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	6*10^88571+77	88572	Robert Price	06/2020
6502	(2^294145+1346)/2	88547	Stefano Morozzi	01/2020
6503	(2*10^88545+7)/9	88545	Erik Branger	03/2011
6504	2^294137-133	88545	Lelio R Paula	10/2012
6505	(2^294109+3494)/2	88536	Stefano Morozzi	01/2020
6506	23515^5818+5818^23515	88529	Hans Havermann	08/2020
6507	(2^294092-1017)/1171	88528	Lelio R Paula	01/2013
6509	4^147036+147036^4+1	88525	Robert Price	04/2014
6508	22541^8458+8458^22541	88525	Hans Havermann	08/2020
6510	(14^77213-5^77213)/9	88496	Robert Price	04/2013
6511	2^293965+2793377	88493	Enzo Doria	03/2016
6512	(2^293956+3306)/2	88490	Stefano Morozzi	01/2020
6513	11^84971-150	88489	Enzo Doria	08/2012
6514	(2^293944+1066)/2	88486	Stefano Morozzi	01/2020
6515	48^52626-47	88478	Norbert Schneider	08/2018
6516	(2^293956-1017)/39851376696677	88476	Lelio R Paula	01/2013
6517	11^84958-2190	88475	Enzo Doria	12/2012
6518	(2^293902+3070)/2	88474	Stefano Morozzi	01/2020
6519	2^293880-111347	88467	Enzo Doria	05/2014
6520	(106*10^88459-1)/3	88461	Serge Batalov	12/2014
6521	10^88457+278733	88458	Patrick De Geest	07/2017
6522	10^88457-401	88457	Robert Price	06/2017
6523	(2^293834+3018)/2	88453	Stefano Morozzi	01/2020
6524	(2^293747+1626)/2	88427	Stefano Morozzi	01/2020
6525	22080^10109+10109^22080	88424	Hans Havermann	08/2020
6526	11^84908-1680	88423	Enzo Doria	12/2012
6527	(2^293703+3486)/2	88414	Stefano Morozzi	01/2020
6528	2^293679-112075	88407	Enzo Doria	06/2014
6529	6^113608-65	88405	Lelio R Paula	12/2015
6530	2^293624+82875	88390	Lelio R Paula	10/2013
6531	(2^293618+918)/2	88388	Stefano Morozzi	01/2020
6532	2^293612-112337	88387	Enzo Doria	06/2014
6533	758^30693+30693^758	88386	Norbert Schneider	05/2017
6534	gcd(V(1062695),5F(212539)(F(212539)-1)+1)	88383	Serge Batalov	04/2015
6535	5*10^88377+77	88378	Robert Price	06/2016
6536	(2^293584+1558)/2	88378	Stefano Morozzi	01/2020
6537	(5*2^293526+1)/303	88359	Lelio R Paula	01/2013
6538	20918^16743+16743^20918	88355	Hans Havermann	08/2020
6539	(2^293499+2390)/2	88352	Stefano Morozzi	01/2020
6540	20727^18292+18292^20727	88344	Hans Havermann	08/2020
6541	2^293461-2785843	88341	Enzo Doria	03/2016
6543	2^293416-1037	88328	Yves Minet	11/2012
6542	6*10^88327+43	88328	Robert Price	07/2020
6544	25109^3292+3292^25109	88320	Hans Havermann	08/2020
6545	(2^293384-7)/3	88317	Lelio R Paula	01/2013
6546	(3^185092-5)/4	88311	Lelio R Paula	01/2013
6547	(5*10^88303-173)/3	88304	Robert Price	11/2017
6548	14^77039-57	88297	Lelio R Paula	11/2015
6549	3*10^88293-59	88294	Robert Price	10/2017
6550	5^126303+42	88283	Lelio R Paula	10/2015
6552	19^69025-18	88266	Theodore Burton	01/2006
6551	140^41128+139	88266	Norbert Schneider	04/2019
6553	5*10^88261-3	88262	Dmitry Domanov	11/2010
6554	(2^293195+2238)/2	88261	Stefano Morozzi	01/2020
6555	8^97731-7^(97731-1)	88260	Robert Price	04/2016
6556	5*10^88254+59	88255	Robert Price	09/2016
6558	4*3^184968-7	88253	Lelio R Paula	08/2014
6557	34*10^88251-9	88253	Robert Price	06/2020
6559	7^104426+88	88251	Lelio R Paula	10/2015
6560	2^293142+99	88245	Lelio R Paula	10/2012
6561	11^84736-2130	88244	Enzo Doria	12/2012
6562	23884^4945+4945^23884	88232	Hans Havermann	08/2020
6563	22080^9907+9907^22080	88231	Hans Havermann	08/2020
