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 ?
9251	13739^4600+4600^13739	50323	Hans Havermann	10/2015
9252	11508^12391+12391^11508	50320	Norbert Schneider	06/2014
9253	2^167132-2163	50312	Yves Minet	08/2013
9254	7^59527-62	50307	Lelio R Paula	06/2012
9255	(310027^9161+1)/310028	50302	Faysal YAtim	04/2008
9256	(12301^12301+74)/3^2/5^3/11/17/1151	50302	Makoto Morimoto	07/2016
9257	2^167083-112519	50297	Enzo Doria	06/2014
9258	272^20659-20659^272	50296	Norbert Schneider	09/2015
9259	25337!!-16	50290	Robert Price	06/2015
9260	9722^12611-12611^9722	50290	Norbert Schneider	12/2016
9262	(15*2^167013+1)/649	50275	Lelio R Paula	07/2012
9261	19^39315-12	50275	Lelio R Paula	01/2013
9263	5^71925-36	50274	Lelio R Paula	06/2012
9264	2^167002+2799139	50273	Enzo Doria	04/2016
9265	10957^12444-12444^10957	50270	Norbert Schneider	07/2013
9266	8*10^50253-99	50254	Robert Price	02/2017
9268	5^71894-54	50252	Lelio R Paula	06/2012
9267	(127^23887+1)/128	50252	Richard Fischer	04/2017
9269	18^40028-5	50247	Lelio R Paula	01/2013
9270	(3*2^166904+1)/1279	50241	Lelio R Paula	07/2012
9271	24^36397+23	50236	Norbert Schneider	12/2013
9272	7984*29^34345+21	50230	Curtis Bright	05/2015
9273	3^105248-13528	50217	Enzo Doria	02/2013
9274	6^64532-65	50216	Lelio R Paula	06/2012
9275	5^71834-20616	50210	Enzo Doria	03/2013
9276	(31*2^166778-1)/3651	50204	Lelio R Paula	01/2014
9277	2^166752-112397	50198	Enzo Doria	06/2014
9278	(12277^12277+1746)/17/37/151	50197	Makoto Morimoto	07/2016
9279	11^48199-930	50195	Enzo Doria	11/2012
9280	3*10^50194-7	50195	Erik Branger	11/2013
9281	9992^12549+12549^9992	50192	Norbert Schneider	10/2015
9282	2^166708+157	50185	Lelio R Paula	01/2011
9283	(1338272^8192+1)/65537	50184	Syoichiro Yamada	06/2008
9284	7*2^166685+3	50179	Lelio R Paula	02/2014
9285	7*2^166671-9	50174	Lelio R Paula	02/2014
9286	9*2^166670+7	50174	Lelio R Paula	02/2014
9287	2^166670-112541	50173	Enzo Doria	06/2014
9288	2^166657+465	50169	Lelio R Paula	11/2011
9289	17^40768-20	50163	Lelio R Paula	01/2013
9290	2^166596-78795	50151	Lelio R Paula	07/2011
9291	135^23541+134	50151	Norbert Schneider	04/2015
9292	24^36335-673	50150	Enzo Doria	03/2013
9293	(12269^12269+291)/2^8/5/7/19/41/109/10426349	50150	Makoto Morimoto	07/2016
9294	(28*10^50147-97)/3	50148	Robert Price	07/2016
9295	263^20718-20718^263	50137	Norbert Schneider	09/2015
9296	t(167020)	50133	Robert Price	01/2015
9297	(12263^12263+1442)/127/5479	50133	Makoto Morimoto	07/2016
9298	2868(2340(29023#-29527)(2340(29023#-29527)+3)+1)(2868(2340(29023#-29527)(2340*(29023#-29527)	50129	Pierre CAMI	06/2008
9299	12^46445-19	50123	Lelio R Paula	12/2012
9300	2^166501-14593	50122	Enzo Doria	04/2013
