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	(2^42643801/10^3670320)%10^50000	50000	Michael Vang	05/2016
9252	(2^37156667/10^412682)%10^50000	50000	Michael Vang	05/2016
9253	(2^32582657/10^7836670)%10^50000	50000	Michael Vang	05/2016
9254	(2^24036583/10^3069021)%10^50000	50000	Michael Vang	05/2016
9255	(2^25964951/10^5214128)%10^50000	50000	Michael Vang	05/2016
9256	(2^13466917/10^157937)%10^50000	50000	Michael Vang	05/2016
9257	(2^20996011/10^6193479)%10^50000	50000	Michael Vang	05/2016
9258	(2^6972593/10^381525)%10^50000	50000	Michael Vang	05/2016
9259	(2^30402457/10^1629036)%10^50000	50000	Michael Vang	05/2016
9260	(2^3021377/10^702316)%10^50000	50000	Michael Vang	05/2016
9261	(2^1398269/10^37827)%10^50000	50000	Michael Vang	05/2016
9262	(2^2976221/10^767789)%10^50000	50000	Michael Vang	05/2016
9263	(2^859433/10^42285)%10^50000	50000	Michael Vang	06/2016
9264	(2^1257787/10^119173)%10^50000	50000	Michael Vang	06/2016
9265	(2^756839/10^136257)%10^50000	50000	Michael Vang	06/2016
9266	2*10^49999+363	50000	Makoto Morimoto	09/2016
9267	10^49999-4149	49999	Patrick De Geest	02/2009
9268	10484^12433-12433^10484	49988	Norbert Schneider	07/2013
9269	2^166052+145	49987	Lelio R Paula	01/2011
9270	(10^50001+10936)/(2^319241587200315974507)	49983	Makoto Morimoto	09/2016
9271	1111*2^166022-555	49981	Henri Lifchitz	02/2005
9272	11^47993+30	49980	Lelio R Paula	10/2012
9273	2^166000-78795	49971	Lelio R Paula	07/2011
9275	13517!-13517#+1	49970		03/2005
9276	2^165995-113227	49970	Enzo Doria	07/2014
9274	(12227^12227+1092)/5/11/17/37^2	49970	Makoto Morimoto	07/2016
9277	17^40609+14	49968	Lelio R Paula	11/2012
9279	(1257656^8192+1)/65537	49963	Syoichiro Yamada	06/2008
9278	(3^104735-8)/1493199931	49963	Lelio R Paula	03/2012
9280	2^165969-112711	49962	Enzo Doria	06/2014
9281	2^165910-7605	49944	Lelio R Paula	04/2009
9282	36313!3-59049	49942	Robert Price	12/2015
9283	2^165884-45	49937	Lelio R Paula	08/2010
9285	(1246892^8192+1)/65537	49933	Syoichiro Yamada	06/2008
9284	3^104654+104	49933	Lelio R Paula	07/2012
9286	7452^12895-12895^7452	49933	Norbert Schneider	05/2017
9287	9035^12622+12622^9035	49932	Norbert Schneider	01/2016
9288	(22699*2^165838+1)/3287	49924	Lelio R Paula	05/2014
9289	6^64149-85	49918	Lelio R Paula	06/2012
9290	(7*10^49913+71)/3	49914	Robert Price	03/2016
9291	2^165799-114817	49911	Enzo Doria	05/2015
9292	2^165789+35	49908	Lelio R Paula	08/2010
9293	2^165783-121	49906	Lelio R Paula	01/2011
9294	2^165760-112649	49899	Enzo Doria	06/2014
9295	(11*2^165758+1)/135	49898	Lelio R Paula	01/2012
9296	2^165747+63	49895	Lelio R Paula	04/2009
9297	(7*10^49893-13)/3	49894	Robert Price	06/2016
