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 (> 50000)	Who ?	When ?
8251	2^214055-159	64437	Lelio R Paula	08/2011
8252	10^64436-53	64436	Robert Price	05/2011
8253	(3^135043-lucasV(1,3,135043)+1)/3	64432	Paul Vanderveen	11/2017
8254	Phi(128878,10)/39503297927	64428	Maksym Voznyy	11/2015
8255	3^135027+100	64425	Lelio R Paula	05/2013
8256	(3^134972-7)/2	64398	Lelio R Paula	04/2012
8257	6*10^64387+7	64388	Dmitry Domanov	11/2010
8258	2^213864-18377	64380	Enzo Doria	05/2013
8259	17929^3892+3892^17929	64369	Hans Havermann	06/2019
8260	(2^213821+9)/209	64365	Lelio R Paula	04/2012
8261	2^213788+135	64357	Lelio R Paula	08/2011
8262	17703^4316+4316^17703	64352	Hans Havermann	06/2019
8263	(3^134883+2)/48313	64351	Lelio R Paula	04/2012
8264	(49^38069-46^38069)/3	64344	Serge Batalov	12/2016
8265	(11^61781+2^61781)/13	64338	Robert Price	02/2013
8266	6^82670+37	64330	Lelio R Paula	07/2013
8267	(3^134839+4)/32312959	64328	Lelio R Paula	04/2012
8268	(22*10^64326+161)/3	64327	Robert Price	02/2017
8269	11^61767-4050	64324	Enzo Doria	12/2012
8270	2^213645-114853	64314	Enzo Doria	05/2015
8271	13^57733+18	64312	Lelio R Paula	07/2013
8272	2^213621+72707	64307	Enzo Doria	04/2016
8273	10^64305+136791	64306	Patrick De Geest	05/2011
8274	10^64305-9	64305	Alexander Gramolin	01/2011
8275	V(307652)	64295	Serge Batalov	03/2015
8276	4*10^64286-89	64287	Robert Price	08/2017
8277	(2^213546-5)/2221	64281	Lelio R Paula	04/2012
8278	2^213438-58695	64252	Lelio R Paula	10/2011
8279	2^213367-105	64230	Lelio R Paula	08/2011
8280	595^23148+23148^595	64225	Norbert Schneider	07/2016
8282	3^134601+8680	64221	Lelio R Paula	05/2013
8281	(26*10^64220+61)/3	64221	Robert Price	06/2017
8283	500^23793+23793^500	64217	Norbert Schneider	08/2016
8284	179^28504-2	64216	Lelio R Paula	10/2017
8285	2^213314-455	64214	Yves Minet	02/2012
8286	39^40359-38	64214	Norbert Schneider	05/2014
8287	2^213292-16085	64208	Enzo Doria	04/2013
8288	(72524!5+1)/25	64203	Joe McLean	10/2018
8289	2^213274-77	64202	Lelio R Paula	08/2011
8290	19^50203+78	64198	Lelio R Paula	08/2013
8291	(44*10^64192-233)/9	64193	Robert Price	10/2017
8292	2^213240-112865	64192	Enzo Doria	06/2014
8293	2^213190-112391	64177	Enzo Doria	06/2014
8294	(9913*2^213184-1)/9657	64175	Lelio R Paula	04/2015
8295	14^55991+27	64173	Lelio R Paula	07/2013
8296	2^213158-112581	64167	Enzo Doria	06/2014
8297	2^213148+91	64164	Lelio R Paula	08/2011
8298	(96^32369+1)/97	64163	Paul Bourdelais	08/2017
8300	6^82439+125	64151	Lelio R Paula	07/2013
8299	7*2^213102+9	64151	Lelio R Paula	04/2014
8301	L(306854)+F(306855)	64129	Henri Lifchitz	01/2007
8302	15621^12736+12736^15621	64125	Hans Havermann	07/2019
8303	15633^12622+12622^15633	64113	Hans Havermann	07/2019
8304	610^23017+23017^610	64110	Norbert Schneider	07/2016
8305	2^212950-64875	64105	Lelio R Paula	10/2011
8306	(266*10^64102-17)/3	64104	Robert Price	06/2016
8307	p(13679)#/2+64	64097	Robert Price	03/2017
8308	19^50119+94	64090	Lelio R Paula	08/2013
8309	2^212880-147	64084	Lelio R Paula	08/2011
8310	11^61523-4590	64070	Enzo Doria	01/2013
8311	5^91663+38	64070	Lelio R Paula	05/2013
8312	5^91650+52	64061	Lelio R Paula	05/2013
8313	2^212770+69	64051	Lelio R Paula	08/2011
