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	2^246906-1215	74327	Lelio R Paula	05/2013
5502	2^246848+111	74309	Lelio R Paula	03/2012
5503	6^95490-18443	74306	Enzo Doria	03/2013
5504	18^59188-2369	74298	Enzo Doria	03/2013
5505	(13632^246767+1)/(35713^2*743)	74281	Jens K. Andersen	09/2007
5506	2^246744+40755	74278	Lelio R Paula	05/2013
5507	(29*10^74276+91)/3	74277	Robert Price	03/2016
5508	6^95441+163	74268	Lelio R Paula	01/2015
5509	V(390863)	74258	Serge Batalov	03/2015
5510	10^74254+91	74255	Robert Price	03/2011
5511	(19*10^74253-1)/9	74254	Ray Chandler	02/2012
5512	10^74254-130569	74254	Patrick De Geest	05/2013
5513	771^25718+25718^771	74250	Norbert Schneider	10/2016
5514	2^246618+427	74240	Henri Lifchitz	02/2005
5515	88*10^74234+3	74236	Robert Price	11/2016
5516	8*10^74234-49	74235	Robert Price	04/2016
5517	2^246578+12285	74228	Lelio R Paula	05/2013
5518	(3^155569-5)/2	74225	Lelio R Paula	06/2012
5519	13^66628+46	74220	Lelio R Paula	01/2015
5520	2^246476-17295	74197	Lelio R Paula	05/2013
5521	(15185*2^246432-1)/13	74187	Lelio R Paula	04/2015
5522	5*2^246413-3	74179	Lelio R Paula	05/2014
5523	2^246386-28635	74170	Lelio R Paula	05/2013
5524	2^246334-111245	74154	Enzo Doria	05/2014
5525	39^77708+7^77708-24^77708-3	74153	Mike Oakes	12/2010
5526	15^63045+82	74147	Lelio R Paula	01/2015
5527	19255!+19255#+1	74140	D. Gazzoni Filho & Lucas Teixeira	06/2005
5528	2^246268-110507	74135	Enzo Doria	05/2014
5529	3^155328+2660	74111	Lelio R Paula	01/2015
5530	2^246148-2786249	74098	Enzo Doria	03/2016
5531	(16*10^74092-19)/3	74093	Robert Price	03/2016
5532	2^246115-110767	74088	Enzo Doria	05/2014
5533	7^87666-68	74087	Lelio R Paula	08/2014
5534	10^74079+1145141919	74080	Marisa Kirisame	03/2015
5535	10^74079+6219	74080	Patrick De Geest	03/2016
5536	10^74079-282707	74079	Patrick De Geest	03/2016
5537	129^35098+2	74078	Lelio R Paula	05/2013
5538	2^246025-112123	74061	Enzo Doria	06/2014
5539	(67*10^74045+17)/3	74047	Robert Price	02/2017
5540	2^245823+66831	74001	Marek Hubal	02/2017
5541	5^105869+42	74000	Lelio R Paula	08/2014
5542	(21*2^245806+1)/634555	73991	Lelio R Paula	08/2012
5543	(22699*2^245762+1)/119	73985	Lelio R Paula	06/2014
5544	(3^155048-7)/262	73975	Lelio R Paula	06/2012
5545	9998*2^245696+3	73966	Donovan Johnson	10/2004
5546	13^66400-80	73966	Lelio R Paula	01/2015
5547	(2^245704+9)/25	73963	Lelio R Paula	07/2012
5548	11^71023-7170	73963	Enzo Doria	01/2013
5549	(31*2^245660-1)/114195	73948	Lelio R Paula	01/2014
5550	2^245629-2797813	73942	Eric Chen	03/2016
5551	2^245557-153	73921	Lelio R Paula	03/2012
5552	2^245525+1869881	73911	Enzo Doria	06/2016
5553	2^245522+159	73910	Lelio R Paula	03/2012
5554	19^57783-56	73891	Lelio R Paula	01/2015
5555	7*10^73888+79	73889	Robert Price	02/2017
5556	6^94948+174281	73884	Mike Oakes	02/2011
5557	11^70939-4860	73876	Enzo Doria	01/2013
5558	2^245372+54615	73865	Lelio R Paula	05/2013
5559	2^245362-143	73862	Lelio R Paula	03/2012
5560	7^87396+6^(87396-1)	73859	Robert Price	03/2016
5561	(22*10^73853-37)/3	73854	Robert Price	05/2017
5562	5^105646-14246	73844	Enzo Doria	02/2013
5564	2^245290-41	73840	Lelio R Paula	03/2012
