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	7^90833-60	76763	Lelio R Paula	02/2015
6252	13^68901-56	76752	Lelio R Paula	03/2015
6253	2^254961+1869917	76751	Enzo Doria	05/2016
6254	9*5^109791-8	76742	Lelio R Paula	10/2014
6255	82^40089+40089^82	76723	Serge Batalov	02/2012
6256	2^254861-2790013	76721	Enzo Doria	03/2016
6257	(10^278+1)*(10^115926+1)/(10^834+1)/(10^38642+1)/20459779741	76718	Makoto Kamada	03/2019
6258	10^76705+13	76706	Robert Price	01/2011
6259	10^76705-94077	76705	Patrick De Geest	06/2013
6260	(5*2^254785-1)/999	76696	Lelio R Paula	02/2014
6261	2^254758-110405	76690	Enzo Doria	05/2014
6262	2^254716-3779	76678	Yves Minet	04/2017
6263	2^254708-110507	76675	Enzo Doria	05/2014
6264	(47*10^76672+133)/9	76673	Robert Price	04/2017
6265	2^254670-112901	76664	Enzo Doria	06/2014
6266	(3^160665+7)/981350	76651	Lelio R Paula	10/2012
6267	2^254598-113183	76642	Enzo Doria	07/2014
6268	19^59932+22	76639	Lelio R Paula	01/2015
6269	2^254569-112213	76633	Enzo Doria	06/2014
6270	2*5^109626+9	76626	Lelio R Paula	10/2014
6271	2^254521+1872527	76619	Enzo Doria	05/2016
6272	(76*10^76615+167)/9	76616	Robert Price	08/2016
6273	25^54799-24^54799	76606	Robert Price	07/2012
6274	(24737*2^254464+1)/9	76605	Lelio R Paula	06/2014
6275	12^70961-85	76580	Lelio R Paula	02/2015
6276	7^90590-38	76558	Lelio R Paula	02/2015
6277	2^254304+5227	76554	Lelio R Paula	06/2013
6278	(76*10^76547-211)/9	76548	Robert Price	10/2017
6279	18^60979-5363	76546	Enzo Doria	03/2013
6280	(21181*2^254264+1)/55314379	76538	Lelio R Paula	06/2014
6282	(34*10^76547-7)/9/61/94529/214807	76536	Makoto Morimoto	05/2016
6281	(7*10^76536-313)/9	76536	Robert Price	11/2016
6284	2^254239-27	76534	Lelio R Paula	03/2012
6283	2^254238-1841	76534	Yves Minet	03/2013
6285	(10^76537-1)/9/66127969	76529	Jens K. Andersen	04/2009
6286	2^254189-112225	76519	Enzo Doria	06/2014
6287	18^60938-1397	76494	Enzo Doria	03/2013
6288	2^254075-2788417	76485	Enzo Doria	03/2016
6289	7*10^76483-23	76484	Robert Price	04/2016
6290	2^254042-112913	76475	Enzo Doria	06/2014
6291	14^66723-37	76474	Lelio R Paula	02/2015
6292	2^254037-110305	76473	Enzo Doria	05/2014
6293	2^253931-111109	76441	Enzo Doria	05/2014
6294	2^253926-1167	76440	Lelio R Paula	05/2013
6295	(49*10^76438-13)/9	76439	Robert Price	07/2015
6296	(21*2^253845-1)/143	76415	Lelio R Paula	02/2014
6297	10^76374+31	76375	Robert Price	03/2011
6298	10^76374-222159	76374	Patrick De Geest	05/2013
6299	2^253561-110533	76330	Enzo Doria	05/2014
6300	gcd(V(917285),5F(183457)(F(183457)+1)+1)	76321	Serge Batalov	04/2015
6301	9*5^109182+2	76316	Lelio R Paula	10/2014
6302	11^73279-3690	76313	Enzo Doria	12/2012
6303	(598*10^76309-31)/9	76311	Robert Price	02/2017
6304	11^73274-24000	76308	Enzo Doria	12/2012
6305	7^90291-6	76305	Theodore Burton	11/2005
6306	(21181*2^253432+1)/21437	76291	Lelio R Paula	06/2014
6307	6^98025+145	76279	Lelio R Paula	01/2015
6308	2^253355+1155	76268	Lelio R Paula	05/2013
6309	(73*10^76262+413)/9	76263	Robert Price	10/2017
6310	2^253292-71219	76249	Enzo Doria	04/2016
6311	7^90221-36	76246	Lelio R Paula	02/2015
6312	18^60727-3473	76229	Enzo Doria	03/2013
