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 (> 30000)	Who ?	When ?
7252	2^203642+39	61303	Lelio R Paula	08/2011
7251	floor(Pi*10^61382)%(10^61303)	61303	Serge Batalov	07/2012
7253	11^58849-6040	61285	Enzo Doria	02/2013
7254	43694!3-3	61264	Robert Price	10/2014
7255	58(10^(320420)-1)/111-1	61260	Robert Price	10/2014
7256	2^203490+12909	61257	Lelio R Paula	10/2011
7257	(16*10^61251-31)/3	61252	Robert Price	03/2016
7258	20^47077-5703	61249	Enzo Doria	03/2013
7259	2^203434-113081	61240	Enzo Doria	07/2014
7260	5^87606+4	61234	Wojciech Florek	11/2005
7261	2^203412-167	61234	Lelio R Paula	08/2011
7262	2^203402+1089	61231	Lelio R Paula	10/2011
7263	(8*10^61230+67)/3	61231	Robert Price	01/2017
7264	(2^203408+lucasV(1,2,203408)+1)/(2*32993)	61228	Mike Oakes	11/2016
7265	1265^19732+19732^1265	61211	Serge Batalov	05/2014
7266	2^203330+145	61209	Lelio R Paula	08/2011
7267	6^78647-137	61200	Lelio R Paula	04/2013
7268	85^31718+84	61198	Norbert Schneider	10/2015
7269	11^58763-270	61196	Enzo Doria	07/2012
7270	2^203285-112321	61195	Enzo Doria	06/2014
7271	2^203253-995143	61186	Paul Bourdelais	11/2012
7272	15319^9862+9862^15319	61184	Hans Havermann	07/2016
7273	7^72395-44	61181	Lelio R Paula	04/2013
7274	5*2^203176-7	61163	Lelio R Paula	04/2014
7276	7^72358+54	61150	Lelio R Paula	04/2013
7275	2^203133-111775	61150	Enzo Doria	05/2014
7277	(lucasV(1,2,406356)+2)/(3^251119315836979671743)	61145	Mike Oakes	01/2017
7278	2^203112-18009	61143	Enzo Doria	05/2013
7279	43607!3+729	61129	Robert Price	09/2014
7280	2^203065-114853	61129	Enzo Doria	05/2015
7281	3^128111+196	61125	Lelio R Paula	04/2013
7282	128^29007+29007^128	61124	Serge Batalov	05/2014
7283	4*10^61119+49	61120	Robert Price	08/2017
7284	22355*2^203009-3	61117	Donovan Johnson	03/2004
7285	2^203018+33	61115	Lelio R Paula	08/2011
7286	2^203017-1615	61115	Lelio R Paula	10/2011
7287	16697^4570+4570^16697	61110	Hans Havermann	12/2016
7288	2^202998-17241	61109	Enzo Doria	05/2013
7289	20^46964+93	61102	Lelio R Paula	06/2013
7290	(55*10^61097-1)/9	61098	Ray Chandler	02/2012
7291	20^46960-5463	61097	Enzo Doria	03/2013
7292	(11*10^61095+49)/3	61096	Robert Price	05/2016
7293	2^202934-5955	61090	Lelio R Paula	10/2011
7294	19^47772-68	61089	Lelio R Paula	05/2013
7295	2^202877-499423	61073	Paul Bourdelais	03/2013
7296	2^202763-17125	61038	Enzo Doria	05/2013
7297	(23*2^202756+1)/9	61037	Lelio R Paula	03/2012
7298	14788^13355+13355^14788	61011	Hans Havermann	12/2016
7299	16069^6258+6258^16069	61005	Hans Havermann	12/2016
7300	5^87276-14336	61004	Enzo Doria	02/2013
7301	50^35899-49^35899	60992	Robert Price	12/2012
7302	2^202599-3049	60989	Yves Minet	10/2014
7303	2^202535-111571	60970	Enzo Doria	05/2014
7304	10^60959+57	60960	Patrick De Geest	12/2008
7306	10^60959-60959	60959	Henri Lifchitz	08/2002
7305	10^60959-29177	60959	Patrick De Geest	08/2008
7307	5^87206+4^(87206+1)	60955	Robert Price	07/2016
7308	2^202476-15909	60952	Enzo Doria	04/2013
7309	2^202472-17513	60951	Enzo Doria	05/2013
7310	14858^12651+12651^14858	60950	Hans Havermann	12/2016
7311	2^202389-58695	60926	Lelio R Paula	09/2011
7312	3^127597-34	60880	Lelio R Paula	04/2013
7313	15088^10831+10831^15088	60876	Hans Havermann	12/2016