9301	(31*2^166509-1)/3684077	50120	Lelio R Paula	01/2014
9302	2^166483-169	50117	Lelio R Paula	01/2011
9303	9^52515+2*6^52515-4^52515	50113	Mike Oakes	04/2010
9304	(23*2^166487-1)/33770499	50112	Lelio R Paula	01/2014
9305	2*5^71689-9	50109	Lelio R Paula	09/2014
9306	13495^5154+5154^13495	50096	Hans Havermann	04/2016
9307	6^64369-119	50089	Lelio R Paula	06/2012
9308	9224^12633-12633^9224	50089	Norbert Schneider	12/2016
9309	2^166370-112541	50083	Enzo Doria	06/2014
9310	(12253^12253+1454)/3^3/251/947/292427	50081	Makoto Morimoto	07/2016
9311	2^166339-112321	50074	Enzo Doria	06/2014
9312	5^71637-22	50073	Lelio R Paula	06/2012
9313	Phi(50131,10)/89010999409/9123691040118653/18020045580157867/30621915318063801947	50068	Maksym Voznyy	01/2013
9314	(4*10^50060+137)/3	50061	Robert Price	07/2017
9315	5^71618-13826	50059	Enzo Doria	02/2013
9316	15^42563-2	50058	Lelio R Paula	11/2012
9317	1943^15222+15222^1943	50058	Serge Batalov	05/2014
9318	11641^12310+12310^11641	50053	Norbert Schneider	04/2014
9319	13537!-2^13537+1	50052	Joe McLean	06/2006
9320	2^166227-164467	50040	Gary Barnes	08/2009
9321	12241^12241+4756	50039	Makoto Morimoto	07/2016
9322	(106*10^50035-1)/3	50037	Serge Batalov	12/2014
9323	11^48044-810	50033	Enzo Doria	11/2012
9324	15^42539+88	50030	Lelio R Paula	11/2012
9325	524^18397-523^18397	50028	Jean-Louis Charton	10/2009
9326	2^166159-14497	50019	Enzo Doria	04/2013
9327	2^166155+87855	50018	Lelio R Paula	01/2009
9328	2^166138-11655	50013	Lelio R Paula	07/2011
9329	(L(239313)-1)/5-2^9551	50013	Jorge Menendez	06/2017
9334	2^166104-112625	50003	Enzo Doria	06/2014
9330	(L(239265)-1)/5-2^906	50003	Jorge Menendez	03/2017
9331	(L(239265)-1)/5-2^3152	50003	Jorge Menendez	04/2017
9332	(L(239265)-1)/5-2^20155	50003	Jorge Menendez	04/2017
9333	(L(239265)-1)/5-2^78912	50003	Jorge Menendez	04/2017
9335	2^166100+199015	50002	Lelio R Paula	05/2008
9336	10^50000+65859	50001	Milton L. Brown	02/2006
9337	(598*10^49999-31)/9	50001	Robert Price	02/2017
9358	10^49999+91701	50000	Patrick De Geest	03/2005
9338	10^50000-194303	50000	Patrick De Geest	02/2009
9339	(2^74207281/10^948782)%10^50000	50000	Michael Vang	04/2016
9340	(2^57885161/10^11608093)%10^50000	50000	Michael Vang	05/2016
9341	(2^43112609/10^788658)%10^50000	50000	Michael Vang	05/2016
9342	(2^42643801/10^3670320)%10^50000	50000	Michael Vang	05/2016
9343	(2^37156667/10^412682)%10^50000	50000	Michael Vang	05/2016
9344	(2^32582657/10^7836670)%10^50000	50000	Michael Vang	05/2016
9345	(2^24036583/10^3069021)%10^50000	50000	Michael Vang	05/2016
9346	(2^25964951/10^5214128)%10^50000	50000	Michael Vang	05/2016
9347	(2^13466917/10^157937)%10^50000	50000	Michael Vang	05/2016
