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 ?
7501	(3*2^328311+1)/5	98832	Lelio R Paula	11/2013
7502	(2^328284+9)/1325	98821	Lelio R Paula	10/2013
7503	(21*2^328258+1)/2125	98814	Lelio R Paula	11/2013
7504	(28623^22171-1)/28622	98806	Serge Batalov	06/2022
7505	24746^9825+9825^24746	98795	Hans Havermann	07/2020
7506	26620^5143+5143^26620	98793	Hans Havermann	07/2020
7507	65^54491+48	98788	Lelio R Paula	04/2016
7508	3^207042+98	98785	Lelio R Paula	08/2016
7509	(2^328121+3110)/2	98774	Stefano Morozzi	09/2020
7510	10^98754+73383	98755	Patrick De Geest	02/2021
7513	3^206977-112756	98754	Enzo Doria	07/2014
7512	10^98754-40000000001	98754	Robert Price	09/2020
7511	10^98754-169343	98754	Patrick De Geest	02/2021
7514	7^116846-50	98747	Lelio R Paula	08/2016
7515	(19152^23059-1)/19151	98740	Serge Batalov	06/2022
7516	23267^17512+17512^23267	98730	Hans Havermann	04/2020
7517	2^327967-28635	98728	Lelio R Paula	08/2016
7518	707^34642+34642^707	98710	Norbert Schneider	12/2017
7519	(10771^24481-1)/10770	98710	Serge Batalov	06/2022
7520	6^126850-47	98709	Lelio R Paula	08/2016
7521	(2^327886+2170)/2	98704	Stefano Morozzi	09/2020
7522	(22*10^98697+47)/3	98698	Robert Price	06/2021
7523	8*6^126830-7	98694	Lelio R Paula	11/2014
7524	11^94770-270	98693	Enzo Doria	08/2012
7525	(2^327846+3250)/2	98692	Stefano Morozzi	01/2021
7526	2^327832+43	98688	Lelio R Paula	12/2012
7527	2^327795+761	98677	Lelio R Paula	02/2013
7528	(2^327796+1522)/2	98677	Stefano Morozzi	09/2020
7529	10^98669+147411	98670	Patrick De Geest	11/2016
7531	10^98669-9^(98669-1)	98669	Robert Price	05/2016
7530	10^98669-105249	98669	Patrick De Geest	11/2016
7532	(7911^25309-1)/7910	98657	Serge Batalov	06/2022
7533	2^327671-109801	98639	Enzo Doria	04/2014
7534	24398^11037+11037^24398	98638	Hans Havermann	10/2019
7535	5^141090-14	98618	Lelio R Paula	08/2016
7536	20^75799+47	98617	Lelio R Paula	08/2016
7537	(5452^26393-1)/5451	98616	Serge Batalov	06/2022
7538	28101^3226+3226^28101	98597	Hans Havermann	07/2020
7539	2^327515-1017	98592	Lelio R Paula	08/2016
7540	6^126692+97681	98586	Mike Oakes	04/2011
7541	2^327467-741	98578	Lelio R Paula	08/2016
7542	(2947^28411-1)/2946	98566	Serge Batalov	06/2022
7543	22713^21800+21800^22713	98540	Hans Havermann	05/2020
7544	(2^327329+9)/19	98535	Lelio R Paula	10/2013
7545	7^116577-66	98519	Lelio R Paula	08/2016
7546	(3*2^327250+1)/7	98512	Lelio R Paula	11/2013
7547	23220^17479+17479^23220	98512	Hans Havermann	03/2020
7548	(2^327240+3798)/2	98509	Stefano Morozzi	02/2021
7549	(28514^22111-1)/28513	98502	Serge Batalov	06/2022
7550	(19*2^327192+1)/275	98494	Lelio R Paula	11/2013
7551	2^327162-66945	98486	Lelio R Paula	08/2016
7552	30139^1852+1852^30139	98484	Hans Havermann	02/2020
7553	23182^17703+17703^23182	98479	Hans Havermann	01/2020
7554	4*10^98472-3	98473	Erik Branger	11/2013
7555	26167^5794+5794^26167	98466	Hans Havermann	01/2020
7556	(6883*2^327047-1)/77	98453	Lelio R Paula	05/2015
7557	(71*10^98446+1)/9	98447	Serge Batalov	11/2010
7558	(2009^29803-1)/2008	98436	Serge Batalov	06/2022
7559	13^88363+94	98432	Lelio R Paula	08/2016
7560	48^58543-47^58543	98425	Jean-Louis Charton	11/2005
7561	6^126481+41	98422	Lelio R Paula	08/2016
7562	78*10^98413-7	98415	Robert Price	05/2017
