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	7^91966-32	77721	Lelio R Paula	02/2015
6252	35^50327+2	77709	Lelio R Paula	05/2013
6253	24^56298+23	77704	Norbert Schneider	12/2016
6254	(2^258105+78557)/19	77697	Lelio R Paula	10/2012
6255	2^258079+179	77690	Lelio R Paula	03/2012
6256	2^258062-113111	77685	Enzo Doria	07/2014
6257	80^40807-79	77660	Norbert Schneider	03/2015
6258	(10^77637+359)/9	77637	Serge Batalov	12/2014
6259	2^257862-165	77625	Lelio R Paula	03/2012
6260	(25*2^257853+1)/3	77623	Lelio R Paula	07/2012
6261	(2^257869+1)/(3*18645362967379)	77613	Henri Lifchitz	04/2005
6262	6^99728+71	77604	Lelio R Paula	01/2015
6263	2^257778-112767	77599	Enzo Doria	06/2014
6264	(31*2^257771+1)/537	77596	Lelio R Paula	07/2012
6265	2^257729-73	77585	Lelio R Paula	03/2012
6266	2^257689-63	77573	Lelio R Paula	03/2012
6267	(47*10^77572+493)/9	77573	Robert Price	11/2017
6268	(78557*2^257665+1)/6108725	77564	Lelio R Paula	06/2014
6269	(3^162563+8)/2885	77559	Lelio R Paula	10/2012
6270	2^257636-110235	77557	Enzo Doria	05/2014
6271	(23*10^77556+97)/3	77557	Robert Price	02/2017
6272	2^257621-110071	77552	Enzo Doria	04/2014
6273	2^257567-64875	77536	Lelio R Paula	06/2013
6274	2*7^91674+9	77474	Lelio R Paula	10/2014
6275	(17*10^77427-47)/3	77428	Robert Price	05/2017
6276	10^77418+841683	77419	Patrick De Geest	06/2013
6277	10^77418-33	77418	Robert Price	05/2011
6278	19^60539-36	77415	Lelio R Paula	03/2015
6279	37401!!-1024	77397	Robert Price	11/2015
6280	11^74313-18750	77390	Enzo Doria	12/2012
6282	2^257044-112883	77378	Enzo Doria	06/2014
6281	8*10^77377+51	77378	Robert Price	05/2017
6283	2*7^91553+9	77372	Lelio R Paula	10/2014
6284	713^27118+27118^713	77371	Norbert Schneider	12/2016
6285	2^256920-111155	77341	Enzo Doria	05/2014
6286	2^256896-6555	77334	Lelio R Paula	06/2013
6287	(52*10^77322-7)/9	77323	Robert Price	12/2014
6288	2^256849-112939	77320	Enzo Doria	06/2014
6289	(4*10^77309-31)/9	77309	Erik Branger	05/2011
6290	(3^161988+7)/41864	77284	Lelio R Paula	10/2012
6291	(14^67421-1)/13	77272	Paul Bourdelais	09/2008
6292	5*3^161923-4	77258	Lelio R Paula	06/2014
6293	2^256552-1499	77230	Yves Minet	05/2013
6294	2^256460-112757	77203	Enzo Doria	06/2014
6295	2^256398+23299	77184	Yves Minet	02/2011
6296	2^256391-1155*256391	77182	Henri Lifchitz	03/2005
6297	(2^256391-9)/56593	77177	Lelio R Paula	10/2012
6298	(2^256308+9)/10585	77153	Lelio R Paula	10/2012
6300	21^58348-2	77149	Lelio R Paula	08/2013
6299	(17*2^256291-1)/4785	77149	Lelio R Paula	02/2014
6301	(5*2^256274-1)/2141	77144	Lelio R Paula	02/2014
6302	19^60321+82	77136	Lelio R Paula	03/2015
6303	5*2^256233-3	77135	Lelio R Paula	06/2014
6304	3*2^256149+7	77110	Lelio R Paula	06/2014
6305	3^161594-106	77100	Lelio R Paula	02/2015
6306	2^256114-185	77098	Lelio R Paula	03/2012
6307	8^85349-85349^8	77078	Norbert Schneider	05/2017
6308	2^256043-2786377	77077	Enzo Doria	03/2016
6309	2^255973+1869947	77056	Enzo Doria	05/2016
6310	12^71393-43	77046	Lelio R Paula	02/2015
6311	15^65490+44	77023	Lelio R Paula	02/2015
6312	(3^161411-7)/940	77010	Lelio R Paula	10/2012
6313	lucasU(1107,1,25297)-lucasU(1107,1,25296)	77005	Mike Oakes	05/2009
