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 ?
7251	2^202182+135	60863	Lelio R Paula	08/2011
7252	2^202176+85	60862	Lelio R Paula	08/2011
7253	5183^16384+5182^16384	60860	Henri Lifchitz	01/2007
7254	(31*2^202163+1)/3	60859	Lelio R Paula	03/2012
7255	14708^13707+13707^14708	60847	Hans Havermann	12/2016
7256	2^202112+202112^2-1	60842	Robert Price	04/2014
7257	(13*2^202142-1)/405984274257	60841	Lelio R Paula	01/2014
7258	64743*10^60832+(6^78175-11)/5	60837	Gilbert Mozzo	05/2012
7259	(19*2^202098-1)/6795	60836	Lelio R Paula	01/2014
7260	(6^78175-11)/5	60832	Paul Bourdelais	11/2011
7261	2^202063+1605	60828	Lelio R Paula	09/2011
7262	2^202058+859	60826	Lelio R Paula	09/2011
7263	1576^19021+19021^1576	60821	Serge Batalov	05/2014
7264	(2^202009+3)/6005	60807	Lelio R Paula	03/2012
7265	10^60776+3	60777	Robert Price	01/2011
7266	10^60776-14819	60776	Patrick De Geest	12/2012
7267	(6883*2^201869-1)/35	60771	Lelio R Paula	04/2015
7268	(27*2^201841-1)/43	60760	Lelio R Paula	01/2014
7269	2^201822-177	60755	Lelio R Paula	08/2011
7270	(13*10^60744+17)/3	60745	Robert Price	06/2015
7271	(31*2^201754-1)/99	60734	Lelio R Paula	01/2014
7272	(26*10^60717-71)/9	60718	Robert Price	03/2015
7273	37^38712-2	60709	Lelio R Paula	08/2013
7274	2^201657-112003	60705	Enzo Doria	05/2014
7275	(10^60703+3^60703)/13	60702	Robert Price	01/2013
7276	2^201622-112817	60695	Enzo Doria	06/2014
7277	2^201620-17177	60694	Enzo Doria	05/2013
7278	(2^201615-3)*6-7	60693	Gilbert Mozzo	05/2016
7279	2^201609-49789	60691	Henri Lifchitz	03/2005
7280	2^201582-19061	60683	Enzo Doria	05/2013
7281	43316!3+27	60679	Robert Price	09/2014
7282	(509203*2^201564-1)/5067	60679	Lelio R Paula	04/2015
7283	2^201560+105	60676	Lelio R Paula	08/2011
7284	(27*2^201584-1)/646755486457	60673	Lelio R Paula	01/2014
7285	2^201545-18021	60672	Enzo Doria	05/2013
7286	2^201543+11715	60671	Lelio R Paula	09/2011
7287	2^201512-111755	60662	Enzo Doria	05/2014
7288	p(13013)#/2+64	60662	Robert Price	03/2017
7289	11^58248+16	60660	Lelio R Paula	05/2013
7290	2^201496-27	60657	Lelio R Paula	08/2011
7291	2^201426-16097	60636	Enzo Doria	04/2013
7292	(17*10^60631-11)/3	60632	Robert Price	07/2015
7293	6^77916-77	60631	Lelio R Paula	04/2013
7294	(27*2^201410-1)/491	60630	Lelio R Paula	01/2014
7295	5^86727+98	60620	Lelio R Paula	04/2013
7296	17^49266-26	60620	Lelio R Paula	05/2013
7297	20^46589-33	60614	Lelio R Paula	05/2013
7298	6^77889+65	60610	Lelio R Paula	04/2013
7299	139901#+148387	60595	Nicolas PALAU	09/2016
7301	2^201285-111723	60593	Enzo Doria	05/2014
7300	46199*2^201268+129647	60593	Paul Vanderveen	11/2016
7303	3^126991-100	60591	Lelio R Paula	04/2013
7302	2^201278-111623	60591	Enzo Doria	05/2014
7304	5^86682-16004	60589	Enzo Doria	05/2014
7305	(58*10^60579+221)/9	60580	Robert Price	02/2017
7306	9*2^201231-5	60578	Lelio R Paula	04/2014
7307	(78557*2^201207+1)/13067	60571	Lelio R Paula	06/2014
7308	2^201186-66945	60564	Lelio R Paula	09/2011
7309	2^201186-94395	60564	Lelio R Paula	09/2011
7310	65^33403+32	60557	Lelio R Paula	01/2016
7311	103^30079+102	60545	Norbert Schneider	10/2016
7312	(1000159^10091+1)/1000160	60541	Faysal YAtim	08/2008
7313	2^201098-17717	60537	Enzo Doria	05/2013
