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 ?
9251	11^80096-1830	83412	Enzo Doria	12/2012
9252	3^174801+56	83402	Lelio R Paula	12/2015
9253	2^277033-111973	83396	Enzo Doria	05/2014
9254	120^40105-119	83386	Norbert Schneider	09/2018
9255	(2^276992+2046)/2	83383	Stefano Morozzi	01/2020
9256	(2^276990+474)/2	83382	Stefano Morozzi	01/2020
9257	20519^11572+11572^20519	83378	Hans Havermann	03/2017
9258	20850^9971+9971^20850	83374	Hans Havermann	03/2017
9261	6^107122-18863	83358	Enzo Doria	03/2013
9259	(2^276908+2322)/2	83358	Stefano Morozzi	01/2020
9260	(2^276910+2734)/2	83358	Stefano Morozzi	01/2020
9262	4*10^83354-89	83355	Robert Price	08/2017
9263	3^174697-34	83352	Robert Price	11/2013
9264	(9787*2^276855-1)/2345	83343	Lelio R Paula	04/2015
9265	(2^276860+1678)/2	83343	Stefano Morozzi	01/2020
9266	(2^276841+3354)/2	83338	Stefano Morozzi	01/2020
9268	2^276825+75227	83333	Enzo Doria	04/2016
9267	34*10^83331-9	83333	Robert Price	06/2020
9269	5^119214+84	83328	Lelio R Paula	10/2015
9270	2^276803-159	83327	Lelio R Paula	06/2012
9271	(13*10^83313+137)/3	83314	Robert Price	06/2021
9272	(3*2^276753-1)/25	83311	Lelio R Paula	02/2014
9273	7*10^83297-39	83298	Robert Price	07/2020
9274	114^40495+40495^114	83295	Norbert Schneider	12/2014
9275	39967!2+1024	83282	Robert Price	02/2015
9276	(1894^25411-1)/1893	83279	Serge Batalov	08/2020
9278	2^276641+57	83278	Lelio R Paula	06/2012
9279	35^53934-3414	83278	Enzo Doria	03/2013
9277	21777^6670+6670^21777	83278	Hans Havermann	06/2020
9280	(2^276655+78557)/365425	83276	Lelio R Paula	12/2012
9281	2^276615-4035	83270	Lelio R Paula	08/2013
9282	2^276588+1155	83262	Lelio R Paula	08/2013
9283	2^276587-937	83261	Yves Minet	10/2009
9284	2^276584-113183	83261	Enzo Doria	07/2014
9285	(2^276592-1017)/13843739	83256	Lelio R Paula	12/2012
9286	2^276547-109591	83249	Enzo Doria	04/2014
9287	13^74733-32	83249	Lelio R Paula	11/2015
9288	2^276523-2587	83242	Yves Minet	07/2014
9289	18^66311-43	83239	Lelio R Paula	11/2015
9290	11^79919-1530	83228	Enzo Doria	12/2012
9291	2^276468-109745	83226	Enzo Doria	04/2014
9292	2^276462+5385	83224	Lelio R Paula	08/2013
9293	3*10^83219-17	83220	Robert Price	03/2021
9294	(9787*2^276422-1)/3	83215	Lelio R Paula	04/2015
9296	2^276391-15	83202	Lelio R Paula	06/2012
9295	(4*10^83201+173)/3	83202	Robert Price	01/2017
9297	(259*10^83186-1)/3	83188	Robert Price	12/2020
9298	(2^276327+534)/2	83183	Stefano Morozzi	01/2020
9299	2^276316-109655	83180	Enzo Doria	04/2014
9300	2^276305-112063	83177	Enzo Doria	06/2014
9301	(2^276296+3406)/2	83174	Stefano Morozzi	01/2020
9302	(10^(241585+1)+5410^41585-1)/9	83171	Robert Price	04/2017
9303	(2^276277+3254)/2	83168	Stefano Morozzi	01/2020
9304	74913!4-2	83161	Robert Price	07/2017
9305	(3023^23893-1)/3022	83155	Serge Batalov	08/2020
9306	2^276227-1837207	83153	Enzo Doria	05/2015
9307	(2^276227+3)/7	83152	Lelio R Paula	12/2012
9308	(2^276229+12)/28	83152	Stefano Morozzi	03/2020
9309	(2^276205+1190)/2	83146	Stefano Morozzi	01/2020
9310	2^276184-63389	83140	Paul Bourdelais	02/2012
9311	(2^276165+2046)/2	83134	Stefano Morozzi	01/2020
9312	(2^276105+1274)/2	83116	Stefano Morozzi	01/2020
9313	2^276066-111603	83105	Enzo Doria	05/2014
