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	(2^276165+2046)/2	83134	Stefano Morozzi	01/2020
8252	(2^276105+1274)/2	83116	Stefano Morozzi	01/2020
8253	2^276066-111603	83105	Enzo Doria	05/2014
8254	19438^18837+18837^19438	83098	Hans Havermann	07/2020
8255	(431^31543-1)/430	83097	Serge Batalov	08/2020
8256	(2^276028-3)*6-7	83094	Gilbert Mozzo	09/2016
8257	(26*10^83067+79)/3	83068	Robert Price	09/2020
8258	2^275926-4691	83063	Yves Minet	05/2019
8259	(2^275919+1386)/2	83060	Stefano Morozzi	01/2020
8260	(2^275897+9)/1153	83051	Lelio R Paula	12/2012
8261	2^275879-109807	83048	Enzo Doria	04/2014
8263	F(397379)	83047	Henri Lifchitz	08/2003
8262	U(397379)	83047	Serge Batalov	03/2015
8264	3^174040-14	83039	Robert Price	08/2013
8265	(86*10^83038-221)/9	83039	Robert Price	06/2017
8266	21632^6897+6897^21632	83038	Hans Havermann	05/2020
8267	2^275841-6883	83037	Lelio R Paula	07/2011
8268	19610^17127+17127^19610	83023	Hans Havermann	06/2020
8269	3^174002-140	83021	Lelio R Paula	12/2015
8270	6^106681+77	83014	Lelio R Paula	12/2015
8271	187^36539-2	83011	Lelio R Paula	10/2017
8272	1036^27529+27529^1036	83010	Norbert Schneider	03/2020
8273	11^79701-3150	83001	Enzo Doria	12/2012
8274	(2^275721+1554)/2	83000	Stefano Morozzi	01/2020
8275	(2^275704+1858)/2	82995	Stefano Morozzi	01/2020
8276	(2^275696+1726)/2	82993	Stefano Morozzi	01/2020
8277	(55459*2^275657+1)/21	82985	Lelio R Paula	06/2014
8278	(7*10^82960-457)/9	82960	Robert Price	09/2017
8279	2^275535-6855	82945	Lelio R Paula	08/2013
8280	3^173828-14	82938	Robert Price	08/2013
8281	2^275512-109677	82938	Enzo Doria	04/2014
8282	(2^275450+1698)/2	82919	Stefano Morozzi	01/2020
8283	2^275446-110045	82918	Enzo Doria	04/2014
8284	(2^275473+47)/29526097447	82916	Lelio R Paula	12/2012
8285	3*10^82914-83	82915	Robert Price	02/2021
8286	3^173755-14	82903	Robert Price	08/2013
8287	(182*10^82898+43)/9	82900	Robert Price	11/2017
8288	2^275363-112309	82893	Enzo Doria	06/2014
8289	61^46427-60	82888	Norbert Schneider	10/2014
8290	3*10^82880-7^82880	82881	Mike Oakes	02/2010
8291	2^275290+90195	82871	Lelio R Paula	07/2013
8292	(35*10^82870-71)/9	82871	Robert Price	05/2015
8293	2^275270-1859621	82865	Enzo Doria	03/2016
8294	2^275259+81	82862	Henri Lifchitz	01/2007
8295	21436^7335+7335^21436	82859	Hans Havermann	05/2020
8296	(2^275247+1590)/2	82858	Stefano Morozzi	01/2020
8297	22515^4784+4784^22515	82851	Hans Havermann	05/2020
8298	6*10^82842-31	82843	Robert Price	07/2020
8299	(10013^20707-1)/10012	82836	Serge Batalov	08/2020
8300	(113703^16384+1)/2	82834	Richard Fischer	04/2018
8301	(2^275146+954)/2	82827	Stefano Morozzi	01/2020
8302	7^98003+98003^7+1	82823	Robert Price	05/2014
8303	(2^275101+3566)/2	82814	Stefano Morozzi	01/2020
8304	(2^275050+3150)/2	82798	Stefano Morozzi	01/2020
8305	(2^275044+2482)/2	82797	Stefano Morozzi	01/2020
8306	10^82790+126043	82791	Patrick De Geest	07/2013
8307	10^82790-47	82790	Robert Price	05/2011
8308	20762^9711+9711^20762	82784	Hans Havermann	05/2020
8309	2^274985-112663	82779	Enzo Doria	06/2014
8310	2^274935+15015	82764	Lelio R Paula	07/2013
8311	(17*2^274922+1)/3	82761	Lelio R Paula	12/2012
8312	[(55^5)^9511-(22434^2)^9511]/19	82759	Richard Fischer	11/2019