9298	298^20163-20163^298	49888	Norbert Schneider	08/2015
9299	(49885^49885)/(10^184474)	49885	James G. Merickel	08/2015
9300	17^40540+36	49883	Lelio R Paula	11/2012
9301	(12211^12211+4312)/13/17/31/1297/1483/1627/9923/36433	49882	Makoto Morimoto	07/2016
9302	2^165676-112949	49874	Enzo Doria	06/2014
9303	(12203^12203+992)/11	49867	Makoto Morimoto	07/2016
9304	7784^12811-12811^7784	49851	Norbert Schneider	03/2017
9305	2^165581-745	49845	Yves Minet	01/2012
9306	2^165576+74821	49844	Enzo Doria	04/2016
9307	13318^5527+5527^13318	49843	Hans Havermann	04/2016
9309	2^165561-2155	49839	Yves Minet	08/2013
9308	(12197^12197+1755)/2^4	49839	Makoto Morimoto	07/2016
9310	7406^12879+12879^7406	49837	Norbert Schneider	03/2016
9311	8530^12677+12677^8530	49833	Norbert Schneider	01/2016
9312	(3^52222-69)^2-71	49833	Jorge Menendez	02/2017
9313	12^46175+29	49832	Lelio R Paula	10/2012
9314	2^165488-12969	49817	Enzo Doria	10/2012
9315	2^165473+58905	49813	Lelio R Paula	04/2009
9316	20^38284+49	49809	Lelio R Paula	11/2012
9317	3^104388-20	49806	Lelio R Paula	07/2012
9318	(10^49806+119)/3	49806	Serge Batalov	12/2014
9319	(1202206^8192+1)/65537	49803	Syoichiro Yamada	06/2008
9320	(4*10^49801+11)/3	49802	Erik Branger	05/2013
9321	5^71240-15476	49795	Enzo Doria	02/2013
9322	7*3^104334-4	49781	Lelio R Paula	03/2014
9323	(136*10^49774-1)/9	49776	Serge Batalov	12/2014
9324	3^104297+8680	49763	Lelio R Paula	07/2012
9325	(F(10)^28579-F(9)^28579)/F(8)	49737	Wayne Halsdorf	03/2010
9326	(3^104243+1)/4	49736	Kamil Duszenko	05/2004
9327	(10223*2^165183+1)/55	49728	Lelio R Paula	05/2014
9328	6^63895+101	49720	Lelio R Paula	06/2012
9329	3^104194+100	49714	Lelio R Paula	07/2012
9330	10^49711-701	49711	Robert Price	06/2017
9331	U(356793)	49710	Serge Batalov	03/2015
9332	13321^5388+5388^13321	49707	Hans Havermann	04/2016
9333	12166^12166+565	49700	Henri Lifchitz	11/2004
9334	(89*10^49689-53)/9	49690	Erik Branger	05/2013
9335	(1163126^8192+1)/65537	49685	Syoichiro Yamada	06/2008
9336	11^47709+42	49684	Lelio R Paula	10/2012
9338	(35*10^49682+1)/9	49683	Serge Batalov	05/2010
9337	(12163^12163+1194)/37/193	49683	Makoto Morimoto	07/2016
9339	3^104124+92	49680	Lelio R Paula	07/2012
9341	2^165025+165029	49678	Henri Lifchitz	04/2005
9340	14063^3408+3408^14063	49678	Hans Havermann	04/2016
9342	(2^165031+3)/48439	49675	Lelio R Paula	01/2012
9343	(7*2^165020-1)/261	49675	Lelio R Paula	01/2014
9344	2^165000+5227	49670	Lelio R Paula	05/2011
9345	(12161^12161+765)/2/13/29/277/311	49670	Makoto Morimoto	07/2016
9346	(110051^9851+1)/110052	49660	Faysal YAtim	09/2007
9347	2^164962-639791	49659	Paul Bourdelais	11/2012
9348	10^49657+31	49658	Robert Price	01/2011