7314	(3^126881+8)/4829	60534	Lelio R Paula	03/2012
7315	2^201074+75049	60530	Enzo Doria	04/2016
7316	11^58111-1290	60517	Enzo Doria	11/2012
7317	(509203*2^201012-1)/9	60516	Lelio R Paula	04/2015
7318	2^200911+5711	60481	Lelio R Paula	10/2011
7319	(2^200912-3)/23	60480	Lelio R Paula	03/2012
7320	18^48179-17^48179	60478	Jean-Louis Charton	12/2010
7322	38^38281-37^38281	60476	Robert Price	09/2012
7321	4*7^71560-3	60476	Lelio R Paula	09/2014
7323	(10^(230232+1)+1510^30232-1)/3	60465	Robert Price	04/2016
7324	lucasV(1,2,401712)+2	60464	Mike Oakes	01/2017
7325	2^200833-18493	60457	Enzo Doria	05/2013
7326	20^46465-5043	60453	Enzo Doria	03/2013
7327	2^200810-18257	60450	Enzo Doria	05/2013
7328	5^86466-14336	60438	Enzo Doria	02/2013
7329	Phi(145558,10)/103928413/161714939/14779231531/36075385837/242411419853	60432	Maksym Voznyy	10/2011
7330	(29*2^200703-1)/231	60417	Lelio R Paula	01/2014
7331	2^200682-1016831	60412	Paul Bourdelais	11/2012
7332	2^200617-17881	60392	Enzo Doria	05/2013
7333	(25^43201+1)/26	60391	Robert Price	06/2013
7335	2^200609-133	60390	Lelio R Paula	08/2011
7334	2^200608-12837	60390	Enzo Doria	10/2012
7336	2^200607-17121	60389	Enzo Doria	05/2013
7337	11^57975-1620	60375	Enzo Doria	11/2012
7338	(9913*2^200538-1)/3801	60369	Lelio R Paula	04/2015
7339	5^86342+64	60351	Lelio R Paula	04/2013
7340	(14*10^60346-23)/9	60347	Robert Price	04/2015
7341	2^200457-8295	60344	Lelio R Paula	09/2011
7342	6^77546+113	60343	Lelio R Paula	04/2013
7344	37^38461-36^38461	60315	Robert Price	06/2012
7343	2^200361-17593	60315	Enzo Doria	05/2013
7345	10103^15059-106	60304	Enzo Doria	07/2012
7346	2^200301-17401	60297	Enzo Doria	05/2013
7347	(37*10^60290+71)/9	60291	Robert Price	04/2015
7348	2^200266-94395	60287	Lelio R Paula	09/2011
7349	2^200261-111613	60285	Enzo Doria	05/2014
7350	46^36238-45	60256	Norbert Schneider	07/2014
7351	13^54091+94	60255	Lelio R Paula	05/2013
7352	311^24171-154	60253	Enzo Doria	07/2012
7353	2^200120-81089	60243	Paul Bourdelais	01/2012
7354	3^126262+8680	60243	Lelio R Paula	04/2013
7355	43031!3-59049	60239	Robert Price	12/2015
7356	2^200100-111269	60237	Enzo Doria	05/2014
7357	(29*2^200069-1)/5373	60225	Lelio R Paula	01/2014
7358	20^46283-1923	60216	Enzo Doria	03/2013
7359	2^200011-112075	60210	Enzo Doria	05/2014
7360	2^200002+74539	60207	Enzo Doria	04/2016
7361	(386027912^200026-1)/(5778492645749*3427009)	60203	Jens K. Andersen	09/2007
7362	2^199872+93	60168	Donovan Johnson	06/2008
7363	6^77321+77	60168	Lelio R Paula	04/2013
7364	(86*10^60165-77)/9	60166	Robert Price	05/2016
7365	(2^199868+78557)/23373	60162	Lelio R Paula	05/2012
7366	7^71180+82	60155	Lelio R Paula	04/2013
7367	2^199814-112295	60151	Enzo Doria	06/2014
7368	42964!3-81	60135	Robert Price	09/2014
7369	2^199709-51	60119	Lelio R Paula	05/2011
7370	2^199700-111623	60116	Enzo Doria	05/2014
7371	(15185*2^199681-1)/159	60112	Lelio R Paula	04/2015
7372	2^199672+2533	60108	Henri Lifchitz	09/2004
7373	20^46198-11	60105	Lelio R Paula	04/2013
7374	2^199657+93257	60103	Yves Minet	03/2010
7375	3^125967-110	60102	Lelio R Paula	10/2012
7376	2^199654-18813	60102	Enzo Doria	05/2013
7377	(29*10^60100+19)/3	60101	Robert Price	01/2017