6313	(78557*2^253184+1)/3	76221	Lelio R Paula	06/2014
6314	(8*10^76220-83)/3	76221	Robert Price	10/2017
6315	(44791^20480+1)/(44791^4096+1)	76206	Serge Batalov	01/2017
6316	11^73163-2010	76192	Enzo Doria	12/2012
6317	2^253060+54615	76179	Lelio R Paula	05/2013
6318	2^253029+1869761	76170	Enzo Doria	05/2016
6319	2^252955-111007	76148	Enzo Doria	05/2014
6320	2*5^108931+7	76140	Lelio R Paula	10/2014
6321	(86*10^76128+121)/9	76129	Robert Price	03/2017
6322	22154*29^52050+9	76123	Curtis Bright	05/2015
6323	3^159530-112358	76116	Enzo Doria	06/2014
6324	11^73089-48	76115	Lelio R Paula	02/2015
6325	86^39337-85	76098	Norbert Schneider	10/2015
6326	(3^159505-7)/313297316	76095	Lelio R Paula	06/2012
6327	6^97783+77	76090	Lelio R Paula	01/2015
6328	2^252712-105	76074	Lelio R Paula	03/2012
6329	(10^76069-19)/9	76069	Robert Price	10/2017
6331	131^35927+2	76068	Lelio R Paula	05/2013
6330	(41*10^76067+373)/9	76068	Robert Price	04/2017
6332	2^252683-139	76066	Lelio R Paula	03/2012
6333	137^35597-136	76061	Norbert Schneider	05/2015
6334	3^159413+106	76060	Lelio R Paula	01/2015
6335	9^79677+38^79677-24^79677-3*2^79677	76032	Mike Oakes	12/2010
6336	(2^252557-9)/71	76026	Lelio R Paula	07/2012
6337	(85*10^76021-103)/9	76022	Robert Price	10/2017
6338	11^72989+80	76011	Lelio R Paula	02/2015
6339	99877!6-36	75996	Robert Price	11/2018
6340	2^252449-459523	75995	Enzo Doria	05/2015
6341	20^58408+73	75991	Lelio R Paula	01/2015
6342	2^252418-1421	75986	Yves Minet	01/2013
6343	(11*2^252396-1)/5	75980	Lelio R Paula	02/2014
6344	2^252365-110689	75970	Enzo Doria	05/2014
6345	11^72949-1020	75969	Enzo Doria	11/2012
6346	(2^252294+47)/6549	75945	Lelio R Paula	07/2012
6347	2^252261-110595	75939	Enzo Doria	05/2014
6348	7^89853+76	75935	Lelio R Paula	01/2015
6349	3^159132+56	75926	Lelio R Paula	01/2015
6350	730^26513+26513^730	75916	Norbert Schneider	11/2016
6351	(27*2^252163-1)/1945	75907	Lelio R Paula	01/2014
6352	5^108596-14846	75906	Enzo Doria	02/2013
6353	5^108560-14846	75881	Enzo Doria	02/2013
6354	2^252051-110359	75875	Enzo Doria	05/2014
6355	2^251971-110509	75851	Enzo Doria	05/2014
6356	(42457^16384+1)/327682	75819	Lelio R Paula	11/2011
6357	99655!6-2	75811	Robert Price	07/2017
6358	14*10^75798+1089	75800	Jens K. Andersen	11/2007
6359	2^251784-455	75795	Yves Minet	03/2012
6360	2^251780-1289	75794	Yves Minet	01/2013
6361	2^251760-215609	75788	Paul Bourdelais	03/2013
6362	99^37973+2	75781	Lelio R Paula	05/2013
6363	(185*10^75777+7)/3	75779	Robert Price	02/2017
6364	5*2^251690+3	75767	Lelio R Paula	06/2014
6365	6^97366+95	75766	Lelio R Paula	01/2015
6366	s(23010)	75760	Hans Havermann	11/2017
6367	8*6^97337-7	75744	Lelio R Paula	10/2014
6368	2^251588-111677	75736	Enzo Doria	05/2014
6369	5^108346-13256	75731	Enzo Doria	02/2013
6370	(31^50777+1)/32	75726	Robert Price	07/2013
6371	(10^75707+77)/3	75707	Robert Price	01/2017
6372	(174907#+1673)/(723915467899)	75700	Makoto Morimoto	10/2017
6373	2^251466+193	75699	Lelio R Paula	03/2012
6374	(5*2^251464+1)/9423	75695	Lelio R Paula	07/2012
6375	2^251422-109991	75686	Enzo Doria	04/2014
6376	91(10^23+1)(10^1721+1)*(10^118749+1)/(10^69+1)/(10^5163+1)/(10^39583+1)	75680	Makoto Kamada	03/2019
