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	10^99992-28607	99992	Patrick De Geest	02/2020
6502	10^99991+125391	99992	Patrick De Geest	02/2020
6503	10^99991-204573	99991	Patrick De Geest	02/2020
6504	10^99990+13899	99991	Patrick De Geest	02/2020
6505	10^99990-8111	99990	Patrick De Geest	02/2020
6506	2^332141-113073	99985	Enzo Doria	07/2014
6508	(3^209561+2)/728101255	99978	Lelio R Paula	09/2013
6507	23827^15702+15702^23827	99978	Hans Havermann	04/2018
6509	2^332085+1865897	99968	Enzo Doria	03/2016
6510	(9787*2^332070-1)/936402369	99959	Lelio R Paula	05/2015
6511	2^332023+191	99949	Lelio R Paula	02/2011
6512	7*10^99944+27	99945	Robert Price	11/2020
6513	2^331938+71149	99924	Enzo Doria	04/2016
6514	2^331932-78795	99922	Lelio R Paula	09/2016
6515	2^331921+771	99919	Lelio R Paula	01/2013
6516	(3^209419-2)/5132755	99912	Lelio R Paula	09/2013
6517	2^331860-114989	99900	Enzo Doria	05/2015
6518	2^331746-11655	99866	Lelio R Paula	09/2016
6519	11^95891-28	99861	Lelio R Paula	08/2016
6520	(2^331694-5)/11	99849	Lelio R Paula	10/2013
6521	(3^209246+7)/64	99834	Lelio R Paula	09/2013
6522	25062^9617+9617^25062	99823	Hans Havermann	04/2018
6523	15^84866-52	99811	Lelio R Paula	08/2016
6524	13^89600+30	99810	Lelio R Paula	08/2016
6525	2^331527+100280245065	99800	Paul Bourdelais	10/2021
6526	22950^22309+22309^22950	99798	Hans Havermann	03/2018
6527	5^142772-38	99794	Lelio R Paula	08/2016
6528	(23*2^331459+1)/475	99778	Lelio R Paula	11/2013
6529	2^331416-331416+1	99767	Robert Price	10/2014
6530	2^331256-57	99718	Lelio R Paula	12/2012
6531	28192^3443+3443^28192	99714	Hans Havermann	03/2018
6532	2^331185+737	99697	Lelio R Paula	01/2013
6533	(4*10^99693+149)/9	99693	Robert Price	03/2017
6534	2^331154+1880527	99688	Enzo Doria	10/2016
6536	(19^77951+1)/20	99679	Paul Bourdelais	03/2010
6535	24354^12385+12385^24354	99679	Hans Havermann	03/2018
6537	2^331110+1870459	99675	Enzo Doria	05/2016
6538	5*2^331075+7	99665	Lelio R Paula	08/2014
6539	25776^7351+7351^25776	99659	Hans Havermann	02/2018
6540	(16*10^99656-31)/3	99657	Robert Price	03/2016
6541	2^330968+345	99632	Lelio R Paula	09/2016
6542	(2^330969+690)/2	99632	Stefano Morozzi	09/2020
6544	2*5^142528-7	99624	Lelio R Paula	11/2014
6543	2^330942+77329	99624	Enzo Doria	05/2016
6545	14^86914-99	99615	Lelio R Paula	08/2016
6546	(19*2^330902+1)/77	99611	Lelio R Paula	11/2013
6547	22971^21692+21692^22971	99610	Hans Havermann	03/2018
6548	2^330845+71687	99595	Enzo Doria	04/2016
6549	(23*2^330770+1)/3	99573	Lelio R Paula	11/2013
6550	24494^11613+11613^24494	99567	Hans Havermann	03/2018
6551	2^330735+8415	99562	Lelio R Paula	09/2016
6552	2^330720+74071	99557	Enzo Doria	04/2016
6553	31^66738-2	99531	Lelio R Paula	09/2013
6554	7*3^208567+4	99513	Lelio R Paula	08/2014
6555	(13*10^99508+47)/3	99509	Robert Price	01/2017
6556	2^330553+779	99507	Lelio R Paula	01/2013
6557	15^84606-94	99505	Lelio R Paula	08/2016
6558	(10^99497+173)/3	99497	Robert Price	05/2021
6559	9*10^99493-43	99494	Robert Price	09/2021
6560	6^127858+47	99493	Lelio R Paula	08/2016
6561	5^142337+48	99490	Lelio R Paula	08/2016
6562	7^117724-20	99489	Lelio R Paula	08/2016
6563	(29*10^99474-17)/3	99475	Erik Branger	09/2014