9348	(2^20996011/10^6193479)%10^50000	50000	Michael Vang	05/2016
9349	(2^6972593/10^381525)%10^50000	50000	Michael Vang	05/2016
9350	(2^30402457/10^1629036)%10^50000	50000	Michael Vang	05/2016
9351	(2^3021377/10^702316)%10^50000	50000	Michael Vang	05/2016
9352	(2^1398269/10^37827)%10^50000	50000	Michael Vang	05/2016
9353	(2^2976221/10^767789)%10^50000	50000	Michael Vang	05/2016
9354	(2^859433/10^42285)%10^50000	50000	Michael Vang	06/2016
9355	(2^1257787/10^119173)%10^50000	50000	Michael Vang	06/2016
9356	(2^756839/10^136257)%10^50000	50000	Michael Vang	06/2016
9357	2*10^49999+363	50000	Makoto Morimoto	09/2016
9359	10^49999-4149	49999	Patrick De Geest	02/2009
9360	10484^12433-12433^10484	49988	Norbert Schneider	07/2013
9361	2^166052+145	49987	Lelio R Paula	01/2011
9362	(10^50001+10936)/(2^319241587200315974507)	49983	Makoto Morimoto	09/2016
9363	1111*2^166022-555	49981	Henri Lifchitz	02/2005
9364	11^47993+30	49980	Lelio R Paula	10/2012
9365	2^166000-78795	49971	Lelio R Paula	07/2011
9366	13517!-13517#+1	49970		03/2005
9368	2^165995-113227	49970	Enzo Doria	07/2014
9367	(12227^12227+1092)/5/11/17/37^2	49970	Makoto Morimoto	07/2016
9369	17^40609+14	49968	Lelio R Paula	11/2012
9371	(1257656^8192+1)/65537	49963	Syoichiro Yamada	06/2008
9370	(3^104735-8)/1493199931	49963	Lelio R Paula	03/2012
9372	2^165969-112711	49962	Enzo Doria	06/2014
9373	2^165910-7605	49944	Lelio R Paula	04/2009
9374	36313!3-59049	49942	Robert Price	12/2015
9375	2^165884-45	49937	Lelio R Paula	08/2010
9378	(1246892^8192+1)/65537	49933	Syoichiro Yamada	06/2008
9376	3^104654+104	49933	Lelio R Paula	07/2012
9377	7452^12895-12895^7452	49933	Norbert Schneider	05/2017
9379	9035^12622+12622^9035	49932	Norbert Schneider	01/2016
9380	(22699*2^165838+1)/3287	49924	Lelio R Paula	05/2014
9381	6^64149-85	49918	Lelio R Paula	06/2012
9382	(7*10^49913+71)/3	49914	Robert Price	03/2016
9383	2^165799-114817	49911	Enzo Doria	05/2015
9384	2^165789+35	49908	Lelio R Paula	08/2010
9385	2^165783-121	49906	Lelio R Paula	01/2011
9386	2^165760-112649	49899	Enzo Doria	06/2014
9387	(11*2^165758+1)/135	49898	Lelio R Paula	01/2012
9388	2^165747+63	49895	Lelio R Paula	04/2009
9389	(7*10^49893-13)/3	49894	Robert Price	06/2016
9390	298^20163-20163^298	49888	Norbert Schneider	08/2015
9391	(49885^49885)/(10^184474)	49885	James G. Merickel	08/2015
9392	17^40540+36	49883	Lelio R Paula	11/2012
9393	(12211^12211+4312)/13/17/31/1297/1483/1627/9923/36433	49882	Makoto Morimoto	07/2016
9394	2^165676-112949	49874	Enzo Doria	06/2014
9395	(12203^12203+992)/11	49867	Makoto Morimoto	07/2016
9396	7784^12811-12811^7784	49851	Norbert Schneider	03/2017
9397	2^165581-745	49845	Yves Minet	01/2012
