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 ?
5501	2^248816+1111	74902	Lelio R Paula	01/2011
5502	V(388219)	74890	Serge Batalov	03/2015
5503	2*F(358297)-1	74880	Henri Lifchitz	12/2009
5504	(22*10^74874-31)/9	74875	Robert Price	04/2015
5505	11^71892-76800000	74868	Enzo Doria	01/2013
5506	9*5^107107-4	74866	Lelio R Paula	10/2014
5507	2^248678-710111	74860	Paul Bourdelais	03/2013
5508	13^67194+12	74851	Lelio R Paula	01/2015
5509	(7*2^248634+1)/71	74846	Lelio R Paula	08/2012
5510	11^71867-3090	74842	Enzo Doria	12/2012
5511	2^248609+262145	74839	Lelio R Paula	05/2013
5512	3^156852+50	74838	Lelio R Paula	01/2015
5513	18^59607-11	74824	Lelio R Paula	01/2015
5514	2^248556-110507	74823	Enzo Doria	05/2014
5515	7^88531-36	74818	Lelio R Paula	01/2015
5516	p(15738)#/2+1024	74814	Robert Price	07/2017
5517	4*3^156740-5	74785	Lelio R Paula	05/2014
5518	(32*10^74773-41)/9	74774	Robert Price	05/2015
5519	(29*2^248384-1)/13	74772	Lelio R Paula	01/2014
5520	19401!+19401#+1	74765	D. Gazzoni Filho & Lucas Teixeira	06/2005
5521	2^248357-12797413	74763	Enzo Doria	03/2016
5522	42^46057+41	74762	Lelio R Paula	07/2012
5523	11^71784-3000	74756	Enzo Doria	12/2012
5524	19^58458+18	74754	Lelio R Paula	01/2015
5525	12^69265-35	74750	Lelio R Paula	02/2015
5526	11^71771-48000	74742	Enzo Doria	12/2012
5527	(7*10^74741+197)/3	74742	Robert Price	07/2017
5528	(2^248282-5)/50129	74736	Lelio R Paula	06/2012
5529	2^248252-110105	74732	Enzo Doria	04/2014
5530	(7*10^74729+71)/3	74730	Robert Price	03/2016
5531	3^156614-50	74724	Lelio R Paula	01/2015
5532	(7*2^248213+1)/135	74719	Lelio R Paula	07/2012
5533	(2^248173+78557)/767	74705	Lelio R Paula	07/2012
5534	125^35622+124	74697	Norbert Schneider	02/2015
5535	(19*2^248099-1)/29	74686	Lelio R Paula	01/2014
5536	(86*10^74676-41)/9	74677	Robert Price	11/2015
5537	10^74670+31	74671	Robert Price	01/2011
5538	10^74670-122463	74670	Patrick De Geest	05/2013
5539	2^248036-69	74667	Lelio R Paula	03/2012
5540	11^71698-6000	74666	Enzo Doria	12/2012
5541	58(10^(324887)-1)/111-1	74661	Robert Price	10/2014
5542	14^65139-45	74658	Lelio R Paula	01/2015
5543	6^95921-133	74642	Lelio R Paula	01/2015
5544	11^71675+78	74642	Lelio R Paula	02/2015
5545	18^59449-91	74625	Lelio R Paula	01/2015
5546	6^95864-16043	74597	Enzo Doria	02/2013
5547	5*7^88261+6	74590	Lelio R Paula	10/2014
5548	9*5^106710+4	74589	Lelio R Paula	10/2014
5549	(7772^247788+1)/(11754121)	74588	Jens K. Andersen	09/2007
5550	(265*10^74579+17)/3	74581	Robert Price	05/2016
5551	(2^247759-1017)/3318311717	74574	Lelio R Paula	07/2012
5552	5^106682-24	74568	Lelio R Paula	08/2014
5553	474^27863+27863^474	74556	Norbert Schneider	01/2017
5554	(35365^16384+1)/2	74524	Lelio R Paula	11/2011
5555	3^156161+2660	74508	Lelio R Paula	01/2015
5556	2^247474-58695	74498	Lelio R Paula	05/2013
5557	11^71519-90	74480	Enzo Doria	07/2012
5558	(19*2^247419-1)/23202983	74475	Lelio R Paula	01/2014
5560	(2^247394-7)/3	74473	Lelio R Paula	06/2012
5559	18^59328+17	74473	Lelio R Paula	01/2015
5561	2^247379-181	74469	Lelio R Paula	03/2012
5562	(15*2^247370-1)/479	74465	Lelio R Paula	01/2014
5563	2^247344+2047	74458	Lelio R Paula	05/2013
