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	2^195833-17173	58952	Enzo Doria	05/2013
8252	(27*2^195833-1)/53	58952	Lelio R Paula	01/2014
8253	(13*2^195821-1)/122425	58945	Lelio R Paula	01/2014
8254	139^27504-138	58942	Norbert Schneider	10/2015
8255	(418*10^58923+23)/9	58925	Robert Price	08/2017
8256	3^123495+44	58923	Lelio R Paula	10/2012
8257	2^195737-18565	58923	Enzo Doria	05/2013
8258	14^51407+47	58920	Lelio R Paula	03/2013
8259	2^195691-99	58909	Lelio R Paula	04/2011
8260	2^195667-1859827	58902	Enzo Doria	04/2016
8262	2^195642+75499	58895	Enzo Doria	04/2016
8261	(299*10^58893+1)/3	58895	Robert Price	11/2017
8263	8*6^75678+5	58890	Lelio R Paula	09/2014
8265	2^195618+73189	58887	Enzo Doria	04/2016
8264	(3928^20480+1)/(3928^4096+1)	58887	Serge Batalov	01/2017
8266	t(197953)	58881	Robert Price	12/2014
8267	2^195581-16105	58876	Enzo Doria	04/2013
8268	(8*10^58872+67)/3	58873	Robert Price	01/2017
8269	7*2^195542-5	58865	Lelio R Paula	03/2014
8270	2*10^58861+9^58861	58862	Mike Oakes	04/2011
8271	11^56513-1620	58853	Enzo Doria	11/2012
8272	2^195496+165	58851	Lelio R Paula	04/2011
8273	5^84187+66	58845	Lelio R Paula	10/2012
8274	(28*10^58843-43)/3	58844	Robert Price	04/2016
8275	2^195462-17565	58840	Enzo Doria	05/2013
8276	2^195449-4171	58837	Yves Minet	02/2018
8277	2^195435+59273	58832	Yves Minet	01/2011
8278	2^195424-18605	58829	Enzo Doria	05/2013
8279	2^195385-111	58817	Lelio R Paula	04/2011
8280	7*10^58815-83	58816	Robert Price	09/2017
8281	(47*2^195254+1)/268821	58774	Lelio R Paula	03/2015
8282	2^195207-18109	58764	Enzo Doria	05/2013
8283	2^195199-1567	58761	Yves Minet	08/2012
8284	2^195190+73759	58759	Enzo Doria	04/2016
8285	9*7^69525-4	58757	Lelio R Paula	09/2014
8286	2^195170-18045	58753	Enzo Doria	05/2013
8287	2^195166-165	58751	Lelio R Paula	04/2011
8288	(754*10^58748-7)/9	58750	Robert Price	11/2017
8289	(22699*2^195140+1)/175	58746	Lelio R Paula	05/2014
8290	7*3^123109-2	58739	Lelio R Paula	04/2014
8291	(8*10^58738-611)/9	58738	Robert Price	11/2017
8292	18^46790+77	58735	Lelio R Paula	03/2013
8294	2^195095-337297	58730	Gary Barnes	09/2009
8293	(14*10^58729+31)/9	58730	Robert Price	02/2015
8295	99^29424+98	58720	Norbert Schneider	07/2013
8296	(15185*2^195039-1)/219	58715	Lelio R Paula	04/2015
8297	2^195001-69	58702	Lelio R Paula	04/2011
8298	2^194978-487811	58695	Gary Barnes	09/2009
8299	163^26530+26530^163	58690	Serge Batalov	05/2014
8300	2^194940-194940+1	58683	Robert Price	10/2014
8301	(76*10^58669+41)/9	58670	Robert Price	10/2015
8302	14^51186+87	58666	Lelio R Paula	03/2013
8303	2^194878-97305	58665	Lelio R Paula	09/2011
8304	5^83927-18136	58663	Enzo Doria	05/2014
8305	(24737*2^194865+1)/1085	58662	Lelio R Paula	06/2014
8306	7^69411+40	58660	Lelio R Paula	10/2012
8307	6^75382-79	58659	Lelio R Paula	10/2012
8308	2^194854+27	58657	Lelio R Paula	04/2011
8309	2^194801+29835	58641	Lelio R Paula	10/2012
8310	2^194752+195	58627	Lelio R Paula	04/2011
8311	7^69371-6^69371	58626	Predrag Minovic	08/2004
8312	2^194747-112519	58625	Enzo Doria	06/2014
8313	(15*2^194737+1)/59	58622	Lelio R Paula	07/2012