9314	19438^18837+18837^19438	83098	Hans Havermann	07/2020
9315	(431^31543-1)/430	83097	Serge Batalov	08/2020
9316	(2^276028-3)*6-7	83094	Gilbert Mozzo	09/2016
9317	(85*10^83080-139)/9	83081	Robert Price	08/2021
9318	(26*10^83067+79)/3	83068	Robert Price	09/2020
9319	2^275926-4691	83063	Yves Minet	05/2019
9320	(2^275919+1386)/2	83060	Stefano Morozzi	01/2020
9321	(2^275897+9)/1153	83051	Lelio R Paula	12/2012
9322	2^275879-109807	83048	Enzo Doria	04/2014
9324	F(397379)	83047	Henri Lifchitz	08/2003
9323	U(397379)	83047	Serge Batalov	03/2015
9325	3^174040-14	83039	Robert Price	08/2013
9326	(86*10^83038-221)/9	83039	Robert Price	06/2017
9327	21632^6897+6897^21632	83038	Hans Havermann	05/2020
9328	2^275841-6883	83037	Lelio R Paula	07/2011
9329	19610^17127+17127^19610	83023	Hans Havermann	06/2020
9330	3^174002-140	83021	Lelio R Paula	12/2015
9331	6^106681+77	83014	Lelio R Paula	12/2015
9332	187^36539-2	83011	Lelio R Paula	10/2017
9333	1036^27529+27529^1036	83010	Norbert Schneider	03/2020
9334	11^79701-3150	83001	Enzo Doria	12/2012
9335	(2^275721+1554)/2	83000	Stefano Morozzi	01/2020
9336	(2^275704+1858)/2	82995	Stefano Morozzi	01/2020
9337	(2^275696+1726)/2	82993	Stefano Morozzi	01/2020
9338	(22*10^82988-43)/3	82989	Robert Price	10/2021
9339	(55459*2^275657+1)/21	82985	Lelio R Paula	06/2014
9340	(7*10^82960-457)/9	82960	Robert Price	09/2017
9341	2^275535-6855	82945	Lelio R Paula	08/2013
9342	3^173828-14	82938	Robert Price	08/2013
9343	2^275512-109677	82938	Enzo Doria	04/2014
9344	(2^275450+1698)/2	82919	Stefano Morozzi	01/2020
9345	2^275446-110045	82918	Enzo Doria	04/2014
9346	(2^275473+47)/29526097447	82916	Lelio R Paula	12/2012
9347	3*10^82914-83	82915	Robert Price	02/2021
9348	3^173755-14	82903	Robert Price	08/2013
9349	(182*10^82898+43)/9	82900	Robert Price	11/2017
9350	(86*10^82897+103)/9	82898	Robert Price	12/2021
9351	2^275363-112309	82893	Enzo Doria	06/2014
9352	61^46427-60	82888	Norbert Schneider	10/2014
9353	3*10^82880-7^82880	82881	Mike Oakes	02/2010
9354	2^275290+90195	82871	Lelio R Paula	07/2013
9355	(35*10^82870-71)/9	82871	Robert Price	05/2015
9356	2^275270-1859621	82865	Enzo Doria	03/2016
9357	2^275259+81	82862	Henri Lifchitz	01/2007
9358	21436^7335+7335^21436	82859	Hans Havermann	05/2020
9359	(2^275247+1590)/2	82858	Stefano Morozzi	01/2020
9360	22515^4784+4784^22515	82851	Hans Havermann	05/2020
9361	6*10^82842-31	82843	Robert Price	07/2020
9362	(10013^20707-1)/10012	82836	Serge Batalov	08/2020
9363	(113703^16384+1)/2	82834	Richard Fischer	04/2018
9364	(2^275146+954)/2	82827	Stefano Morozzi	01/2020
9365	7^98003+98003^7+1	82823	Robert Price	05/2014
9366	(2^275101+3566)/2	82814	Stefano Morozzi	01/2020
9367	(2^275050+3150)/2	82798	Stefano Morozzi	01/2020
9368	(2^275044+2482)/2	82797	Stefano Morozzi	01/2020
9369	10^82790+126043	82791	Patrick De Geest	07/2013
9370	10^82790-47	82790	Robert Price	05/2011
9371	20762^9711+9711^20762	82784	Hans Havermann	05/2020
9372	2^274985-112663	82779	Enzo Doria	06/2014
9373	2^274935+15015	82764	Lelio R Paula	07/2013
9374	(17*2^274922+1)/3	82761	Lelio R Paula	12/2012
9375	[(55^5)^9511-(22434^2)^9511]/19	82759	Richard Fischer	11/2019
9376	(43*10^82752-61)/9	82753	Robert Price	06/2015