7563	22634^22263+22263^22634	98404	Hans Havermann	07/2020
7564	(47*10^98386+241)/9	98387	Robert Price	06/2022
7565	7^116416+46	98383	Lelio R Paula	08/2016
7566	7^116407-24	98376	Lelio R Paula	07/2016
7567	439^37228+37228^439	98374	Norbert Schneider	08/2018
7568	2^326782-1860671	98372	Enzo Doria	03/2016
7569	17^79948+58	98372	Lelio R Paula	08/2016
7570	22499^22602-22602^22499	98368	Norbert Schneider	08/2020
7571	3^206143-98	98356	Lelio R Paula	08/2016
7572	8*5^140705+7	98350	Lelio R Paula	11/2014
7573	(2^326632+1662)/2	98326	Stefano Morozzi	09/2020
7574	(638^35053-1)/637	98315	Serge Batalov	06/2022
7575	2^326585+11	98312	Lelio R Paula	12/2012
7576	2^326582-459161	98311	Enzo Doria	05/2015
7577	(1266^31687-1)/1265	98304	Serge Batalov	06/2022
7579	(2^326548+9)/5	98301	Lelio R Paula	10/2013
7578	(2^326549+18)/10	98301	Stefano Morozzi	03/2020
7580	2^326538+71659	98298	Enzo Doria	04/2016
7581	(2^326520+2082)/2	98293	Stefano Morozzi	09/2020
7582	(2^326521+1002)/2	98293	Stefano Morozzi	09/2020
7583	15^83575-58	98292	Lelio R Paula	08/2016
7584	10^98288+3	98289	Robert Price	03/2011
7585	10^98288-117017	98288	Patrick De Geest	11/2011
7586	(44*10^98284-719)/9	98285	Robert Price	12/2017
7587	(5985^26021-1)/5984	98280	Serge Batalov	06/2022
7588	23466^15419+15419^23466	98277	Hans Havermann	02/2020
7589	2^326421-2797573	98263	Enzo Doria	04/2016
7590	2^326401+16095	98257	Lelio R Paula	07/2016
7591	(6494^25771-1)/6493	98249	Serge Batalov	06/2022
7592	7^116240-116240^7	98235	Norbert Schneider	05/2017
7593	17^79826-78	98222	Lelio R Paula	08/2016
7594	2^326268-809	98217	Yves Minet	04/2011
7595	22659^21590+21590^22659	98210	Hans Havermann	10/2019
7596	22268^22587-22587^22268	98202	Norbert Schneider	08/2020
7597	(418*10^98199+23)/9	98201	Robert Price	08/2017
7598	12*10^98198-7	98200	Robert Price	11/2017
7599	15^83496-76	98199	Lelio R Paula	08/2016
7600	(10223*2^326179+1)/6125	98190	Lelio R Paula	07/2014
7601	9*5^140471-4	98186	Lelio R Paula	11/2014
7602	(35103^21601-1)/35102	98180	Serge Batalov	06/2022
7604	22774^20455+20455^22774	98175	Hans Havermann	07/2020
7603	(4516^26863-1)/4515	98175	Serge Batalov	06/2022
7605	2^326069-2383	98157	Yves Minet	10/2013
7606	(9661^24631-1)/9660	98152	Serge Batalov	06/2022
7607	(4175^27109-1)/4174	98149	Serge Batalov	06/2022
7608	(57801^20611-1)/57800	98144	Serge Batalov	06/2022
7609	2^325973+1185	98128	Lelio R Paula	07/2016
7610	(25*2^325949-1)/17	98121	Lelio R Paula	02/2014
7611	2^325945-1847269	98120	Enzo Doria	07/2015
7612	8*10^98111-67	98112	Robert Price	10/2017
7613	(2^325902+1138)/2	98106	Stefano Morozzi	09/2020
7614	(215^42061-1)/214	98103	Serge Batalov	06/2022
7615	(6775^25609-1)/6774	98102	Serge Batalov	06/2022
7616	(6718^25633-1)/6717	98100	Serge Batalov	06/2022
7617	2^325866+15	98096	Lelio R Paula	12/2012
7618	22591^21952+21952^22591	98079	Hans Havermann	02/2020
7619	2^325765+1974305	98066	Enzo Doria	06/2016
7620	2^325733-58695	98056	Lelio R Paula	07/2016
7621	(7*10^98055-529)/9	98055	Robert Price	08/2021
7622	2^325717-3645	98051	Lelio R Paula	07/2016
7623	(2^325704+718)/2	98047	Stefano Morozzi	09/2020
7624	(15679^23371-1)/15678	98045	Serge Batalov	06/2022
7625	(23342^22441-1)/23341	98022	Serge Batalov	06/2022
