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 ?
5510	25206!+p(4114)	100001	Henri Lifchitz	09/2005
5511	25206!-p(5447)	100001	Henri Lifchitz	10/2005
5512	25206!-p(12402)	100001	Henri Lifchitz	04/2006
5513	25206!-p(16290)	100001	Henri Lifchitz	09/2006
5514	25206!-p(19647)	100001	Henri Lifchitz	02/2007
5515	2^332194+11473	100001	Henri Lifchitz	03/2007
5505	10^100000+342909	100001	Milton L. Brown	12/2007
5506	10^100000+346579	100001	Robert Price	04/2012
5507	10^100000+829767	100001	Robert Price	05/2012
5508	10^100000+871899	100001	Robert Price	05/2012
5509	10^100000+1475997	100001	Robert Price	07/2012
5501	10^100000+2503087	100001	Robert Price	12/2012
5502	10^100000+2686179	100001	Robert Price	12/2012
5503	10^100000+2688933	100001	Robert Price	12/2012
5504	10^100000+3667159	100001	Robert Price	08/2013
5516	10^99999+309403	100000	Daniel Heuer	01/2004
5517	10^100000-260199	100000	Patrick De Geest	01/2010
5518	10^99999-59511	99999	Patrick De Geest	07/2009
5519	10^99998+235437	99999	Patrick De Geest	02/2020
5520	10^99998-286587	99998	Patrick De Geest	02/2020
5521	10^99997+72297	99998	Patrick De Geest	02/2020
5522	10^99997-402627	99997	Patrick De Geest	02/2020
5523	10^99996+279853	99997	Patrick De Geest	02/2020
5524	10^99997-500000001	99997	Robert Price	12/2020
5525	10^99996-94961	99996	Patrick De Geest	02/2020
5526	10^99995+54633	99996	Patrick De Geest	02/2020
5527	10^99995-101429	99995	Patrick De Geest	02/2020
5528	10^99994+117271	99995	Patrick De Geest	02/2020
5529	10^99994-452289	99994	Patrick De Geest	02/2020
5530	10^99993+371311	99994	Patrick De Geest	02/2020
5531	10^99993-186491	99993	Patrick De Geest	02/2020
5532	10^99992+17431	99993	Patrick De Geest	02/2020
5533	10^99992-28607	99992	Patrick De Geest	02/2020
5534	10^99991+125391	99992	Patrick De Geest	02/2020
5535	10^99991-204573	99991	Patrick De Geest	02/2020
5536	10^99990+13899	99991	Patrick De Geest	02/2020
5537	10^99990-8111	99990	Patrick De Geest	02/2020
5538	2^332141-113073	99985	Enzo Doria	07/2014
5540	(3^209561+2)/728101255	99978	Lelio R Paula	09/2013
5539	23827^15702+15702^23827	99978	Hans Havermann	04/2018
5541	2^332085+1865897	99968	Enzo Doria	03/2016
5542	(9787*2^332070-1)/936402369	99959	Lelio R Paula	05/2015
5543	2^332023+191	99949	Lelio R Paula	02/2011
5544	7*10^99944+27	99945	Robert Price	11/2020
5545	2^331938+71149	99924	Enzo Doria	04/2016
5546	2^331932-78795	99922	Lelio R Paula	09/2016
5547	2^331921+771	99919	Lelio R Paula	01/2013
5548	(3^209419-2)/5132755	99912	Lelio R Paula	09/2013
5549	2^331860-114989	99900	Enzo Doria	05/2015
5550	2^331746-11655	99866	Lelio R Paula	09/2016
5551	11^95891-28	99861	Lelio R Paula	08/2016
5552	(2^331694-5)/11	99849	Lelio R Paula	10/2013
5553	(3^209246+7)/64	99834	Lelio R Paula	09/2013
5554	25062^9617+9617^25062	99823	Hans Havermann	04/2018
5555	15^84866-52	99811	Lelio R Paula	08/2016
5556	13^89600+30	99810	Lelio R Paula	08/2016
5557	22950^22309+22309^22950	99798	Hans Havermann	03/2018
5558	5^142772-38	99794	Lelio R Paula	08/2016
5559	(23*2^331459+1)/475	99778	Lelio R Paula	11/2013
5560	2^331416-331416+1	99767	Robert Price	10/2014
5561	2^331256-57	99718	Lelio R Paula	12/2012
