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	11^56235-7950	58563	Enzo Doria	02/2013
8252	(14*10^58550+211)/9	58551	Robert Price	11/2017
8253	2^194479-113239	58545	Enzo Doria	07/2014
8254	2^194455-112249	58537	Enzo Doria	06/2014
8255	2^194405-111919	58522	Enzo Doria	05/2014
8256	(4*10^58521-19)/3	58522	Robert Price	06/2017
8258	(7^69247-4^69247)/3	58521	Robert Price	06/2012
8257	5*7^69246+8	58521	Lelio R Paula	09/2014
8259	2^194358-1167	58508	Lelio R Paula	05/2011
8260	(2^194366+7)/1373	58507	Lelio R Paula	02/2012
8261	(493*10^58486-7)/9	58488	Robert Price	07/2016
8262	3^122579-340	58486	Lelio R Paula	10/2012
8263	(11*10^58458-149)/3	58459	Robert Price	01/2017
8264	(47*10^58456+133)/9	58457	Robert Price	04/2017
8265	2^194186+85	58456	Lelio R Paula	04/2011
8266	3^122506-2^(122506-1)	58451	Robert Price	01/2016
8267	(74^31267-1)/73	58444	Paul Bourdelais	08/2017
8268	177^25998-2	58443	Lelio R Paula	10/2017
8269	15^49690-26	58440	Lelio R Paula	03/2013
8270	10^58437+110721	58438	Patrick De Geest	12/2012
8271	10^58437-11	58437	Robert Price	05/2011
8272	2^194095+69	58429	Lelio R Paula	04/2011
8273	(29*10^58417-77)/3	58418	Robert Price	01/2017
8274	2^194034+177	58411	Lelio R Paula	04/2011
8275	789^20158+20158^789	58400	Norbert Schneider	06/2016
8276	14^50949+75	58395	Lelio R Paula	03/2013
8277	2^193974-114761	58392	Enzo Doria	05/2015
8278	2^193965+5	58390	Henri Lifchitz	12/2002
8279	(5*10^58384-29)/3	58385	Robert Price	02/2017
8280	3^122360+80	58381	Lelio R Paula	10/2012
8281	10103^14577-114	58373	Enzo Doria	07/2012
8282	(22699*2^193883+1)/21	58368	Lelio R Paula	06/2014
8283	(31*2^193886+1)/140765	58362	Lelio R Paula	07/2012
8284	11^56041-1560	58361	Enzo Doria	11/2012
8285	(2^193881+9)/17699	58360	Lelio R Paula	02/2012
8286	3^122313+58	58359	Lelio R Paula	10/2012
8287	6^74996-119	58359	Lelio R Paula	10/2012
8288	(11*2^193859+1)/13	58358	Lelio R Paula	07/2012
8289	2^193861-112255	58358	Enzo Doria	06/2014
8290	(22699*2^193854+1)/4927	58357	Lelio R Paula	06/2014
8291	18^46487+37	58354	Lelio R Paula	03/2013
8292	17^47419+54	58347	Lelio R Paula	03/2013
8293	(31*2^193791+1)/3	58338	Lelio R Paula	02/2012
8294	(27*2^193805-1)/982249	58337	Lelio R Paula	01/2014
8295	3^122219-2^122219	58314	Mike Oakes	09/2003
8296	(199*10^58306+11)/3	58308	Robert Price	05/2017
8297	2^193674-18825	58302	Lelio R Paula	05/2011
8298	5*10^58275+3	58276	Dmitry Domanov	11/2010
8299	2^193578-112913	58273	Enzo Doria	06/2014
8300	2^193541+1299	58262	Lelio R Paula	05/2011
8301	10^58250+93	58251	Robert Price	01/2011
8302	10^58250-175607	58250	Patrick De Geest	12/2012
8303	2^193492+8415	58247	Lelio R Paula	10/2012
8304	2^193444+157	58233	Lelio R Paula	04/2011
8305	Phi(28754,28754)	58231	Henri Lifchitz	08/2013
8306	2^193430-111881	58229	Enzo Doria	05/2014
8307	10^58225+124579	58226	Patrick De Geest	12/2012
8308	10^58225-93	58225	Robert Price	05/2011
8309	2^193375-295	58212	Yves Minet	05/2013
8310	2^193345+77267	58203	Enzo Doria	05/2016
8311	21^44017-20^44017	58201	Robert Price	05/2012
8312	(17*2^193329-1)/9	58199	Lelio R Paula	01/2014
8313	17^47291+20	58190	Lelio R Paula	03/2013
