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 ?
6251	(2^278428+1750)/2	83815	Stefano Morozzi	01/2020
6252	(8*10^83811-101)/3	83812	Robert Price	10/2017
6253	2^278400+40755	83807	Lelio R Paula	08/2013
6254	(2^278394+3718)/2	83805	Stefano Morozzi	01/2020
6255	(2^278388+3586)/2	83803	Stefano Morozzi	01/2020
6256	(9*2^278381-1)/7	83802	Lelio R Paula	02/2014
6257	39^87813+6^87813+24^87813	83796	Mike Oakes	12/2010
6258	19551^19268+19268^19551	83773	Hans Havermann	05/2017
6259	20625^11522+11522^20625	83770	Hans Havermann	05/2017
6260	(44*10^83768-791)/9	83769	Robert Price	10/2017
6261	(87^43189+1)/88	83764	Paul Bourdelais	08/2017
6262	2^278235-49	83758	Lelio R Paula	06/2012
6263	23543^3610+3610^23543	83755	Hans Havermann	05/2017
6265	18^66711-91	83741	Lelio R Paula	11/2015
6264	4*10^83740-89	83741	Robert Price	08/2017
6266	(3*2^278172-1)/11	83738	Lelio R Paula	02/2014
6267	(15*29^57251+2561)/28	83724	Curtis Bright	05/2015
6268	4*7^99059-9	83716	Lelio R Paula	10/2014
6269	(2^278128-3)/126844724149	83714	Lelio R Paula	12/2012
6270	2^278077+1867211	83710	Enzo Doria	03/2016
6271	2^278059-27	83705	Lelio R Paula	06/2012
6272	214^35917+35917^214	83702	Norbert Schneider	12/2014
6273	(23*10^83693+7)/3	83694	Robert Price	10/2015
6274	85^43375-2	83689	Lelio R Paula	09/2013
6275	5*3^175360+4	83669	Lelio R Paula	07/2014
6276	(23^61441-1)/22	83665	Robert Price	01/2012
6277	20091^14596+14596^20091	83664	Hans Havermann	03/2017
6278	2^277907-110629	83659	Enzo Doria	05/2014
6279	19522^19283+19283^19522	83656	Hans Havermann	04/2017
6280	(2^277881+2570)/2	83651	Stefano Morozzi	01/2020
6281	8*5^119664-3	83643	Lelio R Paula	10/2014
6282	8*3^175299-7	83640	Lelio R Paula	07/2014
6283	(26*10^83638-413)/9	83639	Robert Price	10/2017
6284	3^175250+22	83616	Robert Price	12/2013
6286	11^80285+30	83609	Lelio R Paula	10/2015
6285	26870^1293+1293^26870	83609	Hans Havermann	03/2017
6287	2^277691+1874423	83594	Enzo Doria	06/2016
6288	13^75022-60	83571	Lelio R Paula	11/2015
6289	(2^277593+2622)/2	83564	Stefano Morozzi	01/2020
6290	14^72905-51	83559	Lelio R Paula	11/2015
6291	(17*2^277565-1)/543	83554	Lelio R Paula	02/2014
6292	5^119532-12	83550	Lelio R Paula	10/2015
6293	6^107358-16253	83541	Enzo Doria	02/2013
6294	2^277478-460211	83530	Enzo Doria	06/2015
6295	(2^277474+814)/2	83528	Stefano Morozzi	01/2020
6296	(22*10^83525-7)/3	83526	Erik Branger	09/2014
6297	(30^56543+1)/31	83520	Robert Price	07/2013
6298	2^277417-460783	83511	Paul Bourdelais	04/2013
6299	(2^277404+3582)/2	83507	Stefano Morozzi	01/2020
6300	(22699*2^277387+1)/219	83504	Lelio R Paula	06/2014
6301	(31*2^277383-1)/247	83500	Lelio R Paula	02/2014
6302	21368^8085+8085^21368	83500	Hans Havermann	04/2017
6303	(2^277353+3750)/2	83492	Stefano Morozzi	01/2020
6304	(2^277348+3538)/2	83490	Stefano Morozzi	01/2020
6305	(9*2^277342+1)/13	83489	Lelio R Paula	12/2012
6306	5^119439-66	83485	Lelio R Paula	10/2015
6307	(14*10^83471-101)/3	83472	Robert Price	04/2017
6308	5*6^107263+7	83468	Lelio R Paula	10/2014
6309	(64*10^83461-1)/9	83462	Serge Batalov	11/2010
6310	2^277244-175709	83459	Hans Havermann	10/2018
6311	(2^277230+1450)/2	83455	Stefano Morozzi	01/2020