8313	(43*10^82752-61)/9	82753	Robert Price	06/2015
8314	(3*2^274862+1)/1027	82740	Lelio R Paula	12/2012
8315	(2^274851+3126)/2	82739	Stefano Morozzi	01/2020
8316	(31*2^274848-1)/4065	82736	Lelio R Paula	02/2014
8317	(4^137405+23)/3	82726	Robert Price	02/2017
8318	(2^274798+414)/2	82723	Stefano Morozzi	01/2020
8319	2^274791-110491	82721	Enzo Doria	05/2014
8320	(11*2^274776-1)/95	82715	Lelio R Paula	02/2014
8321	(47*10^82706-119)/9	82707	Robert Price	09/2017
8322	2^274704-111395	82695	Enzo Doria	05/2014
8323	2^274686-3911	82689	Yves Minet	04/2017
8324	(1629^25741-1)/1628	82675	Serge Batalov	08/2020
8325	21474^7075+7075^21474	82670	Hans Havermann	06/2020
8326	(2^274663-1017)/48871318292279	82669	Lelio R Paula	12/2012
8327	(3^173263-5)/14498	82664	Lelio R Paula	12/2012
8328	20488^10815+10815^20488	82650	Hans Havermann	07/2020
8329	(2^274554+894)/2	82649	Stefano Morozzi	01/2020
8331	2^274511-64875	82637	Lelio R Paula	08/2013
8330	(2^274512+1222)/2	82637	Stefano Morozzi	01/2020
8332	12^76572-83	82636	Lelio R Paula	11/2015
8333	3^173191-2^173191	82634	Mike Oakes	02/2004
8334	(2^274500+2970)/2	82633	Stefano Morozzi	01/2020
8335	20507^10698+10698^20507	82629	Hans Havermann	07/2020
8336	(2^274429+3726)/2	82612	Stefano Morozzi	01/2020
8337	14^72072-15	82604	Lelio R Paula	11/2015
8338	(2^274374+2950)/2	82595	Stefano Morozzi	01/2020
8339	(55459*2^274339+1)/3	82589	Lelio R Paula	06/2014
8340	2^274351+123	82588	Lelio R Paula	06/2012
8341	(1017*2^274339-1)/3515	82584	Lelio R Paula	04/2015
8342	21208^7833+7833^21208	82583	Hans Havermann	07/2020
8343	(2^274248+750)/2	82557	Stefano Morozzi	01/2020
8344	(2^274240+822)/2	82555	Stefano Morozzi	01/2020
8345	6^106086+113	82551	Lelio R Paula	12/2015
8346	(17*10^82540-377)/9	82541	Robert Price	11/2017
8347	(3470^23311-1)/3469	82526	Serge Batalov	08/2020
8348	2^274093-58695	82511	Lelio R Paula	07/2013
8349	7*10^82509-47	82510	Robert Price	02/2017
8350	2^274081-6555	82507	Lelio R Paula	07/2013
8352	2^274074-274074+1	82505	Robert Price	10/2014
8353	14^71985+47	82505	Lelio R Paula	11/2015
8351	5*10^82504+21	82505	Robert Price	01/2017
8354	(2^274062+498)/2	82501	Stefano Morozzi	01/2020
8355	6^106014-139	82495	Lelio R Paula	12/2015
8356	(2^274046+47)/753	82494	Lelio R Paula	12/2012
8357	2^274008-1838099	82485	Enzo Doria	05/2015
8358	2^273981-110029	82477	Enzo Doria	04/2014
8359	19^64490-30	82467	Lelio R Paula	12/2015
8360	(2^273864+3150)/2	82441	Stefano Morozzi	01/2020
8361	21328^7333+7333^21328	82439	Hans Havermann	07/2020
8362	20829^9070+9070^20829	82434	Hans Havermann	07/2020
8365	2^273785+11715	82418	Lelio R Paula	07/2013
8364	8*10^82417+51	82418	Robert Price	05/2017
8363	(2^273786+2242)/2	82418	Stefano Morozzi	01/2020
8366	11^79133-10	82409	Theodore Burton	11/2005
8367	(2^273752+1882)/2	82408	Stefano Morozzi	01/2020
8368	91^42063+90	82404	Norbert Schneider	01/2016
8370	2^273662-63	82381	Lelio R Paula	06/2012
8369	2^273661+255	82381	Lelio R Paula	07/2013
8371	(62*10^82377-17)/9	82378	Robert Price	09/2015
8372	2^273608+524287	82365	Paul Underwood	08/2018
8373	8*10^82360-51	82361	Robert Price	10/2017
8374	(79*10^82347-1)/3	82349	Robert Price	11/2017
8375	(11*10^82323+91)/3	82323	Robert Price	02/2017
8376	(189977#+19081)/(19081*17260483)	82317	Makoto Morimoto	10/2017