8314	(3^134227+1)/4	64042	Paul Bourdelais	11/2007
8315	(2*10^64041-17)/3	64041	Robert Price	08/2014
8316	(15^54449+1)/16	64036	Paul Bourdelais	03/2010
8317	(29*10^64027+91)/3	64028	Robert Price	03/2016
8318	(lucasV(1,2,425405)+2)/(17*89)	64027	Mike Oakes	03/2017
8319	16878!+16878#-1	64022	D. Gazzoni Filho & Lucas Teixeira	05/2005
8320	15862^10863+10863^15862	64019	Hans Havermann	06/2019
8321	2^212663+53	64018	Lelio R Paula	08/2011
8322	(4*10^64014+197)/3	64015	Robert Price	03/2017
8323	85402!6-3	64014	Robert Price	08/2018
8324	(140^29819+1)/141	63994	Richard Fischer	05/2018
8325	15313^15094+15094^15313	63991	Hans Havermann	06/2019
8326	10^63986+63	63987	Robert Price	01/2011
8327	10^63986-31557	63986	Patrick De Geest	05/2013
8328	15699^11900+11900^15699	63983	Hans Havermann	07/2019
8329	31487!2-2^31487	63982	Robert Price	09/2015
8330	(21*2^212522-1)/1416323	63971	Lelio R Paula	01/2014
8331	5^91517+98	63968	Lelio R Paula	04/2013
8332	(19*10^63960-43)/3	63961	Robert Price	10/2017
8333	(62*10^63954-17)/9	63955	Robert Price	09/2015
8335	5^91493-4^91493	63951	Predrag Minovic	04/2004
8334	V(364793)	63951	Serge Batalov	03/2015
8338	19^50004+58	63943	Lelio R Paula	05/2013
8336	5*6^82172-7	63943	Lelio R Paula	09/2014
8337	(56*10^63942+223)/9	63943	Robert Price	07/2016
8339	19^50000-24	63938	Lelio R Paula	05/2013
8340	(23*2^212374-1)/27019	63928	Lelio R Paula	01/2014
8341	(9*2^212355-1)/761	63924	Lelio R Paula	01/2014
8343	2^212344-183	63922	Lelio R Paula	08/2011
8342	(58695*2^212336-1)/379	63922	Lelio R Paula	04/2015
8344	10^63916+79	63917	Robert Price	01/2011
8345	10^63916-76823	63916	Patrick De Geest	05/2013
8346	2^212295-25	63908	Lelio R Paula	08/2011
8347	2^212285-2383	63905	Yves Minet	10/2013
8348	267^26336+26336^267	63905	Norbert Schneider	09/2014
8349	(-lucasV(1,2,424552)-2)/1601	63899	Mike Oakes	03/2017
8350	19^49962+60	63890	Lelio R Paula	05/2013
8351	3^133906-113056	63890	Enzo Doria	07/2014
8352	(lucasV(1,2,424451)+2)/3	63886	Mike Oakes	03/2017
8353	3*6^82092+5	63881	Lelio R Paula	09/2014
8354	15441^13706+13706^15441	63879	Hans Havermann	02/2017
8355	2^212154-776351	63865	Paul Bourdelais	03/2013
8356	35^41359+2	63862	Lelio R Paula	05/2013
8357	(61*10^63857-43)/9	63858	Robert Price	09/2015
8358	(2^212131-3)/485	63856	Lelio R Paula	04/2012
8359	2^212112-459995	63853	Enzo Doria	06/2015
8360	15^54290+58	63850	Lelio R Paula	05/2013
8361	3*2^212097-7	63849	Lelio R Paula	04/2014
8362	55^36683-54	63842	Norbert Schneider	08/2014
8363	(509203*2^212056-1)/3	63841	Lelio R Paula	04/2015
8364	(3^133805-7)/172	63839	Lelio R Paula	04/2012
8365	2^212049+149	63834	Lelio R Paula	08/2011
8366	5^91318-18	63829	Lelio R Paula	04/2013
8367	18468^2857+2857^18468	63824	Hans Havermann	03/2017
8368	(2^212024-5)/1111	63823	Lelio R Paula	04/2012
8369	2^211961+12915	63807	Lelio R Paula	02/2013
8371	(3^133707-7)/5780	63791	Lelio R Paula	04/2012
8370	(44*10^63790-161)/9	63791	Robert Price	11/2017
8372	747^22198+22198^747	63782	Norbert Schneider	07/2016
8374	2^211800-17169	63759	Enzo Doria	05/2013
8373	(85*10^63757-1)/3	63759	Robert Price	07/2017
8375	85089!6-8	63757	Robert Price	08/2018