6564	(10^110315+1)/(10^22063+1)/5824812682167648578460281641	88225	Makoto Kamada	04/2019
6565	2^293068-89	88223	Lelio R Paula	10/2012
6566	2126^26511+26511^2126	88218	Norbert Schneider	02/2020
6567	2^293014-109655	88207	Enzo Doria	04/2014
6568	8*7^104371-3	88205	Lelio R Paula	10/2014
6569	2^292995-2145	88201	Lelio R Paula	10/2013
6570	28534^1233+1233^28534	88198	Hans Havermann	08/2020
6571	5*10^88182+77	88183	Robert Price	06/2016
6573	2^292929+43877	88181	Donovan Johnson	04/2005
6572	6^113321+131	88181	Lelio R Paula	12/2015
6574	(2^292919+3366)/2	88178	Stefano Morozzi	01/2020
6575	2^292904-583949	88173	Paul Bourdelais	04/2013
6576	2^292894-111851	88170	Enzo Doria	05/2014
6577	2^292872-2797349	88164	Enzo Doria	03/2016
6578	(2^292864+1042)/2	88161	Stefano Morozzi	01/2020
6579	2^292860-109685	88160	Enzo Doria	04/2014
6580	9*6^113288-5	88157	Lelio R Paula	10/2014
6581	(2^292735+2166)/2	88122	Stefano Morozzi	01/2020
6582	(2^292735+2346)/2	88122	Stefano Morozzi	01/2020
6583	(2^292705+1934)/2	88113	Stefano Morozzi	01/2020
6584	(2*10^88112-23)/3	88112	Robert Price	09/2017
6585	29622^943+943^29622	88111	Hans Havermann	08/2020
6586	(73*10^88105+17)/9	88106	Robert Price	10/2015
6587	(2^292673+3026)/2	88104	Stefano Morozzi	01/2020
6588	11^84588+78	88090	Lelio R Paula	11/2015
6589	(265*10^88077+11)/3	88079	Robert Price	03/2017
6590	91^44959-90^44959	88077	Robert Price	07/2015
6591	6^113177-5^113177	88069	Jean-Louis Charton	01/2009
6592	1316^28233+28233^1316	88066	Norbert Schneider	07/2020
6593	(2^292543+2234)/2	88064	Stefano Morozzi	01/2020
6594	(10^88020+101)/3	88020	Robert Price	04/2016
6595	52^51285-51	88006	Norbert Schneider	09/2018
6596	21002^15501+15501^21002	88006	Hans Havermann	08/2020
6597	20466^19951+19951^20466	88004	Hans Havermann	08/2020
6598	(2^292324+2346)/2	87998	Stefano Morozzi	01/2020
6599	21634^11683+11683^21634	87998	Hans Havermann	08/2020
6600	(6340^23143-1)/6339	87988	Serge Batalov	08/2020
6601	20674^18013+18013^20674	87980	Hans Havermann	08/2020
6602	(10^(243982+1)-610^43982-1)/3	87965	Robert Price	02/2016
6603	(424*10^87930-1)/9	87932	Robert Price	11/2017
6604	(2^292100+3070)/2	87931	Stefano Morozzi	01/2020
6605	p(18225)#/2+128	87929	Robert Price	04/2017
6606	(10607^21841-1)/10606	87919	Serge Batalov	08/2020
6607	(2^292047+1550)/2	87915	Stefano Morozzi	01/2020
6608	4*6^112977+7	87914	Lelio R Paula	10/2014
6609	(2^292016+1062)/2	87906	Stefano Morozzi	01/2020
6610	(11359^21673-1)/11358	87888	Serge Batalov	08/2020
6611	14^76677+69	87882	Lelio R Paula	11/2015
6612	(22*10^87863-1)/3	87864	Robert Price	12/2014
6613	2^291822-2797811	87848	Enzo Doria	04/2016
6614	(2^291730+1614)/2	87820	Stefano Morozzi	01/2020
6615	2^291716-111389	87816	Enzo Doria	05/2014
6616	(782*10^87809-71)/9	87811	Robert Price	06/2017
6617	3^184039+1820	87809	Lelio R Paula	12/2015
6618	12^81356+41	87798	Lelio R Paula	11/2015
6619	21307^13188+13188^21307	87789	Hans Havermann	08/2020
6620	(2527^25801-1)/2526	87788	Serge Batalov	08/2020
6621	(2^291596+1986)/2	87779	Stefano Morozzi	01/2020
6623	6^112792-18983	87770	Enzo Doria	03/2013
6622	(3123^25117-1)/3122	87770	Serge Batalov	08/2020
6624	3*6^112787-5	87766	Lelio R Paula	10/2014