7378	129^28468+28468^129	60085	Serge Batalov	05/2014
7379	2^199572-15873	60078	Enzo Doria	04/2013
7380	9*2^199559+7	60075	Lelio R Paula	03/2014
7381	2^199527-111919	60064	Enzo Doria	05/2014
7382	2^199522+82875	60063	Lelio R Paula	10/2012
7383	5^85928-72	60062	Lelio R Paula	10/2012
7384	39^37749+38	60062	Norbert Schneider	05/2014
7385	6^77182-143	60060	Lelio R Paula	10/2012
7386	2^199502-2145	60057	Lelio R Paula	06/2011
7387	2^199493+4257	60054	Lelio R Paula	06/2011
7388	2^199488+40755	60052	Lelio R Paula	06/2011
7389	(2^199451+9)/25619	60037	Lelio R Paula	02/2012
7390	2^199425-61	60033	Lelio R Paula	05/2011
7391	(85*10^60026+23)/9	60027	Robert Price	11/2015
7392	65^33107+62	60021	Lelio R Paula	01/2016
7394	2^199362-1215	60014	Lelio R Paula	06/2011
7393	2^199362-111633	60014	Enzo Doria	05/2014
7395	1537^18832+18832^1537	60012	Serge Batalov	05/2014
7396	2^199324-17433	60003	Enzo Doria	05/2013
7397	10^60000+204331	60001	Milton L. Brown	04/2006
7398	10^60000+87129	60001	Milton L. Brown	04/2006
7399	10^59999+65197	60000	Patrick De Geest	04/2005
7400	10^60000-32529	60000	Patrick De Geest	08/2009
7414	(10^60000+2249)/9	60000	Makoto Morimoto	09/2016
7415	((2^43112609)/10^24296)%10^60000	60000	Michael Vang	10/2016
7416	(2^57885161/10^105090)%10^60000	60000	Michael Vang	10/2016
7417	(2^42643801/10^58945)%10^60000	60000	Michael Vang	10/2016
7401	(2^37156667/10^243655)%10^60000	60000	Michael Vang	10/2016
7402	(2^30402457/10^69028)%10^60000	60000	Michael Vang	11/2016
7403	(2^32582657/10^248088)%10^60000	60000	Michael Vang	11/2016
7404	(2^32582657/10^238942)%10^60000	60000	Michael Vang	11/2016
7405	(2^24036583/10^13547)%10^60000	60000	Michael Vang	11/2016
7406	(2^20996011/10^131008)%10^60000	60000	Michael Vang	11/2016
7407	(2^13466917/10^79774)%10^60000	60000	Michael Vang	11/2016
7408	(2^13466917/10^102581)%10^60000	60000	Michael Vang	11/2016
7409	(2^6972593/10^339640)%10^60000	60000	Michael Vang	11/2016
7410	(2^2976221/10^65464)%10^60000	60000	Michael Vang	12/2016
7411	(2^1398269/10^61138)%10^60000	60000	Michael Vang	12/2016
7412	(2^3021377/10^418881)%10^60000	60000	Michael Vang	12/2016
7413	(2^1257787/10^164080)%10^60000	60000	Michael Vang	12/2016
7421	10^59999-516267	59999	Patrick De Geest	06/2009
7420	20^46116-41	59999	Lelio R Paula	03/2013
7418	(2^74207281/10^184638)%10^60000	59999	Michael Vang	10/2016
7419	(2^25964951/10^135429)%10^60000	59999	Michael Vang	11/2016
7422	6^77100-55	59996	Lelio R Paula	10/2012
7424	(19*2^199274+1)/161	59987	Lelio R Paula	07/2012
7423	(23^44053+1)/24	59987	Robert Price	06/2013
7425	9^62848+6^62848-2^62848	59973	Mike Oakes	08/2010
7426	15852^6061+6061^15852	59961	Hans Havermann	08/2016
7427	19^46880-20	59948	Lelio R Paula	03/2013
7428	2^199107-17737	59938	Enzo Doria	05/2013
7429	(13*10^59928+83)/3	59929	Robert Price	09/2016
7430	10^59913+108931431	59914	Marisa Kirisame	02/2015
7431	10^59913+48619	59914	Patrick De Geest	04/2016
7432	10^59913-74123	59913	Patrick De Geest	03/2016
7433	t(199528)	59890	Robert Price	01/2015
7434	2^198903-17901	59876	Enzo Doria	05/2013
7435	gcd(V(776555),5F(155311)(F(155311)+1)+1)	59858	Serge Batalov	04/2015
7436	(3^125447+7)/2	59854	Lelio R Paula	04/2012
