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 ?
7251	20091^14596+14596^20091	83664	Hans Havermann	03/2017
7252	2^277907-110629	83659	Enzo Doria	05/2014
7253	19522^19283+19283^19522	83656	Hans Havermann	04/2017
7254	(2^277881+2570)/2	83651	Stefano Morozzi	01/2020
7255	8*5^119664-3	83643	Lelio R Paula	10/2014
7256	8*3^175299-7	83640	Lelio R Paula	07/2014
7257	(26*10^83638-413)/9	83639	Robert Price	10/2017
7258	3^175250+22	83616	Robert Price	12/2013
7260	11^80285+30	83609	Lelio R Paula	10/2015
7259	26870^1293+1293^26870	83609	Hans Havermann	03/2017
7261	(6730^21841-1)/6729	83604	Serge Batalov	08/2020
7262	(2828^24223-1)/2827	83602	Serge Batalov	08/2020
7263	2^277691+1874423	83594	Enzo Doria	06/2016
7264	13^75022-60	83571	Lelio R Paula	11/2015
7265	(2^277593+2622)/2	83564	Stefano Morozzi	01/2020
7266	14^72905-51	83559	Lelio R Paula	11/2015
7267	(17*2^277565-1)/543	83554	Lelio R Paula	02/2014
7268	5^119532-12	83550	Lelio R Paula	10/2015
7269	6^107358-16253	83541	Enzo Doria	02/2013
7270	2^277478-460211	83530	Enzo Doria	06/2015
7271	(2^277474+814)/2	83528	Stefano Morozzi	01/2020
7272	(22*10^83525-7)/3	83526	Erik Branger	09/2014
7273	(30^56543+1)/31	83520	Robert Price	07/2013
7274	2^277417-460783	83511	Paul Bourdelais	04/2013
7275	(2^277404+3582)/2	83507	Stefano Morozzi	01/2020
7276	(22699*2^277387+1)/219	83504	Lelio R Paula	06/2014
7277	(31*2^277383-1)/247	83500	Lelio R Paula	02/2014
7278	21368^8085+8085^21368	83500	Hans Havermann	04/2017
7279	(2^277353+3750)/2	83492	Stefano Morozzi	01/2020
7280	(2^277348+3538)/2	83490	Stefano Morozzi	01/2020
7281	(9*2^277342+1)/13	83489	Lelio R Paula	12/2012
7282	5^119439-66	83485	Lelio R Paula	10/2015
7283	(14*10^83471-101)/3	83472	Robert Price	04/2017
7284	5*6^107263+7	83468	Lelio R Paula	10/2014
7285	(64*10^83461-1)/9	83462	Serge Batalov	11/2010
7286	2^277244-175709	83459	Hans Havermann	10/2018
7287	(2^277230+1450)/2	83455	Stefano Morozzi	01/2020
7288	(2^277232+3658)/2	83455	Stefano Morozzi	01/2020
7289	17^67796-92	83420	Lelio R Paula	11/2015
7290	2^277106-110057	83418	Enzo Doria	04/2014
7291	6^107200-19	83418	Lelio R Paula	12/2015
7292	11^80096-1830	83412	Enzo Doria	12/2012
7293	3^174801+56	83402	Lelio R Paula	12/2015
7294	2^277033-111973	83396	Enzo Doria	05/2014
7295	120^40105-119	83386	Norbert Schneider	09/2018
7296	(2^276992+2046)/2	83383	Stefano Morozzi	01/2020
7297	(2^276990+474)/2	83382	Stefano Morozzi	01/2020
7298	20519^11572+11572^20519	83378	Hans Havermann	03/2017
7299	20850^9971+9971^20850	83374	Hans Havermann	03/2017
7302	6^107122-18863	83358	Enzo Doria	03/2013
7300	(2^276908+2322)/2	83358	Stefano Morozzi	01/2020
7301	(2^276910+2734)/2	83358	Stefano Morozzi	01/2020
7303	4*10^83354-89	83355	Robert Price	08/2017
7304	3^174697-34	83352	Robert Price	11/2013
7306	(9787*2^276855-1)/2345	83343	Lelio R Paula	04/2015
7305	(2^276860+1678)/2	83343	Stefano Morozzi	01/2020
7307	(2^276841+3354)/2	83338	Stefano Morozzi	01/2020
7309	2^276825+75227	83333	Enzo Doria	04/2016
7308	34*10^83331-9	83333	Robert Price	06/2020
7310	5^119214+84	83328	Lelio R Paula	10/2015
7311	2^276803-159	83327	Lelio R Paula	06/2012
7312	(3*2^276753-1)/25	83311	Lelio R Paula	02/2014
7313	7*10^83297-39	83298	Robert Price	07/2020