6377	4*5^108245-3	75661	Lelio R Paula	10/2014
6378	12^70067-11^70067	75615	Jean-Louis Charton	11/2006
6379	12^70066+95	75614	Lelio R Paula	02/2015
6380	-E20534/2063	75607	Thomas Ritschel	02/2017
6381	19^59120-50	75600	Lelio R Paula	01/2015
6382	18^60222-4697	75596	Enzo Doria	03/2013
6383	18^60211-4355	75582	Enzo Doria	03/2013
6384	7*2^251014-9	75564	Lelio R Paula	06/2014
6385	6^97101-25	75560	Lelio R Paula	01/2015
6386	8^83663-7^83663	75556	Jean-Louis Charton	01/2004
6387	3^158331-140	75544	Lelio R Paula	01/2015
6389	(37^48157-1)/36	75519	Robert Price	03/2012
6390	(19*10^75518-43)/3	75519	Robert Price	10/2017
6388	2^250868-4229	75519	Yves Minet	08/2018
6391	10^75516+31467	75517	Patrick De Geest	03/2016
6393	10^75516-10^2256-1	75516	Serge Batalov	01/2011
6392	10^75516-66591	75516	Patrick De Geest	03/2016
6394	2^250851-187	75514	Lelio R Paula	03/2012
6395	(43*10^75498-7)/9	75499	Robert Price	12/2014
6396	(3^158244-5)/247916	75497	Lelio R Paula	06/2012
6397	4*5^107971-3	75470	Lelio R Paula	10/2014
6398	(25*10^75465+71)/3	75466	Robert Price	01/2017
6399	(5*2^250681-1)/999	75461	Lelio R Paula	01/2014
6400	(182*10^75456+1)/3	75458	Robert Price	02/2017
6401	(2^250669-9)/98897729	75451	Lelio R Paula	07/2012
6402	10^75441+13	75442	Robert Price	01/2011
6403	10^75441-9923	75441	Patrick De Geest	05/2013
6404	(27*2^250546-1)/6457	75420	Lelio R Paula	01/2014
6405	5*7^89231-6	75410	Lelio R Paula	10/2014
6407	2^250503-16995	75409	Lelio R Paula	05/2013
6406	11^72411-28	75409	Lelio R Paula	02/2015
6408	3*5^107860-8	75392	Lelio R Paula	10/2014
6409	(34*10^75387-403)/9	75388	Robert Price	10/2017
6411	2^250426+29835	75386	Lelio R Paula	05/2013
6410	8*3^157999-7	75386	Lelio R Paula	05/2014
6412	(88*10^75381-43)/9	75382	Robert Price	11/2015
6413	2^250382-111755	75373	Enzo Doria	05/2014
6414	2^250374-2798051	75371	Eric Chen	03/2016
6415	(22*10^75368-1)/3	75369	Robert Price	12/2014
6416	2^250369-4543	75369	Yves Minet	03/2019
6417	(19*10^75338+119)/3	75339	Robert Price	02/2017
6418	2^250223-1859167	75325	Enzo Doria	03/2016
6419	(3^157854-7)/66025282	75308	Lelio R Paula	06/2012
6420	3^157831-98	75305	Lelio R Paula	01/2015
6421	(46^45281+11^45281)/57	75290	Serge Batalov	12/2016
6422	92^38335-91	75282	Norbert Schneider	01/2016
6423	2^250020+18915	75264	Lelio R Paula	05/2013
6424	2^250002+8193	75259	Lelio R Paula	05/2013
6425	(11*2^249977-7)/15	75251	Renaud Lifchitz	02/2011
6426	(2^249968+78557)/63	75247	Lelio R Paula	07/2012
6427	(5*10^75244+91)/3	75245	Robert Price	11/2016
6428	(10489!)^2+Prime(10489)	75242	Robert Price	08/2014
6429	14^65644+67	75237	Lelio R Paula	01/2015
6430	(2^249928-5)/11859059	75229	Lelio R Paula	06/2012
6431	129^35638+2	75218	Lelio R Paula	05/2013
6432	2^249853-110475	75214	Enzo Doria	05/2014
6433	2^249762+75409	75186	Enzo Doria	04/2016
6434	565^27318+27318^565	75181	Norbert Schneider	12/2016
6435	(2^249741-7)/685	75177	Lelio R Paula	06/2012
6436	2^249726-112181	75176	Enzo Doria	06/2014
6437	2^249721+11715	75174	Lelio R Paula	05/2013
6438	(38661^16384+1)/2	75158	Lelio R Paula	11/2011
6439	2^249658-47355	75155	Lelio R Paula	05/2013
