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 ?
6251	20^58408+73	75991	Lelio R Paula	01/2015
6252	2^252418-1421	75986	Yves Minet	01/2013
6253	(11*2^252396-1)/5	75980	Lelio R Paula	02/2014
6254	2^252365-110689	75970	Enzo Doria	05/2014
6255	11^72949-1020	75969	Enzo Doria	11/2012
6256	(2^252294+47)/6549	75945	Lelio R Paula	07/2012
6257	2^252261-110595	75939	Enzo Doria	05/2014
6258	7^89853+76	75935	Lelio R Paula	01/2015
6259	3^159132+56	75926	Lelio R Paula	01/2015
6260	730^26513+26513^730	75916	Norbert Schneider	11/2016
6261	(27*2^252163-1)/1945	75907	Lelio R Paula	01/2014
6262	5^108596-14846	75906	Enzo Doria	02/2013
6263	5^108560-14846	75881	Enzo Doria	02/2013
6264	2^252051-110359	75875	Enzo Doria	05/2014
6265	2^251971-110509	75851	Enzo Doria	05/2014
6266	(42457^16384+1)/327682	75819	Lelio R Paula	11/2011
6267	99655!6-2	75811	Robert Price	07/2017
6268	14*10^75798+1089	75800	Jens K. Andersen	11/2007
6269	2^251784-455	75795	Yves Minet	03/2012
6270	2^251780-1289	75794	Yves Minet	01/2013
6271	2^251760-215609	75788	Paul Bourdelais	03/2013
6272	99^37973+2	75781	Lelio R Paula	05/2013
6273	(185*10^75777+7)/3	75779	Robert Price	02/2017
6274	5*2^251690+3	75767	Lelio R Paula	06/2014
6275	6^97366+95	75766	Lelio R Paula	01/2015
6276	s(23010)	75760	Hans Havermann	11/2017
6277	8*6^97337-7	75744	Lelio R Paula	10/2014
6278	2^251588-111677	75736	Enzo Doria	05/2014
6279	5^108346-13256	75731	Enzo Doria	02/2013
6280	(31^50777+1)/32	75726	Robert Price	07/2013
6281	(10^75707+77)/3	75707	Robert Price	01/2017
6282	(174907#+1673)/(723915467899)	75700	Makoto Morimoto	10/2017
6283	2^251466+193	75699	Lelio R Paula	03/2012
6284	(5*2^251464+1)/9423	75695	Lelio R Paula	07/2012
6285	2^251422-109991	75686	Enzo Doria	04/2014
6286	4*5^108245-3	75661	Lelio R Paula	10/2014
6287	12^70067-11^70067	75615	Jean-Louis Charton	11/2006
6288	12^70066+95	75614	Lelio R Paula	02/2015
6289	-E20534/2063	75607	Thomas Ritschel	02/2017
6290	19^59120-50	75600	Lelio R Paula	01/2015
6291	18^60222-4697	75596	Enzo Doria	03/2013
6292	18^60211-4355	75582	Enzo Doria	03/2013
6293	7*2^251014-9	75564	Lelio R Paula	06/2014
6294	6^97101-25	75560	Lelio R Paula	01/2015
6295	8^83663-7^83663	75556	Jean-Louis Charton	01/2004
6296	3^158331-140	75544	Lelio R Paula	01/2015
6298	(37^48157-1)/36	75519	Robert Price	03/2012
6297	(19*10^75518-43)/3	75519	Robert Price	10/2017
6299	2^250868-4229	75519	Yves Minet	08/2018
6300	10^75516+31467	75517	Patrick De Geest	03/2016
6302	10^75516-10^2256-1	75516	Serge Batalov	01/2011
6301	10^75516-66591	75516	Patrick De Geest	03/2016
6303	2^250851-187	75514	Lelio R Paula	03/2012
6304	(43*10^75498-7)/9	75499	Robert Price	12/2014
6305	(3^158244-5)/247916	75497	Lelio R Paula	06/2012
6306	4*5^107971-3	75470	Lelio R Paula	10/2014
6307	(25*10^75465+71)/3	75466	Robert Price	01/2017
6308	(5*2^250681-1)/999	75461	Lelio R Paula	01/2014
6309	(182*10^75456+1)/3	75458	Robert Price	02/2017
6310	(2^250669-9)/98897729	75451	Lelio R Paula	07/2012
6311	10^75441+13	75442	Robert Price	01/2011
6312	10^75441-9923	75441	Patrick De Geest	05/2013
6313	(27*2^250546-1)/6457	75420	Lelio R Paula	01/2014