5563	2^245290-94395	73840	Lelio R Paula	05/2013
5565	8*5^105600-7	73813	Lelio R Paula	10/2014
5566	7*5^105573-4	73794	Lelio R Paula	10/2014
5567	18^58742-4805	73738	Enzo Doria	03/2013
5568	13^66179+66	73720	Lelio R Paula	01/2015
5569	(82*10^73714-1)/9	73715	Robert Price	12/2014
5570	(29*2^244856-1)/186121	73706	Lelio R Paula	01/2014
5571	(13*2^244840-1)/2799	73702	Lelio R Paula	01/2014
5572	(13*10^73701+17)/3	73702	Robert Price	06/2015
5573	(2^244787-1017)/28411	73684	Lelio R Paula	07/2012
5574	(3^154421-4)/23	73677	Lelio R Paula	06/2012
5575	8*7^87170+5	73669	Lelio R Paula	10/2014
5576	Phi(40100,-40100)	73651	Henri Lifchitz	06/2013
5577	(4*10^73647-19)/3	73648	Robert Price	06/2017
5578	2^244618-2297	73638	Yves Minet	10/2009
5579	3*5^105344+8	73633	Lelio R Paula	10/2014
5580	5^105334-14096	73626	Enzo Doria	02/2013
5581	(2^244584-7)/13237074243033	73614	Lelio R Paula	07/2012
5582	2^244465-110185	73592	Enzo Doria	05/2014
5583	2^244443+40755	73585	Lelio R Paula	05/2013
5584	2^244404+3841	73573	Yves Minet	03/2011
5585	2^244372-110627	73564	Enzo Doria	05/2014
5586	(3*2^244255+1)/245	73527	Lelio R Paula	08/2012
5587	(11*2^244245+1)/23	73525	Lelio R Paula	08/2012
5588	(15185*2^244187-1)/6111	73509	Lelio R Paula	04/2015
5589	18^58521+65	73460	Lelio R Paula	01/2015
5590	13^65940+36	73454	Lelio R Paula	01/2015
5591	5^105050-14	73427	Lelio R Paula	08/2014
5592	(((((((((((((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
5593	15^62410-46	73400	Lelio R Paula	01/2015
5594	2^243733+1869707	73371	Enzo Doria	05/2016
5595	11^70439-5430	73355	Enzo Doria	01/2013
5596	2^243676-87	73354	Lelio R Paula	03/2012
5597	(101*10^73346-17)/3	73348	Robert Price	08/2016
5598	2^243621-113185	73338	Enzo Doria	07/2014
5599	(5*2^243610-1)/1669	73332	Lelio R Paula	01/2014
5600	2*5^104888-7	73314	Lelio R Paula	10/2014
5601	(58695*2^243516-1)/983	73308	Lelio R Paula	04/2015
5602	(3^153648-2)/33423138097	73299	Lelio R Paula	06/2012
5603	18^58376-5255	73278	Enzo Doria	03/2013
5604	11^70363+32	73276	Lelio R Paula	02/2015
5605	2^243413+4257	73275	Lelio R Paula	05/2013
5606	104824^5+5^104824	73269	Andrey Kulsha	07/2010
5607	7^86689-6^86689	73261	Predrag Minovic	09/2004
5608	2^243296+90195	73240	Lelio R Paula	05/2013
5609	p(15433)#/2-4	73218	Robert Price	12/2016
5610	2^243127+71355	73189	Lelio R Paula	05/2013
5611	2^243116-249419	73186	Paul Bourdelais	03/2013
5612	(58695*2^243085-1)/11	73180	Lelio R Paula	04/2015
5613	11^70262-98	73171	Lelio R Paula	02/2015
5614	(2^243034+47)/722703303	73152	Lelio R Paula	07/2012
5615	(2^242966+47)/46887	73136	Lelio R Paula	07/2012
5616	(43^44773-1)/42	73134	Robert Price	04/2014
5617	6^93980-158359	73131	Mike Oakes	02/2011
5618	6^93915+53	73081	Lelio R Paula	01/2015
5619	(74*10^73076+43)/9	73077	Robert Price	10/2015
5620	(3^153125+2)/1144955	73054	Lelio R Paula	06/2012
5621	2^242632-112199	73040	Enzo Doria	06/2014
5622	V(351646)	73029	Serge Batalov	03/2015
5623	18^58175-85	73026	Lelio R Paula	01/2015
5624	p(15395)#/2-4	73019	Robert Price	12/2016
5625	(4^121271+3^121271)/7	73012	Jean-Louis Charton	03/2011
5626	8*6^93825-5	73011	Lelio R Paula	10/2014