5564	2^247311-1017	74449	Lelio R Paula	05/2013
5565	2^247280+7	74439	Lelio R Paula	03/2012
5566	(68*10^74434+13)/9	74435	Ray Chandler	11/2010
5567	3^156004-62	74433	Lelio R Paula	01/2015
5568	36095!2-64	74416	Robert Price	06/2015
5569	2^247165-3	74405	M. Frind & P. Underwood	07/2002
5570	2^247150+32769	74400	Lelio R Paula	05/2013
5571	12^68911+73	74368	Lelio R Paula	01/2015
5572	2^246999+74903	74355	Enzo Doria	04/2016
5573	2^246989-110643	74352	Enzo Doria	05/2014
5574	10^74350+279439	74351	Patrick De Geest	07/2017
5577	(10^74350+11)/3	74350	Robert Price	11/2014
5575	10^74350-400000001	74350	Robert Price	07/2017
5576	10^74350-716241	74350	Patrick De Geest	07/2017
5578	10^74335+13659	74336	Patrick De Geest	05/2013
5579	10^74335-53	74335	Robert Price	05/2011
5580	2^246906-1215	74327	Lelio R Paula	05/2013
5581	2^246848+111	74309	Lelio R Paula	03/2012
5582	6^95490-18443	74306	Enzo Doria	03/2013
5583	18^59188-2369	74298	Enzo Doria	03/2013
5584	(13632^246767+1)/(35713^2*743)	74281	Jens K. Andersen	09/2007
5585	2^246744+40755	74278	Lelio R Paula	05/2013
5586	(29*10^74276+91)/3	74277	Robert Price	03/2016
5587	6^95441+163	74268	Lelio R Paula	01/2015
5588	V(390863)	74258	Serge Batalov	03/2015
5589	10^74254+91	74255	Robert Price	03/2011
5590	(19*10^74253-1)/9	74254	Ray Chandler	02/2012
5591	10^74254-130569	74254	Patrick De Geest	05/2013
5592	771^25718+25718^771	74250	Norbert Schneider	10/2016
5593	2^246618+427	74240	Henri Lifchitz	02/2005
5594	88*10^74234+3	74236	Robert Price	11/2016
5595	8*10^74234-49	74235	Robert Price	04/2016
5596	2^246578+12285	74228	Lelio R Paula	05/2013
5597	(3^155569-5)/2	74225	Lelio R Paula	06/2012
5598	13^66628+46	74220	Lelio R Paula	01/2015
5599	2^246476-17295	74197	Lelio R Paula	05/2013
5600	(15185*2^246432-1)/13	74187	Lelio R Paula	04/2015
5601	5*2^246413-3	74179	Lelio R Paula	05/2014
5602	2^246386-28635	74170	Lelio R Paula	05/2013
5603	2^246334-111245	74154	Enzo Doria	05/2014
5604	39^77708+7^77708-24^77708-3	74153	Mike Oakes	12/2010
5605	15^63045+82	74147	Lelio R Paula	01/2015
5606	19255!+19255#+1	74140	D. Gazzoni Filho & Lucas Teixeira	06/2005
5607	2^246268-110507	74135	Enzo Doria	05/2014
5608	3^155328+2660	74111	Lelio R Paula	01/2015
5609	2^246148-2786249	74098	Enzo Doria	03/2016
5610	(16*10^74092-19)/3	74093	Robert Price	03/2016
5611	2^246115-110767	74088	Enzo Doria	05/2014
5612	7^87666-68	74087	Lelio R Paula	08/2014
5613	10^74079+1145141919	74080	Marisa Kirisame	03/2015
5614	10^74079+6219	74080	Patrick De Geest	03/2016
5615	10^74079-282707	74079	Patrick De Geest	03/2016
5616	129^35098+2	74078	Lelio R Paula	05/2013
5617	2^246025-112123	74061	Enzo Doria	06/2014
5618	(67*10^74045+17)/3	74047	Robert Price	02/2017
5619	2^245823+66831	74001	Marek Hubal	02/2017
5620	5^105869+42	74000	Lelio R Paula	08/2014
5621	(21*2^245806+1)/634555	73991	Lelio R Paula	08/2012
5622	(22699*2^245762+1)/119	73985	Lelio R Paula	06/2014
5623	(3^155048-7)/262	73975	Lelio R Paula	06/2012
5624	9998*2^245696+3	73966	Donovan Johnson	10/2004
5625	13^66400-80	73966	Lelio R Paula	01/2015
5626	(2^245704+9)/25	73963	Lelio R Paula	07/2012