7626	23968^12293+12293^23968	98021	Hans Havermann	11/2019
7627	(23*2^325583-1)/21	98011	Lelio R Paula	02/2014
7628	(7*10^98007-13)/3	98008	Robert Price	06/2016
7629	(2^325544+1110)/2	97999	Stefano Morozzi	09/2020
7630	2^325512-459959	97989	Enzo Doria	05/2015
7631	(2^325492+682)/2	97983	Stefano Morozzi	09/2020
7632	(3^205354-8)/17	97978	Lelio R Paula	09/2013
7633	2^325433+76817	97966	Enzo Doria	05/2016
7634	5*10^97963+81	97964	Robert Price	08/2017
7635	(13208^23773-1)/13207	97961	Serge Batalov	06/2022
7636	2^325390-109061	97953	Enzo Doria	04/2014
7637	(55*10^97940+323)/9	97941	Robert Price	10/2021
7638	13^87921+24	97940	Lelio R Paula	08/2016
7639	10^97930-7000001	97930	Robert Price	06/2021
7640	961^32831-960^32831	97926	Jean-Louis Charton	02/2011
7641	(17968^23017-1)/17967	97922	Serge Batalov	06/2022
7642	(3337^27793-1)/3336	97922	Serge Batalov	06/2022
7644	22600^21499+21499^22600	97913	Hans Havermann	05/2020
7643	(18703^22921-1)/18702	97913	Serge Batalov	06/2022
7645	2^325215+12909	97900	Lelio R Paula	07/2016
7646	22619^21286+21286^22619	97898	Hans Havermann	04/2020
7647	(85*10^97876-49)/9	97877	Robert Price	12/2020
7648	7*10^97874-69	97875	Robert Price	01/2017
7649	5*10^97869-63	97870	Robert Price	04/2021
7651	(17^79537+5^79537)/22	97865	Robert Price	06/2013
7650	15^83212+22	97865	Lelio R Paula	08/2016
7652	2^325087-109057	97861	Enzo Doria	04/2014
7653	2^325074+1870657	97858	Enzo Doria	05/2016
7655	2^325066-2111	97855	Yves Minet	08/2013
7654	CopelandErdos(97855)	97855	Eric W. Weisstein	10/2015
7656	(8694^24841-1)/8693	97851	Serge Batalov	06/2022
7657	(21159^22621-1)/21158	97843	Serge Batalov	06/2022
7658	26660^4677+4677^26660	97842	Hans Havermann	12/2019
7659	18^77944-89	97841	Lelio R Paula	07/2016
7660	119^47136+118	97833	Norbert Schneider	09/2018
7661	6^125720-17663	97830	Enzo Doria	02/2013
7662	(73640^20101-1)/73639	97829	Serge Batalov	06/2022
7663	2^324972-2069	97827	Yves Minet	05/2013
7664	2^324958-4691	97823	Yves Minet	05/2019
7665	(8087^25033-1)/8086	97820	Serge Batalov	06/2022
7666	2^324944-2788319	97818	Enzo Doria	03/2016
7667	22845^19112+19112^22845	97807	Hans Havermann	10/2019
7668	(2^324898+1270)/2	97804	Stefano Morozzi	09/2020
7670	4*10^97799-9	97800	Erik Branger	11/2013
7669	2^324882+577294575	97800	Lelio R Paula	09/2016
7671	2^324863-1867921	97794	Enzo Doria	04/2016
7672	6^125662-18473	97785	Enzo Doria	03/2013
7673	12^90604+11	97779	Lelio R Paula	07/2016
7674	(29*10^97751+49)/3	97752	Robert Price	09/2021
7675	(37108^21391-1)/37107	97741	Serge Batalov	06/2022
7676	5^139830+24	97737	Lelio R Paula	04/2016
7677	(2^324672+1198)/2	97736	Stefano Morozzi	09/2020
7678	(101*10^97724+7)/9	97726	Robert Price	02/2022
7679	2^324612+1155	97718	Lelio R Paula	07/2016
7680	(2^324597+3542)/2	97714	Stefano Morozzi	09/2020
7681	19^76404-44	97702	Lelio R Paula	07/2016
7682	(5939^25889-1)/5938	97694	Serge Batalov	06/2022
7684	2^324505-2983	97686	Yves Minet	04/2011
7683	(7740^25121-1)/7739	97686	Serge Batalov	06/2022
7685	(144^45259+1)/145	97684	Paul Bourdelais	08/2019
7686	(31*2^324496-1)/45	97683	Lelio R Paula	02/2014
7687	(11234^24109-1)/11233	97651	Serge Batalov	06/2022
7688	6^125488-17843	97649	Enzo Doria	02/2013
7689	(2^324350+3198)/2	97639	Stefano Morozzi	09/2020
