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 ?
8502	3^206977-112756	98754	Enzo Doria	07/2014
8501	10^98754-40000000001	98754	Robert Price	09/2020
8503	7^116846-50	98747	Lelio R Paula	08/2016
8504	(19152^23059-1)/19151	98740	Serge Batalov	06/2022
8505	23267^17512+17512^23267	98730	Hans Havermann	04/2020
8506	2^327967-28635	98728	Lelio R Paula	08/2016
8507	707^34642+34642^707	98710	Norbert Schneider	12/2017
8508	(10771^24481-1)/10770	98710	Serge Batalov	06/2022
8509	6^126850-47	98709	Lelio R Paula	08/2016
8510	(2^327886+2170)/2	98704	Stefano Morozzi	09/2020
8511	(22*10^98697+47)/3	98698	Robert Price	06/2021
8512	8*6^126830-7	98694	Lelio R Paula	11/2014
8513	11^94770-270	98693	Enzo Doria	08/2012
8514	(2^327846+3250)/2	98692	Stefano Morozzi	01/2021
8515	2^327832+43	98688	Lelio R Paula	12/2012
8516	2^327795+761	98677	Lelio R Paula	02/2013
8517	(2^327796+1522)/2	98677	Stefano Morozzi	09/2020
8518	10^98669+147411	98670	Patrick De Geest	11/2016
8520	10^98669-9^(98669-1)	98669	Robert Price	05/2016
8519	10^98669-105249	98669	Patrick De Geest	11/2016
8521	(7911^25309-1)/7910	98657	Serge Batalov	06/2022
8522	2^327671-109801	98639	Enzo Doria	04/2014
8523	24398^11037+11037^24398	98638	Hans Havermann	10/2019
8524	5^141090-14	98618	Lelio R Paula	08/2016
8525	20^75799+47	98617	Lelio R Paula	08/2016
8526	(5452^26393-1)/5451	98616	Serge Batalov	06/2022
8527	28101^3226+3226^28101	98597	Hans Havermann	07/2020
8528	2^327515-1017	98592	Lelio R Paula	08/2016
8529	6^126692+97681	98586	Mike Oakes	04/2011
8530	2^327467-741	98578	Lelio R Paula	08/2016
8531	(2947^28411-1)/2946	98566	Serge Batalov	06/2022
8532	22713^21800+21800^22713	98540	Hans Havermann	05/2020
8533	(2^327329+9)/19	98535	Lelio R Paula	10/2013
8534	7^116577-66	98519	Lelio R Paula	08/2016
8535	(3*2^327250+1)/7	98512	Lelio R Paula	11/2013
8536	23220^17479+17479^23220	98512	Hans Havermann	03/2020
8537	(2^327240+3798)/2	98509	Stefano Morozzi	02/2021
8538	(28514^22111-1)/28513	98502	Serge Batalov	06/2022
8539	(19*2^327192+1)/275	98494	Lelio R Paula	11/2013
8540	2^327162-66945	98486	Lelio R Paula	08/2016
8541	30139^1852+1852^30139	98484	Hans Havermann	02/2020
8542	23182^17703+17703^23182	98479	Hans Havermann	01/2020
8543	4*10^98472-3	98473	Erik Branger	11/2013
8544	26167^5794+5794^26167	98466	Hans Havermann	01/2020
8545	(6883*2^327047-1)/77	98453	Lelio R Paula	05/2015
8546	(71*10^98446+1)/9	98447	Serge Batalov	11/2010
8547	(2009^29803-1)/2008	98436	Serge Batalov	06/2022
8548	13^88363+94	98432	Lelio R Paula	08/2016
8549	48^58543-47^58543	98425	Jean-Louis Charton	11/2005
8550	6^126481+41	98422	Lelio R Paula	08/2016
8551	78*10^98413-7	98415	Robert Price	05/2017
8552	22634^22263+22263^22634	98404	Hans Havermann	07/2020
8553	(47*10^98386+241)/9	98387	Robert Price	06/2022
8554	7^116416+46	98383	Lelio R Paula	08/2016
8555	7^116407-24	98376	Lelio R Paula	07/2016
8556	439^37228+37228^439	98374	Norbert Schneider	08/2018
8557	2^326782-1860671	98372	Enzo Doria	03/2016
8558	17^79948+58	98372	Lelio R Paula	08/2016
8559	22499^22602-22602^22499	98368	Norbert Schneider	08/2020
8560	3^206143-98	98356	Lelio R Paula	08/2016
8561	8*5^140705+7	98350	Lelio R Paula	11/2014
8562	(2^326632+1662)/2	98326	Stefano Morozzi	09/2020
8563	(638^35053-1)/637	98315	Serge Batalov	06/2022
8564	2^326585+11	98312	Lelio R Paula	12/2012
8565	2^326582-459161	98311	Enzo Doria	05/2015
8566	(1266^31687-1)/1265	98304	Serge Batalov	06/2022
8568	(2^326548+9)/5	98301	Lelio R Paula	10/2013
8567	(2^326549+18)/10	98301	Stefano Morozzi	03/2020
8569	2^326538+71659	98298	Enzo Doria	04/2016
8570	(2^326520+2082)/2	98293	Stefano Morozzi	09/2020
8571	(2^326521+1002)/2	98293	Stefano Morozzi	09/2020
8572	15^83575-58	98292	Lelio R Paula	08/2016
8573	10^98288+3	98289	Robert Price	03/2011
8574	10^98288-117017	98288	Patrick De Geest	11/2011
8575	(44*10^98284-719)/9	98285	Robert Price	12/2017
8576	(5985^26021-1)/5984	98280	Serge Batalov	06/2022