6314	(570^27943-1)/569	77005	Serge Batalov	12/2016
6315	2^255750-75	76989	Lelio R Paula	03/2012
6316	3*6^98926-5	76980	Lelio R Paula	10/2014
6317	18^61320-1433	76974	Enzo Doria	03/2013
6318	6^98916-17093	76972	Enzo Doria	02/2013
6319	2^255659-110131	76962	Enzo Doria	04/2014
6320	12^71303+91	76949	Lelio R Paula	02/2015
6321	18^61298+59	76946	Lelio R Paula	02/2015
6322	(223^32768+1)/131074	76945	Lelio R Paula	02/2009
6323	(2^255613-5)/281517	76942	Lelio R Paula	10/2012
6324	18^61290-11	76936	Lelio R Paula	02/2015
6326	63^42752-2	76926	Lelio R Paula	08/2013
6325	(11*2^255545-1)/117	76926	Lelio R Paula	02/2014
6327	2^255517+56387	76919	Yves Minet	02/2011
6328	2^255499-112567	76913	Enzo Doria	06/2014
6329	2^255492+345	76911	Lelio R Paula	06/2013
6330	10^76875+217591	76876	Patrick De Geest	05/2013
6332	10^76875-53	76875	Robert Price	05/2011
6331	11^73819-5880	76875	Enzo Doria	01/2013
6333	2^255313+18915	76857	Lelio R Paula	06/2013
6334	(2^255320-1017)/1446667	76853	Lelio R Paula	10/2012
6335	2^255296+5775	76852	Lelio R Paula	06/2013
6336	14^67052-29	76851	Lelio R Paula	02/2015
6337	(8*10^76840+43)/3	76841	Robert Price	10/2017
6338	(7*10^76818-313)/9	76818	Robert Price	11/2016
6339	10^76801+69	76802	Robert Price	03/2011
6340	10^76801-80943	76801	Patrick De Geest	06/2013
6341	2^255105+57	76795	Lelio R Paula	03/2012
6342	(lucasV(1,2,510187)+2)/(3511)	76789	Mike Oakes	04/2017
6343	(2^255097-7)/20020055	76785	Lelio R Paula	10/2012
6344	2^255055+1869353	76780	Enzo Doria	05/2016
6345	17^62396-90	76776	Lelio R Paula	03/2015
6346	7^90833-60	76763	Lelio R Paula	02/2015
6347	13^68901-56	76752	Lelio R Paula	03/2015
6348	2^254961+1869917	76751	Enzo Doria	05/2016
6349	9*5^109791-8	76742	Lelio R Paula	10/2014
6350	82^40089+40089^82	76723	Serge Batalov	02/2012
6351	2^254861-2790013	76721	Enzo Doria	03/2016
6352	(10^278+1)*(10^115926+1)/(10^834+1)/(10^38642+1)/20459779741	76718	Makoto Kamada	03/2019
6353	10^76705+13	76706	Robert Price	01/2011
6354	10^76705-94077	76705	Patrick De Geest	06/2013
6355	(5*2^254785-1)/999	76696	Lelio R Paula	02/2014
6356	2^254758-110405	76690	Enzo Doria	05/2014
6357	2^254716-3779	76678	Yves Minet	04/2017
6358	2^254708-110507	76675	Enzo Doria	05/2014
6359	(47*10^76672+133)/9	76673	Robert Price	04/2017
6360	2^254670-112901	76664	Enzo Doria	06/2014
6361	(3^160665+7)/981350	76651	Lelio R Paula	10/2012
6362	2^254598-113183	76642	Enzo Doria	07/2014
6363	19^59932+22	76639	Lelio R Paula	01/2015
6364	2^254569-112213	76633	Enzo Doria	06/2014
6365	2*5^109626+9	76626	Lelio R Paula	10/2014
6366	2^254521+1872527	76619	Enzo Doria	05/2016
6367	(76*10^76615+167)/9	76616	Robert Price	08/2016
6368	25^54799-24^54799	76606	Robert Price	07/2012
6369	(24737*2^254464+1)/9	76605	Lelio R Paula	06/2014
6370	12^70961-85	76580	Lelio R Paula	02/2015
6371	7^90590-38	76558	Lelio R Paula	02/2015
6372	2^254304+5227	76554	Lelio R Paula	06/2013
6373	(76*10^76547-211)/9	76548	Robert Price	10/2017
6374	18^60979-5363	76546	Enzo Doria	03/2013
6375	(21181*2^254264+1)/55314379	76538	Lelio R Paula	06/2014
6377	(34*10^76547-7)/9/61/94529/214807	76536	Makoto Morimoto	05/2016