6312	(2^277232+3658)/2	83455	Stefano Morozzi	01/2020
6313	17^67796-92	83420	Lelio R Paula	11/2015
6314	2^277106-110057	83418	Enzo Doria	04/2014
6315	6^107200-19	83418	Lelio R Paula	12/2015
6316	11^80096-1830	83412	Enzo Doria	12/2012
6317	3^174801+56	83402	Lelio R Paula	12/2015
6318	2^277033-111973	83396	Enzo Doria	05/2014
6319	120^40105-119	83386	Norbert Schneider	09/2018
6320	(2^276992+2046)/2	83383	Stefano Morozzi	01/2020
6321	(2^276990+474)/2	83382	Stefano Morozzi	01/2020
6322	20519^11572+11572^20519	83378	Hans Havermann	03/2017
6323	20850^9971+9971^20850	83374	Hans Havermann	03/2017
6326	6^107122-18863	83358	Enzo Doria	03/2013
6324	(2^276908+2322)/2	83358	Stefano Morozzi	01/2020
6325	(2^276910+2734)/2	83358	Stefano Morozzi	01/2020
6327	4*10^83354-89	83355	Robert Price	08/2017
6328	3^174697-34	83352	Robert Price	11/2013
6330	(9787*2^276855-1)/2345	83343	Lelio R Paula	04/2015
6329	(2^276860+1678)/2	83343	Stefano Morozzi	01/2020
6331	(2^276841+3354)/2	83338	Stefano Morozzi	01/2020
6332	2^276825+75227	83333	Enzo Doria	04/2016
6333	5^119214+84	83328	Lelio R Paula	10/2015
6334	2^276803-159	83327	Lelio R Paula	06/2012
6335	(3*2^276753-1)/25	83311	Lelio R Paula	02/2014
6336	114^40495+40495^114	83295	Norbert Schneider	12/2014
6337	39967!2+1024	83282	Robert Price	02/2015
6338	2^276641+57	83278	Lelio R Paula	06/2012
6339	35^53934-3414	83278	Enzo Doria	03/2013
6340	(2^276655+78557)/365425	83276	Lelio R Paula	12/2012
6341	2^276615-4035	83270	Lelio R Paula	08/2013
6342	2^276588+1155	83262	Lelio R Paula	08/2013
6343	2^276587-937	83261	Yves Minet	10/2009
6344	2^276584-113183	83261	Enzo Doria	07/2014
6345	(2^276592-1017)/13843739	83256	Lelio R Paula	12/2012
6346	2^276547-109591	83249	Enzo Doria	04/2014
6347	13^74733-32	83249	Lelio R Paula	11/2015
6348	2^276523-2587	83242	Yves Minet	07/2014
6349	18^66311-43	83239	Lelio R Paula	11/2015
6350	11^79919-1530	83228	Enzo Doria	12/2012
6351	2^276468-109745	83226	Enzo Doria	04/2014
6352	2^276462+5385	83224	Lelio R Paula	08/2013
6353	(9787*2^276422-1)/3	83215	Lelio R Paula	04/2015
6355	2^276391-15	83202	Lelio R Paula	06/2012
6354	(4*10^83201+173)/3	83202	Robert Price	01/2017
6356	(2^276327+534)/2	83183	Stefano Morozzi	01/2020
6357	2^276316-109655	83180	Enzo Doria	04/2014
6358	2^276305-112063	83177	Enzo Doria	06/2014
6359	(2^276296+3406)/2	83174	Stefano Morozzi	01/2020
6360	(10^(241585+1)+5410^41585-1)/9	83171	Robert Price	04/2017
6361	(2^276277+3254)/2	83168	Stefano Morozzi	01/2020
6362	74913!4-2	83161	Robert Price	07/2017
6363	2^276227-1837207	83153	Enzo Doria	05/2015
6365	(2^276227+3)/7	83152	Lelio R Paula	12/2012
6364	(2^276229+12)/28	83152	Stefano Morozzi	03/2020
6366	(2^276205+1190)/2	83146	Stefano Morozzi	01/2020
6367	2^276184-63389	83140	Paul Bourdelais	02/2012
6368	(2^276165+2046)/2	83134	Stefano Morozzi	01/2020
6369	(2^276105+1274)/2	83116	Stefano Morozzi	01/2020
6370	2^276066-111603	83105	Enzo Doria	05/2014
6371	(2^276028-3)*6-7	83094	Gilbert Mozzo	09/2016
6372	2^275926-4691	83063	Yves Minet	05/2019
6373	(2^275919+1386)/2	83060	Stefano Morozzi	01/2020
6374	(2^275897+9)/1153	83051	Lelio R Paula	12/2012
6375	2^275879-109807	83048	Enzo Doria	04/2014
