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 ?
8251	10^60776+3	60777	Robert Price	01/2011
8252	10^60776-14819	60776	Patrick De Geest	12/2012
8253	55*10^60772+7	60774	Robert Price	10/2017
8254	(6883*2^201869-1)/35	60771	Lelio R Paula	04/2015
8255	(27*2^201841-1)/43	60760	Lelio R Paula	01/2014
8256	2^201822-177	60755	Lelio R Paula	08/2011
8257	(13*10^60744+17)/3	60745	Robert Price	06/2015
8258	(31*2^201754-1)/99	60734	Lelio R Paula	01/2014
8259	(26*10^60717-71)/9	60718	Robert Price	03/2015
8260	37^38712-2	60709	Lelio R Paula	08/2013
8261	2^201657-112003	60705	Enzo Doria	05/2014
8262	(10^60703+3^60703)/13	60702	Robert Price	01/2013
8263	2^201622-112817	60695	Enzo Doria	06/2014
8264	2^201620-17177	60694	Enzo Doria	05/2013
8265	(2^201615-3)*6-7	60693	Gilbert Mozzo	05/2016
8266	2^201609-49789	60691	Henri Lifchitz	03/2005
8267	2^201582-19061	60683	Enzo Doria	05/2013
8268	43316!3+27	60679	Robert Price	09/2014
8269	(509203*2^201564-1)/5067	60679	Lelio R Paula	04/2015
8270	2^201560+105	60676	Lelio R Paula	08/2011
8271	(27*2^201584-1)/646755486457	60673	Lelio R Paula	01/2014
8272	2^201545-18021	60672	Enzo Doria	05/2013
8273	2^201543+11715	60671	Lelio R Paula	09/2011
8274	2^201512-111755	60662	Enzo Doria	05/2014
8275	p(13013)#/2+64	60662	Robert Price	03/2017
8276	11^58248+16	60660	Lelio R Paula	05/2013
8277	2^201496-27	60657	Lelio R Paula	08/2011
8278	5*10^60655+57	60656	Robert Price	11/2017
8279	(7*10^60643+197)/3	60644	Robert Price	07/2017
8280	2^201426-16097	60636	Enzo Doria	04/2013
8281	(17*10^60631-11)/3	60632	Robert Price	07/2015
8282	6^77916-77	60631	Lelio R Paula	04/2013
8283	(27*2^201410-1)/491	60630	Lelio R Paula	01/2014
8284	5^86727+98	60620	Lelio R Paula	04/2013
8285	17^49266-26	60620	Lelio R Paula	05/2013
8286	20^46589-33	60614	Lelio R Paula	05/2013
8287	6^77889+65	60610	Lelio R Paula	04/2013
8288	139901#+148387	60595	Nicolas PALAU	09/2016
8289	2^201285-111723	60593	Enzo Doria	05/2014
8290	46199*2^201268+129647	60593	Paul Vanderveen	11/2016
8292	3^126991-100	60591	Lelio R Paula	04/2013
8291	2^201278-111623	60591	Enzo Doria	05/2014
8293	5^86682-16004	60589	Enzo Doria	05/2014
8294	(865*10^60583-1)/9	60585	Robert Price	11/2017
8295	(58*10^60579+221)/9	60580	Robert Price	02/2017
8296	9*2^201231-5	60578	Lelio R Paula	04/2014
8297	4*10^60572-89	60573	Robert Price	08/2017
8298	(78557*2^201207+1)/13067	60571	Lelio R Paula	06/2014
8299	2^201186-66945	60564	Lelio R Paula	09/2011
8300	2^201186-94395	60564	Lelio R Paula	09/2011
8301	65^33403+32	60557	Lelio R Paula	01/2016
8302	103^30079+102	60545	Norbert Schneider	10/2016
8303	(1000159^10091+1)/1000160	60541	Faysal YAtim	08/2008
8304	2^201098-17717	60537	Enzo Doria	05/2013
8305	(3^126881+8)/4829	60534	Lelio R Paula	03/2012
8306	2^201074+75049	60530	Enzo Doria	04/2016
8307	11^58111-1290	60517	Enzo Doria	11/2012
8308	(509203*2^201012-1)/9	60516	Lelio R Paula	04/2015
8309	2^200911+5711	60481	Lelio R Paula	10/2011
8310	(2^200912-3)/23	60480	Lelio R Paula	03/2012
8311	18^48179-17^48179	60478	Jean-Louis Charton	12/2010
8313	38^38281-37^38281	60476	Robert Price	09/2012
8312	4*7^71560-3	60476	Lelio R Paula	09/2014
8314	(10^(230232+1)+1510^30232-1)/3	60465	Robert Price	04/2016
