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 ?
8251	10^99434+155571	99435	Patrick De Geest	04/2020
8252	10^99434-123456789	99434	Robert Price	02/2020
8253	10^99434-191237	99434	Patrick De Geest	04/2020
8254	46^59791-45^59791	99418	Jean-Louis Charton	01/2013
8255	23839^14802+14802^23839	99417	Hans Havermann	02/2018
8256	(2*10^99408+529)/9	99408	Robert Price	01/2017
8257	(2^330216+3510)/2	99405	Stefano Morozzi	09/2020
8258	53^57646-2	99398	Lelio R Paula	09/2013
8259	2^330165+1870025	99390	Enzo Doria	05/2016
8260	7*10^99383+97	99384	Robert Price	09/2021
8261	2^330142-155	99383	Lelio R Paula	12/2012
8262	2^330088-115259	99367	Enzo Doria	06/2015
8263	24216^12671+12671^24216	99354	Hans Havermann	01/2018
8264	Phi(200548,10)/3208769	99354	Makoto Kamada	04/2019
8265	(746*10^99303+1)/9	99305	Robert Price	02/2017
8266	3^208107+40	99293	Lelio R Paula	08/2016
8267	(3939^27617-1)/3938	99291	Serge Batalov	06/2022
8268	(5*2^329833-1)/369	99288	Lelio R Paula	02/2014
8269	8*3^208093+5	99287	Lelio R Paula	08/2014
8270	5^142043+56	99284	Lelio R Paula	08/2016
8271	(13*10^99282-157)/9	99283	Robert Price	05/2021
8272	(10^99284+7)/53/67	99281	Alfred Reich	06/2021
8273	22*10^99275+7	99277	Robert Price	04/2016
8274	2^329778+1876189	99274	Enzo Doria	07/2016
8275	(6580^25997-1)/6579	99259	Serge Batalov	06/2022
8276	(2249^29611-1)/2248	99253	Serge Batalov	06/2022
8277	(10^99239-13)/3	99239	Robert Price	02/2017
8278	(1199^32233-1)/1198	99237	Serge Batalov	06/2022
8280	3^207987+62	99236	Lelio R Paula	08/2016
8279	(62*10^99235+91)/9	99236	Robert Price	07/2021
8281	2^329638+49	99231	Lelio R Paula	12/2012
8282	7^117413-18	99226	Lelio R Paula	08/2016
8283	2^329586-458903	99216	Enzo Doria	04/2015
8284	(6290^26119-1)/6289	99214	Serge Batalov	06/2022
8286	2^329553+101	99206	Lelio R Paula	12/2012
8285	(21297^22921-1)/21296	99206	Serge Batalov	06/2022
8287	2^329551-112897	99205	Enzo Doria	06/2014
8288	(3^207925+7)/50	99204	Lelio R Paula	09/2013
8289	6^127458-17993	99182	Enzo Doria	03/2013
8290	27197^4428+4428^27197	99166	Hans Havermann	10/2017
8291	(46*10^99143-1)/9	99144	Robert Price	12/2014
8292	(64*10^99135+161)/9	99136	Robert Price	08/2022
8293	7*10^99133+69	99134	Robert Price	10/2017
8294	(21701^22861-1)/21700	99132	Serge Batalov	06/2022
8295	18^78968-3065	99127	Enzo Doria	03/2013
8297	25927^6654+6654^25927	99122	Hans Havermann	10/2017
8296	87915!4+16	99122	Robert Price	09/2019
8298	2^329259+189	99117	Lelio R Paula	12/2012
8299	8*10^99113+39	99114	Robert Price	01/2017
8300	6^127364+77	99109	Lelio R Paula	08/2016
8301	(82*10^99103+143)/9	99104	Robert Price	06/2021
8302	(11414^24421-1)/11413	99083	Serge Batalov	06/2022
8303	(2^329135+1110)/2	99080	Stefano Morozzi	09/2020
8304	(22089^22807-1)/22088	99074	Serge Batalov	06/2022
8305	(59*10^99069+391)/9	99070	Robert Price	03/2021
8306	(797*10^99061-41)/9	99063	Robert Price	04/2022
8307	2^329058-287681	99057	Harrison Mesh	06/2022
8308	6^127285+13	99047	Lelio R Paula	08/2016
8309	(228581#+235862)/(2^31171*151)	99044	Makoto Morimoto	10/2017
8310	2^329007+73283	99041	Enzo Doria	04/2016
8311	5*3^207543-8	99024	Lelio R Paula	08/2014
8312	(2^328930+570)/2	99018	Stefano Morozzi	09/2020
8313	2^328885+149	99005	Lelio R Paula	12/2012