9398	2^165576+74821	49844	Enzo Doria	04/2016
9399	13318^5527+5527^13318	49843	Hans Havermann	04/2016
9401	2^165561-2155	49839	Yves Minet	08/2013
9400	(12197^12197+1755)/2^4	49839	Makoto Morimoto	07/2016
9402	7406^12879+12879^7406	49837	Norbert Schneider	03/2016
9403	8530^12677+12677^8530	49833	Norbert Schneider	01/2016
9404	(3^52222-69)^2-71	49833	Jorge Menendez	02/2017
9405	12^46175+29	49832	Lelio R Paula	10/2012
9406	2^165488-12969	49817	Enzo Doria	10/2012
9407	2^165473+58905	49813	Lelio R Paula	04/2009
9408	20^38284+49	49809	Lelio R Paula	11/2012
9410	3^104388-20	49806	Lelio R Paula	07/2012
9409	(10^49806+119)/3	49806	Serge Batalov	12/2014
9411	(1202206^8192+1)/65537	49803	Syoichiro Yamada	06/2008
9412	(4*10^49801+11)/3	49802	Erik Branger	05/2013
9413	5^71240-15476	49795	Enzo Doria	02/2013
9414	7*3^104334-4	49781	Lelio R Paula	03/2014
9415	(136*10^49774-1)/9	49776	Serge Batalov	12/2014
9416	3^104297+8680	49763	Lelio R Paula	07/2012
9417	(F(10)^28579-F(9)^28579)/F(8)	49737	Wayne Halsdorf	03/2010
9418	(3^104243+1)/4	49736	Kamil Duszenko	05/2004
9419	(10223*2^165183+1)/55	49728	Lelio R Paula	05/2014
9420	6^63895+101	49720	Lelio R Paula	06/2012
9421	3^104194+100	49714	Lelio R Paula	07/2012
9422	10^49711+103593	49712	Patrick De Geest	07/2017
9423	10^49711-701	49711	Robert Price	06/2017
9424	U(356793)	49710	Serge Batalov	03/2015
9425	13321^5388+5388^13321	49707	Hans Havermann	04/2016
9426	12166^12166+565	49700	Henri Lifchitz	11/2004
9427	(89*10^49689-53)/9	49690	Erik Branger	05/2013
9428	(1163126^8192+1)/65537	49685	Syoichiro Yamada	06/2008
9429	11^47709+42	49684	Lelio R Paula	10/2012
9431	(35*10^49682+1)/9	49683	Serge Batalov	05/2010
9430	(12163^12163+1194)/37/193	49683	Makoto Morimoto	07/2016
9432	3^104124+92	49680	Lelio R Paula	07/2012
9434	2^165025+165029	49678	Henri Lifchitz	04/2005
9433	14063^3408+3408^14063	49678	Hans Havermann	04/2016
9435	(2^165031+3)/48439	49675	Lelio R Paula	01/2012
9436	(7*2^165020-1)/261	49675	Lelio R Paula	01/2014
9437	2^165000+5227	49670	Lelio R Paula	05/2011
9438	(12161^12161+765)/2/13/29/277/311	49670	Makoto Morimoto	07/2016
9439	(110051^9851+1)/110052	49660	Faysal YAtim	09/2007
9440	2^164962-639791	49659	Paul Bourdelais	11/2012
9441	10^49657+31	49658	Robert Price	01/2011
9442	10^49657-12899	49657	Patrick De Geest	01/2012
9443	2^164937-193	49651	Lelio R Paula	01/2011
9444	21^37549-20^37549	49649	Jean-Louis Charton	02/2012
9445	1417^15754+15754^1417	49647	Serge Batalov	05/2014
9446	(12157^12157+2611)/2^5/11/13/1019/48197/314407	49643	Makoto Morimoto	07/2016
9447	12^45999+25	49642	Lelio R Paula	10/2012
9448	(3^104040+7)/8	49639	Lelio R Paula	03/2012