8314	p(12528)#/2-128	58170	Robert Price	05/2017
8315	2^193214-135	58164	Lelio R Paula	04/2011
8316	19^45483-80	58162	Lelio R Paula	03/2013
8317	(4*10^58155+83)/3	58156	Robert Price	01/2017
8318	14^50739-13	58154	Lelio R Paula	03/2013
8319	(1017*2^193184-1)/4823	58154	Lelio R Paula	04/2015
8320	(2*10^58151+457)/9	58151	Robert Price	01/2017
8321	(9179*2^193183-1)/3999267879	58149	Lelio R Paula	04/2015
8322	(19*2^193114-1)/1186755	58129	Lelio R Paula	01/2014
8324	2^193091-1237	58127	Yves Minet	08/2012
8323	9*7^68780-2	58127	Lelio R Paula	09/2014
8325	2^193083-869688105	58124	Lelio R Paula	10/2012
8326	2^193058-45	58117	Lelio R Paula	04/2011
8327	(14016^14016+14017^14017)/(23710319913)	58115	David Broadhurst	09/2009
8328	11^55795-42	58105	Lelio R Paula	03/2013
8329	3^121779-16	58104	Lelio R Paula	10/2012
8330	(13*10^58103+191)/3	58104	Robert Price	08/2017
8331	2^192986+195	58095	Lelio R Paula	04/2011
8332	7^68740+2*3^68740	58093	Mike Oakes	07/2010
8333	(85*10^58091-1)/3	58093	Robert Price	07/2017
8334	(404*10^58087-53)/9	58089	Robert Price	11/2017
8335	12^53821+11	58083	Lelio R Paula	02/2013
8336	119^27979-118	58072	Norbert Schneider	10/2013
8337	(10223*2^192828+1)/243	58049	Lelio R Paula	05/2014
8338	2^192808-1127	58041	Yves Minet	05/2013
8339	(27*2^192803+1)/9827	58037	Lelio R Paula	07/2012
8341	(2^192781+lucasV(1,2,192781)+1)/4	58033	Mike Oakes	11/2016
8340	3*10^58032-23	58033	Robert Price	11/2017
8342	2^192678+72943	58002	Enzo Doria	04/2016
8343	(13*10^57997-37)/3	57998	Robert Price	08/2017
8344	2^192657-3189	57996	Yves Minet	10/2014
8345	6^74525-149	57992	Lelio R Paula	10/2012
8346	42^35723-41	57988	Norbert Schneider	06/2014
8347	(29*2^192625-1)/183	57986	Lelio R Paula	01/2014
8348	(3^121520-8)/3847	57977	Lelio R Paula	03/2012
8349	(2^192596-5)/139	57976	Lelio R Paula	02/2012
8350	10^57975+67833	57976	Patrick De Geest	09/2013
8351	10^57975-47693	57975	Patrick De Geest	09/2013
8352	(F(7707)^37-F(7706)^37)/F(7705)	57972	Wayne Halsdorf	03/2012
8353	(29*10^57967+673)/9	57968	Robert Price	10/2017
8354	(3^121492-5)/4	57966	Lelio R Paula	03/2012
8355	2^192549+35	57964	Lelio R Paula	04/2011
8356	28799!2+2	57962	Robert Price	10/2012
8357	(7*2^192534-1)/1347	57957	Lelio R Paula	01/2014
8358	7001^15069-100	57943	Enzo Doria	07/2012
8359	L(277273)/11090921	57940	Donovan Johnson	11/2005
8360	(2^192469-1017)/35	57938	Lelio R Paula	02/2012
8361	2^192457-1155*192457	57936	Henri Lifchitz	02/2005
8362	2^192443+1385	57932	Lelio R Paula	05/2011
8363	132^27317-131	57928	Norbert Schneider	03/2015
8364	41522!3-59049	57912	Robert Price	12/2015
8365	(3*2^192380-1)/169	57911	Lelio R Paula	01/2014
8366	2^192339-2515	57900	Yves Minet	07/2014
8367	2^192303+7695	57889	Lelio R Paula	10/2012
8368	2^192273-5955	57880	Lelio R Paula	05/2011
8369	2^192257+16095	57876	Lelio R Paula	05/2011
8370	109^28401-2	57865	Lelio R Paula	10/2017
8371	2^192218-111861	57864	Enzo Doria	05/2014
8372	2^192214-3941	57863	Yves Minet	04/2017
8373	(2^192212+3)/259	57860	Lelio R Paula	02/2012
8374	(3^121270+8)/155939753	57853	Lelio R Paula	03/2012
8375	80^30393-79	57841	Norbert Schneider	03/2015
