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 ?
5501	(2^343974+2670)/2	103547	Stefano Morozzi	09/2020
5502	2^343971-5077	103546	Lelio R Paula	09/2011
5503	(7*10^103531+71)/3	103532	Robert Price	05/2018
5504	2^343899+141	103524	Lelio R Paula	08/2011
5505	(2^343933+1)/(3*98294339989393)	103520	Gord Palameta	08/2018
5506	6^133029-67	103517	Lelio R Paula	11/2016
5507	(17*2^343877+1)/13625	103515	Lelio R Paula	12/2013
5508	66*10^103507+7	103509	Robert Price	07/2020
5509	26297^8614+8614^26297	103485	Hans Havermann	09/2020
5510	(2^343764+2658)/2	103483	Stefano Morozzi	09/2020
5511	26499^8036+8036^26499	103480	Hans Havermann	09/2020
5512	(136*10^103474-1)/9	103476	Serge Batalov	12/2014
5513	5^148014-24	103458	Lelio R Paula	11/2016
5514	28316^4503+4503^28316	103453	Hans Havermann	09/2020
5515	(22*10^103450+53)/3	103451	Robert Price	07/2019
5516	2^343604+9931	103436	Yves Minet	01/2011
5517	2^343601-21189	103435	Enzo Doria	06/2013
5518	(10^103423+173)/3	103423	Robert Price	05/2021
5519	2^343508-115229	103407	Enzo Doria	06/2015
5520	(509203*2^343491-1)/16147	103403	Lelio R Paula	05/2015
5521	3^216685-113056	103386	Enzo Doria	07/2014
5522	24829^14580+14580^24829	103382	Hans Havermann	08/2020
5523	91355!4+1024	103381	Robert Price	09/2019
5524	44^62903-43^62903	103379	Jean-Louis Charton	08/2012
5525	11^99262-20	103371	Lelio R Paula	12/2016
5526	(509203*2^343357-1)/5	103366	Lelio R Paula	05/2015
5527	(2^343363+3570)/2	103363	Stefano Morozzi	09/2020
5528	2^343356-2791889	103361	Enzo Doria	03/2016
5529	(25*10^103360-241)/9	103361	Robert Price	05/2018
5530	Phi(104989,10)/2939693	103350	Maksym Voznyy	09/2015
5531	24826^14511+14511^24826	103319	Hans Havermann	09/2020
5532	2^343182-171	103309	Lelio R Paula	08/2011
5533	(23619^23619+23620^23620)/7187	103294	David Broadhurst	09/2009
5534	2^343079-1835611	103278	Enzo Doria	05/2015
5535	2^343063-1147	103273	Yves Minet	06/2013
5536	24741^14930+14930^24741	103271	Hans Havermann	09/2020
5537	(16*10^103255-73)/3	103256	Robert Price	07/2020
5538	9*6^132689+7	103254	Lelio R Paula	11/2014
5539	2^342979-18085	103247	Enzo Doria	05/2013
5540	(16*10^103244-31)/3	103245	Robert Price	03/2019
5541	2^342966-16995	103244	Lelio R Paula	11/2016
5542	23797^21774+21774^23797	103230	Hans Havermann	09/2020
5543	25388^11637+11637^25388	103224	Hans Havermann	09/2020
5544	(2^342876+2086)/2	103216	Stefano Morozzi	09/2020
5545	(16*10^103214-31)/3	103215	Robert Price	03/2019
5547	(37*10^103211+611)/9	103212	Robert Price	11/2018
5546	(238*10^103210-1)/3	103212	Robert Price	04/2020
5548	5^147650+16	103203	Lelio R Paula	11/2016
5549	gcd(Phi(852060,10),(10^42603+1)^3(10^42603+1-10^21302)+(10^85206+10^42603)(10^21302+1)+10^127809)	103201	Serge Batalov	04/2015
5550	2^342817+2707067	103199	Enzo Doria	03/2016
5551	43^63177-42	103198	Theodore Burton	02/2007
5552	2^342805-21025	103195	Enzo Doria	06/2013
5553	24129^18890+18890^24129	103182	Hans Havermann	09/2020
5554	(622*10^103171-1)/9	103173	Robert Price	11/2021
5555	2^342714+12285	103168	Lelio R Paula	11/2016
5556	18^82178-4481	103156	Enzo Doria	03/2013
5557	2^342665-17349	103153	Enzo Doria	05/2013
5558	30408^2467+2467^30408	103150	Hans Havermann	09/2020
5559	(2^342615+3090)/2	103138	Stefano Morozzi	09/2020
5560	2^342612+175	103137	Lelio R Paula	08/2011