6564	(185*10^99466-11)/3	99468	Robert Price	10/2020
6565	(2^330410+2038)/2	99464	Stefano Morozzi	09/2020
6566	(9*2^330407-1)/7	99463	Lelio R Paula	03/2014
6567	(2^330373+2114)/2	99452	Stefano Morozzi	09/2020
6568	(68*10^99441+7)/3	99443	Robert Price	03/2016
6569	10^99434+155571	99435	Patrick De Geest	04/2020
6570	10^99434-123456789	99434	Robert Price	02/2020
6571	10^99434-191237	99434	Patrick De Geest	04/2020
6572	46^59791-45^59791	99418	Jean-Louis Charton	01/2013
6573	23839^14802+14802^23839	99417	Hans Havermann	02/2018
6574	(2*10^99408+529)/9	99408	Robert Price	01/2017
6575	(2^330216+3510)/2	99405	Stefano Morozzi	09/2020
6576	53^57646-2	99398	Lelio R Paula	09/2013
6577	2^330165+1870025	99390	Enzo Doria	05/2016
6578	7*10^99383+97	99384	Robert Price	09/2021
6579	2^330142-155	99383	Lelio R Paula	12/2012
6580	2^330088-115259	99367	Enzo Doria	06/2015
6581	24216^12671+12671^24216	99354	Hans Havermann	01/2018
6582	Phi(200548,10)/3208769	99354	Makoto Kamada	04/2019
6583	(746*10^99303+1)/9	99305	Robert Price	02/2017
6584	3^208107+40	99293	Lelio R Paula	08/2016
6585	(5*2^329833-1)/369	99288	Lelio R Paula	02/2014
6586	8*3^208093+5	99287	Lelio R Paula	08/2014
6587	5^142043+56	99284	Lelio R Paula	08/2016
6588	(13*10^99282-157)/9	99283	Robert Price	05/2021
6589	(10^99284+7)/53/67	99281	Alfred Reich	06/2021
6590	22*10^99275+7	99277	Robert Price	04/2016
6591	2^329778+1876189	99274	Enzo Doria	07/2016
6592	(10^99239-13)/3	99239	Robert Price	02/2017
6593	3^207987+62	99236	Lelio R Paula	08/2016
6594	(62*10^99235+91)/9	99236	Robert Price	07/2021
6595	2^329638+49	99231	Lelio R Paula	12/2012
6596	7^117413-18	99226	Lelio R Paula	08/2016
6597	2^329586-458903	99216	Enzo Doria	04/2015
6598	2^329553+101	99206	Lelio R Paula	12/2012
6599	2^329551-112897	99205	Enzo Doria	06/2014
6600	(3^207925+7)/50	99204	Lelio R Paula	09/2013
6601	6^127458-17993	99182	Enzo Doria	03/2013
6602	27197^4428+4428^27197	99166	Hans Havermann	10/2017
6603	(46*10^99143-1)/9	99144	Robert Price	12/2014
6604	7*10^99133+69	99134	Robert Price	10/2017
6605	18^78968-3065	99127	Enzo Doria	03/2013
6606	25927^6654+6654^25927	99122	Hans Havermann	10/2017
6607	87915!4+16	99122	Robert Price	09/2019
6608	2^329259+189	99117	Lelio R Paula	12/2012
6609	8*10^99113+39	99114	Robert Price	01/2017
6610	6^127364+77	99109	Lelio R Paula	08/2016
6611	(82*10^99103+143)/9	99104	Robert Price	06/2021
6612	(2^329135+1110)/2	99080	Stefano Morozzi	09/2020
6613	(59*10^99069+391)/9	99070	Robert Price	03/2021
6614	6^127285+13	99047	Lelio R Paula	08/2016
6615	(228581#+235862)/(2^31171*151)	99044	Makoto Morimoto	10/2017
6616	2^329007+73283	99041	Enzo Doria	04/2016
6617	5*3^207543-8	99024	Lelio R Paula	08/2014
6618	(2^328930+570)/2	99018	Stefano Morozzi	09/2020
6619	2^328885+149	99005	Lelio R Paula	12/2012
6620	23392^17075+17075^23392	99004	Hans Havermann	09/2017
6621	(2^328879-9)/119	99001	Lelio R Paula	10/2013
6622	5^141618+54	98987	Lelio R Paula	08/2016
6623	8*10^98982+51	98983	Robert Price	05/2017
6624	(21*2^328809-1)/7709	98979	Lelio R Paula	03/2014
6625	2^328794-2797601	98977	Enzo Doria	04/2016
6626	6^127176+5	98963	Lelio R Paula	11/2014