8315	23392^17075+17075^23392	99004	Hans Havermann	09/2017
8314	(7424^25579-1)/7423	99004	Serge Batalov	06/2022
8316	(2^328879-9)/119	99001	Lelio R Paula	10/2013
8317	5^141618+54	98987	Lelio R Paula	08/2016
8318	8*10^98982+51	98983	Robert Price	05/2017
8319	(21*2^328809-1)/7709	98979	Lelio R Paula	03/2014
8320	2^328794-2797601	98977	Enzo Doria	04/2016
8321	(88331^20011-1)/88330	98972	Serge Batalov	06/2022
8322	6^127176+5	98963	Lelio R Paula	11/2014
8323	2*10^98961-21	98962	Robert Price	09/2020
8324	24262^11989+11989^24262	98960	Hans Havermann	09/2017
8325	(60138^20707-1)/60137	98958	Serge Batalov	06/2022
8326	2^328700-109709	98949	Enzo Doria	04/2014
8327	(2^328698+1810)/2	98948	Stefano Morozzi	01/2021
8328	(1014^32917-1)/1013	98947	Serge Batalov	06/2022
8329	87771!4-128	98944	Robert Price	11/2019
8330	(4576^27031-1)/4575	98943	Serge Batalov	06/2022
8331	(2^328658+3042)/2	98936	Stefano Morozzi	09/2020
8332	(1933^30103-1)/1932	98923	Serge Batalov	06/2022
8333	46711!2-2^46711	98916	Robert Price	09/2015
8334	9*7^117037+4	98909	Lelio R Paula	11/2014
8335	127^47012+126	98905	Norbert Schneider	01/2019
8336	(93826^19891-1)/93825	98900	Serge Batalov	06/2022
8337	(2^328525+1250)/2	98896	Stefano Morozzi	09/2020
8338	(10^98890+149)/3	98890	Serge Batalov	12/2014
8339	22775^21978+21978^22775	98889	Hans Havermann	08/2017
8340	2^328497-216933	98888	Enzo Doria	05/2014
8341	2^328487+32769	98885	Lelio R Paula	08/2016
8342	3^207250-112358	98884	Enzo Doria	06/2014
8343	13^88754-90	98867	Lelio R Paula	08/2016
8344	2^328406+709	98861	Lelio R Paula	02/2013
8345	2*10^98860-21	98861	Robert Price	09/2020
8346	(17*2^328413-1)/16173	98860	Lelio R Paula	03/2014
8347	7^116976+76	98857	Lelio R Paula	08/2016
8348	(2^328378+2710)/2	98852	Stefano Morozzi	09/2020
8349	(25411^22441-1)/25410	98849	Serge Batalov	06/2022
8350	(18668^23143-1)/18667	98842	Serge Batalov	06/2022
8352	2^328335+1155	98839	Lelio R Paula	08/2016
8351	2^328333-349003	98839	Harrison Mesh	06/2022
8354	(3*2^328311+1)/5	98832	Lelio R Paula	11/2013
8353	287^40210+40210^287	98832	Norbert Schneider	11/2014
8355	(2^328284+9)/1325	98821	Lelio R Paula	10/2013
8356	(21*2^328258+1)/2125	98814	Lelio R Paula	11/2013
8357	(28623^22171-1)/28622	98806	Serge Batalov	06/2022
8358	24746^9825+9825^24746	98795	Hans Havermann	07/2020
8359	26620^5143+5143^26620	98793	Hans Havermann	07/2020
8360	65^54491+48	98788	Lelio R Paula	04/2016
8361	3^207042+98	98785	Lelio R Paula	08/2016
8362	(2^328121+3110)/2	98774	Stefano Morozzi	09/2020
8363	10^98754+73383	98755	Patrick De Geest	02/2021
8366	3^206977-112756	98754	Enzo Doria	07/2014
8365	10^98754-40000000001	98754	Robert Price	09/2020
8364	10^98754-169343	98754	Patrick De Geest	02/2021
8367	7^116846-50	98747	Lelio R Paula	08/2016
8368	(19152^23059-1)/19151	98740	Serge Batalov	06/2022
8369	23267^17512+17512^23267	98730	Hans Havermann	04/2020
8370	2^327967-28635	98728	Lelio R Paula	08/2016
8371	707^34642+34642^707	98710	Norbert Schneider	12/2017
8372	(10771^24481-1)/10770	98710	Serge Batalov	06/2022
8373	6^126850-47	98709	Lelio R Paula	08/2016
8374	(2^327886+2170)/2	98704	Stefano Morozzi	09/2020
8375	(22*10^98697+47)/3	98698	Robert Price	06/2021
8376	8*6^126830-7	98694	Lelio R Paula	11/2014