5561	5*2^342585-3	103130	Lelio R Paula	09/2014
5562	(16*10^103127+77)/3	103128	Robert Price	03/2019
5563	(2^342527+3774)/2	103111	Stefano Morozzi	02/2021
5564	2^342503-19209	103104	Enzo Doria	05/2013
5565	(2^342484+2586)/2	103098	Stefano Morozzi	09/2020
5566	2^342476+51	103096	Lelio R Paula	08/2011
5567	2^342460-18885	103091	Enzo Doria	05/2013
5568	(2^342442+862)/2	103086	Stefano Morozzi	02/2021
5569	(194*10^103074-17)/3	103076	Robert Price	09/2020
5570	7^121968+82	103075	Lelio R Paula	10/2016
5571	2^342392-108863	103071	Enzo Doria	03/2014
5572	(2^342389+806)/2	103070	Stefano Morozzi	01/2021
5573	3^216014+28	103065	Lelio R Paula	11/2016
5574	2^342353-108879	103059	Enzo Doria	03/2014
5575	10^103055+276081	103056	Patrick De Geest	12/2016
5576	10^103055-53	103055	Lelio R Paula	11/2016
5577	(58*10^103046+419)/9	103047	Robert Price	05/2019
5578	7^121933+4	103046	Lelio R Paula	11/2014
5579	(71*10^103028-143)/9	103029	Robert Price	10/2021
5580	(2^342235+3618)/2	103023	Stefano Morozzi	09/2020
5581	19^80560-68	103017	Lelio R Paula	10/2016
5582	2^342209+76607	103016	Enzo Doria	05/2016
5584	328^40945+40945^328	103013	Norbert Schneider	12/2014
5583	12^95454-91	103013	Lelio R Paula	10/2016
5585	25833^9716+9716^25833	103009	Hans Havermann	01/2019
5586	(893*10^103004+7)/9	103006	Robert Price	06/2021
5587	65^56809-64^56809	102990	Robert Price	08/2013
5588	5^147338-6	102985	Lelio R Paula	11/2014
5589	2^342084-112739	102978	Enzo Doria	06/2014
5590	9*6^132330+7	102974	Lelio R Paula	11/2014
5591	2^342034-16737	102963	Enzo Doria	05/2013
5592	(9787*2^342011-1)/25	102959	Lelio R Paula	05/2015
5593	(3^215802-5)/124343756	102956	Lelio R Paula	12/2013
5594	2^341991-17421	102950	Enzo Doria	05/2013
5595	2^341969-112225	102943	Enzo Doria	06/2014
5596	(9787*2^341864-1)/3	102915	Lelio R Paula	05/2015
5597	2^341859+1869413	102910	Enzo Doria	05/2016
5598	10^102909+61	102910	Lelio R Paula	11/2016
5599	10^102909-67049	102909	Patrick De Geest	12/2016
5600	23814^20935+20935^23814	102898	Hans Havermann	02/2019
5601	28345^4264+4264^28345	102888	Hans Havermann	02/2019
5602	25665^10204+10204^25665	102886	Hans Havermann	02/2019
5603	26288^8181+8181^26288	102860	Hans Havermann	02/2019
5604	2^341659+1836773	102850	Enzo Doria	03/2016
5605	2^341608-110639	102835	Enzo Doria	05/2014
5606	10^102824+49	102825	Lelio R Paula	11/2016
5607	10^102824-168011	102824	Patrick De Geest	12/2016
5608	11^98708-8	102794	Lelio R Paula	10/2016
5609	2^341466+4429	102792	Lelio R Paula	09/2011
5610	2^341460-107	102790	Lelio R Paula	08/2011
5611	(2^341388+47)/21014943	102761	Lelio R Paula	12/2013
5612	2^341355+21	102759	Lelio R Paula	08/2011
5613	2^341246+40755	102726	Lelio R Paula	11/2016
5614	(2^341256-5)/991699	102723	Lelio R Paula	12/2013
5615	7^121547+78	102720	Lelio R Paula	10/2016
5616	2^341223-461197	102719	Enzo Doria	06/2015
5617	27838^4893+4893^27838	102711	Hans Havermann	03/2019
5619	2^341190-20577	102709	Enzo Doria	06/2013
5618	(27*2^341212+1)/84674449	102709	Lelio R Paula	12/2013
5620	6^131976-65	102698	Lelio R Paula	10/2016
5621	2^341134+2533	102692	Henri Lifchitz	09/2005
5622	13^92184-54	102688	Lelio R Paula	10/2016
5623	2^341116-20873	102687	Enzo Doria	06/2013
5624	2^341094-19953	102680	Enzo Doria	06/2013