6627	2*10^98961-21	98962	Robert Price	09/2020
6628	24262^11989+11989^24262	98960	Hans Havermann	09/2017
6629	2^328700-109709	98949	Enzo Doria	04/2014
6630	(2^328698+1810)/2	98948	Stefano Morozzi	01/2021
6631	87771!4-128	98944	Robert Price	11/2019
6632	(2^328658+3042)/2	98936	Stefano Morozzi	09/2020
6633	46711!2-2^46711	98916	Robert Price	09/2015
6634	9*7^117037+4	98909	Lelio R Paula	11/2014
6635	127^47012+126	98905	Norbert Schneider	01/2019
6636	(2^328525+1250)/2	98896	Stefano Morozzi	09/2020
6637	(10^98890+149)/3	98890	Serge Batalov	12/2014
6638	22775^21978+21978^22775	98889	Hans Havermann	08/2017
6639	2^328497-216933	98888	Enzo Doria	05/2014
6640	2^328487+32769	98885	Lelio R Paula	08/2016
6641	3^207250-112358	98884	Enzo Doria	06/2014
6642	13^88754-90	98867	Lelio R Paula	08/2016
6643	2^328406+709	98861	Lelio R Paula	02/2013
6644	2*10^98860-21	98861	Robert Price	09/2020
6645	(17*2^328413-1)/16173	98860	Lelio R Paula	03/2014
6646	7^116976+76	98857	Lelio R Paula	08/2016
6647	(2^328378+2710)/2	98852	Stefano Morozzi	09/2020
6648	2^328335+1155	98839	Lelio R Paula	08/2016
6650	(3*2^328311+1)/5	98832	Lelio R Paula	11/2013
6649	287^40210+40210^287	98832	Norbert Schneider	11/2014
6651	(2^328284+9)/1325	98821	Lelio R Paula	10/2013
6652	(21*2^328258+1)/2125	98814	Lelio R Paula	11/2013
6653	24746^9825+9825^24746	98795	Hans Havermann	07/2020
6654	26620^5143+5143^26620	98793	Hans Havermann	07/2020
6655	65^54491+48	98788	Lelio R Paula	04/2016
6656	3^207042+98	98785	Lelio R Paula	08/2016
6657	(2^328121+3110)/2	98774	Stefano Morozzi	09/2020
6658	10^98754+73383	98755	Patrick De Geest	02/2021
6661	3^206977-112756	98754	Enzo Doria	07/2014
6660	10^98754-40000000001	98754	Robert Price	09/2020
6659	10^98754-169343	98754	Patrick De Geest	02/2021
6662	7^116846-50	98747	Lelio R Paula	08/2016
6663	23267^17512+17512^23267	98730	Hans Havermann	04/2020
6664	2^327967-28635	98728	Lelio R Paula	08/2016
6665	707^34642+34642^707	98710	Norbert Schneider	12/2017
6666	6^126850-47	98709	Lelio R Paula	08/2016
6667	(2^327886+2170)/2	98704	Stefano Morozzi	09/2020
6668	(22*10^98697+47)/3	98698	Robert Price	06/2021
6669	8*6^126830-7	98694	Lelio R Paula	11/2014
6670	11^94770-270	98693	Enzo Doria	08/2012
6671	(2^327846+3250)/2	98692	Stefano Morozzi	01/2021
6672	2^327832+43	98688	Lelio R Paula	12/2012
6673	2^327795+761	98677	Lelio R Paula	02/2013
6674	(2^327796+1522)/2	98677	Stefano Morozzi	09/2020
6675	10^98669+147411	98670	Patrick De Geest	11/2016
6677	10^98669-9^(98669-1)	98669	Robert Price	05/2016
6676	10^98669-105249	98669	Patrick De Geest	11/2016
6678	2^327671-109801	98639	Enzo Doria	04/2014
6679	24398^11037+11037^24398	98638	Hans Havermann	10/2019
6680	5^141090-14	98618	Lelio R Paula	08/2016
6681	20^75799+47	98617	Lelio R Paula	08/2016
6682	28101^3226+3226^28101	98597	Hans Havermann	07/2020
6683	2^327515-1017	98592	Lelio R Paula	08/2016
6684	6^126692+97681	98586	Mike Oakes	04/2011
6685	2^327467-741	98578	Lelio R Paula	08/2016
6686	22713^21800+21800^22713	98540	Hans Havermann	05/2020
6687	(2^327329+9)/19	98535	Lelio R Paula	10/2013
6688	7^116577-66	98519	Lelio R Paula	08/2016
6689	(3*2^327250+1)/7	98512	Lelio R Paula	11/2013