8377	(189977#+196924)/(271354128874441)	82316	Makoto Morimoto	10/2017
8378	15^69984+32	82308	Lelio R Paula	11/2015
8379	9*6^105746+7	82288	Lelio R Paula	10/2014
8380	89^42211-88	82286	Norbert Schneider	01/2016
8381	gcd(V(1476435),5F(295287)(F(295287)+1)+1)	82281	Serge Batalov	04/2015
8382	20596^9883+9883^20596	82279	Hans Havermann	06/2020
8383	(19*10^82270-43)/3	82271	Robert Price	10/2017
8384	2^273282-110241	82267	Enzo Doria	05/2014
8385	(2^273277+3746)/2	82265	Stefano Morozzi	01/2020
8386	(13^73849+4^73849)/17	82263	Robert Price	05/2013
8388	10^82254+9^(82254+1)	82255	Robert Price	08/2016
8387	10^82254+457773	82255	Patrick De Geest	12/2016
8389	10^82254-99609	82254	Patrick De Geest	12/2016
8390	(754*10^82250-7)/9	82252	Robert Price	11/2017
8391	18^65524+13	82251	Lelio R Paula	11/2015
8392	2^273206-107	82244	Lelio R Paula	06/2012
8393	2^273193-459145	82240	Enzo Doria	05/2015
8395	2^273126+36937	82220	Yves Minet	06/2010
8394	39505!2+128	82220	Robert Price	03/2015
8396	(2^273090+2214)/2	82208	Stefano Morozzi	01/2020
8397	2^273053-112111	82198	Enzo Doria	06/2014
8398	(2^273052+3138)/2	82197	Stefano Morozzi	01/2020
8399	2^273016+1185	82187	Lelio R Paula	07/2013
8400	(2^273008+3)/7	82183	Lelio R Paula	12/2012
8401	(2^272992+2230)/2	82179	Stefano Morozzi	01/2020
8403	5^117554-15386	82167	Enzo Doria	02/2013
8402	21158^7647+7647^21158	82167	Hans Havermann	06/2020
8404	20194^11715+11715^20194	82165	Hans Havermann	06/2020
8405	(38*10^82161+403)/9	82162	Robert Price	11/2017
8406	2^272907-111439	82154	Enzo Doria	05/2014
8407	(67607*2^272901+1)/50790115	82149	Lelio R Paula	06/2014
8408	2^272875-69	82144	Lelio R Paula	06/2012
8409	(3997^22807-1)/3996	82142	Serge Batalov	08/2020
8410	7^97197+4	82141	Robert Price	01/2014
8411	(4*6^105554+1)/5	82137	Serge Batalov	10/2014
8412	2^272826-4433	82129	Yves Minet	03/2019
8413	6^105531-109	82120	Lelio R Paula	12/2015
8414	2^272766-65	82111	Lelio R Paula	06/2012
8415	19^64205-78	82103	Lelio R Paula	12/2015
8416	2^272702+1869979	82092	Enzo Doria	05/2016
8417	(29*2^272687-1)/9	82088	Lelio R Paula	02/2014
8418	(5*10^82085-119)/3	82086	Robert Price	04/2016
8419	(2^272665+1334)/2	82081	Stefano Morozzi	01/2020
8420	2^272660-110049	82079	Enzo Doria	04/2014
8421	6^105474+67	82075	Lelio R Paula	12/2015
8422	2^272637+82875	82072	Lelio R Paula	07/2013
8423	(6330^21589-1)/6329	82065	Serge Batalov	08/2020
8424	2^272587-31	82057	Lelio R Paula	06/2012
8425	(1969^24907-1)/1968	82047	Serge Batalov	08/2020
8426	(41*10^82044-59)/9	82045	Robert Price	10/2017
8427	8*5^117368+9	82038	Lelio R Paula	10/2014
8428	(101525^16384+1)/131074	82023	Lelio R Paula	11/2011
8429	4*5^117343-7	82020	Lelio R Paula	10/2014
8430	(2^272381+506)/2	81995	Stefano Morozzi	01/2020
8431	(265*10^81990+17)/3	81992	Robert Price	05/2016
8432	3^171843+10	81990	Robert Price	10/2013
8433	(2^272361+3762)/2	81989	Stefano Morozzi	01/2020
8434	(7*10^81985+107)/3	81986	Robert Price	02/2017
8435	(3*2^272356+1)/177163	81983	Lelio R Paula	12/2012
8436	2^272296-111149	81970	Enzo Doria	05/2014
8437	(2^272293+2810)/2	81969	Stefano Morozzi	01/2020
8438	(2^272278+2118)/2	81964	Stefano Morozzi	01/2020
8439	(9*2^272243-1)/7	81954	Lelio R Paula	02/2014