8376	20^44455-3123	57838	Enzo Doria	03/2013
8377	2^192122-195	57835	Lelio R Paula	04/2011
8378	(29*10^57834+91)/3	57835	Robert Price	03/2016
8379	8*6^74306+5	57823	Lelio R Paula	09/2014
8380	(39^36341-1)/38	57820	Robert Price	04/2012
8381	2^192037-111805	57809	Enzo Doria	05/2014
8382	2^192023-192023^2	57805	Henri Lifchitz	05/2005
8383	21^43717+2	57804	Ray Chandler	08/2011
8384	8*5^82687+7	57797	Lelio R Paula	09/2014
8385	5^82680-24	57791	Lelio R Paula	10/2012
8386	(2^191915+47)/95	57771	Lelio R Paula	02/2012
8387	(74*10^57763+133)/9	57764	Robert Price	10/2017
8388	6^74227-95	57760	Lelio R Paula	10/2012
8389	2^191861+29835	57756	Lelio R Paula	10/2012
8391	1908^17605+17605^1908	57755	Serge Batalov	05/2014
8390	5*10^57754+59	57755	Robert Price	09/2016
8392	(5*2^191821-1)/8924067	57738	Lelio R Paula	01/2014
8393	38^63917+5^63917-34^63917+3*2^63917	57724	Mike Oakes	11/2010
8394	41399!3-6561	57723	Robert Price	11/2015
8395	(44*10^57721-233)/9	57722	Robert Price	10/2017
8396	2^191745+17	57721	Lelio R Paula	04/2011
8397	2^191730-761	57717	Yves Minet	01/2012
8398	(2^191733-3)/2251	57715	Lelio R Paula	02/2012
8399	2^191698-111	57707	Lelio R Paula	04/2011
8400	(13*10^57691+23)/9	57692	Robert Price	02/2015
8401	20^44340-5423	57688	Enzo Doria	03/2013
8402	(27*2^191629+1)/125	57686	Lelio R Paula	07/2012
8403	410^57684+37^57684	57685	Mike Oakes	11/2010
8404	2*3^120898+5	57684	Lelio R Paula	04/2014
8405	(6883*2^191610-1)/7347	57681	Lelio R Paula	04/2015
8406	6^74117-49	57675	Lelio R Paula	10/2012
8407	2^191586-113201	57674	Enzo Doria	07/2014
8408	2^191580+193	57672	Lelio R Paula	04/2011
8409	(103*29^39433+10401)/4	57669	Curtis Bright	05/2015
8410	2^191560+255255	57666	Lelio R Paula	05/2011
8411	2^191515-85	57652	Lelio R Paula	04/2011
8412	2^191502-1127	57648	Yves Minet	05/2013
8413	2*5^82473-3^82473	57647	Mike Oakes	08/2010
8414	(13*10^57634-61)/3	57635	Robert Price	08/2017
8415	85^29868-29868^85	57628	Norbert Schneider	11/2017
8416	2^191430+103	57627	Lelio R Paula	04/2011
8417	3*2^191408+5	57621	Lelio R Paula	03/2014
8418	2^191382-1858931	57612	Enzo Doria	04/2016
8419	6*7^68163+5	57606	Lelio R Paula	09/2014
8420	91^29403-2	57602	Lelio R Paula	08/2013
8421	11^55308-7950	57598	Enzo Doria	02/2013
8422	2^191329+65	57596	Lelio R Paula	04/2011
8423	11^55302-240	57592	Enzo Doria	07/2012
8424	2^191299-1031467	57587	Paul Bourdelais	11/2012
8425	2^191295-111991	57586	Enzo Doria	05/2014
8426	2^191279-1297	57581	Yves Minet	08/2012
8427	3*6^73961+5	57554	Lelio R Paula	09/2014
8428	(3^120623+5)/52144	57548	Lelio R Paula	04/2012
8429	(17*10^57543-29)/3	57544	Robert Price	09/2017
8430	42^35445-41	57537	Norbert Schneider	06/2014
8431	(71^31079-1)/70	57534	Paul Bourdelais	08/2017
8432	2^191069-723403	57518	Paul Bourdelais	11/2012
8433	4*10^57506-3	57507	Serge Batalov	11/2010
8434	10^57501+67359	57502	Patrick De Geest	06/2016
8435	10^57501-1000000001	57501	Robert Price	05/2016
8436	10^57501-249861	57501	Patrick De Geest	06/2016
8437	(9^60251+4^60251)/13	57493	Robert Price	02/2013
8438	20^44184-6003	57485	Enzo Doria	03/2013