8314	(23*2^194700+1)/3	58612	Lelio R Paula	02/2012
8315	10^58608+55273	58609	Patrick De Geest	07/2017
8316	10^58608-800001	58608	Robert Price	06/2017
8317	10^58608-60119	58608	Patrick De Geest	07/2017
8318	5^83836+76	58599	Lelio R Paula	10/2012
8319	18^46664+31	58577	Lelio R Paula	03/2013
8320	(34*10^58577-7)/9/19/463	58574	Makoto Morimoto	04/2016
8321	2^194574+165	58573	Lelio R Paula	04/2011
8322	2^194569-12211	58572	Enzo Doria	06/2014
8323	10^58571+5^58571+2^58571	58572	Robert Price	12/2016
8324	10^58571+202837	58572	Patrick De Geest	02/2017
8325	(10^58571+41)/3	58571	Robert Price	01/2017
8326	10^58571-343629	58571	Patrick De Geest	02/2017
8327	(43*10^58563-403)/9	58564	Robert Price	04/2017
8328	11^56235-7950	58563	Enzo Doria	02/2013
8329	(14*10^58550+211)/9	58551	Robert Price	11/2017
8330	2^194479-113239	58545	Enzo Doria	07/2014
8331	2^194455-112249	58537	Enzo Doria	06/2014
8332	2^194405-111919	58522	Enzo Doria	05/2014
8333	(4*10^58521-19)/3	58522	Robert Price	06/2017
8335	(7^69247-4^69247)/3	58521	Robert Price	06/2012
8334	5*7^69246+8	58521	Lelio R Paula	09/2014
8336	2^194358-1167	58508	Lelio R Paula	05/2011
8337	(2^194366+7)/1373	58507	Lelio R Paula	02/2012
8338	(493*10^58486-7)/9	58488	Robert Price	07/2016
8339	3^122579-340	58486	Lelio R Paula	10/2012
8340	(11*10^58458-149)/3	58459	Robert Price	01/2017
8341	(47*10^58456+133)/9	58457	Robert Price	04/2017
8342	2^194186+85	58456	Lelio R Paula	04/2011
8343	3^122506-2^(122506-1)	58451	Robert Price	01/2016
8344	(74^31267-1)/73	58444	Paul Bourdelais	08/2017
8345	177^25998-2	58443	Lelio R Paula	10/2017
8346	15^49690-26	58440	Lelio R Paula	03/2013
8347	10^58437+110721	58438	Patrick De Geest	12/2012
8348	10^58437-11	58437	Robert Price	05/2011
8349	2^194095+69	58429	Lelio R Paula	04/2011
8350	(29*10^58417-77)/3	58418	Robert Price	01/2017
8351	2^194034+177	58411	Lelio R Paula	04/2011
8352	789^20158+20158^789	58400	Norbert Schneider	06/2016
8353	14^50949+75	58395	Lelio R Paula	03/2013
8354	2^193974-114761	58392	Enzo Doria	05/2015
8355	2^193965+5	58390	Henri Lifchitz	12/2002
8356	(5*10^58384-29)/3	58385	Robert Price	02/2017
8357	3^122360+80	58381	Lelio R Paula	10/2012
8358	10103^14577-114	58373	Enzo Doria	07/2012
8359	(22699*2^193883+1)/21	58368	Lelio R Paula	06/2014
8360	(31*2^193886+1)/140765	58362	Lelio R Paula	07/2012
8361	11^56041-1560	58361	Enzo Doria	11/2012
8362	(2^193881+9)/17699	58360	Lelio R Paula	02/2012
8363	3^122313+58	58359	Lelio R Paula	10/2012
8364	6^74996-119	58359	Lelio R Paula	10/2012
8365	(11*2^193859+1)/13	58358	Lelio R Paula	07/2012
8366	2^193861-112255	58358	Enzo Doria	06/2014
8367	(22699*2^193854+1)/4927	58357	Lelio R Paula	06/2014
8368	18^46487+37	58354	Lelio R Paula	03/2013
8369	17^47419+54	58347	Lelio R Paula	03/2013
8370	(31*2^193791+1)/3	58338	Lelio R Paula	02/2012
8371	(27*2^193805-1)/982249	58337	Lelio R Paula	01/2014
8372	3^122219-2^122219	58314	Mike Oakes	09/2003
8373	(199*10^58306+11)/3	58308	Robert Price	05/2017
8374	2^193674-18825	58302	Lelio R Paula	05/2011
8375	5*10^58275+3	58276	Dmitry Domanov	11/2010
8376	2^193578-112913	58273	Enzo Doria	06/2014