5628	11^71023-7170	73963	Enzo Doria	01/2013
5627	3*10^73962+13	73963	Robert Price	08/2017
5629	(31*2^245660-1)/114195	73948	Lelio R Paula	01/2014
5630	2^245629-2797813	73942	Eric Chen	03/2016
5631	2^245557-153	73921	Lelio R Paula	03/2012
5632	2^245525+1869881	73911	Enzo Doria	06/2016
5633	2^245522+159	73910	Lelio R Paula	03/2012
5634	(13*10^73891-43)/3	73892	Robert Price	08/2017
5635	19^57783-56	73891	Lelio R Paula	01/2015
5636	7*10^73888+79	73889	Robert Price	02/2017
5637	6^94948+174281	73884	Mike Oakes	02/2011
5638	11^70939-4860	73876	Enzo Doria	01/2013
5639	2^245372+54615	73865	Lelio R Paula	05/2013
5640	2^245362-143	73862	Lelio R Paula	03/2012
5641	7^87396+6^(87396-1)	73859	Robert Price	03/2016
5642	(22*10^73853-37)/3	73854	Robert Price	05/2017
5643	5^105646-14246	73844	Enzo Doria	02/2013
5645	2^245290-41	73840	Lelio R Paula	03/2012
5644	2^245290-94395	73840	Lelio R Paula	05/2013
5646	8*5^105600-7	73813	Lelio R Paula	10/2014
5647	7*5^105573-4	73794	Lelio R Paula	10/2014
5648	18^58742-4805	73738	Enzo Doria	03/2013
5649	13^66179+66	73720	Lelio R Paula	01/2015
5650	(82*10^73714-1)/9	73715	Robert Price	12/2014
5651	(29*2^244856-1)/186121	73706	Lelio R Paula	01/2014
5652	(13*2^244840-1)/2799	73702	Lelio R Paula	01/2014
5653	(13*10^73701+17)/3	73702	Robert Price	06/2015
5654	(2^244787-1017)/28411	73684	Lelio R Paula	07/2012
5655	(3^154421-4)/23	73677	Lelio R Paula	06/2012
5656	8*7^87170+5	73669	Lelio R Paula	10/2014
5657	Phi(40100,-40100)	73651	Henri Lifchitz	06/2013
5658	(4*10^73647-19)/3	73648	Robert Price	06/2017
5659	2^244618-2297	73638	Yves Minet	10/2009
5660	3*5^105344+8	73633	Lelio R Paula	10/2014
5661	5^105334-14096	73626	Enzo Doria	02/2013
5662	(2^244584-7)/13237074243033	73614	Lelio R Paula	07/2012
5663	2^244465-110185	73592	Enzo Doria	05/2014
5664	2^244443+40755	73585	Lelio R Paula	05/2013
5665	2^244404+3841	73573	Yves Minet	03/2011
5666	2^244372-110627	73564	Enzo Doria	05/2014
5667	(3*2^244255+1)/245	73527	Lelio R Paula	08/2012
5668	(11*2^244245+1)/23	73525	Lelio R Paula	08/2012
5669	(15185*2^244187-1)/6111	73509	Lelio R Paula	04/2015
5670	(91^37507+1)/92	73476	Paul Bourdelais	08/2017
5671	18^58521+65	73460	Lelio R Paula	01/2015
5672	13^65940+36	73454	Lelio R Paula	01/2015
5673	5^105050-14	73427	Lelio R Paula	08/2014
5674	(((((((((((((30201^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2	73401	Serge Batalov	07/2016
5675	15^62410-46	73400	Lelio R Paula	01/2015
5676	2^243733+1869707	73371	Enzo Doria	05/2016
5677	11^70439-5430	73355	Enzo Doria	01/2013
5678	2^243676-87	73354	Lelio R Paula	03/2012
5679	(101*10^73346-17)/3	73348	Robert Price	08/2016
5680	2^243621-113185	73338	Enzo Doria	07/2014
5681	(5*2^243610-1)/1669	73332	Lelio R Paula	01/2014
5682	2*5^104888-7	73314	Lelio R Paula	10/2014
5683	(58695*2^243516-1)/983	73308	Lelio R Paula	04/2015
5684	(3^153648-2)/33423138097	73299	Lelio R Paula	06/2012
5685	18^58376-5255	73278	Enzo Doria	03/2013
5686	11^70363+32	73276	Lelio R Paula	02/2015
5687	2^243413+4257	73275	Lelio R Paula	05/2013
5688	104824^5+5^104824	73269	Andrey Kulsha	07/2010
5689	7^86689-6^86689	73261	Predrag Minovic	09/2004