7314	2^202198-113261	60868	Enzo Doria	07/2014
7315	2^202182+135	60863	Lelio R Paula	08/2011
7316	2^202176+85	60862	Lelio R Paula	08/2011
7317	5183^16384+5182^16384	60860	Henri Lifchitz	01/2007
7318	(31*2^202163+1)/3	60859	Lelio R Paula	03/2012
7319	14708^13707+13707^14708	60847	Hans Havermann	12/2016
7320	2^202112+202112^2-1	60842	Robert Price	04/2014
7321	(13*2^202142-1)/405984274257	60841	Lelio R Paula	01/2014
7322	64743*10^60832+(6^78175-11)/5	60837	Gilbert Mozzo	05/2012
7323	(19*2^202098-1)/6795	60836	Lelio R Paula	01/2014
7324	(6^78175-11)/5	60832	Paul Bourdelais	11/2011
7325	2^202063+1605	60828	Lelio R Paula	09/2011
7326	2^202058+859	60826	Lelio R Paula	09/2011
7327	1576^19021+19021^1576	60821	Serge Batalov	05/2014
7328	(2^202009+3)/6005	60807	Lelio R Paula	03/2012
7329	10^60776+3	60777	Robert Price	01/2011
7330	10^60776-14819	60776	Patrick De Geest	12/2012
7331	(6883*2^201869-1)/35	60771	Lelio R Paula	04/2015
7332	(27*2^201841-1)/43	60760	Lelio R Paula	01/2014
7333	2^201822-177	60755	Lelio R Paula	08/2011
7334	(13*10^60744+17)/3	60745	Robert Price	06/2015
7335	(31*2^201754-1)/99	60734	Lelio R Paula	01/2014
7336	(26*10^60717-71)/9	60718	Robert Price	03/2015
7337	37^38712-2	60709	Lelio R Paula	08/2013
7338	2^201657-112003	60705	Enzo Doria	05/2014
7339	(10^60703+3^60703)/13	60702	Robert Price	01/2013
7340	2^201622-112817	60695	Enzo Doria	06/2014
7341	2^201620-17177	60694	Enzo Doria	05/2013
7342	(2^201615-3)*6-7	60693	Gilbert Mozzo	05/2016
7343	2^201609-49789	60691	Henri Lifchitz	03/2005
7344	2^201582-19061	60683	Enzo Doria	05/2013
7345	43316!3+27	60679	Robert Price	09/2014
7346	(509203*2^201564-1)/5067	60679	Lelio R Paula	04/2015
7347	2^201560+105	60676	Lelio R Paula	08/2011
7348	(27*2^201584-1)/646755486457	60673	Lelio R Paula	01/2014
7349	2^201545-18021	60672	Enzo Doria	05/2013
7350	2^201543+11715	60671	Lelio R Paula	09/2011
7352	2^201512-111755	60662	Enzo Doria	05/2014
7351	p(13013)#/2+64	60662	Robert Price	03/2017
7353	11^58248+16	60660	Lelio R Paula	05/2013
7354	2^201496-27	60657	Lelio R Paula	08/2011
7355	(7*10^60643+197)/3	60644	Robert Price	07/2017
7356	2^201426-16097	60636	Enzo Doria	04/2013
7357	(17*10^60631-11)/3	60632	Robert Price	07/2015
7358	6^77916-77	60631	Lelio R Paula	04/2013
7359	(27*2^201410-1)/491	60630	Lelio R Paula	01/2014
7360	5^86727+98	60620	Lelio R Paula	04/2013
7361	17^49266-26	60620	Lelio R Paula	05/2013
7362	20^46589-33	60614	Lelio R Paula	05/2013
7363	6^77889+65	60610	Lelio R Paula	04/2013
7364	139901#+148387	60595	Nicolas PALAU	09/2016
7365	2^201285-111723	60593	Enzo Doria	05/2014
7366	46199*2^201268+129647	60593	Paul Vanderveen	11/2016
7368	3^126991-100	60591	Lelio R Paula	04/2013
7367	2^201278-111623	60591	Enzo Doria	05/2014
7369	5^86682-16004	60589	Enzo Doria	05/2014
7370	(58*10^60579+221)/9	60580	Robert Price	02/2017
7371	9*2^201231-5	60578	Lelio R Paula	04/2014
7372	4*10^60572-89	60573	Robert Price	08/2017
7373	(78557*2^201207+1)/13067	60571	Lelio R Paula	06/2014
7374	2^201186-66945	60564	Lelio R Paula	09/2011
7375	2^201186-94395	60564	Lelio R Paula	09/2011
7376	65^33403+32	60557	Lelio R Paula	01/2016
7377	103^30079+102	60545	Norbert Schneider	10/2016
7378	(1000159^10091+1)/1000160	60541	Faysal YAtim	08/2008