9377	(3*2^274862+1)/1027	82740	Lelio R Paula	12/2012
9378	(2^274851+3126)/2	82739	Stefano Morozzi	01/2020
9379	(31*2^274848-1)/4065	82736	Lelio R Paula	02/2014
9380	(4^137405+23)/3	82726	Robert Price	02/2017
9381	(2^274798+414)/2	82723	Stefano Morozzi	01/2020
9382	2^274791-110491	82721	Enzo Doria	05/2014
9383	(11*2^274776-1)/95	82715	Lelio R Paula	02/2014
9384	(47*10^82706-119)/9	82707	Robert Price	09/2017
9385	2^274704-111395	82695	Enzo Doria	05/2014
9386	2^274686-3911	82689	Yves Minet	04/2017
9387	(1629^25741-1)/1628	82675	Serge Batalov	08/2020
9388	21474^7075+7075^21474	82670	Hans Havermann	06/2020
9389	(2^274663-1017)/48871318292279	82669	Lelio R Paula	12/2012
9390	(3^173263-5)/14498	82664	Lelio R Paula	12/2012
9391	20488^10815+10815^20488	82650	Hans Havermann	07/2020
9392	(2^274554+894)/2	82649	Stefano Morozzi	01/2020
9394	2^274511-64875	82637	Lelio R Paula	08/2013
9393	(2^274512+1222)/2	82637	Stefano Morozzi	01/2020
9395	12^76572-83	82636	Lelio R Paula	11/2015
9396	3^173191-2^173191	82634	Mike Oakes	02/2004
9397	(2^274500+2970)/2	82633	Stefano Morozzi	01/2020
9398	20507^10698+10698^20507	82629	Hans Havermann	07/2020
9399	2^274464-238319	82622	Harrison Mesh	10/2021
9400	(2^274429+3726)/2	82612	Stefano Morozzi	01/2020
9401	14^72072-15	82604	Lelio R Paula	11/2015
9402	(2^274374+2950)/2	82595	Stefano Morozzi	01/2020
9403	(55459*2^274339+1)/3	82589	Lelio R Paula	06/2014
9404	2^274351+123	82588	Lelio R Paula	06/2012
9405	(1017*2^274339-1)/3515	82584	Lelio R Paula	04/2015
9406	21208^7833+7833^21208	82583	Hans Havermann	07/2020
9407	(2^274248+750)/2	82557	Stefano Morozzi	01/2020
9408	(2^274240+822)/2	82555	Stefano Morozzi	01/2020
9409	6^106086+113	82551	Lelio R Paula	12/2015
9410	(17*10^82540-377)/9	82541	Robert Price	11/2017
9411	(3470^23311-1)/3469	82526	Serge Batalov	08/2020
9412	(7*10^82517+173)/9	82517	Robert Price	01/2022
9413	2^274093-58695	82511	Lelio R Paula	07/2013
9414	7*10^82509-47	82510	Robert Price	02/2017
9415	2^274081-6555	82507	Lelio R Paula	07/2013
9417	2^274074-274074+1	82505	Robert Price	10/2014
9418	14^71985+47	82505	Lelio R Paula	11/2015
9416	5*10^82504+21	82505	Robert Price	01/2017
9419	(2^274062+498)/2	82501	Stefano Morozzi	01/2020
9420	6^106014-139	82495	Lelio R Paula	12/2015
9421	(2^274046+47)/753	82494	Lelio R Paula	12/2012
9422	2^274008-1838099	82485	Enzo Doria	05/2015
9423	2^273981-110029	82477	Enzo Doria	04/2014
9424	19^64490-30	82467	Lelio R Paula	12/2015
9425	(2^273864+3150)/2	82441	Stefano Morozzi	01/2020
9426	21328^7333+7333^21328	82439	Hans Havermann	07/2020
9427	20829^9070+9070^20829	82434	Hans Havermann	07/2020
9429	2^273785+11715	82418	Lelio R Paula	07/2013
9430	8*10^82417+51	82418	Robert Price	05/2017
9428	(2^273786+2242)/2	82418	Stefano Morozzi	01/2020
9431	11^79133-10	82409	Theodore Burton	11/2005
9432	(2^273752+1882)/2	82408	Stefano Morozzi	01/2020
9433	91^42063+90	82404	Norbert Schneider	01/2016
9434	10140^20567-20567^10140	82393	Norbert Schneider	11/2021
9436	2^273662-63	82381	Lelio R Paula	06/2012
9435	2^273661+255	82381	Lelio R Paula	07/2013
9437	(62*10^82377-17)/9	82378	Robert Price	09/2015
9438	2^273608+524287	82365	Paul Underwood	08/2018