8376	(14*10^63747-11)/3	63748	Erik Branger	09/2014
8377	91*19^49848+6	63746	Curtis Bright	05/2015
8378	18855^2402+2402^18855	63741	Hans Havermann	03/2017
8379	(142*10^63734-7)/9	63736	Robert Price	02/2017
8380	2^211699-111	63728	Lelio R Paula	08/2011
8381	11^61192-5550	63725	Enzo Doria	01/2013
8382	(11*10^63718+7)/9	63719	Serge Batalov	06/2011
8383	6^81872-13	63709	Lelio R Paula	04/2013
8384	3^133522+98	63707	Lelio R Paula	05/2013
8386	2^211607-61	63701	Lelio R Paula	08/2011
8385	5^91135+8	63701	Lelio R Paula	04/2013
8387	11^61157-270	63689	Enzo Doria	07/2012
8388	10^63685+1145141919	63686	Marisa Kirisame	03/2015
8389	10^63685+103837	63686	Patrick De Geest	03/2016
8390	10^63685-130797	63685	Patrick De Geest	03/2016
8391	2^211547+1155*211547	63682	Henri Lifchitz	02/2005
8392	2^211543+45	63681	Lelio R Paula	08/2011
8393	2^211534+43	63679	Lelio R Paula	08/2011
8394	11^61140-60	63671	Enzo Doria	07/2012
8395	2^211491-112321	63666	Enzo Doria	06/2014
8396	19085^2164+2164^19085	63654	Hans Havermann	03/2017
8397	(2^211430-5)/859	63644	Lelio R Paula	04/2012
8398	2^211401-91	63639	Lelio R Paula	08/2011
8399	(6883*2^211378-1)/69	63634	Lelio R Paula	04/2015
8400	(F(152232)^3-F(152231)^3)/F(152230)	63629	Wayne Halsdorf	03/2012
8401	(29*2^211384-1)/50122621	63627	Lelio R Paula	01/2014
8402	2^211333+15015	63618	Lelio R Paula	01/2013
8403	33^41889-32	63610	Norbert Schneider	03/2014
8404	13^57093+18	63599	Lelio R Paula	05/2013
8405	(5*2^211219-1)/9	63583	Lelio R Paula	01/2014
8406	(107*10^63576-17)/9	63578	Robert Price	02/2017
8407	23^46687-1020	63575	Enzo Doria	08/2012
8408	(67607*2^211188+1)/5234319	63573	Lelio R Paula	06/2014
8409	(3^133243+7)/10726	63570	Lelio R Paula	04/2012
8410	(7*2^211181+1)/2745	63570	Lelio R Paula	06/2012
8412	(20^48859-1)/19	63566	Paul Bourdelais	03/2010
8411	2*3^133227+5	63566	Lelio R Paula	04/2014
8413	2^211155+113	63564	Lelio R Paula	08/2011
8414	2^211134+345	63558	Lelio R Paula	09/2011
8415	2^211121+16385	63554	Lelio R Paula	09/2011
8416	16996^5483+5483^16996	63549	Hans Havermann	02/2017
8417	(2^211079+9)/364283	63536	Lelio R Paula	03/2012
8418	3*10^63522+13	63523	Robert Price	08/2017
8419	15852^10157+10157^15852	63516	Hans Havermann	02/2017
8420	2^210948-15873	63502	Enzo Doria	04/2013
8421	7^75136+6	63498	Lelio R Paula	04/2013
8422	2^210928+12915	63496	Lelio R Paula	02/2013
8423	7*10^63493+39	63494	Robert Price	07/2016
8424	2^210909+135	63490	Lelio R Paula	08/2011
8425	(3*2^210832+1)/7	63467	Lelio R Paula	07/2012
8426	8*7^75098-3	63467	Lelio R Paula	09/2014
8427	17683^3882+3882^17683	63466	Hans Havermann	03/2017
8429	Pell-LucasQ(165799)/2	63464	Eric W. Weisstein	11/2006
8428	2^210820-16905	63464	Enzo Doria	05/2013
8430	5^90795-36	63463	Lelio R Paula	04/2013
8431	84731!6-48	63463	Robert Price	08/2018
8432	2^210816-13197	63462	Enzo Doria	10/2012
8433	2^210750+133	63443	Lelio R Paula	08/2011
8434	291^25742+25742^291	63426	Norbert Schneider	09/2014
8435	(3^132908+8)/279859	63408	Lelio R Paula	04/2012
8436	6^81480-139	63404	Lelio R Paula	04/2013
8437	2^210576-173	63390	Lelio R Paula	08/2011
8438	18^50497+55	63388	Lelio R Paula	05/2013
8439	2^210545+11	63381	Lelio R Paula	08/2011