6314	5*7^89231-6	75410	Lelio R Paula	10/2014
6316	2^250503-16995	75409	Lelio R Paula	05/2013
6315	11^72411-28	75409	Lelio R Paula	02/2015
6317	3*5^107860-8	75392	Lelio R Paula	10/2014
6318	(34*10^75387-403)/9	75388	Robert Price	10/2017
6320	2^250426+29835	75386	Lelio R Paula	05/2013
6319	8*3^157999-7	75386	Lelio R Paula	05/2014
6321	(88*10^75381-43)/9	75382	Robert Price	11/2015
6322	2^250382-111755	75373	Enzo Doria	05/2014
6323	2^250374-2798051	75371	Eric Chen	03/2016
6324	(22*10^75368-1)/3	75369	Robert Price	12/2014
6325	(19*10^75338+119)/3	75339	Robert Price	02/2017
6326	2^250223-1859167	75325	Enzo Doria	03/2016
6327	(3^157854-7)/66025282	75308	Lelio R Paula	06/2012
6328	3^157831-98	75305	Lelio R Paula	01/2015
6329	(46^45281+11^45281)/57	75290	Serge Batalov	12/2016
6330	92^38335-91	75282	Norbert Schneider	01/2016
6331	2^250020+18915	75264	Lelio R Paula	05/2013
6332	2^250002+8193	75259	Lelio R Paula	05/2013
6333	(11*2^249977-7)/15	75251	Renaud Lifchitz	02/2011
6334	(2^249968+78557)/63	75247	Lelio R Paula	07/2012
6335	(5*10^75244+91)/3	75245	Robert Price	11/2016
6336	(10489!)^2+Prime(10489)	75242	Robert Price	08/2014
6337	14^65644+67	75237	Lelio R Paula	01/2015
6338	(2^249928-5)/11859059	75229	Lelio R Paula	06/2012
6339	129^35638+2	75218	Lelio R Paula	05/2013
6340	2^249853-110475	75214	Enzo Doria	05/2014
6341	2^249762+75409	75186	Enzo Doria	04/2016
6342	565^27318+27318^565	75181	Norbert Schneider	12/2016
6343	(2^249741-7)/685	75177	Lelio R Paula	06/2012
6344	2^249726-112181	75176	Enzo Doria	06/2014
6345	2^249721+11715	75174	Lelio R Paula	05/2013
6346	(38661^16384+1)/2	75158	Lelio R Paula	11/2011
6347	2^249658-47355	75155	Lelio R Paula	05/2013
6348	155^34311+2	75153	Lelio R Paula	05/2013
6349	(10^87682+1)/(10^12526+1)/990099009901	75145	Maksym Voznyy	06/2015
6350	(23*2^249602+1)/93	75138	Lelio R Paula	08/2012
6351	2^249522+8415	75114	Lelio R Paula	05/2013
6352	2^249489-110911	75104	Enzo Doria	05/2014
6353	(28*10^75078+131)/3	75079	Robert Price	02/2017
6354	(206*10^75073-17)/9	75075	Robert Price	03/2017
6355	2^249368-110573	75068	Enzo Doria	05/2014
6356	NaturalLogarithmOf10(75067)	75067	Eric W. Weisstein	10/2015
6357	(2^249375+78557)/45056125	75062	Lelio R Paula	07/2012
6358	(26*10^75055-173)/3	75056	Robert Price	10/2017
6359	2^249272+193	75039	Lelio R Paula	03/2012
6360	14^65468+43	75035	Lelio R Paula	01/2015
6361	37^47844+36	75030	Norbert Schneider	05/2014
6362	(52*10^75027-7)/9	75028	Robert Price	12/2014
6363	20^57653+89	75009	Lelio R Paula	01/2015
6364	2^249061-1868353	74975	Enzo Doria	04/2016
6365	7^88713+2*3^88713	74972	Mike Oakes	07/2010
6366	2*6^96313+5	74947	Lelio R Paula	10/2014
6367	(8*10^74944+49)/3	74945	Robert Price	03/2016
6368	300^30247+30247^300	74926	Norbert Schneider	11/2014
6369	2^248866-171	74917	Lelio R Paula	03/2012
6370	6*5^107168-7	74908	Lelio R Paula	10/2014
6371	11^71926+78	74904	Lelio R Paula	02/2015
6372	2^248824+1869391	74904	Enzo Doria	05/2016
6373	2^248816+1111	74902	Lelio R Paula	01/2011
6374	V(388219)	74890	Serge Batalov	03/2015
6375	159^34017+158	74885	Norbert Schneider	12/2018
6376	2*F(358297)-1	74880	Henri Lifchitz	12/2009