8315	lucasV(1,2,401712)+2	60464	Mike Oakes	01/2017
8316	2^200833-18493	60457	Enzo Doria	05/2013
8317	20^46465-5043	60453	Enzo Doria	03/2013
8318	2^200810-18257	60450	Enzo Doria	05/2013
8319	((2)^(2*100400-1)+(2)^(100400-1)+1)+26672	60447	Faysal YAtim	04/2018
8320	5^86466-14336	60438	Enzo Doria	02/2013
8321	Phi(145558,10)/103928413/161714939/14779231531/36075385837/242411419853	60432	Maksym Voznyy	10/2011
8322	(29*2^200703-1)/231	60417	Lelio R Paula	01/2014
8323	2^200682-1016831	60412	Paul Bourdelais	11/2012
8324	2^200617-17881	60392	Enzo Doria	05/2013
8325	(25^43201+1)/26	60391	Robert Price	06/2013
8327	2^200609-133	60390	Lelio R Paula	08/2011
8326	2^200608-12837	60390	Enzo Doria	10/2012
8328	2^200607-17121	60389	Enzo Doria	05/2013
8329	11^57975-1620	60375	Enzo Doria	11/2012
8330	(9913*2^200538-1)/3801	60369	Lelio R Paula	04/2015
8331	5^86342+64	60351	Lelio R Paula	04/2013
8332	(14*10^60346-23)/9	60347	Robert Price	04/2015
8333	2^200457-8295	60344	Lelio R Paula	09/2011
8334	6^77546+113	60343	Lelio R Paula	04/2013
8336	37^38461-36^38461	60315	Robert Price	06/2012
8335	2^200361-17593	60315	Enzo Doria	05/2013
8337	10103^15059-106	60304	Enzo Doria	07/2012
8338	2^200301-17401	60297	Enzo Doria	05/2013
8339	(37*10^60290+71)/9	60291	Robert Price	04/2015
8340	2^200266-94395	60287	Lelio R Paula	09/2011
8341	2^200261-111613	60285	Enzo Doria	05/2014
8342	46^36238-45	60256	Norbert Schneider	07/2014
8343	13^54091+94	60255	Lelio R Paula	05/2013
8344	311^24171-154	60253	Enzo Doria	07/2012
8345	2^200120-81089	60243	Paul Bourdelais	01/2012
8346	3^126262+8680	60243	Lelio R Paula	04/2013
8347	43031!3-59049	60239	Robert Price	12/2015
8348	2^200100-111269	60237	Enzo Doria	05/2014
8349	(29*2^200069-1)/5373	60225	Lelio R Paula	01/2014
8350	20^46283-1923	60216	Enzo Doria	03/2013
8351	2^200011-112075	60210	Enzo Doria	05/2014
8352	2^200002+74539	60207	Enzo Doria	04/2016
8353	(386027912^200026-1)/(5778492645749*3427009)	60203	Jens K. Andersen	09/2007
8354	(28*10^60180+149)/3	60181	Robert Price	10/2017
8355	2^199872+93	60168	Donovan Johnson	06/2008
8356	6^77321+77	60168	Lelio R Paula	04/2013
8357	(86*10^60165-77)/9	60166	Robert Price	05/2016
8358	(2^199868+78557)/23373	60162	Lelio R Paula	05/2012
8359	7^71180+82	60155	Lelio R Paula	04/2013
8361	2^199814-112295	60151	Enzo Doria	06/2014
8360	(51^35227-1)/50	60151	Paul Bourdelais	08/2017
8362	42964!3-81	60135	Robert Price	09/2014
8363	2^199709-51	60119	Lelio R Paula	05/2011
8364	2^199700-111623	60116	Enzo Doria	05/2014
8365	(15185*2^199681-1)/159	60112	Lelio R Paula	04/2015
8366	2^199672+2533	60108	Henri Lifchitz	09/2004
8367	20^46198-11	60105	Lelio R Paula	04/2013
8368	2^199657+93257	60103	Yves Minet	03/2010
8369	3^125967-110	60102	Lelio R Paula	10/2012
8370	2^199654-18813	60102	Enzo Doria	05/2013
8371	(29*10^60100+19)/3	60101	Robert Price	01/2017
8372	2^199615-2*199615+1	60091	Robert Price	04/2018
8373	129^28468+28468^129	60085	Serge Batalov	05/2014
8374	2^199572-15873	60078	Enzo Doria	04/2013
8375	9*2^199559+7	60075	Lelio R Paula	03/2014
8376	2^199527-111919	60064	Enzo Doria	05/2014
8377	2^199522+82875	60063	Lelio R Paula	10/2012
8378	5^85928-72	60062	Lelio R Paula	10/2012