6440	155^34311+2	75153	Lelio R Paula	05/2013
6441	(10^87682+1)/(10^12526+1)/990099009901	75145	Maksym Voznyy	06/2015
6442	(23*2^249602+1)/93	75138	Lelio R Paula	08/2012
6443	2^249522+8415	75114	Lelio R Paula	05/2013
6444	2^249489-110911	75104	Enzo Doria	05/2014
6445	(28*10^75078+131)/3	75079	Robert Price	02/2017
6446	(206*10^75073-17)/9	75075	Robert Price	03/2017
6447	2^249368-110573	75068	Enzo Doria	05/2014
6448	NaturalLogarithmOf10(75067)	75067	Eric W. Weisstein	10/2015
6449	(2^249375+78557)/45056125	75062	Lelio R Paula	07/2012
6450	(26*10^75055-173)/3	75056	Robert Price	10/2017
6451	2^249272+193	75039	Lelio R Paula	03/2012
6452	14^65468+43	75035	Lelio R Paula	01/2015
6453	37^47844+36	75030	Norbert Schneider	05/2014
6454	(52*10^75027-7)/9	75028	Robert Price	12/2014
6455	20^57653+89	75009	Lelio R Paula	01/2015
6456	2^249061-1868353	74975	Enzo Doria	04/2016
6457	7^88713+2*3^88713	74972	Mike Oakes	07/2010
6458	2*6^96313+5	74947	Lelio R Paula	10/2014
6459	(8*10^74944+49)/3	74945	Robert Price	03/2016
6460	300^30247+30247^300	74926	Norbert Schneider	11/2014
6461	2^248866-171	74917	Lelio R Paula	03/2012
6462	6*5^107168-7	74908	Lelio R Paula	10/2014
6463	11^71926+78	74904	Lelio R Paula	02/2015
6464	2^248824+1869391	74904	Enzo Doria	05/2016
6465	2^248816+1111	74902	Lelio R Paula	01/2011
6466	V(388219)	74890	Serge Batalov	03/2015
6467	159^34017+158	74885	Norbert Schneider	12/2018
6468	2*F(358297)-1	74880	Henri Lifchitz	12/2009
6469	(22*10^74874-31)/9	74875	Robert Price	04/2015
6470	11^71892-76800000	74868	Enzo Doria	01/2013
6471	9*5^107107-4	74866	Lelio R Paula	10/2014
6472	2^248678-710111	74860	Paul Bourdelais	03/2013
6473	(14*10^74858+211)/9	74859	Robert Price	11/2017
6474	13^67194+12	74851	Lelio R Paula	01/2015
6475	(7*2^248634+1)/71	74846	Lelio R Paula	08/2012
6476	11^71867-3090	74842	Enzo Doria	12/2012
6477	2^248609+262145	74839	Lelio R Paula	05/2013
6478	3^156852+50	74838	Lelio R Paula	01/2015
6479	18^59607-11	74824	Lelio R Paula	01/2015
6480	2^248556-110507	74823	Enzo Doria	05/2014
6481	7^88531-36	74818	Lelio R Paula	01/2015
6482	p(15738)#/2+1024	74814	Robert Price	07/2017
6483	4*3^156740-5	74785	Lelio R Paula	05/2014
6484	(32*10^74773-41)/9	74774	Robert Price	05/2015
6485	(29*2^248384-1)/13	74772	Lelio R Paula	01/2014
6486	19401!+19401#+1	74765	D. Gazzoni Filho & Lucas Teixeira	06/2005
6487	2^248357-12797413	74763	Enzo Doria	03/2016
6488	42^46057+41	74762	Lelio R Paula	07/2012
6489	11^71784-3000	74756	Enzo Doria	12/2012
6490	19^58458+18	74754	Lelio R Paula	01/2015
6491	12^69265-35	74750	Lelio R Paula	02/2015
6492	11^71771-48000	74742	Enzo Doria	12/2012
6493	(7*10^74741+197)/3	74742	Robert Price	07/2017
6494	(2^248282-5)/50129	74736	Lelio R Paula	06/2012
6495	2^248252-110105	74732	Enzo Doria	04/2014
6496	(7*10^74729+71)/3	74730	Robert Price	03/2016
6497	3^156614-50	74724	Lelio R Paula	01/2015
6498	(7*2^248213+1)/135	74719	Lelio R Paula	07/2012
6499	(2^248173+78557)/767	74705	Lelio R Paula	07/2012
6500	125^35622+124	74697	Norbert Schneider	02/2015

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Probable Primes Top 10000

(252675 PRPs in the top)