7379	2^201098-17717	60537	Enzo Doria	05/2013
7380	(3^126881+8)/4829	60534	Lelio R Paula	03/2012
7381	2^201074+75049	60530	Enzo Doria	04/2016
7382	11^58111-1290	60517	Enzo Doria	11/2012
7383	(509203*2^201012-1)/9	60516	Lelio R Paula	04/2015
7384	2^200911+5711	60481	Lelio R Paula	10/2011
7385	(2^200912-3)/23	60480	Lelio R Paula	03/2012
7386	18^48179-17^48179	60478	Jean-Louis Charton	12/2010
7388	38^38281-37^38281	60476	Robert Price	09/2012
7387	4*7^71560-3	60476	Lelio R Paula	09/2014
7389	(10^(230232+1)+1510^30232-1)/3	60465	Robert Price	04/2016
7390	lucasV(1,2,401712)+2	60464	Mike Oakes	01/2017
7391	2^200833-18493	60457	Enzo Doria	05/2013
7392	20^46465-5043	60453	Enzo Doria	03/2013
7393	2^200810-18257	60450	Enzo Doria	05/2013
7394	5^86466-14336	60438	Enzo Doria	02/2013
7395	Phi(145558,10)/103928413/161714939/14779231531/36075385837/242411419853	60432	Maksym Voznyy	10/2011
7396	(29*2^200703-1)/231	60417	Lelio R Paula	01/2014
7397	2^200682-1016831	60412	Paul Bourdelais	11/2012
7398	2^200617-17881	60392	Enzo Doria	05/2013
7399	(25^43201+1)/26	60391	Robert Price	06/2013
7401	2^200609-133	60390	Lelio R Paula	08/2011
7400	2^200608-12837	60390	Enzo Doria	10/2012
7402	2^200607-17121	60389	Enzo Doria	05/2013
7403	11^57975-1620	60375	Enzo Doria	11/2012
7404	(9913*2^200538-1)/3801	60369	Lelio R Paula	04/2015
7405	5^86342+64	60351	Lelio R Paula	04/2013
7406	(14*10^60346-23)/9	60347	Robert Price	04/2015
7407	2^200457-8295	60344	Lelio R Paula	09/2011
7408	6^77546+113	60343	Lelio R Paula	04/2013
7410	37^38461-36^38461	60315	Robert Price	06/2012
7409	2^200361-17593	60315	Enzo Doria	05/2013
7411	10103^15059-106	60304	Enzo Doria	07/2012
7412	2^200301-17401	60297	Enzo Doria	05/2013
7413	(37*10^60290+71)/9	60291	Robert Price	04/2015
7414	2^200266-94395	60287	Lelio R Paula	09/2011
7415	2^200261-111613	60285	Enzo Doria	05/2014
7416	46^36238-45	60256	Norbert Schneider	07/2014
7417	13^54091+94	60255	Lelio R Paula	05/2013
7418	311^24171-154	60253	Enzo Doria	07/2012
7419	2^200120-81089	60243	Paul Bourdelais	01/2012
7420	3^126262+8680	60243	Lelio R Paula	04/2013
7421	43031!3-59049	60239	Robert Price	12/2015
7422	2^200100-111269	60237	Enzo Doria	05/2014
7423	(29*2^200069-1)/5373	60225	Lelio R Paula	01/2014
7424	20^46283-1923	60216	Enzo Doria	03/2013
7425	2^200011-112075	60210	Enzo Doria	05/2014
7426	2^200002+74539	60207	Enzo Doria	04/2016
7427	(386027912^200026-1)/(5778492645749*3427009)	60203	Jens K. Andersen	09/2007
7428	2^199872+93	60168	Donovan Johnson	06/2008
7429	6^77321+77	60168	Lelio R Paula	04/2013
7430	(86*10^60165-77)/9	60166	Robert Price	05/2016
7431	(2^199868+78557)/23373	60162	Lelio R Paula	05/2012
7432	7^71180+82	60155	Lelio R Paula	04/2013
7433	2^199814-112295	60151	Enzo Doria	06/2014
7434	42964!3-81	60135	Robert Price	09/2014
7435	2^199709-51	60119	Lelio R Paula	05/2011
7436	2^199700-111623	60116	Enzo Doria	05/2014
7437	(15185*2^199681-1)/159	60112	Lelio R Paula	04/2015
7438	2^199672+2533	60108	Henri Lifchitz	09/2004
7439	20^46198-11	60105	Lelio R Paula	04/2013
7440	2^199657+93257	60103	Yves Minet	03/2010
7441	3^125967-110	60102	Lelio R Paula	10/2012
7442	2^199654-18813	60102	Enzo Doria	05/2013