8377	2^193541+1299	58262	Lelio R Paula	05/2011
8378	10^58250+93	58251	Robert Price	01/2011
8379	10^58250-175607	58250	Patrick De Geest	12/2012
8380	(107^28703+1)/108	58248	Richard Fischer	05/2018
8381	2^193492+8415	58247	Lelio R Paula	10/2012
8382	2^193444+157	58233	Lelio R Paula	04/2011
8383	Phi(28754,28754)	58231	Henri Lifchitz	08/2013
8384	2^193430-111881	58229	Enzo Doria	05/2014
8385	10^58225+124579	58226	Patrick De Geest	12/2012
8386	10^58225-93	58225	Robert Price	05/2011
8387	2^193375-295	58212	Yves Minet	05/2013
8388	2^193345+77267	58203	Enzo Doria	05/2016
8389	21^44017-20^44017	58201	Robert Price	05/2012
8390	(17*2^193329-1)/9	58199	Lelio R Paula	01/2014
8391	17^47291+20	58190	Lelio R Paula	03/2013
8392	p(12528)#/2-128	58170	Robert Price	05/2017
8393	2^193214-135	58164	Lelio R Paula	04/2011
8394	19^45483-80	58162	Lelio R Paula	03/2013
8395	(4*10^58155+83)/3	58156	Robert Price	01/2017
8396	14^50739-13	58154	Lelio R Paula	03/2013
8397	(1017*2^193184-1)/4823	58154	Lelio R Paula	04/2015
8398	(2*10^58151+457)/9	58151	Robert Price	01/2017
8399	(9179*2^193183-1)/3999267879	58149	Lelio R Paula	04/2015
8400	(19*2^193114-1)/1186755	58129	Lelio R Paula	01/2014
8402	2^193091-1237	58127	Yves Minet	08/2012
8401	9*7^68780-2	58127	Lelio R Paula	09/2014
8403	2^193083-869688105	58124	Lelio R Paula	10/2012
8404	2^193058-45	58117	Lelio R Paula	04/2011
8405	(14016^14016+14017^14017)/(23710319913)	58115	David Broadhurst	09/2009
8406	11^55795-42	58105	Lelio R Paula	03/2013
8407	3^121779-16	58104	Lelio R Paula	10/2012
8408	(13*10^58103+191)/3	58104	Robert Price	08/2017
8409	2^192986+195	58095	Lelio R Paula	04/2011
8410	7^68740+2*3^68740	58093	Mike Oakes	07/2010
8411	(85*10^58091-1)/3	58093	Robert Price	07/2017
8412	(404*10^58087-53)/9	58089	Robert Price	11/2017
8413	12^53821+11	58083	Lelio R Paula	02/2013
8414	119^27979-118	58072	Norbert Schneider	10/2013
8415	(10223*2^192828+1)/243	58049	Lelio R Paula	05/2014
8416	2^192808-1127	58041	Yves Minet	05/2013
8417	(27*2^192803+1)/9827	58037	Lelio R Paula	07/2012
8419	(2^192781+lucasV(1,2,192781)+1)/4	58033	Mike Oakes	11/2016
8418	3*10^58032-23	58033	Robert Price	11/2017
8420	2^192678+72943	58002	Enzo Doria	04/2016
8421	(13*10^57997-37)/3	57998	Robert Price	08/2017
8422	2^192657-3189	57996	Yves Minet	10/2014
8423	6^74525-149	57992	Lelio R Paula	10/2012
8424	42^35723-41	57988	Norbert Schneider	06/2014
8425	(29*2^192625-1)/183	57986	Lelio R Paula	01/2014
8426	(3^121520-8)/3847	57977	Lelio R Paula	03/2012
8427	(2^192596-5)/139	57976	Lelio R Paula	02/2012
8428	10^57975+67833	57976	Patrick De Geest	09/2013
8429	10^57975-47693	57975	Patrick De Geest	09/2013
8430	(F(7707)^37-F(7706)^37)/F(7705)	57972	Wayne Halsdorf	03/2012
8431	(29*10^57967+673)/9	57968	Robert Price	10/2017
8432	(3^121492-5)/4	57966	Lelio R Paula	03/2012
8433	2^192549+35	57964	Lelio R Paula	04/2011
8434	28799!2+2	57962	Robert Price	10/2012
8435	(7*2^192534-1)/1347	57957	Lelio R Paula	01/2014
8436	7001^15069-100	57943	Enzo Doria	07/2012
8437	L(277273)/11090921	57940	Donovan Johnson	11/2005
8438	(2^192469-1017)/35	57938	Lelio R Paula	02/2012