7437	5^85630+4^(85630-1)	59853	Robert Price	03/2016
7438	2^198824-2135	59852	Yves Minet	06/2013
7439	2^198799-16117	59845	Enzo Doria	04/2013
7440	7^70811+6^(70811+1)	59843	Robert Price	07/2016
7441	2^198774-15945	59837	Enzo Doria	04/2013
7442	2^198753-15873	59831	Enzo Doria	04/2013
7443	(31*2^198748-1)/45	59829	Lelio R Paula	01/2014
7444	2^198725+69	59823	Lelio R Paula	04/2011
7445	(68*10^59821+31)/9	59822	Robert Price	10/2015
7446	(37*25^42785+1867)/8	59812	Curtis Bright	05/2015
7448	3^125354+2660	59810	Lelio R Paula	10/2012
7447	105^29591-104	59810	Norbert Schneider	08/2013
7449	4*5^85565-3	59808	Lelio R Paula	09/2014
7450	13963842222*Bern(19550)/55727275	59803	Thomas Ritschel	03/2014
7452	125330^3+3^125330	59798	Anatoly F. Selevich	06/2010
7451	2^198643-3189	59798	Yves Minet	10/2014
7453	(7*10^59796-1)/3	59797	Erik Branger	03/2014
7454	2^198595+153	59784	Lelio R Paula	04/2011
7455	(19*10^59766+161)/9	59767	Robert Price	07/2016
7456	2^198510-1965	59758	Lelio R Paula	06/2011
7457	2^198506-19077	59757	Enzo Doria	05/2013
7458	2^198484-16005	59750	Enzo Doria	04/2013
7459	2^198473-16821	59747	Enzo Doria	05/2013
7460	(2^198481-5)/28311	59745	Lelio R Paula	02/2012
7461	2^198400-189	59725	Lelio R Paula	04/2011
7462	2^198384-12837	59720	Enzo Doria	10/2012
7463	42694!3-729	59719	Robert Price	09/2014
7464	2^198320-18717	59701	Enzo Doria	05/2013
7465	20^45881-1183	59693	Enzo Doria	03/2013
7466	2^198224-6855	59672	Lelio R Paula	05/2011
7467	2^198181-19101	59659	Enzo Doria	05/2013
7468	2^198149-112213	59649	Enzo Doria	06/2014
7469	2^198138+73699	59646	Enzo Doria	04/2016
7470	2^198129-55	59643	Lelio R Paula	04/2011
7471	5^85318-14636	59635	Enzo Doria	02/2013
7472	(2^198119+47)/1560935	59634	Lelio R Paula	02/2012
7473	2^198090-16097	59632	Enzo Doria	04/2013
7474	9*10^59617+89	59618	Robert Price	11/2016
7475	42625!3+81	59612	Robert Price	09/2014
7476	5^85277-84	59607	Lelio R Paula	10/2012
7477	2^197984-18245	59600	Enzo Doria	05/2013
7478	2^197951-2137	59590	Yves Minet	06/2013
7479	66^32749-65^32749	59589	Robert Price	09/2013
7480	5*10^59586-3	59587	Dmitry Domanov	11/2010
7481	2^197932-3959	59584	Yves Minet	04/2017
7482	2^197909-18961	59577	Enzo Doria	05/2013
7483	(3^124871+2)/45031	59574	Lelio R Paula	04/2012
7485	2^197872+81	59566	Henri Lifchitz	10/2005
7484	2^197873-18469	59566	Enzo Doria	05/2013
7486	(22*10^59558-31)/9	59559	Robert Price	04/2015
7488	2^197840-465	59556	Lelio R Paula	05/2011
7487	(31*2^197856-1)/3889605	59556	Lelio R Paula	01/2014
7489	2^197808-17805	59547	Enzo Doria	05/2013
7490	2^197781-17905	59539	Enzo Doria	05/2013
7491	2^197777-17473	59537	Enzo Doria	05/2013
7492	6^76507-149	59535	Lelio R Paula	10/2012
7494	Phi(61456,109)	59526	Enzo Doria	05/2012
7493	18^47420+23	59526	Lelio R Paula	03/2013
7495	3^124747+94	59520	Lelio R Paula	10/2012
7496	17^48370+18	59517	Lelio R Paula	03/2013
7497	20^45740-1523	59510	Enzo Doria	03/2013
7498	(7*2^197642-1)/3051	59494	Lelio R Paula	01/2014
7499	18^47390-1853	59488	Enzo Doria	03/2013
7500	(2^197581-7)/1915	59475	Lelio R Paula	02/2012

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PRP Records

Probable Primes Top 10000

(174961 PRPs in the top)