^54547)/37	69751	Robert Price	08/2013
8554	(2^231707+998)/2	69751	Stefano Morozzi	01/2020
8556	(23*2^231697-1)/45	69748	Lelio R Paula	01/2014
8557	2^231696-1861499	69748	Enzo Doria	03/2016
8558	2^231684-147	69744	Lelio R Paula	02/2012
8559	(23*2^231686-1)/1183	69743	Lelio R Paula	01/2014
8560	2^231591-477397	69716	Paul Bourdelais	03/2013
8561	16916^13209+13209^16916	69709	Hans Havermann	09/2019
8562	16568^16095+16095^16568	69697	Hans Havermann	09/2019
8563	11^66916-420	69686	Enzo Doria	08/2012
8564	5^99680-13706	69674	Enzo Doria	02/2013
8565	(8*10^69674-53)/9	69674	Robert Price	11/2014
8566	(44*10^69663-413)/9	69664	Robert Price	10/2017
8567	18950^4743+4743^18950	69662	Hans Havermann	10/2019
8568	(77*10^69656-23)/9	69657	Robert Price	10/2015
8569	(2^231385+3710)/2	69654	Stefano Morozzi	01/2020
8570	6^89509+131	69652	Lelio R Paula	09/2013
8571	(2^231364+3030)/2	69648	Stefano Morozzi	01/2020
8572	(78557*2^231349+1)/35	69647	Lelio R Paula	06/2014
8573	(11*10^69645+19)/3	69646	Robert Price	03/2016
8574	11^66875-28	69644	Lelio R Paula	09/2013
8575	2^231347+71483	69643	Enzo Doria	04/2016
8576	(14^60763+3^60763)/17	69641	Robert Price	04/2013
8577	(2^231340+3126)/2	69640	Stefano Morozzi	01/2020
8578	(4*10^69626+173)/3	69627	Robert Price	01/2017
8579	2^231289+255	69625	Lelio R Paula	04/2012
8580	19794^3287+3287^19794	69612	Hans Havermann	09/2019
8581	2^231234-112913	69609	Enzo Doria	06/2014
8582	(265*10^69602-7)/3	69604	Robert Price	07/2016
8583	2^231182-112841	69593	Enzo Doria	06/2014
8584	(15*2^231129+1)/23	69577	Lelio R Paula	08/2012
8585	3^145806-28	69568	Lelio R Paula	09/2013
8586	(265*10^69554-7)/3	69556	Robert Price	07/2016
8587	2^231052-113159	69554	Enzo Doria	07/2014
8588	(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
8589	11^66784-8	69549	Lelio R Paula	09/2013
8590	Phi(104409,10)/2296999	69546	Maksym Voznyy	07/2015
8591	(2^231023+1758)/2	69545	Stefano Morozzi	01/2020
8592	2^231016-110523	69543	Enzo Doria	05/2014
8593	2^231014+577294575	69543	Lelio R Paula	02/2016
8594	(2^230982+970)/2	69533	Stefano Morozzi	01/2020
8595	14^60658+67	69522	Lelio R Paula	09/2013
8596	(2^230898+2422)/2	69507	Stefano Morozzi	01/2020
8597	5^99418+36	69491	Lelio R Paula	06/2013
8598	7^82203-30	69470	Lelio R Paula	09/2013
8599	(63^38609-1)/62	69469	Paul Bourdelais	08/2017
8600	(2^230746+3114)/2	69462	Stefano Morozzi	01/2020
8601	5^99359-2^99360	69449	Mike Oakes	12/2010
8602	(29*2^230684+1)/1395	69442	Lelio R Paula	08/2012
8603	17692^8411+8411^17692	69439	Hans Havermann	09/2019
8604	(2^230638+1278)/2	69429	Stefano Morozzi	01/2020
8605	(19*10^69424+77)/3	69425	Robert Price	08/2016
8606	(2^230610+1222)/2	69421	Stefano Morozzi	01/2020
8607	19^54287-96	69420	Lelio R Paula	09/2013
8608	20739^2222+2222^20739	69409	Hans Havermann	09/2019
8610	2^230541+58905	69400	Lelio R Paula	04/2012
8609	(2^230540+2818)/2	69400	Stefano Morozzi	01/2020
8611	2^230506+12705	69390	Lelio R Paula	02/2013
8612	8*6^89156-5	69378	Lelio R Paula	09/2014
8613	(2^230443+3594)/2	69370	Stefano Morozzi	01/2020
8614	2^230438-111347	69369	Enzo Doria	05/2014
8615	(2^230434+3150)/2	69368	Stefano Morozzi	01/2020
8616	2^230428-99	69366	Lelio R Paula	02/2012
8617	(62^38699+1)/63	69362	Paul Bourdelais	08/2017
8618	(2^230413+3090)/2	69361	Stefano Morozzi	01/2020
8619	3*10^69354+17	69355	Robert Price	03/2017