8379	39^37749+38	60062	Norbert Schneider	05/2014
8380	6^77182-143	60060	Lelio R Paula	10/2012
8381	2^199502-2145	60057	Lelio R Paula	06/2011
8382	2^199493+4257	60054	Lelio R Paula	06/2011
8383	2^199488+40755	60052	Lelio R Paula	06/2011
8384	(2^199451+9)/25619	60037	Lelio R Paula	02/2012
8385	2^199425-61	60033	Lelio R Paula	05/2011
8386	(85*10^60026+23)/9	60027	Robert Price	11/2015
8387	65^33107+62	60021	Lelio R Paula	01/2016
8388	2^199362-1215	60014	Lelio R Paula	06/2011
8389	2^199362-111633	60014	Enzo Doria	05/2014
8390	1537^18832+18832^1537	60012	Serge Batalov	05/2014
8391	2^199324-17433	60003	Enzo Doria	05/2013
8393	10^60000+204331	60001	Milton L. Brown	04/2006
8394	10^60000+87129	60001	Milton L. Brown	04/2006
8392	143^27838-2	60001	Lelio R Paula	10/2017
8395	10^59999+65197	60000	Patrick De Geest	04/2005
8409	10^60000-32529	60000	Patrick De Geest	08/2009
8410	(10^60000+2249)/9	60000	Makoto Morimoto	09/2016
8411	((2^43112609)/10^24296)%10^60000	60000	Michael Vang	10/2016
8412	(2^57885161/10^105090)%10^60000	60000	Michael Vang	10/2016
8413	(2^42643801/10^58945)%10^60000	60000	Michael Vang	10/2016
8396	(2^37156667/10^243655)%10^60000	60000	Michael Vang	10/2016
8397	(2^30402457/10^69028)%10^60000	60000	Michael Vang	11/2016
8398	(2^32582657/10^248088)%10^60000	60000	Michael Vang	11/2016
8399	(2^32582657/10^238942)%10^60000	60000	Michael Vang	11/2016
8400	(2^24036583/10^13547)%10^60000	60000	Michael Vang	11/2016
8401	(2^20996011/10^131008)%10^60000	60000	Michael Vang	11/2016
8402	(2^13466917/10^79774)%10^60000	60000	Michael Vang	11/2016
8403	(2^13466917/10^102581)%10^60000	60000	Michael Vang	11/2016
8404	(2^6972593/10^339640)%10^60000	60000	Michael Vang	11/2016
8405	(2^2976221/10^65464)%10^60000	60000	Michael Vang	12/2016
8406	(2^1398269/10^61138)%10^60000	60000	Michael Vang	12/2016
8407	(2^3021377/10^418881)%10^60000	60000	Michael Vang	12/2016
8408	(2^1257787/10^164080)%10^60000	60000	Michael Vang	12/2016
8416	10^59999-516267	59999	Patrick De Geest	06/2009
8417	20^46116-41	59999	Lelio R Paula	03/2013
8414	(2^74207281/10^184638)%10^60000	59999	Michael Vang	10/2016
8415	(2^25964951/10^135429)%10^60000	59999	Michael Vang	11/2016
8418	6^77100-55	59996	Lelio R Paula	10/2012
8420	(19*2^199274+1)/161	59987	Lelio R Paula	07/2012
8419	(23^44053+1)/24	59987	Robert Price	06/2013
8421	9^62848+6^62848-2^62848	59973	Mike Oakes	08/2010
8422	15852^6061+6061^15852	59961	Hans Havermann	08/2016
8423	19^46880-20	59948	Lelio R Paula	03/2013
8424	2^199107-17737	59938	Enzo Doria	05/2013
8425	(13*10^59928+83)/3	59929	Robert Price	09/2016
8426	10^59913+108931431	59914	Marisa Kirisame	02/2015
8427	10^59913+48619	59914	Patrick De Geest	04/2016
8428	10^59913-74123	59913	Patrick De Geest	03/2016
8429	t(199528)	59890	Robert Price	01/2015
8430	2^198903-17901	59876	Enzo Doria	05/2013
8431	9*10^59862-19	59863	Robert Price	10/2017
8432	gcd(V(776555),5F(155311)(F(155311)+1)+1)	59858	Serge Batalov	04/2015
8433	(3^125447+7)/2	59854	Lelio R Paula	04/2012
8434	5^85630+4^(85630-1)	59853	Robert Price	03/2016
8435	2^198824-2135	59852	Yves Minet	06/2013
8436	(124^28591-1)/123	59851	Richard Fischer	10/2017