6377	(22*10^74874-31)/9	74875	Robert Price	04/2015
6378	11^71892-76800000	74868	Enzo Doria	01/2013
6379	9*5^107107-4	74866	Lelio R Paula	10/2014
6380	2^248678-710111	74860	Paul Bourdelais	03/2013
6381	(14*10^74858+211)/9	74859	Robert Price	11/2017
6382	13^67194+12	74851	Lelio R Paula	01/2015
6383	(7*2^248634+1)/71	74846	Lelio R Paula	08/2012
6384	11^71867-3090	74842	Enzo Doria	12/2012
6385	2^248609+262145	74839	Lelio R Paula	05/2013
6386	3^156852+50	74838	Lelio R Paula	01/2015
6387	18^59607-11	74824	Lelio R Paula	01/2015
6388	2^248556-110507	74823	Enzo Doria	05/2014
6389	7^88531-36	74818	Lelio R Paula	01/2015
6390	p(15738)#/2+1024	74814	Robert Price	07/2017
6391	4*3^156740-5	74785	Lelio R Paula	05/2014
6392	(32*10^74773-41)/9	74774	Robert Price	05/2015
6393	(29*2^248384-1)/13	74772	Lelio R Paula	01/2014
6394	19401!+19401#+1	74765	D. Gazzoni Filho & Lucas Teixeira	06/2005
6395	2^248357-12797413	74763	Enzo Doria	03/2016
6396	42^46057+41	74762	Lelio R Paula	07/2012
6397	11^71784-3000	74756	Enzo Doria	12/2012
6398	19^58458+18	74754	Lelio R Paula	01/2015
6399	12^69265-35	74750	Lelio R Paula	02/2015
6400	11^71771-48000	74742	Enzo Doria	12/2012
6401	(7*10^74741+197)/3	74742	Robert Price	07/2017
6402	(2^248282-5)/50129	74736	Lelio R Paula	06/2012
6403	2^248252-110105	74732	Enzo Doria	04/2014
6404	(7*10^74729+71)/3	74730	Robert Price	03/2016
6405	3^156614-50	74724	Lelio R Paula	01/2015
6406	(7*2^248213+1)/135	74719	Lelio R Paula	07/2012
6407	(2^248173+78557)/767	74705	Lelio R Paula	07/2012
6408	125^35622+124	74697	Norbert Schneider	02/2015
6409	(19*2^248099-1)/29	74686	Lelio R Paula	01/2014
6410	(86*10^74676-41)/9	74677	Robert Price	11/2015
6411	(p(15711)#-4)/2	74672	Robert Price	09/2017
6412	10^74670+31	74671	Robert Price	01/2011
6413	10^74670-122463	74670	Patrick De Geest	05/2013
6414	2^248036-69	74667	Lelio R Paula	03/2012
6415	11^71698-6000	74666	Enzo Doria	12/2012
6416	58(10^(324887)-1)/111-1	74661	Robert Price	10/2014
6417	14^65139-45	74658	Lelio R Paula	01/2015
6418	6^95921-133	74642	Lelio R Paula	01/2015
6419	11^71675+78	74642	Lelio R Paula	02/2015
6420	18^59449-91	74625	Lelio R Paula	01/2015
6421	6^95864-16043	74597	Enzo Doria	02/2013
6422	5*7^88261+6	74590	Lelio R Paula	10/2014
6423	9*5^106710+4	74589	Lelio R Paula	10/2014
6424	(7772^247788+1)/(11754121)	74588	Jens K. Andersen	09/2007
6425	(265*10^74579+17)/3	74581	Robert Price	05/2016
6426	(2^247759-1017)/3318311717	74574	Lelio R Paula	07/2012
6427	5^106682-24	74568	Lelio R Paula	08/2014
6428	474^27863+27863^474	74556	Norbert Schneider	01/2017
6429	(14*10^74540+79)/3	74541	Robert Price	11/2017
6430	(35365^16384+1)/2	74524	Lelio R Paula	11/2011
6431	3^156161+2660	74508	Lelio R Paula	01/2015
6432	2^247474-58695	74498	Lelio R Paula	05/2013
6433	11^71519-90	74480	Enzo Doria	07/2012
6434	(19*2^247419-1)/23202983	74475	Lelio R Paula	01/2014
6436	(2^247394-7)/3	74473	Lelio R Paula	06/2012
6435	18^59328+17	74473	Lelio R Paula	01/2015
6437	2^247379-181	74469	Lelio R Paula	03/2012
6438	(15*2^247370-1)/479	74465	Lelio R Paula	01/2014
6439	2^247344+2047	74458	Lelio R Paula	05/2013