5562	28192^3443+3443^28192	99714	Hans Havermann	03/2018
5563	2^331185+737	99697	Lelio R Paula	01/2013
5564	(4*10^99693+149)/9	99693	Robert Price	03/2017
5565	2^331154+1880527	99688	Enzo Doria	10/2016
5567	(19^77951+1)/20	99679	Paul Bourdelais	03/2010
5566	24354^12385+12385^24354	99679	Hans Havermann	03/2018
5568	2^331110+1870459	99675	Enzo Doria	05/2016
5569	5*2^331075+7	99665	Lelio R Paula	08/2014
5570	25776^7351+7351^25776	99659	Hans Havermann	02/2018
5571	(16*10^99656-31)/3	99657	Robert Price	03/2016
5573	2^330968+345	99632	Lelio R Paula	09/2016
5572	(2^330969+690)/2	99632	Stefano Morozzi	09/2020
5575	2*5^142528-7	99624	Lelio R Paula	11/2014
5574	2^330942+77329	99624	Enzo Doria	05/2016
5576	14^86914-99	99615	Lelio R Paula	08/2016
5577	(19*2^330902+1)/77	99611	Lelio R Paula	11/2013
5578	22971^21692+21692^22971	99610	Hans Havermann	03/2018
5579	2^330845+71687	99595	Enzo Doria	04/2016
5580	(23*2^330770+1)/3	99573	Lelio R Paula	11/2013
5581	24494^11613+11613^24494	99567	Hans Havermann	03/2018
5582	2^330735+8415	99562	Lelio R Paula	09/2016
5583	2^330720+74071	99557	Enzo Doria	04/2016
5584	31^66738-2	99531	Lelio R Paula	09/2013
5585	7*3^208567+4	99513	Lelio R Paula	08/2014
5586	(13*10^99508+47)/3	99509	Robert Price	01/2017
5587	2^330553+779	99507	Lelio R Paula	01/2013
5588	15^84606-94	99505	Lelio R Paula	08/2016
5589	6^127858+47	99493	Lelio R Paula	08/2016
5590	5^142337+48	99490	Lelio R Paula	08/2016
5591	7^117724-20	99489	Lelio R Paula	08/2016
5592	(29*10^99474-17)/3	99475	Erik Branger	09/2014
5593	(185*10^99466-11)/3	99468	Robert Price	10/2020
5594	(2^330410+2038)/2	99464	Stefano Morozzi	09/2020
5595	(9*2^330407-1)/7	99463	Lelio R Paula	03/2014
5596	(2^330373+2114)/2	99452	Stefano Morozzi	09/2020
5597	(68*10^99441+7)/3	99443	Robert Price	03/2016
5598	10^99434+155571	99435	Patrick De Geest	04/2020
5599	10^99434-123456789	99434	Robert Price	02/2020
5600	10^99434-191237	99434	Patrick De Geest	04/2020
5601	46^59791-45^59791	99418	Jean-Louis Charton	01/2013
5602	23839^14802+14802^23839	99417	Hans Havermann	02/2018
5603	(2*10^99408+529)/9	99408	Robert Price	01/2017
5604	(2^330216+3510)/2	99405	Stefano Morozzi	09/2020
5605	53^57646-2	99398	Lelio R Paula	09/2013
5606	2^330165+1870025	99390	Enzo Doria	05/2016
5607	2^330142-155	99383	Lelio R Paula	12/2012
5608	2^330088-115259	99367	Enzo Doria	06/2015
5610	24216^12671+12671^24216	99354	Hans Havermann	01/2018
5609	Phi(200548,10)/3208769	99354	Makoto Kamada	04/2019
5611	(746*10^99303+1)/9	99305	Robert Price	02/2017
5612	3^208107+40	99293	Lelio R Paula	08/2016
5613	(5*2^329833-1)/369	99288	Lelio R Paula	02/2014
5614	8*3^208093+5	99287	Lelio R Paula	08/2014
5615	5^142043+56	99284	Lelio R Paula	08/2016
5616	22*10^99275+7	99277	Robert Price	04/2016
5617	2^329778+1876189	99274	Enzo Doria	07/2016
5618	(10^99239-13)/3	99239	Robert Price	02/2017
5619	3^207987+62	99236	Lelio R Paula	08/2016
5620	2^329638+49	99231	Lelio R Paula	12/2012
5621	7^117413-18	99226	Lelio R Paula	08/2016
5622	2^329586-458903	99216	Enzo Doria	04/2015
5623	2^329553+101	99206	Lelio R Paula	12/2012
5624	2^329551-112897	99205	Enzo Doria	06/2014
5625	(3^207925+7)/50	99204	Lelio R Paula	09/2013
5626	6^127458-17993	99182	Enzo Doria	03/2013