5690	2^243296+90195	73240	Lelio R Paula	05/2013
5691	p(15433)#/2-4	73218	Robert Price	12/2016
5692	2^243127+71355	73189	Lelio R Paula	05/2013
5693	2^243116-249419	73186	Paul Bourdelais	03/2013
5694	(58695*2^243085-1)/11	73180	Lelio R Paula	04/2015
5695	11^70262-98	73171	Lelio R Paula	02/2015
5696	(2^243034+47)/722703303	73152	Lelio R Paula	07/2012
5697	(2^242966+47)/46887	73136	Lelio R Paula	07/2012
5698	(43^44773-1)/42	73134	Robert Price	04/2014
5699	6^93980-158359	73131	Mike Oakes	02/2011
5700	6^93915+53	73081	Lelio R Paula	01/2015
5701	(74*10^73076+43)/9	73077	Robert Price	10/2015
5702	(3^153125+2)/1144955	73054	Lelio R Paula	06/2012
5703	2^242632-112199	73040	Enzo Doria	06/2014
5704	V(351646)	73029	Serge Batalov	03/2015
5705	18^58175-85	73026	Lelio R Paula	01/2015
5706	p(15395)#/2-4	73019	Robert Price	12/2016
5707	(4^121271+3^121271)/7	73012	Jean-Louis Charton	03/2011
5708	8*6^93825-5	73011	Lelio R Paula	10/2014
5710	(F(220)^1601-F(219)^1601)/F(218)	73005	Wayne Halsdorf	08/2013
5709	(73^39181+1)/74	73005	Paul Bourdelais	08/2017
5711	6^93815+143	73003	Lelio R Paula	01/2015
5712	6^93812+5	73000	Wojciech Florek	03/2006
5713	19^57078-62	72989	Lelio R Paula	01/2015
5714	(29*10^72985+91)/3	72986	Robert Price	03/2016
5715	11^70082-2520	72983	Enzo Doria	12/2012
5716	6^93773+133	72970	Lelio R Paula	01/2015
5717	2^242328-59	72948	Lelio R Paula	03/2012
5718	5^104358-13016	72944	Enzo Doria	02/2013
5719	(75*10^72941-57)/99	72941	Ray Chandler	03/2011
5720	12^67585-95	72937	Lelio R Paula	02/2015
5721	2^242230-113285	72919	Enzo Doria	07/2014
5722	(5*10^72916-11)/3	72917	Erik Branger	12/2013
5723	2^242220-110399	72916	Enzo Doria	05/2014
5724	2^242205-113413	72911	Enzo Doria	07/2014
5725	(3^152809+3^76405+1)/7	72908	Serge Batalov	03/2014
5726	2^242175+74243	72902	Yves Minet	03/2011
5727	2^242150+17659	72895	Lelio R Paula	11/2009
5728	11^69982-2340	72879	Enzo Doria	12/2012
5729	(23*2^242093+1)/10117	72875	Lelio R Paula	08/2012
5730	(67607*2^242043+1)/33263	72863	Lelio R Paula	06/2014
5731	2^242032+87	72859	Lelio R Paula	03/2012
5732	2^241968-110595	72840	Enzo Doria	05/2014
5733	(10^72821+71)/9	72821	Robert Price	11/2014
5734	2^241852-64875	72805	Lelio R Paula	05/2013
5735	F(348307)/20562890865908093	72776	Donovan Johnson	07/2007
5736	(67*10^72772+23)/9	72773	Ray Chandler	11/2010
5737	(8*10^72759+67)/3	72760	Robert Price	01/2017
5738	2^241670+145	72750	Lelio R Paula	03/2012
5739	5^104074+52	72745	Lelio R Paula	08/2014
5740	(3^152466-5)/724	72742	Lelio R Paula	06/2012
5741	20^55908-41	72738	Lelio R Paula	01/2015
5742	(73*10^72735+53)/9	72736	Robert Price	10/2015
5743	10^72730+224011	72731	Patrick De Geest	05/2013
5744	10^72730-99	72730	Robert Price	05/2011
5745	(11^69833+3^69833)/14	72723	Robert Price	03/2013
5746	(88*10^72711-43)/9	72712	Robert Price	11/2015
5747	3^152379+280	72704	Lelio R Paula	01/2015
5748	(25*10^72703-241)/9	72704	Robert Price	01/2017
5749	(47*10^72696+133)/9	72697	Robert Price	04/2017
5750	17^59077-90	72692	Lelio R Paula	01/2015

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Probable Primes Top 10000

(181746 PRPs in the top)