7314	114^40495+40495^114	83295	Norbert Schneider	12/2014
7315	39967!2+1024	83282	Robert Price	02/2015
7316	(1894^25411-1)/1893	83279	Serge Batalov	08/2020
7318	2^276641+57	83278	Lelio R Paula	06/2012
7319	35^53934-3414	83278	Enzo Doria	03/2013
7317	21777^6670+6670^21777	83278	Hans Havermann	06/2020
7320	(2^276655+78557)/365425	83276	Lelio R Paula	12/2012
7321	2^276615-4035	83270	Lelio R Paula	08/2013
7322	2^276588+1155	83262	Lelio R Paula	08/2013
7323	2^276587-937	83261	Yves Minet	10/2009
7324	2^276584-113183	83261	Enzo Doria	07/2014
7325	(2^276592-1017)/13843739	83256	Lelio R Paula	12/2012
7326	2^276547-109591	83249	Enzo Doria	04/2014
7327	13^74733-32	83249	Lelio R Paula	11/2015
7328	2^276523-2587	83242	Yves Minet	07/2014
7329	18^66311-43	83239	Lelio R Paula	11/2015
7330	11^79919-1530	83228	Enzo Doria	12/2012
7331	2^276468-109745	83226	Enzo Doria	04/2014
7332	2^276462+5385	83224	Lelio R Paula	08/2013
7333	(9787*2^276422-1)/3	83215	Lelio R Paula	04/2015
7335	2^276391-15	83202	Lelio R Paula	06/2012
7334	(4*10^83201+173)/3	83202	Robert Price	01/2017
7336	(2^276327+534)/2	83183	Stefano Morozzi	01/2020
7337	2^276316-109655	83180	Enzo Doria	04/2014
7338	2^276305-112063	83177	Enzo Doria	06/2014
7339	(2^276296+3406)/2	83174	Stefano Morozzi	01/2020
7340	(10^(241585+1)+5410^41585-1)/9	83171	Robert Price	04/2017
7341	(2^276277+3254)/2	83168	Stefano Morozzi	01/2020
7342	74913!4-2	83161	Robert Price	07/2017
7343	(3023^23893-1)/3022	83155	Serge Batalov	08/2020
7344	2^276227-1837207	83153	Enzo Doria	05/2015
7346	(2^276227+3)/7	83152	Lelio R Paula	12/2012
7345	(2^276229+12)/28	83152	Stefano Morozzi	03/2020
7347	(2^276205+1190)/2	83146	Stefano Morozzi	01/2020
7348	2^276184-63389	83140	Paul Bourdelais	02/2012
7349	(2^276165+2046)/2	83134	Stefano Morozzi	01/2020
7350	(2^276105+1274)/2	83116	Stefano Morozzi	01/2020
7351	2^276066-111603	83105	Enzo Doria	05/2014
7352	19438^18837+18837^19438	83098	Hans Havermann	07/2020
7353	(431^31543-1)/430	83097	Serge Batalov	08/2020
7354	(2^276028-3)*6-7	83094	Gilbert Mozzo	09/2016
7355	(26*10^83067+79)/3	83068	Robert Price	09/2020
7356	2^275926-4691	83063	Yves Minet	05/2019
7357	(2^275919+1386)/2	83060	Stefano Morozzi	01/2020
7358	(2^275897+9)/1153	83051	Lelio R Paula	12/2012
7359	2^275879-109807	83048	Enzo Doria	04/2014
7361	F(397379)	83047	Henri Lifchitz	08/2003
7360	U(397379)	83047	Serge Batalov	03/2015
7362	3^174040-14	83039	Robert Price	08/2013
7363	(86*10^83038-221)/9	83039	Robert Price	06/2017
7364	21632^6897+6897^21632	83038	Hans Havermann	05/2020
7365	2^275841-6883	83037	Lelio R Paula	07/2011
7366	19610^17127+17127^19610	83023	Hans Havermann	06/2020
7367	3^174002-140	83021	Lelio R Paula	12/2015
7368	6^106681+77	83014	Lelio R Paula	12/2015
7369	187^36539-2	83011	Lelio R Paula	10/2017
7370	1036^27529+27529^1036	83010	Norbert Schneider	03/2020
7371	11^79701-3150	83001	Enzo Doria	12/2012
7372	(2^275721+1554)/2	83000	Stefano Morozzi	01/2020
7373	(2^275704+1858)/2	82995	Stefano Morozzi	01/2020
7374	(2^275696+1726)/2	82993	Stefano Morozzi	01/2020
7375	(55459*2^275657+1)/21	82985	Lelio R Paula	06/2014
7376	(7*10^82960-457)/9	82960	Robert Price	09/2017
7377	2^275535-6855	82945	Lelio R Paula	08/2013