5627	27197^4428+4428^27197	99166	Hans Havermann	10/2017
5628	(46*10^99143-1)/9	99144	Robert Price	12/2014
5629	7*10^99133+69	99134	Robert Price	10/2017
5630	18^78968-3065	99127	Enzo Doria	03/2013
5631	25927^6654+6654^25927	99122	Hans Havermann	10/2017
5632	87915!4+16	99122	Robert Price	09/2019
5633	2^329259+189	99117	Lelio R Paula	12/2012
5634	8*10^99113+39	99114	Robert Price	01/2017
5635	6^127364+77	99109	Lelio R Paula	08/2016
5636	(2^329135+1110)/2	99080	Stefano Morozzi	09/2020
5637	(59*10^99069+391)/9	99070	Robert Price	03/2021
5638	6^127285+13	99047	Lelio R Paula	08/2016
5639	(228581#+235862)/(2^31171*151)	99044	Makoto Morimoto	10/2017
5640	2^329007+73283	99041	Enzo Doria	04/2016
5641	5*3^207543-8	99024	Lelio R Paula	08/2014
5642	(2^328930+570)/2	99018	Stefano Morozzi	09/2020
5643	2^328885+149	99005	Lelio R Paula	12/2012
5644	23392^17075+17075^23392	99004	Hans Havermann	09/2017
5645	(2^328879-9)/119	99001	Lelio R Paula	10/2013
5646	5^141618+54	98987	Lelio R Paula	08/2016
5647	8*10^98982+51	98983	Robert Price	05/2017
5648	(21*2^328809-1)/7709	98979	Lelio R Paula	03/2014
5649	2^328794-2797601	98977	Enzo Doria	04/2016
5650	6^127176+5	98963	Lelio R Paula	11/2014
5651	2*10^98961-21	98962	Robert Price	09/2020
5652	24262^11989+11989^24262	98960	Hans Havermann	09/2017
5653	2^328700-109709	98949	Enzo Doria	04/2014
5654	(2^328698+1810)/2	98948	Stefano Morozzi	01/2021
5655	87771!4-128	98944	Robert Price	11/2019
5656	(2^328658+3042)/2	98936	Stefano Morozzi	09/2020
5657	46711!2-2^46711	98916	Robert Price	09/2015
5658	9*7^117037+4	98909	Lelio R Paula	11/2014
5659	127^47012+126	98905	Norbert Schneider	01/2019
5660	(2^328525+1250)/2	98896	Stefano Morozzi	09/2020
5661	(10^98890+149)/3	98890	Serge Batalov	12/2014
5662	22775^21978+21978^22775	98889	Hans Havermann	08/2017
5663	2^328497-216933	98888	Enzo Doria	05/2014
5664	2^328487+32769	98885	Lelio R Paula	08/2016
5665	3^207250-112358	98884	Enzo Doria	06/2014
5666	13^88754-90	98867	Lelio R Paula	08/2016
5668	2^328406+709	98861	Lelio R Paula	02/2013
5667	2*10^98860-21	98861	Robert Price	09/2020
5669	(17*2^328413-1)/16173	98860	Lelio R Paula	03/2014
5670	7^116976+76	98857	Lelio R Paula	08/2016
5671	(2^328378+2710)/2	98852	Stefano Morozzi	09/2020
5672	2^328335+1155	98839	Lelio R Paula	08/2016
5674	(3*2^328311+1)/5	98832	Lelio R Paula	11/2013
5673	287^40210+40210^287	98832	Norbert Schneider	11/2014
5675	(2^328284+9)/1325	98821	Lelio R Paula	10/2013
5676	(21*2^328258+1)/2125	98814	Lelio R Paula	11/2013
5677	24746^9825+9825^24746	98795	Hans Havermann	07/2020
5678	26620^5143+5143^26620	98793	Hans Havermann	07/2020
5679	65^54491+48	98788	Lelio R Paula	04/2016
5680	3^207042+98	98785	Lelio R Paula	08/2016
5681	(2^328121+3110)/2	98774	Stefano Morozzi	09/2020
5682	10^98754+73383	98755	Patrick De Geest	02/2021
5684	3^206977-112756	98754	Enzo Doria	07/2014
5685	10^98754-40000000001	98754	Robert Price	09/2020
5683	10^98754-169343	98754	Patrick De Geest	02/2021
5686	7^116846-50	98747	Lelio R Paula	08/2016
5687	23267^17512+17512^23267	98730	Hans Havermann	04/2020
5688	2^327967-28635	98728	Lelio R Paula	08/2016
5689	707^34642+34642^707	98710	Norbert Schneider	12/2017