8437	2^198799-16117	59845	Enzo Doria	04/2013
8438	7^70811+6^(70811+1)	59843	Robert Price	07/2016
8439	2^198774-15945	59837	Enzo Doria	04/2013
8440	2^198753-15873	59831	Enzo Doria	04/2013
8441	(31*2^198748-1)/45	59829	Lelio R Paula	01/2014
8442	2^198725+69	59823	Lelio R Paula	04/2011
8443	(68*10^59821+31)/9	59822	Robert Price	10/2015
8444	(37*25^42785+1867)/8	59812	Curtis Bright	05/2015
8445	3^125354+2660	59810	Lelio R Paula	10/2012
8446	105^29591-104	59810	Norbert Schneider	08/2013
8447	4*5^85565-3	59808	Lelio R Paula	09/2014
8448	13963842222*Bern(19550)/55727275	59803	Thomas Ritschel	03/2014
8450	125330^3+3^125330	59798	Anatoly F. Selevich	06/2010
8449	2^198643-3189	59798	Yves Minet	10/2014
8451	(13*10^59797+191)/3	59798	Robert Price	08/2017
8452	(7*10^59796-1)/3	59797	Erik Branger	03/2014
8453	2^198595+153	59784	Lelio R Paula	04/2011
8454	(19*10^59766+161)/9	59767	Robert Price	07/2016
8455	2^198510-1965	59758	Lelio R Paula	06/2011
8456	2^198506-19077	59757	Enzo Doria	05/2013
8457	2^198484-16005	59750	Enzo Doria	04/2013
8458	2^198473-16821	59747	Enzo Doria	05/2013
8459	(2^198481-5)/28311	59745	Lelio R Paula	02/2012
8460	2^198400-189	59725	Lelio R Paula	04/2011
8461	2^198384-12837	59720	Enzo Doria	10/2012
8462	42694!3-729	59719	Robert Price	09/2014
8463	2^198320-18717	59701	Enzo Doria	05/2013
8464	20^45881-1183	59693	Enzo Doria	03/2013
8465	2^198224-6855	59672	Lelio R Paula	05/2011
8466	2^198181-19101	59659	Enzo Doria	05/2013
8467	5*10^59650+41	59651	Robert Price	08/2017
8468	2^198149-112213	59649	Enzo Doria	06/2014
8469	2^198138+73699	59646	Enzo Doria	04/2016
8470	2^198129-55	59643	Lelio R Paula	04/2011
8471	5^85318-14636	59635	Enzo Doria	02/2013
8472	(2^198119+47)/1560935	59634	Lelio R Paula	02/2012
8473	2^198090-16097	59632	Enzo Doria	04/2013
8474	9*10^59617+89	59618	Robert Price	11/2016
8475	42625!3+81	59612	Robert Price	09/2014
8476	5^85277-84	59607	Lelio R Paula	10/2012
8477	(871*10^59599-7)/9	59601	Robert Price	11/2017
8478	2^197984-18245	59600	Enzo Doria	05/2013
8479	2^197951-2137	59590	Yves Minet	06/2013
8480	(38*10^59589+187)/9	59590	Robert Price	11/2017
8481	66^32749-65^32749	59589	Robert Price	09/2013
8482	5*10^59586-3	59587	Dmitry Domanov	11/2010
8483	(35*10^59584-197)/9	59585	Robert Kinser	10/2017
8484	2^197932-3959	59584	Yves Minet	04/2017
8485	2^197909-18961	59577	Enzo Doria	05/2013
8486	(3^124871+2)/45031	59574	Lelio R Paula	04/2012
8487	2^197872+81	59566	Henri Lifchitz	10/2005
8488	2^197873-18469	59566	Enzo Doria	05/2013
8489	(22*10^59558-31)/9	59559	Robert Price	04/2015
8491	2^197840-465	59556	Lelio R Paula	05/2011
8490	(31*2^197856-1)/3889605	59556	Lelio R Paula	01/2014
8492	2^197808-17805	59547	Enzo Doria	05/2013
8493	2^197781-17905	59539	Enzo Doria	05/2013
8494	2^197777-17473	59537	Enzo Doria	05/2013
8495	6^76507-149	59535	Lelio R Paula	10/2012
8497	Phi(61456,109)	59526	Enzo Doria	05/2012
8496	18^47420+23	59526	Lelio R Paula	03/2013
8498	(59^33613+1)/60	59522	Paul Bourdelais	08/2017
8499	3^124747+94	59520	Lelio R Paula	10/2012
8500	17^48370+18	59517	Lelio R Paula	03/2013

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PRP Records

Probable Primes Top 10000

(247113 PRPs in the top)