5627	(F(220)^1601-F(219)^1601)/F(218)	73005	Wayne Halsdorf	08/2013
5628	6^93815+143	73003	Lelio R Paula	01/2015
5629	6^93812+5	73000	Wojciech Florek	03/2006
5630	19^57078-62	72989	Lelio R Paula	01/2015
5631	(29*10^72985+91)/3	72986	Robert Price	03/2016
5632	11^70082-2520	72983	Enzo Doria	12/2012
5633	6^93773+133	72970	Lelio R Paula	01/2015
5634	2^242328-59	72948	Lelio R Paula	03/2012
5635	5^104358-13016	72944	Enzo Doria	02/2013
5636	(75*10^72941-57)/99	72941	Ray Chandler	03/2011
5637	12^67585-95	72937	Lelio R Paula	02/2015
5638	2^242230-113285	72919	Enzo Doria	07/2014
5639	(5*10^72916-11)/3	72917	Erik Branger	12/2013
5640	2^242220-110399	72916	Enzo Doria	05/2014
5641	2^242205-113413	72911	Enzo Doria	07/2014
5642	(3^152809+3^76405+1)/7	72908	Serge Batalov	03/2014
5643	2^242175+74243	72902	Yves Minet	03/2011
5644	2^242150+17659	72895	Lelio R Paula	11/2009
5645	11^69982-2340	72879	Enzo Doria	12/2012
5646	(23*2^242093+1)/10117	72875	Lelio R Paula	08/2012
5647	(67607*2^242043+1)/33263	72863	Lelio R Paula	06/2014
5648	2^242032+87	72859	Lelio R Paula	03/2012
5649	2^241968-110595	72840	Enzo Doria	05/2014
5650	(10^72821+71)/9	72821	Robert Price	11/2014
5651	2^241852-64875	72805	Lelio R Paula	05/2013
5652	F(348307)/20562890865908093	72776	Donovan Johnson	07/2007
5653	(67*10^72772+23)/9	72773	Ray Chandler	11/2010
5654	(8*10^72759+67)/3	72760	Robert Price	01/2017
5655	2^241670+145	72750	Lelio R Paula	03/2012
5656	5^104074+52	72745	Lelio R Paula	08/2014
5657	(3^152466-5)/724	72742	Lelio R Paula	06/2012
5658	20^55908-41	72738	Lelio R Paula	01/2015
5659	(73*10^72735+53)/9	72736	Robert Price	10/2015
5660	10^72730+224011	72731	Patrick De Geest	05/2013
5661	10^72730-99	72730	Robert Price	05/2011
5662	(11^69833+3^69833)/14	72723	Robert Price	03/2013
5663	(88*10^72711-43)/9	72712	Robert Price	11/2015
5664	3^152379+280	72704	Lelio R Paula	01/2015
5665	(25*10^72703-241)/9	72704	Robert Price	01/2017
5666	(47*10^72696+133)/9	72697	Robert Price	04/2017
5667	17^59077-90	72692	Lelio R Paula	01/2015
5668	65^40096+58	72691	Lelio R Paula	01/2016
5669	(29*2^241446-1)/245	72682	Lelio R Paula	01/2014
5671	11^69783-38400000	72672	Enzo Doria	01/2013
5670	2^241409-112903	72672	Enzo Doria	06/2014
5672	(3^152287+1)/4	72659	Paul Bourdelais	04/2008
5673	3^152249-56	72642	Lelio R Paula	01/2015
5674	10^72631+37	72632	Robert Price	01/2011
5675	10^72631-8813	72631	Patrick De Geest	05/2013
5676	(19*2^241254+1)/101	72624	Lelio R Paula	08/2012
5677	(9^76103+8^76103)/17	72620	Robert Price	12/2012
5678	2^241220-112337	72615	Enzo Doria	06/2014
5679	(82*10^72612+449)/9	72613	Robert Price	02/2017
5680	2^241169-15793	72600	Enzo Doria	04/2013
5681	9*10^72595+11	72596	Robert Kinser	01/2017
5682	(25*2^241048+1)/89	72563	Lelio R Paula	08/2012
5683	(22*10^72560+17)/3	72561	Robert Price	09/2015
5684	2^241032-23	72558	Lelio R Paula	02/2012
5685	34485*10^72550+2^241004-3	72555	Gilbert Mozzo	12/2012
5686	2^241004-3	72550	M. Frind & P. Underwood	07/2002
5687	97*10^72522-3	72524	Robert Price	01/2017
5688	(68*10^72516+7)/3	72518	Robert Price	03/2016
5689	(78557*2^240844+1)/63	72505	Lelio R Paula	06/2014
5690	67^39701-66	72497	Norbert Schneider	11/2014