9349	10^49657-12899	49657	Patrick De Geest	01/2012
9350	2^164937-193	49651	Lelio R Paula	01/2011
9351	21^37549-20^37549	49649	Jean-Louis Charton	02/2012
9352	1417^15754+15754^1417	49647	Serge Batalov	05/2014
9353	(12157^12157+2611)/2^5/11/13/1019/48197/314407	49643	Makoto Morimoto	07/2016
9354	12^45999+25	49642	Lelio R Paula	10/2012
9355	(3^104040+7)/8	49639	Lelio R Paula	03/2012
9356	2^164882-1017	49635	Lelio R Paula	06/2008
9357	(3^104053-8)/381830020743455	49632	Lelio R Paula	03/2012
9358	11^47658-180	49631	Enzo Doria	07/2012
9359	2^164859-1237	49628	Yves Minet	08/2012
9360	17^40331+98	49626	Lelio R Paula	11/2012
9361	1638^15437+15437^1638	49620	Serge Batalov	05/2014
9362	113^24160+112	49603	Norbert Schneider	09/2013
9363	13^44527+16	49601	Lelio R Paula	11/2012
9364	83^25844+82	49597	Norbert Schneider	01/2013
9365	(12143^12143+1306)/3/7/59	49593	Makoto Morimoto	07/2016
9366	114667#-p(114667)	49591	Henri Lifchitz	03/2007
9367	2^164731-1833847	49589	Enzo Doria	05/2015
9368	(625^17737+1)/626	49588	Richard Fischer	06/2013
9369	2^164714+29835	49584	Lelio R Paula	11/2011
9370	7*10^49580-69	49581	Robert Price	01/2017
9371	7*5^70922+4	49574	Lelio R Paula	09/2014
9372	(229*10^49571-1)/3	49573	Robert Price	12/2016
9373	277^20295-290	49571	Enzo Doria	06/2012
9374	2^164662-112883	49569	Enzo Doria	06/2014
9375	(1125424^8192+1)/65537	49568	Syoichiro Yamada	06/2008
9376	6^63698-35	49567	Lelio R Paula	06/2012
9377	(2^164652-3)*6-7	49566	Gilbert Mozzo	04/2016
9378	(11*10^49552+43)/9	49553	Erik Branger	05/2013
9379	2^164606+43	49552	Lelio R Paula	08/2010
9380	2^164598-113111	49549	Enzo Doria	07/2014
9381	11^47575-8100	49545	Enzo Doria	02/2013
9382	9420^12467-12467^9420	49545	Norbert Schneider	07/2013
9383	2^164581-819253	49544	Paul Bourdelais	11/2012
9384	9001^12528-12528^9001	49540	Norbert Schneider	11/2016
9385	(lucasV(1,2,329135)+2)/(5^217910247)	49533	Mike Oakes	02/2017
9387	(4*10^49529-31)/9	49529	Erik Branger	05/2011
9386	13875^3712+3712^13875	49529	Hans Havermann	03/2016
9388	7^58604-62	49527	Lelio R Paula	06/2012
9389	2^164508+105	49522	Lelio R Paula	04/2009
9390	24^35878-937	49520	Enzo Doria	03/2013
9391	(89*10^49516-17)/9	49517	Erik Branger	05/2013
9392	2^164478-167	49513	Lelio R Paula	01/2011
9393	13^44446+30	49511	Lelio R Paula	11/2012
9394	2^164466-790241	49510	Paul Bourdelais	11/2012
9395	-lucasV(-1,2,328901)	49505	Mike Oakes	01/2017
9396	(21*2^164421-1)/533	49495	Lelio R Paula	01/2014
9397	35^32052-206	49491	Enzo Doria	03/2013
9398	3^103726-11878	49490	Enzo Doria	02/2013
9399	(3^103726+7)/512	49488	Lelio R Paula	03/2012
9400	(12119^12119+6270)/13	49487	Makoto Morimoto	07/2016