8440	2^272177-111223	81934	Enzo Doria	05/2014
8441	(2^272127+3878)/2	81919	Stefano Morozzi	01/2020
8443	(151009^15817+1)/151010	81912	Faysal YAtim	06/2017
8442	(2^272104+1950)/2	81912	Stefano Morozzi	01/2020
8444	23160^3437+3437^23160	81898	Hans Havermann	05/2020
8445	(16*10^81896-19)/3	81897	Robert Price	03/2016
8446	(16*10^81872-73)/3	81873	Robert Price	07/2020
8447	(2^271922+78557)/63	81855	Lelio R Paula	12/2012
8448	(10^81848+77)/3	81848	Robert Price	01/2017
8449	(24737*2^271883+1)/3757	81846	Lelio R Paula	06/2014
8450	(2^271885+1670)/2	81846	Stefano Morozzi	01/2020
8451	18813^19144-19144^18813	81831	Norbert Schneider	02/2020
8452	(14*10^81818-89)/3	81819	Robert Price	05/2020
8453	19492^15731+15731^19492	81804	Hans Havermann	07/2020
8454	20420^10137+10137^20420	81801	Hans Havermann	06/2020
8455	(2^271734+3942)/2	81800	Stefano Morozzi	01/2020
8456	(15429^19531-1)/15428	81799	Serge Batalov	08/2020
8457	10^81778+39	81779	Robert Price	03/2011
8458	10^81778-171999	81778	Patrick De Geest	07/2013
8459	(2^271652+2886)/2	81776	Stefano Morozzi	01/2020
8460	(14*10^81767-11)/3	81768	Erik Branger	09/2014
8461	(2^271546+610)/2	81744	Stefano Morozzi	01/2020
8462	2^271541+1868417	81742	Enzo Doria	04/2016
8463	(2^271549-1)/238749682487	81734	Jens K. Andersen	02/2009
8464	19339^16836+16836^19339	81732	Hans Havermann	06/2020
8465	2^271484-167	81725	Lelio R Paula	06/2012
8467	(8*10^81709-611)/9	81709	Robert Price	11/2017
8466	(2^271431+1790)/2	81709	Stefano Morozzi	01/2020
8468	19648^14399+14399^19648	81703	Hans Havermann	05/2020
8469	2^271382+12909	81695	Lelio R Paula	07/2013
8470	49^48334+48	81694	Norbert Schneider	07/2014
8471	7^96668+48	81694	Lelio R Paula	10/2015
8472	11^78435-1410	81682	Enzo Doria	12/2012
8473	19575^14882+14882^19575	81680	Hans Havermann	04/2020
8474	5*10^81653+9	81654	Dmitry Domanov	11/2010
8475	(2^271224+1230)/2	81647	Stefano Morozzi	01/2020
8476	(2^271211-1)/613961495159	81631	Jens K. Andersen	02/2009
8477	(2^271168+1806)/2	81630	Stefano Morozzi	01/2020
8478	3^171068+52	81621	Lelio R Paula	12/2015
8479	2^271115-110407	81614	Enzo Doria	05/2014
8480	2^271111-110635	81613	Enzo Doria	05/2014
8481	2^271098-111	81609	Lelio R Paula	06/2012
8482	(77*10^81606+13)/9	81607	Robert Price	10/2015
8483	2^271064-2790209	81599	Enzo Doria	03/2016
8484	(13*2^271053-1)/3095	81593	Lelio R Paula	02/2014
8485	2^271040-57	81592	Lelio R Paula	06/2012
8486	(14*10^81585+73)/3	81586	Robert Price	04/2016
8487	127^38779+126	81584	Norbert Schneider	02/2015
8488	18^64966-43	81551	Lelio R Paula	11/2015
8489	19406^15909+15909^19406	81538	Hans Havermann	06/2020
8490	(17*10^81535-161)/9	81536	Robert Price	02/2021
8491	(2^270843+1074)/2	81532	Stefano Morozzi	01/2020
8492	(2^270840+47)/591	81529	Lelio R Paula	12/2012
8493	20^62654+87	81515	Lelio R Paula	01/2016
8494	20120^11241+11241^20120	81503	Hans Havermann	05/2020
8495	(19*10^81488+191)/3	81489	Robert Price	01/2017
8496	8*10^81487+21	81488	Robert Price	02/2017
8497	(73*10^81485+107)/9	81486	Robert Price	08/2016
8498	536^29847+29847^536	81458	Norbert Schneider	03/2017
8499	8*7^96378+9	81450	Lelio R Paula	10/2014
8500	(2^270560+3862)/2	81447	Stefano Morozzi	01/2020

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