8439	2^190948+12705	57482	Lelio R Paula	10/2012
8440	2^190945+29	57481	Henri Lifchitz	06/2005
8441	2^190922-401	57474	Yves Minet	01/2012
8442	15^48860+46	57464	Lelio R Paula	02/2013
8443	3^120434+20	57462	Lelio R Paula	10/2012
8444	7^67964-38	57437	Lelio R Paula	10/2012
8445	2^190799-113065	57437	Enzo Doria	07/2014
8446	9*5^82159+2	57428	Lelio R Paula	09/2014
8447	(F(22898)^13-F(22897)^13)/F(22896)	57422	Wayne Halsdorf	03/2012
8450	lucasU(432,25,21787)-5*lucasU(432,25,21786)	57416	Mike Oakes	05/2009
8448	(103*10^57414-1)/3	57416	Serge Batalov	12/2014
8449	(1654*30^38869-1)/29	57416	Karsten Bonath	05/2017
8451	2*10^57410+9^57410	57411	Mike Oakes	04/2011
8452	2^190704-1595	57408	Lelio R Paula	05/2011
8453	11^55121-1740	57403	Enzo Doria	11/2012
8454	2^190644-185	57390	Lelio R Paula	04/2011
8455	41182!3-3^41182	57389	Robert Price	08/2015
8456	2^190629-112255	57386	Enzo Doria	06/2014
8457	(2*10^57384-71)/3	57384	Robert Price	01/2017
8458	2*6^73735+5^73735	57378	Mike Oakes	11/2009
8459	2^190605+59	57378	Lelio R Paula	04/2011
8460	6^73727-7	57371	Lelio R Paula	10/2012
8461	2^190561-112225	57365	Enzo Doria	06/2014
8462	10^57358+170899	57359	Patrick De Geest	06/2016
8463	10^57358-8001	57358	Robert Price	03/2016
8464	18^45687-11	57350	Lelio R Paula	02/2013
8465	11^55069-210	57349	Enzo Doria	07/2012
8466	11^55068-12	57348	Lelio R Paula	02/2013
8467	19^44839+54	57339	Lelio R Paula	02/2013
8468	(7*2^190468-1)/8511	57334	Lelio R Paula	01/2014
8469	(23*10^57333-59)/9	57334	Robert Price	03/2017
8470	2^190455-1155*190455	57333	Henri Lifchitz	02/2005
8471	65^31620+28	57325	Lelio R Paula	01/2016
8472	2^190403+16095	57318	Lelio R Paula	05/2011
8473	(19*10^57316+119)/3	57317	Robert Price	02/2017
8475	(21*2^190393+1)/211	57314	Lelio R Paula	07/2012
8474	2^190392-112025	57314	Enzo Doria	05/2014
8476	(24737*2^190234+1)/9	57270	Lelio R Paula	05/2014
8477	(7*2^190230+1)/23	57265	Lelio R Paula	07/2012
8478	(10223*2^190197+1)/3211	57256	Lelio R Paula	05/2014
8479	18^45590-97	57228	Lelio R Paula	02/2013
8480	(3*2^190105-1)/19205	57224	Lelio R Paula	01/2014
8481	(16*10^57219-31)/3	57220	Robert Price	03/2016
8482	(2^190074+47)/51	57217	Lelio R Paula	02/2012
8483	3^119894-140	57204	Lelio R Paula	10/2012
8485	(37^36473-1)/36	57196	Robert Price	03/2012
8484	2^190000-2163	57196	Yves Minet	08/2013
8486	2^189987-2798107	57192	Enzo Doria	04/2016
8487	2^189935-112117	57177	Enzo Doria	05/2014
8488	2^189909-112231	57169	Enzo Doria	06/2014
8489	132049#+149053	57161	Makoto Morimoto	12/2015
8490	41032!3-27	57158	Robert Price	09/2014
8491	19^44694+22	57153	Lelio R Paula	02/2013
8492	12^52956-17	57150	Lelio R Paula	02/2013
8493	2^189823-967	57143	Yves Minet	01/2012
8494	(25*10^57138-61)/9	57139	Robert Price	02/2015
8495	5^81743-4^(81743+1)	57136	Robert Price	04/2016
8496	7^67593-54	57123	Lelio R Paula	10/2012
8497	7*3^119712+2	57118	Lelio R Paula	03/2014
8498	5^81700+16	57106	Lelio R Paula	10/2012
8499	2^189700+76561	57106	Enzo Doria	05/2016
8500	4*6^73374+5	57097	Lelio R Paula	09/2014

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Probable Primes Top 10000

(205869 PRPs in the top)