9401	10^49484+16537	49485	Patrick De Geest	01/2016
9403	10^49484-10^5384-1	49484	Serge Batalov	01/2011
9402	10^49484-91539	49484	Patrick De Geest	01/2016
9404	3*2^164365-7	49480	Lelio R Paula	02/2014
9405	(7^58543-5^58543)/2	49475	Robert Price	05/2012
9406	8482^12591+12591^8482	49464	Norbert Schneider	11/2015
9407	(29*2^164309-1)/20907	49460	Lelio R Paula	01/2014
9408	(12113^12113+3627)/2^2/5/19/14496299	49451	Makoto Morimoto	07/2016
9409	5^70746-16016	49450	Enzo Doria	02/2013
9411	(2^164258+9)/13	49446	Lelio R Paula	01/2012
9410	2^164255-112687	49446	Enzo Doria	06/2014
9412	(21*2^164222-1)/1717	49434	Lelio R Paula	01/2014
9413	2^164212+12705	49433	Lelio R Paula	11/2011
9414	3*2^164205+7	49432	Lelio R Paula	02/2014
9415	2^164203+577294575	49431	Lelio R Paula	02/2013
9416	(12109^12109+2534)/3^2/23/24763/781021	49430	Makoto Morimoto	07/2016
9417	Pell-LucasQ(129127)/2	49427	Eric W. Weisstein	05/2006
9418	2^164187+7695	49426	Lelio R Paula	11/2011
9419	3^103585-26	49423	Lelio R Paula	07/2012
9420	(3*2^164194+1)/14255017	49421	Lelio R Paula	07/2012
9421	10^49415+76837	49416	Patrick De Geest	01/2016
9424	10^49415-6^49415-4^49415-1	49415	Mike Oakes	01/2010
9422	10^49415-32813	49415	Patrick De Geest	01/2016
9423	12943^6574+6574^12943	49415	Hans Havermann	02/2016
9425	(6^63497-61)/25	49409	Lelio R Paula	05/2014
9426	11376^12181+12181^11376	49407	Norbert Schneider	12/2013
9427	2^164110-17	49403	Lelio R Paula	08/2010
9428	12^45773+41	49398	Lelio R Paula	10/2012
9429	2^164090+4257	49397	Lelio R Paula	04/2009
9430	(12101^12101+1403)/2^4/193/349/160231/6927689	49389	Makoto Morimoto	07/2016
9431	2^164061-3889	49388	Yves Minet	04/2017
9432	2^164046+25	49383	Lelio R Paula	01/2009
9433	(24737*2^164045+1)/5906585	49381	Lelio R Paula	05/2014
9434	(12097^12097+1922)/3/139/2253409	49380	Makoto Morimoto	07/2016
9436	5^70640-18296	49376	Enzo Doria	02/2013
9435	(9179*2^164010-1)/5	49376	Lelio R Paula	03/2015
9437	(-lucasV(1,2,328052)+2)/108961	49372	Mike Oakes	02/2017
9438	9*2^164002-7	49371	Lelio R Paula	02/2014
9439	5^70626-44	49366	Lelio R Paula	06/2012
9440	11^47396-1050	49358	Enzo Doria	11/2012
9441	(13*2^163956+1)/7	49356	Lelio R Paula	07/2012
9443	2^163934-135	49350	Lelio R Paula	01/2011
9442	3^103431+20	49350	Lelio R Paula	07/2012
9444	7192^12795-12795^7192	49349	Norbert Schneider	03/2017
9445	13^44300+22	49348	Lelio R Paula	11/2012
9446	(2^163904+3)/7	49340	Lelio R Paula	01/2012
9447	2^163872+12915	49331	Lelio R Paula	11/2011
9448	130^23332-129	49323	Norbert Schneider	03/2015
9449	7^58357-38	49318	Lelio R Paula	06/2012
9450	7760^12677-12677^7760	49312	Norbert Schneider	01/2017
9451	13^44265-2	49309	Lelio R Paula	11/2012