7443	(29*10^60100+19)/3	60101	Robert Price	01/2017
7444	129^28468+28468^129	60085	Serge Batalov	05/2014
7445	2^199572-15873	60078	Enzo Doria	04/2013
7446	9*2^199559+7	60075	Lelio R Paula	03/2014
7447	2^199527-111919	60064	Enzo Doria	05/2014
7448	2^199522+82875	60063	Lelio R Paula	10/2012
7449	5^85928-72	60062	Lelio R Paula	10/2012
7450	39^37749+38	60062	Norbert Schneider	05/2014
7451	6^77182-143	60060	Lelio R Paula	10/2012
7452	2^199502-2145	60057	Lelio R Paula	06/2011
7453	2^199493+4257	60054	Lelio R Paula	06/2011
7454	2^199488+40755	60052	Lelio R Paula	06/2011
7455	(2^199451+9)/25619	60037	Lelio R Paula	02/2012
7456	2^199425-61	60033	Lelio R Paula	05/2011
7457	(85*10^60026+23)/9	60027	Robert Price	11/2015
7458	65^33107+62	60021	Lelio R Paula	01/2016
7460	2^199362-1215	60014	Lelio R Paula	06/2011
7459	2^199362-111633	60014	Enzo Doria	05/2014
7461	1537^18832+18832^1537	60012	Serge Batalov	05/2014
7462	2^199324-17433	60003	Enzo Doria	05/2013
7463	10^60000+204331	60001	Milton L. Brown	04/2006
7464	10^60000+87129	60001	Milton L. Brown	04/2006
7465	10^59999+65197	60000	Patrick De Geest	04/2005
7466	10^60000-32529	60000	Patrick De Geest	08/2009
7467	(10^60000+2249)/9	60000	Makoto Morimoto	09/2016
7468	((2^43112609)/10^24296)%10^60000	60000	Michael Vang	10/2016
7469	(2^57885161/10^105090)%10^60000	60000	Michael Vang	10/2016
7470	(2^42643801/10^58945)%10^60000	60000	Michael Vang	10/2016
7471	(2^37156667/10^243655)%10^60000	60000	Michael Vang	10/2016
7472	(2^30402457/10^69028)%10^60000	60000	Michael Vang	11/2016
7473	(2^32582657/10^248088)%10^60000	60000	Michael Vang	11/2016
7474	(2^32582657/10^238942)%10^60000	60000	Michael Vang	11/2016
7475	(2^24036583/10^13547)%10^60000	60000	Michael Vang	11/2016
7476	(2^20996011/10^131008)%10^60000	60000	Michael Vang	11/2016
7477	(2^13466917/10^79774)%10^60000	60000	Michael Vang	11/2016
7478	(2^13466917/10^102581)%10^60000	60000	Michael Vang	11/2016
7479	(2^6972593/10^339640)%10^60000	60000	Michael Vang	11/2016
7480	(2^2976221/10^65464)%10^60000	60000	Michael Vang	12/2016
7481	(2^1398269/10^61138)%10^60000	60000	Michael Vang	12/2016
7482	(2^3021377/10^418881)%10^60000	60000	Michael Vang	12/2016
7483	(2^1257787/10^164080)%10^60000	60000	Michael Vang	12/2016
7486	10^59999-516267	59999	Patrick De Geest	06/2009
7485	20^46116-41	59999	Lelio R Paula	03/2013
7487	(2^74207281/10^184638)%10^60000	59999	Michael Vang	10/2016
7484	(2^25964951/10^135429)%10^60000	59999	Michael Vang	11/2016
7488	6^77100-55	59996	Lelio R Paula	10/2012
7490	(19*2^199274+1)/161	59987	Lelio R Paula	07/2012
7489	(23^44053+1)/24	59987	Robert Price	06/2013
7491	9^62848+6^62848-2^62848	59973	Mike Oakes	08/2010
7492	15852^6061+6061^15852	59961	Hans Havermann	08/2016
7493	19^46880-20	59948	Lelio R Paula	03/2013
7494	2^199107-17737	59938	Enzo Doria	05/2013
7495	(13*10^59928+83)/3	59929	Robert Price	09/2016
7496	10^59913+108931431	59914	Marisa Kirisame	02/2015
7497	10^59913+48619	59914	Patrick De Geest	04/2016
7498	10^59913-74123	59913	Patrick De Geest	03/2016
7499	t(199528)	59890	Robert Price	01/2015
7500	2^198903-17901	59876	Enzo Doria	05/2013

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Probable Primes Top 10000

(180278 PRPs in the top)