6376	(7*10^76536-313)/9	76536	Robert Price	11/2016
6379	2^254239-27	76534	Lelio R Paula	03/2012
6378	2^254238-1841	76534	Yves Minet	03/2013
6380	(10^76537-1)/9/66127969	76529	Jens K. Andersen	04/2009
6381	2^254189-112225	76519	Enzo Doria	06/2014
6382	18^60938-1397	76494	Enzo Doria	03/2013
6383	2^254075-2788417	76485	Enzo Doria	03/2016
6384	7*10^76483-23	76484	Robert Price	04/2016
6385	2^254042-112913	76475	Enzo Doria	06/2014
6386	14^66723-37	76474	Lelio R Paula	02/2015
6387	2^254037-110305	76473	Enzo Doria	05/2014
6388	2^253931-111109	76441	Enzo Doria	05/2014
6389	2^253926-1167	76440	Lelio R Paula	05/2013
6390	(49*10^76438-13)/9	76439	Robert Price	07/2015
6391	(21*2^253845-1)/143	76415	Lelio R Paula	02/2014
6392	10^76374+31	76375	Robert Price	03/2011
6393	10^76374-222159	76374	Patrick De Geest	05/2013
6394	2^253561-110533	76330	Enzo Doria	05/2014
6395	gcd(V(917285),5F(183457)(F(183457)+1)+1)	76321	Serge Batalov	04/2015
6396	9*5^109182+2	76316	Lelio R Paula	10/2014
6397	11^73279-3690	76313	Enzo Doria	12/2012
6398	(598*10^76309-31)/9	76311	Robert Price	02/2017
6399	11^73274-24000	76308	Enzo Doria	12/2012
6400	7^90291-6	76305	Theodore Burton	11/2005
6401	(21181*2^253432+1)/21437	76291	Lelio R Paula	06/2014
6402	6^98025+145	76279	Lelio R Paula	01/2015
6403	2^253355+1155	76268	Lelio R Paula	05/2013
6404	(73*10^76262+413)/9	76263	Robert Price	10/2017
6405	2^253292-71219	76249	Enzo Doria	04/2016
6406	7^90221-36	76246	Lelio R Paula	02/2015
6407	18^60727-3473	76229	Enzo Doria	03/2013
6408	(78557*2^253184+1)/3	76221	Lelio R Paula	06/2014
6409	(8*10^76220-83)/3	76221	Robert Price	10/2017
6410	(44791^20480+1)/(44791^4096+1)	76206	Serge Batalov	01/2017
6411	11^73163-2010	76192	Enzo Doria	12/2012
6412	2^253060+54615	76179	Lelio R Paula	05/2013
6413	2^253029+1869761	76170	Enzo Doria	05/2016
6414	2^252955-111007	76148	Enzo Doria	05/2014
6415	2*5^108931+7	76140	Lelio R Paula	10/2014
6416	(86*10^76128+121)/9	76129	Robert Price	03/2017
6417	22154*29^52050+9	76123	Curtis Bright	05/2015
6418	3^159530-112358	76116	Enzo Doria	06/2014
6419	11^73089-48	76115	Lelio R Paula	02/2015
6420	86^39337-85	76098	Norbert Schneider	10/2015
6421	(3^159505-7)/313297316	76095	Lelio R Paula	06/2012
6422	6^97783+77	76090	Lelio R Paula	01/2015
6423	2^252712-105	76074	Lelio R Paula	03/2012
6424	(10^76069-19)/9	76069	Robert Price	10/2017
6426	131^35927+2	76068	Lelio R Paula	05/2013
6425	(41*10^76067+373)/9	76068	Robert Price	04/2017
6427	2^252683-139	76066	Lelio R Paula	03/2012
6428	137^35597-136	76061	Norbert Schneider	05/2015
6429	3^159413+106	76060	Lelio R Paula	01/2015
6430	9^79677+38^79677-24^79677-3*2^79677	76032	Mike Oakes	12/2010
6431	(2^252557-9)/71	76026	Lelio R Paula	07/2012
6432	(85*10^76021-103)/9	76022	Robert Price	10/2017
6433	11^72989+80	76011	Lelio R Paula	02/2015
6434	99877!6-36	75996	Robert Price	11/2018
6435	2^252449-459523	75995	Enzo Doria	05/2015
6436	20^58408+73	75991	Lelio R Paula	01/2015
6437	2^252418-1421	75986	Yves Minet	01/2013
6438	(11*2^252396-1)/5	75980	Lelio R Paula	02/2014
6439	2^252365-110689	75970	Enzo Doria	05/2014