7378	3^173828-14	82938	Robert Price	08/2013
7379	2^275512-109677	82938	Enzo Doria	04/2014
7380	(2^275450+1698)/2	82919	Stefano Morozzi	01/2020
7381	2^275446-110045	82918	Enzo Doria	04/2014
7382	(2^275473+47)/29526097447	82916	Lelio R Paula	12/2012
7383	3^173755-14	82903	Robert Price	08/2013
7384	(182*10^82898+43)/9	82900	Robert Price	11/2017
7385	2^275363-112309	82893	Enzo Doria	06/2014
7386	61^46427-60	82888	Norbert Schneider	10/2014
7387	3*10^82880-7^82880	82881	Mike Oakes	02/2010
7388	2^275290+90195	82871	Lelio R Paula	07/2013
7389	(35*10^82870-71)/9	82871	Robert Price	05/2015
7390	2^275270-1859621	82865	Enzo Doria	03/2016
7391	2^275259+81	82862	Henri Lifchitz	01/2007
7392	21436^7335+7335^21436	82859	Hans Havermann	05/2020
7393	(2^275247+1590)/2	82858	Stefano Morozzi	01/2020
7394	22515^4784+4784^22515	82851	Hans Havermann	05/2020
7395	6*10^82842-31	82843	Robert Price	07/2020
7396	(10013^20707-1)/10012	82836	Serge Batalov	08/2020
7397	(113703^16384+1)/2	82834	Richard Fischer	04/2018
7398	(2^275146+954)/2	82827	Stefano Morozzi	01/2020
7399	7^98003+98003^7+1	82823	Robert Price	05/2014
7400	(2^275101+3566)/2	82814	Stefano Morozzi	01/2020
7401	(2^275050+3150)/2	82798	Stefano Morozzi	01/2020
7402	(2^275044+2482)/2	82797	Stefano Morozzi	01/2020
7403	10^82790+126043	82791	Patrick De Geest	07/2013
7404	10^82790-47	82790	Robert Price	05/2011
7405	20762^9711+9711^20762	82784	Hans Havermann	05/2020
7406	2^274985-112663	82779	Enzo Doria	06/2014
7407	2^274935+15015	82764	Lelio R Paula	07/2013
7408	(17*2^274922+1)/3	82761	Lelio R Paula	12/2012
7409	[(55^5)^9511-(22434^2)^9511]/19	82759	Richard Fischer	11/2019
7410	(43*10^82752-61)/9	82753	Robert Price	06/2015
7411	(3*2^274862+1)/1027	82740	Lelio R Paula	12/2012
7412	(2^274851+3126)/2	82739	Stefano Morozzi	01/2020
7413	(31*2^274848-1)/4065	82736	Lelio R Paula	02/2014
7414	(4^137405+23)/3	82726	Robert Price	02/2017
7415	(2^274798+414)/2	82723	Stefano Morozzi	01/2020
7416	2^274791-110491	82721	Enzo Doria	05/2014
7417	(11*2^274776-1)/95	82715	Lelio R Paula	02/2014
7418	(47*10^82706-119)/9	82707	Robert Price	09/2017
7419	2^274704-111395	82695	Enzo Doria	05/2014
7420	2^274686-3911	82689	Yves Minet	04/2017
7421	(1629^25741-1)/1628	82675	Serge Batalov	08/2020
7422	21474^7075+7075^21474	82670	Hans Havermann	06/2020
7423	(2^274663-1017)/48871318292279	82669	Lelio R Paula	12/2012
7424	(3^173263-5)/14498	82664	Lelio R Paula	12/2012
7425	20488^10815+10815^20488	82650	Hans Havermann	07/2020
7426	(2^274554+894)/2	82649	Stefano Morozzi	01/2020
7428	2^274511-64875	82637	Lelio R Paula	08/2013
7427	(2^274512+1222)/2	82637	Stefano Morozzi	01/2020
7429	12^76572-83	82636	Lelio R Paula	11/2015
7430	3^173191-2^173191	82634	Mike Oakes	02/2004
7431	(2^274500+2970)/2	82633	Stefano Morozzi	01/2020
7432	20507^10698+10698^20507	82629	Hans Havermann	07/2020
7433	(2^274429+3726)/2	82612	Stefano Morozzi	01/2020
7434	14^72072-15	82604	Lelio R Paula	11/2015
7435	(2^274374+2950)/2	82595	Stefano Morozzi	01/2020
7436	(55459*2^274339+1)/3	82589	Lelio R Paula	06/2014
7437	2^274351+123	82588	Lelio R Paula	06/2012
7438	(1017*2^274339-1)/3515	82584	Lelio R Paula	04/2015
7439	21208^7833+7833^21208	82583	Hans Havermann	07/2020