6625	7^103848+82	87762	Lelio R Paula	10/2015
6626	(19*2^291534-1)/178696395	87754	Lelio R Paula	02/2014
6627	(2^291506+918)/2	87752	Stefano Morozzi	01/2020
6628	24411^3932+3932^24411	87749	Hans Havermann	08/2020
6629	(3^183915+5)/128	87748	Lelio R Paula	01/2013
6630	19^68619+24	87747	Lelio R Paula	12/2015
6632	2^291480+1185	87745	Lelio R Paula	10/2013
6631	2^291482+1867369	87745	Enzo Doria	03/2016
6633	2^291467-937	87741	Yves Minet	05/2013
6634	(25*10^87726+161)/3	87727	Robert Price	01/2017
6635	11^84239-2850	87726	Enzo Doria	12/2012
6636	10^87720+215541	87721	Patrick De Geest	01/2011
6637	10^87720-3	87720	Markus Tervooren	07/2010
6638	(2^291383+3078)/2	87715	Stefano Morozzi	01/2020
6640	(5*10^87712-473)/9	87712	Robert Price	12/2017
6639	(2^291373+2946)/2	87712	Stefano Morozzi	01/2020
6641	22591^7630+7630^22591	87711	Hans Havermann	08/2020
6642	22081^9378+9378^22081	87709	Hans Havermann	08/2020
6643	(2^291357+5)/6847	87704	Lelio R Paula	01/2013
6644	(2^291280+462)/2	87684	Stefano Morozzi	01/2020
6645	20749^16816+16816^20749	87680	Hans Havermann	08/2020
6647	93^44541-2	87679	Lelio R Paula	09/2013
6646	2^291261-109561	87679	Enzo Doria	04/2014
6648	(4*10^87669+149)/9	87669	Robert Price	03/2017
6649	2^291217+4257	87666	Lelio R Paula	10/2013
6650	22748^7137+7137^22748	87660	Hans Havermann	08/2020
6651	2*12^81214-5^81214	87645	Mike Oakes	12/2010
6652	(5005^23689-1)/5004	87632	Serge Batalov	08/2020
6653	(5*10^87622-473)/9	87622	Robert Price	12/2017
6654	12^81188+85	87617	Lelio R Paula	11/2015
6655	(2^291030+3462)/2	87609	Stefano Morozzi	01/2020
6656	(21*2^290980-1)/5	87595	Lelio R Paula	02/2014
6657	(2^290980+1150)/2	87594	Stefano Morozzi	01/2020
6658	2^290958+127	87588	Lelio R Paula	09/2012
6659	78531!4-8	87580	Robert Price	11/2019
6660	2^290923-67	87577	Lelio R Paula	09/2012
6661	3*10^87573-97	87574	Robert Price	08/2017
6662	(13*10^87565+11)/3	87566	Robert Price	05/2015
6663	(2^290881+1022)/2	87564	Stefano Morozzi	01/2020
6664	(2^290857-7)/55	87555	Lelio R Paula	01/2013
6665	(2^290808+1498)/2	87542	Stefano Morozzi	01/2020
6666	2^290802+82875	87541	Lelio R Paula	10/2013
6667	(509203*2^290792-1)/7560987	87536	Lelio R Paula	04/2015
6668	3^183441+236	87524	Lelio R Paula	12/2015
6669	2^290618-33	87485	Lelio R Paula	09/2012
6670	(184*10^87473-1)/3	87475	Robert Price	02/2017
6671	2^290534-115151	87460	Enzo Doria	06/2015
6672	2^290512-109757	87453	Enzo Doria	04/2014
6673	(32*10^87448-41)/9	87449	Robert Price	05/2015
6674	(2^290493+3074)/2	87447	Stefano Morozzi	01/2020
6675	(2^290491+9)/3179	87444	Lelio R Paula	01/2013
6676	(25*2^290489-1)/51809	87443	Lelio R Paula	02/2014
6677	2^290426+82875	87427	Lelio R Paula	11/2013
6678	3*2^290415-7	87425	Lelio R Paula	08/2014
6681	10^87408+57	87409	Robert Price	03/2011
6680	2^290366+74779	87409	Enzo Doria	04/2016
6679	22284^8365+8365^22284	87409	Hans Havermann	08/2020
6682	10^87408-123569	87408	Patrick De Geest	07/2013
6683	21517^11536+11536^21517	87404	Hans Havermann	08/2020
6684	6*10^87396+77	87397	Robert Price	06/2020
6685	(2^290268+3882)/2	87380	Stefano Morozzi	01/2020
6686	2^290265+58905	87379	Lelio R Paula	10/2013
6687	7^103391+16	87376	Lelio R Paula	10/2015
6688	(115*10^87368-7)/9	87370	Robert Price	11/2017