6377	F(397379)	83047	Henri Lifchitz	08/2003
6376	U(397379)	83047	Serge Batalov	03/2015
6378	3^174040-14	83039	Robert Price	08/2013
6379	(86*10^83038-221)/9	83039	Robert Price	06/2017
6380	2^275841-6883	83037	Lelio R Paula	07/2011
6381	3^174002-140	83021	Lelio R Paula	12/2015
6382	6^106681+77	83014	Lelio R Paula	12/2015
6383	187^36539-2	83011	Lelio R Paula	10/2017
6384	1036^27529+27529^1036	83010	Norbert Schneider	03/2020
6385	11^79701-3150	83001	Enzo Doria	12/2012
6386	(2^275721+1554)/2	83000	Stefano Morozzi	01/2020
6387	(2^275704+1858)/2	82995	Stefano Morozzi	01/2020
6388	(2^275696+1726)/2	82993	Stefano Morozzi	01/2020
6389	(55459*2^275657+1)/21	82985	Lelio R Paula	06/2014
6390	(7*10^82960-457)/9	82960	Robert Price	09/2017
6391	2^275535-6855	82945	Lelio R Paula	08/2013
6392	3^173828-14	82938	Robert Price	08/2013
6393	2^275512-109677	82938	Enzo Doria	04/2014
6394	(2^275450+1698)/2	82919	Stefano Morozzi	01/2020
6395	2^275446-110045	82918	Enzo Doria	04/2014
6396	(2^275473+47)/29526097447	82916	Lelio R Paula	12/2012
6397	3^173755-14	82903	Robert Price	08/2013
6398	(182*10^82898+43)/9	82900	Robert Price	11/2017
6399	2^275363-112309	82893	Enzo Doria	06/2014
6400	61^46427-60	82888	Norbert Schneider	10/2014
6401	3*10^82880-7^82880	82881	Mike Oakes	02/2010
6402	2^275290+90195	82871	Lelio R Paula	07/2013
6403	(35*10^82870-71)/9	82871	Robert Price	05/2015
6404	2^275270-1859621	82865	Enzo Doria	03/2016
6405	2^275259+81	82862	Henri Lifchitz	01/2007
6406	(2^275247+1590)/2	82858	Stefano Morozzi	01/2020
6407	(113703^16384+1)/2	82834	Richard Fischer	04/2018
6408	(2^275146+954)/2	82827	Stefano Morozzi	01/2020
6409	7^98003+98003^7+1	82823	Robert Price	05/2014
6410	(2^275101+3566)/2	82814	Stefano Morozzi	01/2020
6411	(2^275050+3150)/2	82798	Stefano Morozzi	01/2020
6412	(2^275044+2482)/2	82797	Stefano Morozzi	01/2020
6413	10^82790+126043	82791	Patrick De Geest	07/2013
6414	10^82790-47	82790	Robert Price	05/2011
6415	2^274985-112663	82779	Enzo Doria	06/2014
6416	2^274935+15015	82764	Lelio R Paula	07/2013
6417	(17*2^274922+1)/3	82761	Lelio R Paula	12/2012
6418	[(55^5)^9511-(22434^2)^9511]/19	82759	Richard Fischer	11/2019
6419	(43*10^82752-61)/9	82753	Robert Price	06/2015
6420	(3*2^274862+1)/1027	82740	Lelio R Paula	12/2012
6421	(2^274851+3126)/2	82739	Stefano Morozzi	01/2020
6422	(31*2^274848-1)/4065	82736	Lelio R Paula	02/2014
6423	(4^137405+23)/3	82726	Robert Price	02/2017
6424	(2^274798+414)/2	82723	Stefano Morozzi	01/2020
6425	2^274791-110491	82721	Enzo Doria	05/2014
6426	(11*2^274776-1)/95	82715	Lelio R Paula	02/2014
6427	(47*10^82706-119)/9	82707	Robert Price	09/2017
6428	2^274704-111395	82695	Enzo Doria	05/2014
6429	2^274686-3911	82689	Yves Minet	04/2017
6430	(2^274663-1017)/48871318292279	82669	Lelio R Paula	12/2012
6431	(3^173263-5)/14498	82664	Lelio R Paula	12/2012
6432	(2^274554+894)/2	82649	Stefano Morozzi	01/2020
6434	2^274511-64875	82637	Lelio R Paula	08/2013
6433	(2^274512+1222)/2	82637	Stefano Morozzi	01/2020
6435	12^76572-83	82636	Lelio R Paula	11/2015
6436	3^173191-2^173191	82634	Mike Oakes	02/2004
6437	(2^274500+2970)/2	82633	Stefano Morozzi	01/2020
6438	(2^274429+3726)/2	82612	Stefano Morozzi	01/2020