7440	(2^274248+750)/2	82557	Stefano Morozzi	01/2020
7441	(2^274240+822)/2	82555	Stefano Morozzi	01/2020
7442	6^106086+113	82551	Lelio R Paula	12/2015
7443	(17*10^82540-377)/9	82541	Robert Price	11/2017
7444	(3470^23311-1)/3469	82526	Serge Batalov	08/2020
7445	2^274093-58695	82511	Lelio R Paula	07/2013
7446	7*10^82509-47	82510	Robert Price	02/2017
7447	2^274081-6555	82507	Lelio R Paula	07/2013
7449	2^274074-274074+1	82505	Robert Price	10/2014
7450	14^71985+47	82505	Lelio R Paula	11/2015
7448	5*10^82504+21	82505	Robert Price	01/2017
7451	(2^274062+498)/2	82501	Stefano Morozzi	01/2020
7452	6^106014-139	82495	Lelio R Paula	12/2015
7453	(2^274046+47)/753	82494	Lelio R Paula	12/2012
7454	2^274008-1838099	82485	Enzo Doria	05/2015
7455	2^273981-110029	82477	Enzo Doria	04/2014
7456	19^64490-30	82467	Lelio R Paula	12/2015
7457	(2^273864+3150)/2	82441	Stefano Morozzi	01/2020
7458	21328^7333+7333^21328	82439	Hans Havermann	07/2020
7459	20829^9070+9070^20829	82434	Hans Havermann	07/2020
7462	2^273785+11715	82418	Lelio R Paula	07/2013
7461	8*10^82417+51	82418	Robert Price	05/2017
7460	(2^273786+2242)/2	82418	Stefano Morozzi	01/2020
7463	11^79133-10	82409	Theodore Burton	11/2005
7464	(2^273752+1882)/2	82408	Stefano Morozzi	01/2020
7465	91^42063+90	82404	Norbert Schneider	01/2016
7467	2^273662-63	82381	Lelio R Paula	06/2012
7466	2^273661+255	82381	Lelio R Paula	07/2013
7468	(62*10^82377-17)/9	82378	Robert Price	09/2015
7469	2^273608+524287	82365	Paul Underwood	08/2018
7470	8*10^82360-51	82361	Robert Price	10/2017
7471	(79*10^82347-1)/3	82349	Robert Price	11/2017
7472	(11*10^82323+91)/3	82323	Robert Price	02/2017
7473	(189977#+19081)/(19081*17260483)	82317	Makoto Morimoto	10/2017
7474	(189977#+196924)/(271354128874441)	82316	Makoto Morimoto	10/2017
7475	15^69984+32	82308	Lelio R Paula	11/2015
7476	9*6^105746+7	82288	Lelio R Paula	10/2014
7477	89^42211-88	82286	Norbert Schneider	01/2016
7478	gcd(V(1476435),5F(295287)(F(295287)+1)+1)	82281	Serge Batalov	04/2015
7479	20596^9883+9883^20596	82279	Hans Havermann	06/2020
7480	(19*10^82270-43)/3	82271	Robert Price	10/2017
7481	2^273282-110241	82267	Enzo Doria	05/2014
7482	(2^273277+3746)/2	82265	Stefano Morozzi	01/2020
7483	(13^73849+4^73849)/17	82263	Robert Price	05/2013
7484	10^82254+9^(82254+1)	82255	Robert Price	08/2016
7485	10^82254+457773	82255	Patrick De Geest	12/2016
7486	10^82254-99609	82254	Patrick De Geest	12/2016
7487	(754*10^82250-7)/9	82252	Robert Price	11/2017
7488	18^65524+13	82251	Lelio R Paula	11/2015
7489	2^273206-107	82244	Lelio R Paula	06/2012
7490	2^273193-459145	82240	Enzo Doria	05/2015
7492	2^273126+36937	82220	Yves Minet	06/2010
7491	39505!2+128	82220	Robert Price	03/2015
7493	(2^273090+2214)/2	82208	Stefano Morozzi	01/2020
7494	2^273053-112111	82198	Enzo Doria	06/2014
7495	(2^273052+3138)/2	82197	Stefano Morozzi	01/2020
7496	2^273016+1185	82187	Lelio R Paula	07/2013
7497	(2^273008+3)/7	82183	Lelio R Paula	12/2012
7498	(2^272992+2230)/2	82179	Stefano Morozzi	01/2020
7500	5^117554-15386	82167	Enzo Doria	02/2013
7499	21158^7647+7647^21158	82167	Hans Havermann	06/2020

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Probable Primes Top 10000

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