6689	(92^44491-1)/91	87369	Paul Bourdelais	08/2017
6690	8*7^103379+3	87367	Lelio R Paula	10/2014
6691	(2^290226+7)/71	87365	Lelio R Paula	01/2013
6692	(3216^24907-1)/3215	87354	Serge Batalov	08/2020
6693	(2^290160+2686)/2	87347	Stefano Morozzi	01/2020
6694	13^78407-30	87341	Lelio R Paula	11/2015
6695	4*10^87337-99	87338	Robert Price	12/2016
6696	7*10^87319+39	87320	Robert Price	07/2016
6697	3*5^124921+2	87317	Lelio R Paula	10/2014
6698	78315!4-16	87316	Robert Price	11/2019
6699	3^182984+88	87306	Lelio R Paula	12/2015
6700	(10^87323-1)/(9*33909262597306826117)	87303	Alfred Reich	02/2019
6701	(2^290008+958)/2	87301	Stefano Morozzi	01/2020
6702	(10536^21701-1)/10535	87293	Serge Batalov	08/2020
6703	4*10^87287-99	87288	Robert Price	12/2016
6705	11^83813-1860	87283	Enzo Doria	12/2012
6704	(3068^25033-1)/3067	87283	Serge Batalov	08/2020
6706	734^30453+30453^734	87270	Norbert Schneider	04/2017
6707	12^80855+29	87258	Lelio R Paula	11/2015
6708	22209^8482+8482^22209	87249	Hans Havermann	08/2020
6709	3*6^112119-5	87247	Lelio R Paula	10/2014
6710	12^80806+79	87205	Lelio R Paula	11/2015
6711	91382^9+9^91382	87201	Andrey Kulsha	11/2004
6712	(21181*2^289657+1)/81	87198	Lelio R Paula	06/2014
6713	6^112054-47	87195	Lelio R Paula	12/2015
6714	(55459*2^289632+1)/55	87191	Lelio R Paula	06/2014
6715	15^74131-68	87185	Lelio R Paula	11/2015
6716	2^289583-741	87174	Lelio R Paula	10/2013
6717	7^103146+12	87169	Lelio R Paula	10/2015
6718	(2^289562+2182)/2	87167	Stefano Morozzi	01/2020
6719	5*2^289556-3	87166	Lelio R Paula	08/2014
6720	2^289543-112735	87162	Enzo Doria	06/2014
6721	20204^20243-20243^20204	87155	Norbert Schneider	04/2020
6722	8*3^182655-7	87150	Lelio R Paula	08/2014
6723	2*10^87144+81	87145	Robert Price	01/2017
6724	20541^17468+17468^20541	87140	Hans Havermann	07/2020
6725	7^103106+2*3^103106	87135	Mike Oakes	08/2010
6726	8*3^182614+7	87130	Lelio R Paula	08/2014
6727	(4982^23563-1)/4981	87119	Serge Batalov	08/2020
6728	(2^289368-509203)/9	87108	Lelio R Paula	01/2013
6729	3^182566+14	87107	Robert Price	09/2013
6730	1738^26881+26881^1738	87096	Norbert Schneider	04/2020
6731	24290^3849+3849^24290	87089	Hans Havermann	08/2020
6732	(3^182385-5)/2	87020	Lelio R Paula	01/2013
6733	11^83534-8	86992	Lelio R Paula	11/2015
6734	4^144479-14267	86986	Mike Oakes	03/2011
6735	(145*10^86982-1)/9	86984	Serge Batalov	12/2014
6737	(151*10^86963-1)/3	86965	Robert Price	04/2017
6736	(2^288892+826)/2	86965	Stefano Morozzi	01/2020
6738	15^73940-58	86961	Lelio R Paula	11/2015
6739	2^288761-113143	86926	Enzo Doria	07/2014
6740	24440^3603+3603^24440	86925	Hans Havermann	08/2020
6742	2^288747+3083	86922	Yves Minet	03/2011
6741	(2^288749+3102)/2	86922	Stefano Morozzi	01/2020
6743	30^58842+29	86917	Norbert Schneider	03/2017
6744	(2^288705+2186)/2	86909	Stefano Morozzi	01/2020
6745	(10^86906-13)/3	86906	Robert Price	02/2017
6746	2^288692-110027	86905	Enzo Doria	04/2014
6747	(2^288682+7)/259895449	86894	Lelio R Paula	01/2013
6748	(26*10^86885+79)/3	86886	Robert Price	09/2020
6749	(2^288636+47)/1293	86885	Lelio R Paula	01/2013
6750	3^182089-34	86879	Robert Price	11/2013

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Probable Primes Top 10000

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