6439	14^72072-15	82604	Lelio R Paula	11/2015
6440	(2^274374+2950)/2	82595	Stefano Morozzi	01/2020
6441	(55459*2^274339+1)/3	82589	Lelio R Paula	06/2014
6442	2^274351+123	82588	Lelio R Paula	06/2012
6443	(1017*2^274339-1)/3515	82584	Lelio R Paula	04/2015
6444	(2^274248+750)/2	82557	Stefano Morozzi	01/2020
6445	(2^274240+822)/2	82555	Stefano Morozzi	01/2020
6446	6^106086+113	82551	Lelio R Paula	12/2015
6447	(17*10^82540-377)/9	82541	Robert Price	11/2017
6448	2^274093-58695	82511	Lelio R Paula	07/2013
6449	7*10^82509-47	82510	Robert Price	02/2017
6450	2^274081-6555	82507	Lelio R Paula	07/2013
6452	2^274074-274074+1	82505	Robert Price	10/2014
6453	14^71985+47	82505	Lelio R Paula	11/2015
6451	5*10^82504+21	82505	Robert Price	01/2017
6454	(2^274062+498)/2	82501	Stefano Morozzi	01/2020
6455	6^106014-139	82495	Lelio R Paula	12/2015
6456	(2^274046+47)/753	82494	Lelio R Paula	12/2012
6457	2^274008-1838099	82485	Enzo Doria	05/2015
6458	2^273981-110029	82477	Enzo Doria	04/2014
6459	19^64490-30	82467	Lelio R Paula	12/2015
6460	(2^273864+3150)/2	82441	Stefano Morozzi	01/2020
6463	2^273785+11715	82418	Lelio R Paula	07/2013
6462	8*10^82417+51	82418	Robert Price	05/2017
6461	(2^273786+2242)/2	82418	Stefano Morozzi	01/2020
6464	11^79133-10	82409	Theodore Burton	11/2005
6465	(2^273752+1882)/2	82408	Stefano Morozzi	01/2020
6466	91^42063+90	82404	Norbert Schneider	01/2016
6468	2^273662-63	82381	Lelio R Paula	06/2012
6467	2^273661+255	82381	Lelio R Paula	07/2013
6469	(62*10^82377-17)/9	82378	Robert Price	09/2015
6470	2^273608+524287	82365	Paul Underwood	08/2018
6471	8*10^82360-51	82361	Robert Price	10/2017
6472	(79*10^82347-1)/3	82349	Robert Price	11/2017
6473	(11*10^82323+91)/3	82323	Robert Price	02/2017
6474	(189977#+19081)/(19081*17260483)	82317	Makoto Morimoto	10/2017
6475	(189977#+196924)/(271354128874441)	82316	Makoto Morimoto	10/2017
6476	15^69984+32	82308	Lelio R Paula	11/2015
6477	9*6^105746+7	82288	Lelio R Paula	10/2014
6478	89^42211-88	82286	Norbert Schneider	01/2016
6479	gcd(V(1476435),5F(295287)(F(295287)+1)+1)	82281	Serge Batalov	04/2015
6480	(19*10^82270-43)/3	82271	Robert Price	10/2017
6481	2^273282-110241	82267	Enzo Doria	05/2014
6482	(2^273277+3746)/2	82265	Stefano Morozzi	01/2020
6483	(13^73849+4^73849)/17	82263	Robert Price	05/2013
6485	10^82254+9^(82254+1)	82255	Robert Price	08/2016
6484	10^82254+457773	82255	Patrick De Geest	12/2016
6486	10^82254-99609	82254	Patrick De Geest	12/2016
6487	(754*10^82250-7)/9	82252	Robert Price	11/2017
6488	18^65524+13	82251	Lelio R Paula	11/2015
6489	2^273206-107	82244	Lelio R Paula	06/2012
6490	2^273193-459145	82240	Enzo Doria	05/2015
6492	2^273126+36937	82220	Yves Minet	06/2010
6491	39505!2+128	82220	Robert Price	03/2015
6493	(2^273090+2214)/2	82208	Stefano Morozzi	01/2020
6494	2^273053-112111	82198	Enzo Doria	06/2014
6495	(2^273052+3138)/2	82197	Stefano Morozzi	01/2020
6496	2^273016+1185	82187	Lelio R Paula	07/2013
6497	(2^273008+3)/7	82183	Lelio R Paula	12/2012
6498	(2^272992+2230)/2	82179	Stefano Morozzi	01/2020
6499	5^117554-15386	82167	Enzo Doria	02/2013
6500	(38*10^82161+403)/9	82162	Robert Price	11/2017

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