8439	2^192457-1155*192457	57936	Henri Lifchitz	02/2005
8440	2^192443+1385	57932	Lelio R Paula	05/2011
8441	132^27317-131	57928	Norbert Schneider	03/2015
8442	41522!3-59049	57912	Robert Price	12/2015
8443	(3*2^192380-1)/169	57911	Lelio R Paula	01/2014
8444	2^192339-2515	57900	Yves Minet	07/2014
8445	2^192303+7695	57889	Lelio R Paula	10/2012
8446	2^192273-5955	57880	Lelio R Paula	05/2011
8447	2^192257+16095	57876	Lelio R Paula	05/2011
8448	109^28401-2	57865	Lelio R Paula	10/2017
8449	2^192218-111861	57864	Enzo Doria	05/2014
8450	2^192214-3941	57863	Yves Minet	04/2017
8451	(2^192212+3)/259	57860	Lelio R Paula	02/2012
8452	(3^121270+8)/155939753	57853	Lelio R Paula	03/2012
8453	80^30393-79	57841	Norbert Schneider	03/2015
8454	20^44455-3123	57838	Enzo Doria	03/2013
8455	2^192122-195	57835	Lelio R Paula	04/2011
8456	(29*10^57834+91)/3	57835	Robert Price	03/2016
8457	8*6^74306+5	57823	Lelio R Paula	09/2014
8458	(39^36341-1)/38	57820	Robert Price	04/2012
8459	2^192037-111805	57809	Enzo Doria	05/2014
8460	2^192023-192023^2	57805	Henri Lifchitz	05/2005
8461	21^43717+2	57804	Ray Chandler	08/2011
8462	8*5^82687+7	57797	Lelio R Paula	09/2014
8463	5^82680-24	57791	Lelio R Paula	10/2012
8464	(2^191915+47)/95	57771	Lelio R Paula	02/2012
8465	(74*10^57763+133)/9	57764	Robert Price	10/2017
8466	6^74227-95	57760	Lelio R Paula	10/2012
8467	2^191861+29835	57756	Lelio R Paula	10/2012
8469	1908^17605+17605^1908	57755	Serge Batalov	05/2014
8468	5*10^57754+59	57755	Robert Price	09/2016
8470	(5*2^191821-1)/8924067	57738	Lelio R Paula	01/2014
8471	38^63917+5^63917-34^63917+3*2^63917	57724	Mike Oakes	11/2010
8472	41399!3-6561	57723	Robert Price	11/2015
8473	(44*10^57721-233)/9	57722	Robert Price	10/2017
8474	2^191745+17	57721	Lelio R Paula	04/2011
8475	2^191730-761	57717	Yves Minet	01/2012
8476	(2^191733-3)/2251	57715	Lelio R Paula	02/2012
8477	2^191698-111	57707	Lelio R Paula	04/2011
8478	(13*10^57691+23)/9	57692	Robert Price	02/2015
8479	20^44340-5423	57688	Enzo Doria	03/2013
8480	(27*2^191629+1)/125	57686	Lelio R Paula	07/2012
8481	410^57684+37^57684	57685	Mike Oakes	11/2010
8482	2*3^120898+5	57684	Lelio R Paula	04/2014
8483	(6883*2^191610-1)/7347	57681	Lelio R Paula	04/2015
8484	6^74117-49	57675	Lelio R Paula	10/2012
8485	2^191586-113201	57674	Enzo Doria	07/2014
8486	2^191580+193	57672	Lelio R Paula	04/2011
8487	(103*29^39433+10401)/4	57669	Curtis Bright	05/2015
8488	2^191560+255255	57666	Lelio R Paula	05/2011
8489	2^191515-85	57652	Lelio R Paula	04/2011
8490	2^191502-1127	57648	Yves Minet	05/2013
8491	2*5^82473-3^82473	57647	Mike Oakes	08/2010
8492	(13*10^57634-61)/3	57635	Robert Price	08/2017
8493	85^29868-29868^85	57628	Norbert Schneider	11/2017
8494	2^191430+103	57627	Lelio R Paula	04/2011
8495	3*2^191408+5	57621	Lelio R Paula	03/2014
8496	2^191382-1858931	57612	Enzo Doria	04/2016
8497	6*7^68163+5	57606	Lelio R Paula	09/2014
8498	91^29403-2	57602	Lelio R Paula	08/2013
8499	11^55308-7950	57598	Enzo Doria	02/2013
8500	2^191329+65	57596	Lelio R Paula	04/2011

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PRP Records

Probable Primes Top 10000

(212140 PRPs in the top)