5691	(185*10^72484+7)/3	72486	Robert Price	02/2017
5693	(293*27^50631-1736)/13	72473	Curtis Bright	05/2015
5692	103^36005-102	72473	Norbert Schneider	10/2016
5694	15^61616+88	72467	Lelio R Paula	01/2015
5695	45^43831+2	72462	Lelio R Paula	05/2013
5696	2^240692-492389	72456	Paul Bourdelais	03/2013
5697	(646*10^72446-7)/9	72448	Robert Price	07/2016
5698	9*6^93083+7	72434	Lelio R Paula	10/2014
5699	2^240617-3645	72433	Lelio R Paula	05/2013
5700	11^69531-24000	72410	Enzo Doria	12/2012
5701	(22699*2^240396+1)/55	72370	Lelio R Paula	06/2014
5702	6^92995+13	72365	Lelio R Paula	01/2015
5703	(11*10^72362-149)/3	72363	Robert Price	01/2017
5704	(2^240381+3)/51655	72358	Lelio R Paula	05/2012
5705	6^92974-55	72348	Lelio R Paula	01/2015
5706	2^240295+11	72337	Lelio R Paula	02/2012
5707	(14*10^72326-53)/3	72327	Robert Price	12/2016
5708	15^61493-46	72322	Lelio R Paula	01/2015
5709	lucasU(46,1,43497)-lucasU(46,1,43496)	72315	Mike Oakes	04/2009
5711	5*10^72302+9	72303	Dmitry Domanov	11/2010
5710	(9787*2^240179-1)/265	72303	Lelio R Paula	04/2015
5712	11^69419-3120	72293	Enzo Doria	12/2012
5713	10^72267+33	72268	Robert Price	01/2011
5714	10^72267-553947	72267	Patrick De Geest	05/2013
5715	11^69389-1380	72262	Enzo Doria	12/2012
5716	(16^60013-5^60013)/11	72262	Robert Price	07/2013
5717	7^85507-30	72262	Lelio R Paula	08/2014
5718	(19*2^240026-1)/15	72256	Lelio R Paula	02/2014
5719	(3^151426-2)/661337	72243	Lelio R Paula	06/2012
5720	gcd(V(1296375),5F(259275)(F(259275)-1)+1)	72227	Serge Batalov	04/2015
5721	2^239863-112267	72206	Enzo Doria	06/2014
5722	2^239853-114853	72203	Enzo Doria	05/2015
5723	(4*10^72174+149)/9	72174	Robert Price	03/2017
5725	(2^239671+9)/296131	72143	Lelio R Paula	05/2012
5724	2^239651-110665	72143	Enzo Doria	05/2014
5726	(29*2^239650-1)/3305	72140	Lelio R Paula	01/2014
5727	241^30280+30280^241	72128	Norbert Schneider	11/2014
5728	(68*10^72120-23)/9	72121	Robert Price	10/2015
5729	(9^75571+8^75571)/17	72112	Robert Price	12/2012
5730	(15*2^239530-1)/173	72105	Lelio R Paula	01/2014
5731	2^239513-112519	72101	Enzo Doria	06/2014
5732	(10^72097+149)/3	72097	Serge Batalov	12/2014
5733	2^239442-6555	72080	Lelio R Paula	05/2012
5734	2*5^103106+3	72069	Lelio R Paula	10/2014
5735	2^239402-197	72068	Lelio R Paula	02/2012
5736	2^239356-111875	72054	Enzo Doria	05/2014
5737	(38*10^72050-119)/9	72051	Robert Price	11/2016
5738	2^239339+15015	72049	Lelio R Paula	01/2013
5739	159^32728+2	72048	Lelio R Paula	05/2013
5740	15^61259-38	72047	Lelio R Paula	01/2015
5741	92^36683-91^36683	72038	Robert Price	08/2015
5742	2^239280+54615	72031	Lelio R Paula	05/2012
5743	(47*2^239267+1)/77	72027	Lelio R Paula	04/2015
5744	(85*10^72025-1)/3	72027	Robert Price	07/2017
5745	2^239236-97305	72018	Lelio R Paula	05/2012
5746	2^239169+59	71998	Lelio R Paula	02/2012
5748	lucasU(2010,1,21796)-lucasU(2010,1,21795)	71994	Mike Oakes	05/2009
5747	(15*2^239171-1)/106301	71994	Lelio R Paula	01/2014
5749	(29^49211-1)/28	71965	Robert Price	04/2012
5750	V(344293)	71953	Serge Batalov	03/2015

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Probable Primes Top 10000

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