9439	8*10^82360-51	82361	Robert Price	10/2017
9440	(79*10^82347-1)/3	82349	Robert Price	11/2017
9441	(11*10^82323+91)/3	82323	Robert Price	02/2017
9442	(189977#+19081)/(19081*17260483)	82317	Makoto Morimoto	10/2017
9443	(189977#+196924)/(271354128874441)	82316	Makoto Morimoto	10/2017
9444	15^69984+32	82308	Lelio R Paula	11/2015
9445	9*6^105746+7	82288	Lelio R Paula	10/2014
9446	89^42211-88	82286	Norbert Schneider	01/2016
9447	gcd(V(1476435),5F(295287)(F(295287)+1)+1)	82281	Serge Batalov	04/2015
9448	20596^9883+9883^20596	82279	Hans Havermann	06/2020
9449	(19*10^82270-43)/3	82271	Robert Price	10/2017
9450	2^273282-110241	82267	Enzo Doria	05/2014
9451	(2^273277+3746)/2	82265	Stefano Morozzi	01/2020
9452	(13^73849+4^73849)/17	82263	Robert Price	05/2013
9454	10^82254+9^(82254+1)	82255	Robert Price	08/2016
9453	10^82254+457773	82255	Patrick De Geest	12/2016
9455	10^82254-99609	82254	Patrick De Geest	12/2016
9456	(754*10^82250-7)/9	82252	Robert Price	11/2017
9457	18^65524+13	82251	Lelio R Paula	11/2015
9458	2^273206-107	82244	Lelio R Paula	06/2012
9459	2^273193-459145	82240	Enzo Doria	05/2015
9461	2^273126+36937	82220	Yves Minet	06/2010
9460	39505!2+128	82220	Robert Price	03/2015
9462	(2^273090+2214)/2	82208	Stefano Morozzi	01/2020
9463	2^273053-112111	82198	Enzo Doria	06/2014
9464	(2^273052+3138)/2	82197	Stefano Morozzi	01/2020
9465	2^273016+1185	82187	Lelio R Paula	07/2013
9466	(2^273008+3)/7	82183	Lelio R Paula	12/2012
9467	(2^272992+2230)/2	82179	Stefano Morozzi	01/2020
9469	5^117554-15386	82167	Enzo Doria	02/2013
9468	21158^7647+7647^21158	82167	Hans Havermann	06/2020
9470	20194^11715+11715^20194	82165	Hans Havermann	06/2020
9471	(38*10^82161+403)/9	82162	Robert Price	11/2017
9472	2^272907-111439	82154	Enzo Doria	05/2014
9473	(67607*2^272901+1)/50790115	82149	Lelio R Paula	06/2014
9474	2^272875-69	82144	Lelio R Paula	06/2012
9475	(3997^22807-1)/3996	82142	Serge Batalov	08/2020
9476	7^97197+4	82141	Robert Price	01/2014
9477	(4*6^105554+1)/5	82137	Serge Batalov	10/2014
9478	2^272826-4433	82129	Yves Minet	03/2019
9479	6^105531-109	82120	Lelio R Paula	12/2015
9480	2^272766-65	82111	Lelio R Paula	06/2012
9481	19^64205-78	82103	Lelio R Paula	12/2015
9482	2^272702+1869979	82092	Enzo Doria	05/2016
9483	(29*2^272687-1)/9	82088	Lelio R Paula	02/2014
9484	(5*10^82085-119)/3	82086	Robert Price	04/2016
9485	(2^272665+1334)/2	82081	Stefano Morozzi	01/2020
9486	2^272660-110049	82079	Enzo Doria	04/2014
9487	6^105474+67	82075	Lelio R Paula	12/2015
9488	2^272637+82875	82072	Lelio R Paula	07/2013
9489	(6330^21589-1)/6329	82065	Serge Batalov	08/2020
9490	2^272587-31	82057	Lelio R Paula	06/2012
9491	(1969^24907-1)/1968	82047	Serge Batalov	08/2020
9493	(41*10^82044-59)/9	82045	Robert Price	10/2017
9492	92*10^82043-9	82045	Robert Price	12/2021
9494	8*5^117368+9	82038	Lelio R Paula	10/2014
9495	(101525^16384+1)/131074	82023	Lelio R Paula	11/2011
9496	4*5^117343-7	82020	Lelio R Paula	10/2014
9497	(2^272381+506)/2	81995	Stefano Morozzi	01/2020
9498	(265*10^81990+17)/3	81992	Robert Price	05/2016
9499	3^171843+10	81990	Robert Price	10/2013
9500	(2^272361+3762)/2	81989	Stefano Morozzi	01/2020

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