6440	11^72949-1020	75969	Enzo Doria	11/2012
6441	(2^252294+47)/6549	75945	Lelio R Paula	07/2012
6442	2^252261-110595	75939	Enzo Doria	05/2014
6443	7^89853+76	75935	Lelio R Paula	01/2015
6444	3^159132+56	75926	Lelio R Paula	01/2015
6445	730^26513+26513^730	75916	Norbert Schneider	11/2016
6446	(27*2^252163-1)/1945	75907	Lelio R Paula	01/2014
6447	5^108596-14846	75906	Enzo Doria	02/2013
6448	5^108560-14846	75881	Enzo Doria	02/2013
6449	2^252051-110359	75875	Enzo Doria	05/2014
6450	2^251971-110509	75851	Enzo Doria	05/2014
6451	(42457^16384+1)/327682	75819	Lelio R Paula	11/2011
6452	2^251842-4715	75812	Yves Minet	05/2019
6453	99655!6-2	75811	Robert Price	07/2017
6454	14*10^75798+1089	75800	Jens K. Andersen	11/2007
6455	2^251784-455	75795	Yves Minet	03/2012
6456	2^251780-1289	75794	Yves Minet	01/2013
6457	2^251760-215609	75788	Paul Bourdelais	03/2013
6458	99^37973+2	75781	Lelio R Paula	05/2013
6459	(185*10^75777+7)/3	75779	Robert Price	02/2017
6460	5*2^251690+3	75767	Lelio R Paula	06/2014
6461	6^97366+95	75766	Lelio R Paula	01/2015
6462	s(23010)	75760	Hans Havermann	11/2017
6463	8*6^97337-7	75744	Lelio R Paula	10/2014
6464	2^251588-111677	75736	Enzo Doria	05/2014
6465	5^108346-13256	75731	Enzo Doria	02/2013
6466	(31^50777+1)/32	75726	Robert Price	07/2013
6467	(10^75707+77)/3	75707	Robert Price	01/2017
6468	(174907#+1673)/(723915467899)	75700	Makoto Morimoto	10/2017
6469	2^251466+193	75699	Lelio R Paula	03/2012
6470	(5*2^251464+1)/9423	75695	Lelio R Paula	07/2012
6471	2^251422-109991	75686	Enzo Doria	04/2014
6472	91(10^23+1)(10^1721+1)*(10^118749+1)/(10^69+1)/(10^5163+1)/(10^39583+1)	75680	Makoto Kamada	03/2019
6473	4*5^108245-3	75661	Lelio R Paula	10/2014
6474	12^70067-11^70067	75615	Jean-Louis Charton	11/2006
6475	12^70066+95	75614	Lelio R Paula	02/2015
6476	-E20534/2063	75607	Thomas Ritschel	02/2017
6477	19^59120-50	75600	Lelio R Paula	01/2015
6478	18^60222-4697	75596	Enzo Doria	03/2013
6479	18^60211-4355	75582	Enzo Doria	03/2013
6480	7*2^251014-9	75564	Lelio R Paula	06/2014
6481	6^97101-25	75560	Lelio R Paula	01/2015
6482	8^83663-7^83663	75556	Jean-Louis Charton	01/2004
6483	3^158331-140	75544	Lelio R Paula	01/2015
6485	(37^48157-1)/36	75519	Robert Price	03/2012
6484	(19*10^75518-43)/3	75519	Robert Price	10/2017
6486	2^250868-4229	75519	Yves Minet	08/2018
6487	10^75516+31467	75517	Patrick De Geest	03/2016
6489	10^75516-10^2256-1	75516	Serge Batalov	01/2011
6488	10^75516-66591	75516	Patrick De Geest	03/2016
6490	2^250851-187	75514	Lelio R Paula	03/2012
6491	(43*10^75498-7)/9	75499	Robert Price	12/2014
6492	(3^158244-5)/247916	75497	Lelio R Paula	06/2012
6493	4*5^107971-3	75470	Lelio R Paula	10/2014
6494	(25*10^75465+71)/3	75466	Robert Price	01/2017
6495	(5*2^250681-1)/999	75461	Lelio R Paula	01/2014
6496	(182*10^75456+1)/3	75458	Robert Price	02/2017
6497	(2^250669-9)/98897729	75451	Lelio R Paula	07/2012
6498	10^75441+13	75442	Robert Price	01/2011
6499	10^75441-9923	75441	Patrick De Geest	05/2013
6500	(27*2^250546-1)/6457	75420	Lelio R Paula	01/2014

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PRP Records

Probable Primes Top 10000

(252932 PRPs in the top)