8377	11^94770-270	98693	Enzo Doria	08/2012
8378	(2^327846+3250)/2	98692	Stefano Morozzi	01/2021
8379	2^327832+43	98688	Lelio R Paula	12/2012
8380	2^327795+761	98677	Lelio R Paula	02/2013
8381	(2^327796+1522)/2	98677	Stefano Morozzi	09/2020
8382	10^98669+147411	98670	Patrick De Geest	11/2016
8384	10^98669-9^(98669-1)	98669	Robert Price	05/2016
8383	10^98669-105249	98669	Patrick De Geest	11/2016
8385	(7911^25309-1)/7910	98657	Serge Batalov	06/2022
8386	2^327671-109801	98639	Enzo Doria	04/2014
8387	24398^11037+11037^24398	98638	Hans Havermann	10/2019
8388	5^141090-14	98618	Lelio R Paula	08/2016
8389	20^75799+47	98617	Lelio R Paula	08/2016
8390	(5452^26393-1)/5451	98616	Serge Batalov	06/2022
8391	28101^3226+3226^28101	98597	Hans Havermann	07/2020
8392	2^327515-1017	98592	Lelio R Paula	08/2016
8393	6^126692+97681	98586	Mike Oakes	04/2011
8394	2^327467-741	98578	Lelio R Paula	08/2016
8395	(2947^28411-1)/2946	98566	Serge Batalov	06/2022
8396	22713^21800+21800^22713	98540	Hans Havermann	05/2020
8397	(2^327329+9)/19	98535	Lelio R Paula	10/2013
8398	7^116577-66	98519	Lelio R Paula	08/2016
8399	(3*2^327250+1)/7	98512	Lelio R Paula	11/2013
8400	23220^17479+17479^23220	98512	Hans Havermann	03/2020
8401	(2^327240+3798)/2	98509	Stefano Morozzi	02/2021
8402	(28514^22111-1)/28513	98502	Serge Batalov	06/2022
8403	(19*2^327192+1)/275	98494	Lelio R Paula	11/2013
8404	2^327162-66945	98486	Lelio R Paula	08/2016
8405	30139^1852+1852^30139	98484	Hans Havermann	02/2020
8406	23182^17703+17703^23182	98479	Hans Havermann	01/2020
8407	4*10^98472-3	98473	Erik Branger	11/2013
8408	26167^5794+5794^26167	98466	Hans Havermann	01/2020
8409	(6883*2^327047-1)/77	98453	Lelio R Paula	05/2015
8410	(71*10^98446+1)/9	98447	Serge Batalov	11/2010
8411	(2009^29803-1)/2008	98436	Serge Batalov	06/2022
8412	13^88363+94	98432	Lelio R Paula	08/2016
8413	48^58543-47^58543	98425	Jean-Louis Charton	11/2005
8414	6^126481+41	98422	Lelio R Paula	08/2016
8415	78*10^98413-7	98415	Robert Price	05/2017
8416	22634^22263+22263^22634	98404	Hans Havermann	07/2020
8417	(47*10^98386+241)/9	98387	Robert Price	06/2022
8418	7^116416+46	98383	Lelio R Paula	08/2016
8419	7^116407-24	98376	Lelio R Paula	07/2016
8420	439^37228+37228^439	98374	Norbert Schneider	08/2018
8421	2^326782-1860671	98372	Enzo Doria	03/2016
8422	17^79948+58	98372	Lelio R Paula	08/2016
8423	22499^22602-22602^22499	98368	Norbert Schneider	08/2020
8424	3^206143-98	98356	Lelio R Paula	08/2016
8425	8*5^140705+7	98350	Lelio R Paula	11/2014
8426	(2^326632+1662)/2	98326	Stefano Morozzi	09/2020
8427	(638^35053-1)/637	98315	Serge Batalov	06/2022
8428	2^326585+11	98312	Lelio R Paula	12/2012
8429	2^326582-459161	98311	Enzo Doria	05/2015
8430	(1266^31687-1)/1265	98304	Serge Batalov	06/2022
8432	(2^326548+9)/5	98301	Lelio R Paula	10/2013
8431	(2^326549+18)/10	98301	Stefano Morozzi	03/2020
8433	2^326538+71659	98298	Enzo Doria	04/2016
8434	(2^326520+2082)/2	98293	Stefano Morozzi	09/2020
8435	(2^326521+1002)/2	98293	Stefano Morozzi	09/2020
8436	15^83575-58	98292	Lelio R Paula	08/2016
8437	10^98288+3	98289	Robert Price	03/2011
8438	10^98288-117017	98288	Patrick De Geest	11/2011
8439	(44*10^98284-719)/9	98285	Robert Price	12/2017
8440	(5985^26021-1)/5984	98280	Serge Batalov	06/2022