7690	(75638^20011-1)/75637	97624	Serge Batalov	06/2022
7691	7^115515-2	97622	Lelio R Paula	09/2013
7692	(15672^23269-1)/15671	97613	Serge Batalov	06/2022
7693	(89^50069-1)/88	97603	Paul Bourdelais	08/2017
7694	6^125418-5	97595	Lelio R Paula	11/2014
7695	(2^324193+3522)/2	97592	Stefano Morozzi	09/2020
7696	(2422^28837-1)/2421	97587	Serge Batalov	06/2022
7697	(2^324172+666)/2	97586	Stefano Morozzi	09/2020
7698	2^324091+111546435	97562	Paul Bourdelais	10/2021
7699	2^324076+1155	97557	Lelio R Paula	07/2016
7700	(2^324074+9)/13	97555	Lelio R Paula	10/2013
7701	(11*10^97539-71)/3	97540	Robert Price	04/2022
7702	(55459*2^323993+1)/21	97536	Lelio R Paula	07/2014
7703	13^87557-12^87557	97534	Jean-Louis Charton	12/2008
7704	2^323946+73939	97518	Enzo Doria	04/2016
7705	2^323937+1866947	97515	Enzo Doria	03/2016
7706	(98339^19531-1)/98338	97508	Serge Batalov	06/2022
7708	6^125290-18533	97495	Enzo Doria	03/2013
7707	(2^323870+1650)/2	97495	Stefano Morozzi	09/2020
7709	2^323845+101	97488	Lelio R Paula	12/2012
7710	18^77662+65	97487	Lelio R Paula	07/2016
7711	22634^20265+20265^22634	97479	Hans Havermann	04/2020
7712	(5533^26041-1)/5532	97467	Serge Batalov	06/2022
7713	2^323772+76771	97466	Enzo Doria	05/2016
7714	2^323765-112213	97463	Enzo Doria	06/2014
7715	22730^19389+19389^22730	97457	Hans Havermann	02/2020
7716	2^323720-6555	97450	Lelio R Paula	07/2016
7717	2^323694-1860401	97442	Enzo Doria	03/2016
7718	20^74886+3	97429	Lelio R Paula	06/2016
7719	24476^9561+9561^24476	97427	Hans Havermann	01/2020
7720	(2^323623+1766)/2	97420	Stefano Morozzi	09/2020
7721	(3250^27739-1)/3249	97413	Serge Batalov	06/2022
7723	3*10^97399+73	97400	Robert Price	04/2016
7722	7^115252-50	97400	Lelio R Paula	07/2016
7724	(4715^26513-1)/4714	97392	Serge Batalov	06/2022
7725	224737#+393581	97389	Nicolas PALAU	12/2016
7726	(2^323468+3186)/2	97374	Stefano Morozzi	09/2020
7727	(2^323456+538)/2	97370	Stefano Morozzi	09/2020
7728	23277^15236+15236^23277	97365	Hans Havermann	07/2020
7730	(26*10^97353+31)/3	97354	Robert Price	07/2016
7729	(2^323403+3510)/2	97354	Stefano Morozzi	09/2020
7731	23756^12519+12519^23756	97342	Hans Havermann	07/2020
7732	10^97335-4000001	97335	Robert Price	07/2021
7733	(637*10^97331+11)/9	97333	Robert Price	10/2021
7734	23991^11402+11402^23991	97332	Hans Havermann	07/2020
7735	61^54517-60^54517	97331	Jean-Louis Charton	09/2005
7736	(38*10^97329+187)/9	97330	Robert Price	11/2017
7737	(31147^21661-1)/31146	97328	Serge Batalov	06/2022
7738	86455!4+8	97319	Robert Price	09/2019
7739	22591^20310+20310^22591	97316	Hans Havermann	06/2020
7740	2^323261-431173	97312	Harrison Mesh	06/2022
7741	(3996^27017-1)/3995	97302	Serge Batalov	06/2022
7742	25101^7520+7520^25101	97297	Hans Havermann	05/2020
7743	(233*10^97294+7)/3	97296	Robert Price	03/2022
7744	p(19982)#/2-1024	97293	Robert Price	09/2017
7745	(65*10^97288+277)/9	97289	Robert Price	08/2021
7746	6^125021-85	97286	Lelio R Paula	08/2016
7747	2^323164-47355	97283	Lelio R Paula	07/2016
7748	(3^203902+4)/36051015157	97276	Lelio R Paula	09/2013
7749	2^323054-6555	97249	Lelio R Paula	07/2016
7750	22822^18247+18247^22822	97249	Hans Havermann	02/2020

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