5625	23761^20950+20950^23761	102676	Hans Havermann	03/2019
5626	2^341053+129	102668	Lelio R Paula	08/2011
5628	(31*2^341006-1)/3	102655	Lelio R Paula	03/2014
5627	7^121471+94	102655	Lelio R Paula	10/2016
5630	2^341004-173	102653	Lelio R Paula	08/2011
5629	20^78901+3	102653	Lelio R Paula	10/2016
5631	(2^341001+1674)/2	102652	Stefano Morozzi	09/2020
5632	5^146853-52	102646	Lelio R Paula	10/2016
5633	2^340969-216931	102642	Enzo Doria	05/2014
5634	122^49196+121	102641	Norbert Schneider	10/2018
5635	2^340952+1870021	102637	Enzo Doria	05/2016
5636	5*2^340940-3	102634	Lelio R Paula	08/2014
5637	(6^131891+1)/7	102631	Paul Bourdelais	01/2010
5638	(11*10^102629-23)/3	102630	Robert Price	09/2021
5639	25876^9239+9239^25876	102615	Hans Havermann	02/2019
5640	(4*10^102612+83)/3	102613	Robert Price	02/2018
5641	75^54717+74	102598	Norbert Schneider	01/2015
5642	(17*10^102597+13)/3	102598	Robert Price	01/2019
5643	2^340806-20393	102593	Enzo Doria	06/2013
5644	(2^340790+5)/138267	102583	Lelio R Paula	12/2013
5645	6^131821+77	102577	Lelio R Paula	10/2016
5646	(203*10^102561-11)/3	102563	Robert Price	12/2020
5647	2^340688-29	102558	Henri Lifchitz	05/2005
5648	2^340685-109101	102557	Enzo Doria	04/2014
5649	65^56567-64	102552	Norbert Schneider	11/2014
5650	26230^8121+8121^26230	102550	Hans Havermann	03/2019
5651	(8*10^102541+49)/3	102542	Robert Price	05/2020
5652	(536*10^102533-23)/9	102535	Robert Price	02/2020
5653	2^340547-108897	102515	Enzo Doria	03/2014
5654	(2^340536+778)/2	102512	Stefano Morozzi	09/2020
5655	25592^10119+10119^25592	102500	Hans Havermann	02/2019
5656	7^121268+82	102484	Lelio R Paula	10/2016
5657	(6883*2^340443-1)/162401	102483	Lelio R Paula	05/2015
5658	2^340434-5955	102481	Lelio R Paula	11/2016
5659	(7*10^102480-19)/3	102481	Robert Price	10/2020
5660	(2^340381+47)/7	102465	Lelio R Paula	12/2013
5661	111^50095+110	102461	Norbert Schneider	04/2017
5662	2^340291-20301	102438	Enzo Doria	06/2013
5663	12^94915+89	102431	Lelio R Paula	10/2016
5664	(106*10^102422+17)/3	102424	Robert Price	04/2021
5665	24466^15349+15349^24466	102417	Hans Havermann	03/2019
5666	2^340212+111546435	102415	Paul Bourdelais	10/2021
5667	2^340208-20373	102413	Enzo Doria	06/2013
5668	6^131598-17273	102404	Enzo Doria	02/2013
5669	(2^340132+1182)/2	102390	Stefano Morozzi	09/2020
5670	(2^340133+1166)/2	102390	Stefano Morozzi	09/2020
5671	2^340115-21181	102385	Enzo Doria	06/2013
5672	(55459*2^340090+1)/1591	102379	Lelio R Paula	07/2014
5673	(2^340064+3630)/2	102370	Stefano Morozzi	09/2020
5674	89^52511-88^52511	102365	Robert Price	06/2015
5675	3^214539-112756	102362	Enzo Doria	07/2014
5676	23159^23450-23450^23159	102353	Norbert Schneider	12/2019
5677	2^340000-19877	102351	Enzo Doria	06/2013
5678	2^339990-114845	102348	Enzo Doria	05/2015
5679	(3^214516-2)/51383	102346	Lelio R Paula	12/2013
5680	20^78661-99	102341	Lelio R Paula	09/2016
5681	2^339951-19585	102336	Enzo Doria	05/2013
5682	(13*2^339943+1)/45	102333	Lelio R Paula	12/2013
5683	(236282#+121441)/(121441*25499429)	102332	Makoto Morimoto	08/2020
5684	5*10^102323-91	102324	Robert Price	03/2021
5686	2^339889+29327	102317	Yves Minet	06/2010
5685	(167*10^102315-17)/3	102317	Robert Price	03/2020
5687	26348^7641+7641^26348	102314	Hans Havermann	03/2019