6440	2^247311-1017	74449	Lelio R Paula	05/2013
6441	2^247280+7	74439	Lelio R Paula	03/2012
6442	(68*10^74434+13)/9	74435	Ray Chandler	11/2010
6443	3^156004-62	74433	Lelio R Paula	01/2015
6444	36095!2-64	74416	Robert Price	06/2015
6445	2^247165-3	74405	M. Frind & P. Underwood	07/2002
6446	2^247150+32769	74400	Lelio R Paula	05/2013
6447	12^68911+73	74368	Lelio R Paula	01/2015
6448	2^246999+74903	74355	Enzo Doria	04/2016
6449	2^246989-110643	74352	Enzo Doria	05/2014
6450	10^74350+279439	74351	Patrick De Geest	07/2017
6453	(10^74350+11)/3	74350	Robert Price	11/2014
6451	10^74350-400000001	74350	Robert Price	07/2017
6452	10^74350-716241	74350	Patrick De Geest	07/2017
6454	10^74335+13659	74336	Patrick De Geest	05/2013
6455	10^74335-53	74335	Robert Price	05/2011
6456	2^246906-1215	74327	Lelio R Paula	05/2013
6457	2^246848+111	74309	Lelio R Paula	03/2012
6458	6^95490-18443	74306	Enzo Doria	03/2013
6459	18^59188-2369	74298	Enzo Doria	03/2013
6460	(13632^246767+1)/(35713^2*743)	74281	Jens K. Andersen	09/2007
6461	2^246744+40755	74278	Lelio R Paula	05/2013
6462	(29*10^74276+91)/3	74277	Robert Price	03/2016
6463	6^95441+163	74268	Lelio R Paula	01/2015
6464	V(390863)	74258	Serge Batalov	03/2015
6465	10^74254+91	74255	Robert Price	03/2011
6467	(19*10^74253-1)/9	74254	Ray Chandler	02/2012
6466	10^74254-130569	74254	Patrick De Geest	05/2013
6468	771^25718+25718^771	74250	Norbert Schneider	10/2016
6469	2^246618+427	74240	Henri Lifchitz	02/2005
6470	88*10^74234+3	74236	Robert Price	11/2016
6471	8*10^74234-49	74235	Robert Price	04/2016
6472	2^246578+12285	74228	Lelio R Paula	05/2013
6473	(3^155569-5)/2	74225	Lelio R Paula	06/2012
6474	13^66628+46	74220	Lelio R Paula	01/2015
6475	2^246476-17295	74197	Lelio R Paula	05/2013
6476	(61*10^74189-1)/3	74191	Robert Price	11/2017
6477	(15185*2^246432-1)/13	74187	Lelio R Paula	04/2015
6478	5*2^246413-3	74179	Lelio R Paula	05/2014
6479	2^246386-28635	74170	Lelio R Paula	05/2013
6480	2^246334-111245	74154	Enzo Doria	05/2014
6481	39^77708+7^77708-24^77708-3	74153	Mike Oakes	12/2010
6482	15^63045+82	74147	Lelio R Paula	01/2015
6483	19255!+19255#+1	74140	D. Gazzoni Filho & Lucas Teixeira	06/2005
6484	2^246268-110507	74135	Enzo Doria	05/2014
6485	3^155328+2660	74111	Lelio R Paula	01/2015
6486	2^246148-2786249	74098	Enzo Doria	03/2016
6487	(16*10^74092-19)/3	74093	Robert Price	03/2016
6488	2^246115-110767	74088	Enzo Doria	05/2014
6489	7^87666-68	74087	Lelio R Paula	08/2014
6490	10^74079+1145141919	74080	Marisa Kirisame	03/2015
6491	10^74079+6219	74080	Patrick De Geest	03/2016
6492	10^74079-282707	74079	Patrick De Geest	03/2016
6493	129^35098+2	74078	Lelio R Paula	05/2013
6494	2^246025-112123	74061	Enzo Doria	06/2014
6495	(67*10^74045+17)/3	74047	Robert Price	02/2017
6496	2^245823+66831	74001	Marek Hubal	02/2017
6497	5^105869+42	74000	Lelio R Paula	08/2014
6498	(21*2^245806+1)/634555	73991	Lelio R Paula	08/2012
6499	(22699*2^245762+1)/119	73985	Lelio R Paula	06/2014
6500	(3^155048-7)/262	73975	Lelio R Paula	06/2012

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PRP Records

Probable Primes Top 10000

(252538 PRPs in the top)