6690	23220^17479+17479^23220	98512	Hans Havermann	03/2020
6691	(2^327240+3798)/2	98509	Stefano Morozzi	02/2021
6692	(19*2^327192+1)/275	98494	Lelio R Paula	11/2013
6693	2^327162-66945	98486	Lelio R Paula	08/2016
6694	30139^1852+1852^30139	98484	Hans Havermann	02/2020
6695	23182^17703+17703^23182	98479	Hans Havermann	01/2020
6696	4*10^98472-3	98473	Erik Branger	11/2013
6697	26167^5794+5794^26167	98466	Hans Havermann	01/2020
6698	(6883*2^327047-1)/77	98453	Lelio R Paula	05/2015
6699	(71*10^98446+1)/9	98447	Serge Batalov	11/2010
6700	13^88363+94	98432	Lelio R Paula	08/2016
6701	48^58543-47^58543	98425	Jean-Louis Charton	11/2005
6702	6^126481+41	98422	Lelio R Paula	08/2016
6703	78*10^98413-7	98415	Robert Price	05/2017
6704	22634^22263+22263^22634	98404	Hans Havermann	07/2020
6705	7^116416+46	98383	Lelio R Paula	08/2016
6706	7^116407-24	98376	Lelio R Paula	07/2016
6707	439^37228+37228^439	98374	Norbert Schneider	08/2018
6708	2^326782-1860671	98372	Enzo Doria	03/2016
6709	17^79948+58	98372	Lelio R Paula	08/2016
6710	22499^22602-22602^22499	98368	Norbert Schneider	08/2020
6711	3^206143-98	98356	Lelio R Paula	08/2016
6712	8*5^140705+7	98350	Lelio R Paula	11/2014
6713	(2^326632+1662)/2	98326	Stefano Morozzi	09/2020
6714	2^326585+11	98312	Lelio R Paula	12/2012
6715	2^326582-459161	98311	Enzo Doria	05/2015
6717	(2^326548+9)/5	98301	Lelio R Paula	10/2013
6716	(2^326549+18)/10	98301	Stefano Morozzi	03/2020
6718	2^326538+71659	98298	Enzo Doria	04/2016
6719	(2^326520+2082)/2	98293	Stefano Morozzi	09/2020
6720	(2^326521+1002)/2	98293	Stefano Morozzi	09/2020
6721	15^83575-58	98292	Lelio R Paula	08/2016
6722	10^98288+3	98289	Robert Price	03/2011
6723	10^98288-117017	98288	Patrick De Geest	11/2011
6724	(44*10^98284-719)/9	98285	Robert Price	12/2017
6725	23466^15419+15419^23466	98277	Hans Havermann	02/2020
6726	2^326421-2797573	98263	Enzo Doria	04/2016
6727	2^326401+16095	98257	Lelio R Paula	07/2016
6728	7^116240-116240^7	98235	Norbert Schneider	05/2017
6729	17^79826-78	98222	Lelio R Paula	08/2016
6730	2^326268-809	98217	Yves Minet	04/2011
6731	22659^21590+21590^22659	98210	Hans Havermann	10/2019
6732	22268^22587-22587^22268	98202	Norbert Schneider	08/2020
6733	(418*10^98199+23)/9	98201	Robert Price	08/2017
6734	12*10^98198-7	98200	Robert Price	11/2017
6735	15^83496-76	98199	Lelio R Paula	08/2016
6736	(10223*2^326179+1)/6125	98190	Lelio R Paula	07/2014
6737	9*5^140471-4	98186	Lelio R Paula	11/2014
6738	22774^20455+20455^22774	98175	Hans Havermann	07/2020
6739	2^326069-2383	98157	Yves Minet	10/2013
6740	2^325973+1185	98128	Lelio R Paula	07/2016
6741	(25*2^325949-1)/17	98121	Lelio R Paula	02/2014
6742	2^325945-1847269	98120	Enzo Doria	07/2015
6743	8*10^98111-67	98112	Robert Price	10/2017
6744	(2^325902+1138)/2	98106	Stefano Morozzi	09/2020
6745	2^325866+15	98096	Lelio R Paula	12/2012
6746	22591^21952+21952^22591	98079	Hans Havermann	02/2020
6747	2^325765+1974305	98066	Enzo Doria	06/2016
6748	2^325733-58695	98056	Lelio R Paula	07/2016
6749	(7*10^98055-529)/9	98055	Robert Price	08/2021
6750	2^325717-3645	98051	Lelio R Paula	07/2016

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Probable Primes Top 10000

(288949 PRPs in the top)