5688	Phi(239414,10)/6333218543	102303	Makoto Kamada	08/2019
5689	2^339834-109493	102301	Enzo Doria	04/2014
5690	(16*10^102299-19)/3	102300	Robert Price	02/2019
5691	(11^98221-5^98221)/6	102286	Robert Price	01/2013
5692	3^214365+1820	102279	Lelio R Paula	10/2016
5693	31978^1579+1579^31978	102278	Hans Havermann	03/2019
5694	(11*2^339705-1)/183	102261	Lelio R Paula	03/2014
5695	2^339694-16995	102259	Lelio R Paula	09/2016
5696	(56*10^102255+691)/9	102256	Robert Price	05/2019
5697	122^49008+121	102249	Norbert Schneider	10/2018
5698	(2^339652+3178)/2	102246	Stefano Morozzi	09/2020
5699	7^120985-38	102245	Lelio R Paula	10/2016
5700	10^102244+122961	102245	Patrick De Geest	12/2016
5701	10^102244-27	102244	Lelio R Paula	09/2016
5702	7^120982-62	102242	Lelio R Paula	10/2016
5703	(2^339640+2670)/2	102242	Stefano Morozzi	09/2020
5704	4*6^131382-5	102236	Lelio R Paula	11/2014
5705	(2^339607+3290)/2	102232	Stefano Morozzi	02/2021
5706	2^339586-1091	102226	Yves Minet	11/2012
5707	11^98161-3072000	102225	Enzo Doria	12/2012
5708	9*7^120961-4	102225	Lelio R Paula	11/2014
5709	5*3^214250+2	102224	Serge Batalov	10/2010
5710	12^94713-59	102213	Lelio R Paula	10/2016
5711	12^94705+89	102204	Lelio R Paula	10/2016
5712	2^339407-177	102172	Lelio R Paula	08/2011
5713	4*10^102163-57	102164	Robert Price	10/2018
5714	2^339355+65	102157	Lelio R Paula	07/2011
5715	(28*10^102142-31)/3	102143	Robert Price	12/2019
5716	(2^339323+47)/880715	102141	Lelio R Paula	12/2013
5717	(2^339268+1758)/2	102130	Stefano Morozzi	09/2020
5718	s(178551)	102122	Robert Price	05/2020
5719	(797*10^102112-23)/9	102114	Robert Price	01/2022
5720	(2^339175+2790)/2	102102	Stefano Morozzi	02/2021
5723	2^339168+21	102100	Lelio R Paula	07/2011
5722	2^339167-108807	102100	Enzo Doria	03/2014
5721	(2^339169+42)/2	102100	Stefano Morozzi	09/2020
5724	2^339156+163	102097	Lelio R Paula	08/2011
5725	(2^339149+746)/2	102094	Stefano Morozzi	09/2020
5726	(25*10^102076-67)/3	102077	Robert Price	06/2019
5727	2^339081-4543	102074	Yves Minet	03/2019
5728	2*10^102062+77	102063	Robert Price	08/2020
5729	24327^15668+15668^24327	102053	Hans Havermann	02/2019
5730	10^102052-7000001	102052	Robert Price	06/2021
5731	2^339000-175635	102050	Stefano Morozzi	12/2021
5732	2^339000-151667	102050	Stefano Morozzi	12/2021
5733	2^338999+79289	102049	Stefano Morozzi	01/2022
5734	2^338975+28355	102042	Stefano Morozzi	01/2022
5736	25080^11711+11711^25080	102041	Hans Havermann	02/2019
5735	2^338972+152343	102041	Stefano Morozzi	12/2021
5737	2^338968+53461	102040	Stefano Morozzi	01/2022
5738	2^338963-127455	102039	Stefano Morozzi	12/2021
5740	(2^338982-7)/1754517	102038	Lelio R Paula	12/2013
5739	2^338960+53935	102038	Stefano Morozzi	01/2022
5741	2^338954-177003	102036	Stefano Morozzi	12/2021
5742	2^338954+154207	102036	Stefano Morozzi	01/2022
5743	2^338950+175077	102035	Stefano Morozzi	12/2021
5744	2^338951-51687	102035	Stefano Morozzi	12/2021
5745	2^338943+127103	102033	Stefano Morozzi	12/2021
5746	2^338940+78607	102032	Stefano Morozzi	01/2022
5747	2^338939+151569	102031	Stefano Morozzi	12/2021
5748	2^338931+2349	102029	Stefano Morozzi	12/2021
5749	2^338928+2367	102028	Stefano Morozzi	12/2021
5750	2^338927+52779	102028	Stefano Morozzi	01/2022

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