9453	(19*2^163785+1)/2043	49303	Lelio R Paula	01/2012
9452	2^163781-1741	49303	Yves Minet	09/2012
9454	4*5^70529+3	49299	Lelio R Paula	09/2014
9455	(2^163742-3)/131	49290	Lelio R Paula	01/2012
9456	5^70514-17216	49288	Enzo Doria	02/2013
9457	2^163727-1741	49287	Yves Minet	09/2012
9458	Linear(0,1,1,-1,327433)	49283	Henri Lifchitz	04/2007
9459	5^70498-17576	49276	Enzo Doria	02/2013
9460	(12073^12073+1070)/3/13/31063	49274	Makoto Morimoto	07/2016
9461	2^163667+72113	49269	Enzo Doria	04/2016
9462	5^70484-17696	49267	Enzo Doria	02/2013
9463	(12071^12071+4263)/2/101/11489	49265	Makoto Morimoto	07/2016
9464	7^58293+66	49264	Lelio R Paula	06/2012
9465	(52*10^49261-1)/3	49263	Robert Price	02/2017
9467	2671^14376-114	49262	Enzo Doria	06/2012
9466	(15185*2^163636-1)/209	49262	Lelio R Paula	03/2015
9468	2^163630+183	49258	Lelio R Paula	01/2011
9469	2^163560+15	49237	Lelio R Paula	08/2010
9471	3^103189+110	49234	Lelio R Paula	07/2012
9470	(41*10^49233+31)/9	49234	Erik Branger	05/2013
9472	(1023052^8192+1)/65537	49229	Syoichiro Yamada	05/2008
9473	2*10^49216+93	49217	Robert Price	07/2016
9474	2^163453+885	49205	Lelio R Paula	10/2011
9475	(67607*2^163432+1)/3	49203	Lelio R Paula	05/2014
9476	15^41835-46	49202	Lelio R Paula	11/2012
9477	10^49190+45507	49191	Patrick De Geest	01/2016
9479	10^49190-6018659	49190	Marisa Kirisame	02/2015
9478	10^49190-154431	49190	Patrick De Geest	01/2016
9480	2^163385+94395	49184	Henri Lifchitz	01/2005
9481	2^163382-2021	49183	Yves Minet	03/2013
9483	(55*10^49169-1)/9	49170	Ray Chandler	02/2012
9482	2^163336-15177	49170	Enzo Doria	04/2013
9484	8323^12542-12542^8323	49169	Norbert Schneider	11/2016
9485	(10^49165-991)/9	49165	Serge Batalov	07/2010
9486	7^58169-6^(58169+1)	49159	Robert Price	06/2016
9488	(F(5)^70327-F(4)^70327)/F(3)	49157	Wayne Halsdorf	01/2010
9487	(5^70327-3^70327)/2	49157	Robert Price	08/2011
9489	2^163283+54615	49154	Lelio R Paula	04/2009
9490	18388^471+471^18388	49152	Anatoly F. Selevich	12/2006
9491	(782*10^49148-71)/9	49150	Robert Price	06/2017
9492	(12043^12043+799)/2/157	49142	Makoto Morimoto	07/2016
9493	14^42875+69	49141	Lelio R Paula	11/2012
9494	(2^163243+9)/17	49140	Lelio R Paula	01/2012
9495	(F(770)^307-F(769)^307)/F(768)	49136	Wayne Halsdorf	02/2010
9496	(12041^12041+467)/2^2/23/47	49132	Makoto Morimoto	07/2016
9497	5^70290-19446	49131	Enzo Doria	03/2013
9498	(F(760)^311-F(759)^311)/F(758)	49130	Wayne Halsdorf	02/2010
9499	5^70286-20046	49128	Enzo Doria	03/2013
9500	12^45519-91	49124	Lelio R Paula	10/2012

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Probable Primes Top 10000

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