8620	(493*10^69340-7)/9	69342	Robert Price	07/2016
8621	(2^230325+590)/2	69335	Stefano Morozzi	01/2020
8623	(41*10^69321+373)/9	69322	Robert Price	04/2017
8622	(2^230282+1990)/2	69322	Stefano Morozzi	01/2020
8624	6^89072+53	69312	Lelio R Paula	09/2013
8625	155^31639+2	69300	Lelio R Paula	05/2013
8626	(2^230117+3462)/2	69272	Stefano Morozzi	01/2020
8627	3*7^81965-4	69269	Lelio R Paula	09/2014
8628	(16*10^69265+41)/3	69266	Robert Price	10/2017
8629	(86*10^69260-77)/9	69261	Robert Price	05/2016
8630	9*5^99087+4	69260	Lelio R Paula	09/2014
8631	3^145145+2660	69252	Lelio R Paula	09/2013
8632	11^66492-1140	69245	Enzo Doria	11/2012
8633	5*3^145129-4	69245	Lelio R Paula	04/2014
8634	7*3^145126+8	69244	Lelio R Paula	04/2014
8635	11^66480-2370	69232	Enzo Doria	12/2012
8636	(2^229965+3482)/2	69227	Stefano Morozzi	01/2020
8637	(2^229968+3010)/2	69227	Stefano Morozzi	01/2020
8638	2^229962-65	69226	Lelio R Paula	02/2012
8639	2^229958-110733	69225	Enzo Doria	05/2014
8640	V(332407)	69225	Serge Batalov	03/2015
8641	6^88959+7	69224	Lelio R Paula	09/2013
8642	15^58855-94	69219	Lelio R Paula	09/2013
8643	(2^229941+774)/2	69219	Stefano Morozzi	01/2020
8644	(2^229931+3270)/2	69216	Stefano Morozzi	01/2020
8645	159773#-p(159773)	69212	Henri Lifchitz	12/2018
8646	20223^2638+2638^20223	69189	Hans Havermann	09/2019
8648	(2^229838+47)/12081	69185	Lelio R Paula	04/2012
8647	(2^229828+3810)/2	69185	Stefano Morozzi	01/2020
8649	3^144952+98	69160	Lelio R Paula	09/2013
8650	5^98941-72	69157	Lelio R Paula	06/2013
8651	63329!4+256	69147	Robert Price	09/2019
8652	16422^16229+16229^16422	69142	Hans Havermann	09/2019
8653	(17*2^229604-1)/229	69117	Lelio R Paula	01/2014
8654	2^229585-1063	69112	Yves Minet	11/2012
8655	(13*2^229567-1)/19	69107	Lelio R Paula	01/2014
8656	(2^229419+1946)/2	69062	Stefano Morozzi	01/2020
8657	(2^229399+1890)/2	69056	Stefano Morozzi	01/2020
8658	(13*2^229393-1)/5	69055	Lelio R Paula	01/2014
8659	(2^229388+3666)/2	69053	Stefano Morozzi	01/2020
8660	(53*10^69050-17)/9	69051	Robert Price	09/2015
8661	(43*10^69048+47)/9	69049	Robert Price	12/2017
8662	2^229305-1868533	69028	Enzo Doria	04/2016
8663	2^229297+1385	69026	Lelio R Paula	04/2012
8664	18^54986-2441	69023	Enzo Doria	03/2013
8665	(34*10^69021-7)/9/3/67	69020	Makoto Morimoto	04/2016
8666	5^98736-14636	69014	Enzo Doria	02/2013
8667	(2^229252+2346)/2	69012	Stefano Morozzi	01/2020
8669	(13^61949-5^61949)/8	69007	Robert Price	03/2013
8668	(2^229235+2966)/2	69007	Stefano Morozzi	01/2020
8670	(2^229227+5)/611	69002	Lelio R Paula	04/2012
8671	2^229216-113279	69001	Enzo Doria	07/2014
8672	10^68994+51913	68995	Patrick De Geest	03/2016
8674	10^68994-10^5814-1	68994	Serge Batalov	01/2011
8673	10^68994-82947	68994	Patrick De Geest	03/2016
8675	(2^229182+814)/2	68991	Stefano Morozzi	01/2020
8676	(17*2^229136-1)/2381	68975	Lelio R Paula	01/2014
8677	2^229113+107	68970	Lelio R Paula	02/2012
8678	16877^12198+12198^16877	68965	Hans Havermann	09/2019
8679	(2^229056+2010)/2	68953	Stefano Morozzi	01/2020
8680	11^66202-4410	68943	Enzo Doria	01/2013
8681	12^63883+5	68942	Lelio R Paula	07/2013
8683	(9913*2^229002-1)/399903	68935	Lelio R Paula	04/2015
8682	(2^228997+2454)/2	68935	Stefano Morozzi	01/2020
8684	(2^228982+3118)/2	68931	Stefano Morozzi	01/2020
8685	(2^228982+3490)/2	68931	Stefano Morozzi	01/2020