5690	6^126850-47	98709	Lelio R Paula	08/2016
5691	(2^327886+2170)/2	98704	Stefano Morozzi	09/2020
5692	8*6^126830-7	98694	Lelio R Paula	11/2014
5693	11^94770-270	98693	Enzo Doria	08/2012
5694	(2^327846+3250)/2	98692	Stefano Morozzi	01/2021
5695	2^327832+43	98688	Lelio R Paula	12/2012
5696	2^327795+761	98677	Lelio R Paula	02/2013
5697	(2^327796+1522)/2	98677	Stefano Morozzi	09/2020
5698	10^98669+147411	98670	Patrick De Geest	11/2016
5700	10^98669-9^(98669-1)	98669	Robert Price	05/2016
5699	10^98669-105249	98669	Patrick De Geest	11/2016
5701	2^327671-109801	98639	Enzo Doria	04/2014
5702	24398^11037+11037^24398	98638	Hans Havermann	10/2019
5703	5^141090-14	98618	Lelio R Paula	08/2016
5704	20^75799+47	98617	Lelio R Paula	08/2016
5705	28101^3226+3226^28101	98597	Hans Havermann	07/2020
5706	2^327515-1017	98592	Lelio R Paula	08/2016
5707	6^126692+97681	98586	Mike Oakes	04/2011
5708	2^327467-741	98578	Lelio R Paula	08/2016
5709	22713^21800+21800^22713	98540	Hans Havermann	05/2020
5710	(2^327329+9)/19	98535	Lelio R Paula	10/2013
5711	7^116577-66	98519	Lelio R Paula	08/2016
5713	(3*2^327250+1)/7	98512	Lelio R Paula	11/2013
5712	23220^17479+17479^23220	98512	Hans Havermann	03/2020
5714	(2^327240+3798)/2	98509	Stefano Morozzi	02/2021
5715	(19*2^327192+1)/275	98494	Lelio R Paula	11/2013
5716	2^327162-66945	98486	Lelio R Paula	08/2016
5717	30139^1852+1852^30139	98484	Hans Havermann	02/2020
5718	23182^17703+17703^23182	98479	Hans Havermann	01/2020
5719	4*10^98472-3	98473	Erik Branger	11/2013
5720	26167^5794+5794^26167	98466	Hans Havermann	01/2020
5721	(6883*2^327047-1)/77	98453	Lelio R Paula	05/2015
5722	(71*10^98446+1)/9	98447	Serge Batalov	11/2010
5723	13^88363+94	98432	Lelio R Paula	08/2016
5724	48^58543-47^58543	98425	Jean-Louis Charton	11/2005
5725	6^126481+41	98422	Lelio R Paula	08/2016
5726	78*10^98413-7	98415	Robert Price	05/2017
5727	22634^22263+22263^22634	98404	Hans Havermann	07/2020
5728	7^116416+46	98383	Lelio R Paula	08/2016
5729	7^116407-24	98376	Lelio R Paula	07/2016
5730	439^37228+37228^439	98374	Norbert Schneider	08/2018
5732	2^326782-1860671	98372	Enzo Doria	03/2016
5731	17^79948+58	98372	Lelio R Paula	08/2016
5733	22499^22602-22602^22499	98368	Norbert Schneider	08/2020
5734	3^206143-98	98356	Lelio R Paula	08/2016
5735	8*5^140705+7	98350	Lelio R Paula	11/2014
5736	(2^326632+1662)/2	98326	Stefano Morozzi	09/2020
5737	2^326585+11	98312	Lelio R Paula	12/2012
5738	2^326582-459161	98311	Enzo Doria	05/2015
5740	(2^326548+9)/5	98301	Lelio R Paula	10/2013
5739	(2^326549+18)/10	98301	Stefano Morozzi	03/2020
5741	2^326538+71659	98298	Enzo Doria	04/2016
5742	(2^326520+2082)/2	98293	Stefano Morozzi	09/2020
5743	(2^326521+1002)/2	98293	Stefano Morozzi	09/2020
5744	15^83575-58	98292	Lelio R Paula	08/2016
5745	10^98288+3	98289	Robert Price	03/2011
5746	10^98288-117017	98288	Patrick De Geest	11/2011
5747	(44*10^98284-719)/9	98285	Robert Price	12/2017
5748	23466^15419+15419^23466	98277	Hans Havermann	02/2020
5749	2^326421-2797573	98263	Enzo Doria	04/2016
5750	2^326401+16095	98257	Lelio R Paula	07/2016

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PRP Records

Probable Primes Top 10000

(280932 PRPs in the top)