8440	2^210543+63	63380	Lelio R Paula	08/2011
8441	155^28929-154	63365	Norbert Schneider	12/2018
8442	83^33016+82	63361	Norbert Schneider	04/2015
8443	2^210464+98765331	63356	Jason Earls	12/2008
8444	7*10^63351+9	63352	Dmitry Domanov	11/2010
8445	p(13534)#/2+512	63348	Robert Price	05/2017
8446	1741^19546+19546^1741	63345	Serge Batalov	05/2014
8447	10^63336+19819	63337	Patrick De Geest	12/2013
8448	10^63336-122883	63336	Patrick De Geest	12/2013
8449	(19^49523-2^49523)/17	63327	Robert Price	09/2013
8450	(2^210378+47)/95516931	63323	Lelio R Paula	03/2012
8451	31191!2+256	63316	Robert Price	01/2015
8452	16458^7031+7031^16458	63315	Hans Havermann	01/2017
8453	(lucasV(1,2,420636)-2)/(731^2210319)	63303	Mike Oakes	03/2017
8454	156^28864+155	63303	Norbert Schneider	12/2018
8455	(2^210283+7)/1691145	63296	Lelio R Paula	03/2012
8456	2^210217+1299	63282	Lelio R Paula	09/2011
8457	(2^210221-3)/269	63281	Lelio R Paula	04/2012
8458	Phi(193404,10)/386809/8122969	63268	Maksym Voznyy	10/2011
8459	96^31913-95	63261	Norbert Schneider	04/2016
8460	3^132572+280	63253	Lelio R Paula	04/2013
8461	3^132570-2^(132570-1)	63252	Robert Price	01/2016
8462	11^60734-4920	63248	Enzo Doria	01/2013
8464	2^210061+21	63235	Donovan Johnson	06/2006
8463	18^50375+95	63235	Lelio R Paula	05/2013
8465	85^32773-2	63233	Lelio R Paula	08/2013
8466	(-lucasV(1,2,420115)-2)/(3*5^3)	63232	Mike Oakes	02/2017
8467	(2^210054-1017)/671	63230	Lelio R Paula	04/2012
8468	3*2^210022+5	63224	Lelio R Paula	04/2014
8469	15^53756+32	63222	Lelio R Paula	05/2013
8471	17^51380+22	63221	Lelio R Paula	05/2013
8470	(lucasV(1,2,420045)+2)/257	63221	Mike Oakes	02/2017
8472	43^38700+42	63216	Norbert Schneider	06/2014
8473	5^90431-96	63209	Lelio R Paula	04/2013
8474	(172*10^63202-1)/9	63204	Serge Batalov	12/2014
8475	(43*10^63200+83)/9	63201	Robert Price	08/2017
8476	2^209914-16005	63191	Enzo Doria	04/2013
8477	3*6^81190-5	63179	Lelio R Paula	09/2014
8478	2^209820+4257	63163	Lelio R Paula	10/2011
8479	99^31648+2	63158	Lelio R Paula	05/2013
8480	16976^5253+5253^16976	63158	Hans Havermann	01/2017
8481	2^209790+67	63154	Lelio R Paula	08/2011
8482	145878#-p(145878)	63152	Henri Lifchitz	12/2018
8483	2^209759+90195	63144	Lelio R Paula	02/2013
8484	145823#+211507	63142	Arkadiusz Wesolowski	03/2013
8486	2^209707+513	63129	Lelio R Paula	10/2011
8485	(3^132314-8)/17	63129	Lelio R Paula	04/2012
8487	(2*10^63117+7)/9	63117	Erik Branger	03/2011
8488	9*2^209654-7	63114	Lelio R Paula	04/2014
8489	84304!6-9	63112	Robert Price	08/2018
8490	11^60598-14	63107	Lelio R Paula	05/2013
8491	15103^15078+15078^15103	63106	Hans Havermann	01/2017
8492	15346^12941+12941^15346	63103	Hans Havermann	01/2017
8493	3^132253+76	63101	Lelio R Paula	04/2013
8494	(56*10^63100+403)/9	63101	Robert Price	10/2017
8495	17549^3936+3936^17549	63090	Hans Havermann	01/2017
8496	(55459*2^209553+1)/423	63084	Lelio R Paula	06/2014
8497	(331^25033-1)/330	63077	Eric Chen	09/2017
8499	20^48480+31	63074	Lelio R Paula	06/2013
8498	(26*10^63073-23)/3	63074	Robert Price	08/2016
8500	2^209499+76253	63066	Enzo Doria	04/2016

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PRP Records

Probable Primes Top 10000

(253476 PRPs in the top)