8441	23466^15419+15419^23466	98277	Hans Havermann	02/2020
8442	2^326421-2797573	98263	Enzo Doria	04/2016
8443	2^326401+16095	98257	Lelio R Paula	07/2016
8444	(6494^25771-1)/6493	98249	Serge Batalov	06/2022
8445	7^116240-116240^7	98235	Norbert Schneider	05/2017
8446	17^79826-78	98222	Lelio R Paula	08/2016
8447	2^326268-809	98217	Yves Minet	04/2011
8448	22659^21590+21590^22659	98210	Hans Havermann	10/2019
8449	22268^22587-22587^22268	98202	Norbert Schneider	08/2020
8450	(418*10^98199+23)/9	98201	Robert Price	08/2017
8451	12*10^98198-7	98200	Robert Price	11/2017
8452	15^83496-76	98199	Lelio R Paula	08/2016
8453	(10223*2^326179+1)/6125	98190	Lelio R Paula	07/2014
8454	9*5^140471-4	98186	Lelio R Paula	11/2014
8455	(35103^21601-1)/35102	98180	Serge Batalov	06/2022
8457	22774^20455+20455^22774	98175	Hans Havermann	07/2020
8456	(4516^26863-1)/4515	98175	Serge Batalov	06/2022
8458	2^326069-2383	98157	Yves Minet	10/2013
8459	(9661^24631-1)/9660	98152	Serge Batalov	06/2022
8460	(4175^27109-1)/4174	98149	Serge Batalov	06/2022
8461	(57801^20611-1)/57800	98144	Serge Batalov	06/2022
8462	2^325973+1185	98128	Lelio R Paula	07/2016
8463	(25*2^325949-1)/17	98121	Lelio R Paula	02/2014
8464	2^325945-1847269	98120	Enzo Doria	07/2015
8465	8*10^98111-67	98112	Robert Price	10/2017
8466	(2^325902+1138)/2	98106	Stefano Morozzi	09/2020
8467	(215^42061-1)/214	98103	Serge Batalov	06/2022
8468	(6775^25609-1)/6774	98102	Serge Batalov	06/2022
8469	(6718^25633-1)/6717	98100	Serge Batalov	06/2022
8470	2^325866+15	98096	Lelio R Paula	12/2012
8471	22591^21952+21952^22591	98079	Hans Havermann	02/2020
8472	2^325765+1974305	98066	Enzo Doria	06/2016
8473	2^325733-58695	98056	Lelio R Paula	07/2016
8474	(7*10^98055-529)/9	98055	Robert Price	08/2021
8475	2^325717-3645	98051	Lelio R Paula	07/2016
8476	(2^325704+718)/2	98047	Stefano Morozzi	09/2020
8477	(15679^23371-1)/15678	98045	Serge Batalov	06/2022
8478	(23342^22441-1)/23341	98022	Serge Batalov	06/2022
8479	23968^12293+12293^23968	98021	Hans Havermann	11/2019
8480	(23*2^325583-1)/21	98011	Lelio R Paula	02/2014
8481	(7*10^98007-13)/3	98008	Robert Price	06/2016
8482	(2^325544+1110)/2	97999	Stefano Morozzi	09/2020
8483	2^325512-459959	97989	Enzo Doria	05/2015
8484	(2^325492+682)/2	97983	Stefano Morozzi	09/2020
8485	(3^205354-8)/17	97978	Lelio R Paula	09/2013
8486	2^325433+76817	97966	Enzo Doria	05/2016
8487	5*10^97963+81	97964	Robert Price	08/2017
8488	(13208^23773-1)/13207	97961	Serge Batalov	06/2022
8489	2^325390-109061	97953	Enzo Doria	04/2014
8490	(55*10^97940+323)/9	97941	Robert Price	10/2021
8491	13^87921+24	97940	Lelio R Paula	08/2016
8492	10^97930+188277	97931	Patrick De Geest	09/2022
8494	10^97930-7000001	97930	Robert Price	06/2021
8493	10^97930-66951	97930	Patrick De Geest	09/2022
8495	961^32831-960^32831	97926	Jean-Louis Charton	02/2011
8496	(17968^23017-1)/17967	97922	Serge Batalov	06/2022
8497	(3337^27793-1)/3336	97922	Serge Batalov	06/2022
8499	22600^21499+21499^22600	97913	Hans Havermann	05/2020
8498	(18703^22921-1)/18702	97913	Serge Batalov	06/2022
8500	2^325215+12909	97900	Lelio R Paula	07/2016

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Probable Primes Top 10000

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