8686	2^228962-111581	68925	Enzo Doria	05/2014
8687	2^228944+81	68920	Henri Lifchitz	01/2007
8688	11^66174-54	68914	Lelio R Paula	09/2013
8689	(2^228926+694)/2	68914	Stefano Morozzi	01/2020
8690	16756^12959+12959^16756	68911	Hans Havermann	09/2019
8691	2^228913-111265	68910	Enzo Doria	05/2014
8692	18917^4392+4392^18917	68909	Hans Havermann	09/2019
8694	2^228902+73519	68907	Enzo Doria	04/2016
8693	(2^228903+3018)/2	68907	Stefano Morozzi	01/2020
8695	(2^228892+3046)/2	68904	Stefano Morozzi	01/2020
8696	(47*2^228884+1)/63	68901	Lelio R Paula	04/2015
8697	(2^228857+3782)/2	68893	Stefano Morozzi	01/2020
8698	16542^14591+14591^16542	68883	Hans Havermann	09/2019
8699	2^228821+76427	68882	Enzo Doria	05/2016
8700	(2^228798+442)/2	68875	Stefano Morozzi	01/2020
8701	(2^228784+1222)/2	68871	Stefano Morozzi	01/2020
8702	3^144340+50	68868	Lelio R Paula	09/2013
8703	(2^228766+3850)/2	68866	Stefano Morozzi	01/2020
8704	2^228758-112967	68864	Enzo Doria	06/2014
8705	2^228743-111379	68859	Enzo Doria	05/2014
8706	2^228741-110911	68858	Enzo Doria	05/2014
8708	lucasU(1926,1,20964)-lucasU(1926,1,20963)	68857	Mike Oakes	05/2009
8707	3*5^98511-8	68857	Lelio R Paula	09/2014
8709	2^228717+467	68851	Lelio R Paula	02/2011
8710	(2^228714+2110)/2	68850	Stefano Morozzi	01/2020
8711	Phi(153218,10)/2211855049/23592660859/497714117291	68849	Maksym Voznyy	10/2011
8712	(2^228704+3990)/2	68847	Stefano Morozzi	01/2020
8713	(509203*2^228665-1)/35	68840	Lelio R Paula	04/2015
8714	(2^228648+2910)/2	68830	Stefano Morozzi	01/2020
8715	8^76213-7^76213	68828	Ananda Tallur & Jean-Louis Charton	11/2003
8716	(2^228580+3762)/2	68810	Stefano Morozzi	01/2020
8717	11^66074-1050	68809	Enzo Doria	11/2012
8718	(68*10^68798-11)/3	68800	Robert Price	10/2017
8719	2^228484+181	68781	Lelio R Paula	02/2012
8720	2^228479-58695	68780	Lelio R Paula	04/2012
8721	2^228465-15853	68775	Enzo Doria	04/2013
8722	11^66040-5400	68774	Enzo Doria	01/2013
8723	(13*2^228441-1)/575	68766	Lelio R Paula	01/2014
8724	(17*2^228393+1)/295	68752	Lelio R Paula	08/2012
8725	17859^7072+7072^17859	68749	Hans Havermann	09/2019
8726	(2^228368+1950)/2	68746	Stefano Morozzi	01/2020
8727	2*10^68744+41	68745	Robert Price	01/2017
8728	11^66011-150	68744	Enzo Doria	08/2012
8729	(2^228307+3570)/2	68727	Stefano Morozzi	01/2020
8730	(13*2^228304-1)/81	68726	Lelio R Paula	01/2014
8731	2^228295-111079	68724	Enzo Doria	05/2014
8733	(3^144039+7)/22	68723	Lelio R Paula	04/2012
8732	(8*10^68722+49)/3	68723	Robert Price	03/2016
8734	(35*10^68718+1)/9	68719	Serge Batalov	11/2010
8735	2^228271-228271	68717	Henri Lifchitz	11/2004
8736	2^228257+82875	68713	Lelio R Paula	02/2013
8737	3^144013+40	68712	Lelio R Paula	09/2013
8738	13^61671-86	68699	Lelio R Paula	09/2013
8739	(46*10^68698+683)/9	68699	Robert Price	12/2017
8740	17^55828-72	68694	Lelio R Paula	09/2013
8741	18675^4762+4762^18675	68683	Hans Havermann	09/2019
8742	6^88259+61	68679	Lelio R Paula	09/2013
8743	18^54699-5	68663	Lelio R Paula	09/2013
8744	33^45216+2	68662	Lelio R Paula	05/2013
8746	(2^228073-5)/3	68657	Lelio R Paula	04/2012
8745	(2^(6*38012+1)-5)/3	68657	Kevin Acres	11/2013
8747	2^228055-111607	68652	Enzo Doria	05/2014
8748	2^228054-114761	68652	Enzo Doria	05/2015
8749	2^228041+1185	68648	Lelio R Paula	04/2012
8750	2^228040-1037	68647	Yves Minet	11/2012

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