9449	2^164882-1017	49635	Lelio R Paula	06/2008
9450	(3^104053-8)/381830020743455	49632	Lelio R Paula	03/2012
9451	11^47658-180	49631	Enzo Doria	07/2012
9452	2^164859-1237	49628	Yves Minet	08/2012
9453	17^40331+98	49626	Lelio R Paula	11/2012
9454	1638^15437+15437^1638	49620	Serge Batalov	05/2014
9455	113^24160+112	49603	Norbert Schneider	09/2013
9456	13^44527+16	49601	Lelio R Paula	11/2012
9457	83^25844+82	49597	Norbert Schneider	01/2013
9458	(12143^12143+1306)/3/7/59	49593	Makoto Morimoto	07/2016
9459	114667#-p(114667)	49591	Henri Lifchitz	03/2007
9460	2^164731-1833847	49589	Enzo Doria	05/2015
9461	(625^17737+1)/626	49588	Richard Fischer	06/2013
9462	2^164714+29835	49584	Lelio R Paula	11/2011
9463	7*10^49580-69	49581	Robert Price	01/2017
9464	7*5^70922+4	49574	Lelio R Paula	09/2014
9465	(229*10^49571-1)/3	49573	Robert Price	12/2016
9466	277^20295-290	49571	Enzo Doria	06/2012
9467	2^164662-112883	49569	Enzo Doria	06/2014
9468	(1125424^8192+1)/65537	49568	Syoichiro Yamada	06/2008
9469	6^63698-35	49567	Lelio R Paula	06/2012
9470	(2^164652-3)*6-7	49566	Gilbert Mozzo	04/2016
9471	(11*10^49552+43)/9	49553	Erik Branger	05/2013
9472	2^164606+43	49552	Lelio R Paula	08/2010
9473	2^164598-113111	49549	Enzo Doria	07/2014
9474	11^47575-8100	49545	Enzo Doria	02/2013
9475	9420^12467-12467^9420	49545	Norbert Schneider	07/2013
9476	2^164581-819253	49544	Paul Bourdelais	11/2012
9477	9001^12528-12528^9001	49540	Norbert Schneider	11/2016
9478	(lucasV(1,2,329135)+2)/(5^217910247)	49533	Mike Oakes	02/2017
9479	(4*10^49529-31)/9	49529	Erik Branger	05/2011
9480	13875^3712+3712^13875	49529	Hans Havermann	03/2016
9481	7^58604-62	49527	Lelio R Paula	06/2012
9482	2^164508+105	49522	Lelio R Paula	04/2009
9483	24^35878-937	49520	Enzo Doria	03/2013
9484	(89*10^49516-17)/9	49517	Erik Branger	05/2013
9485	2^164478-167	49513	Lelio R Paula	01/2011
9486	13^44446+30	49511	Lelio R Paula	11/2012
9487	2^164466-790241	49510	Paul Bourdelais	11/2012
9488	-lucasV(-1,2,328901)	49505	Mike Oakes	01/2017
9489	(21*2^164421-1)/533	49495	Lelio R Paula	01/2014
9490	35^32052-206	49491	Enzo Doria	03/2013
9491	3^103726-11878	49490	Enzo Doria	02/2013
9492	(3^103726+7)/512	49488	Lelio R Paula	03/2012
9493	(12119^12119+6270)/13	49487	Makoto Morimoto	07/2016
9494	10^49484+16537	49485	Patrick De Geest	01/2016
9496	10^49484-10^5384-1	49484	Serge Batalov	01/2011
9495	10^49484-91539	49484	Patrick De Geest	01/2016
9497	3*2^164365-7	49480	Lelio R Paula	02/2014
9498	(7^58543-5^58543)/2	49475	Robert Price	05/2012
9499	8482^12591+12591^8482	49464	Norbert Schneider	11/2015
9500	(29*2^164309-1)/20907	49460	Lelio R Paula	01/2014

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