8577	23466^15419+15419^23466	98277	Hans Havermann	02/2020
8578	2^326421-2797573	98263	Enzo Doria	04/2016
8579	2^326401+16095	98257	Lelio R Paula	07/2016
8580	(6494^25771-1)/6493	98249	Serge Batalov	06/2022
8581	7^116240-116240^7	98235	Norbert Schneider	05/2017
8582	17^79826-78	98222	Lelio R Paula	08/2016
8583	2^326268-809	98217	Yves Minet	04/2011
8584	22659^21590+21590^22659	98210	Hans Havermann	10/2019
8585	22268^22587-22587^22268	98202	Norbert Schneider	08/2020
8586	(418*10^98199+23)/9	98201	Robert Price	08/2017
8587	12*10^98198-7	98200	Robert Price	11/2017
8588	15^83496-76	98199	Lelio R Paula	08/2016
8589	(10223*2^326179+1)/6125	98190	Lelio R Paula	07/2014
8590	9*5^140471-4	98186	Lelio R Paula	11/2014
8591	(35103^21601-1)/35102	98180	Serge Batalov	06/2022
8593	22774^20455+20455^22774	98175	Hans Havermann	07/2020
8592	(4516^26863-1)/4515	98175	Serge Batalov	06/2022
8594	2^326069-2383	98157	Yves Minet	10/2013
8595	(9661^24631-1)/9660	98152	Serge Batalov	06/2022
8596	(4175^27109-1)/4174	98149	Serge Batalov	06/2022
8597	(57801^20611-1)/57800	98144	Serge Batalov	06/2022
8598	2^325973+1185	98128	Lelio R Paula	07/2016
8599	(25*2^325949-1)/17	98121	Lelio R Paula	02/2014
8600	2^325945-1847269	98120	Enzo Doria	07/2015
8601	8*10^98111-67	98112	Robert Price	10/2017
8602	(2^325902+1138)/2	98106	Stefano Morozzi	09/2020
8603	(215^42061-1)/214	98103	Serge Batalov	06/2022
8604	(6775^25609-1)/6774	98102	Serge Batalov	06/2022
8605	(6718^25633-1)/6717	98100	Serge Batalov	06/2022
8606	2^325866+15	98096	Lelio R Paula	12/2012
8607	22591^21952+21952^22591	98079	Hans Havermann	02/2020
8608	2^325765+1974305	98066	Enzo Doria	06/2016
8609	2^325733-58695	98056	Lelio R Paula	07/2016
8610	(7*10^98055-529)/9	98055	Robert Price	08/2021
8611	2^325717-3645	98051	Lelio R Paula	07/2016
8612	(2^325704+718)/2	98047	Stefano Morozzi	09/2020
8613	(15679^23371-1)/15678	98045	Serge Batalov	06/2022
8614	(23342^22441-1)/23341	98022	Serge Batalov	06/2022
8615	23968^12293+12293^23968	98021	Hans Havermann	11/2019
8616	(23*2^325583-1)/21	98011	Lelio R Paula	02/2014
8617	(7*10^98007-13)/3	98008	Robert Price	06/2016
8618	(2^325544+1110)/2	97999	Stefano Morozzi	09/2020
8619	2^325512-459959	97989	Enzo Doria	05/2015
8620	(2^325492+682)/2	97983	Stefano Morozzi	09/2020
8621	(3^205354-8)/17	97978	Lelio R Paula	09/2013
8622	2^325433+76817	97966	Enzo Doria	05/2016
8623	5*10^97963+81	97964	Robert Price	08/2017
8624	(13208^23773-1)/13207	97961	Serge Batalov	06/2022
8625	2^325390-109061	97953	Enzo Doria	04/2014
8626	(55*10^97940+323)/9	97941	Robert Price	10/2021
8627	13^87921+24	97940	Lelio R Paula	08/2016
8628	10^97930+188277	97931	Patrick De Geest	09/2022
8630	10^97930-7000001	97930	Robert Price	06/2021
8629	10^97930-66951	97930	Patrick De Geest	09/2022
8631	961^32831-960^32831	97926	Jean-Louis Charton	02/2011
8632	(17968^23017-1)/17967	97922	Serge Batalov	06/2022
8633	(3337^27793-1)/3336	97922	Serge Batalov	06/2022
8635	22600^21499+21499^22600	97913	Hans Havermann	05/2020
8634	(18703^22921-1)/18702	97913	Serge Batalov	06/2022
8636	2^325215+12909	97900	Lelio R Paula	07/2016
8637	22619^21286+21286^22619	97898	Hans Havermann	04/2020
8638	(85*10^97876-49)/9	97877	Robert Price	12/2020
8639	7*10^97874-69	97875	Robert Price	01/2017
8640	5*10^97869-63	97870	Robert Price	04/2021
8642	(17^79537+5^79537)/22	97865	Robert Price	06/2013
8641	15^83212+22	97865	Lelio R Paula	08/2016
8643	2^325087-109057	97861	Enzo Doria	04/2014
8644	2^325074+1870657	97858	Enzo Doria	05/2016
8646	2^325066-2111	97855	Yves Minet	08/2013
8645	CopelandErdos(97855)	97855	Eric W. Weisstein	10/2015
8647	(8694^24841-1)/8693	97851	Serge Batalov	06/2022
8648	(21159^22621-1)/21158	97843	Serge Batalov	06/2022
8649	26660^4677+4677^26660	97842	Hans Havermann	12/2019
8650	18^77944-89	97841	Lelio R Paula	07/2016
8651	119^47136+118	97833	Norbert Schneider	09/2018
8652	6^125720-17663	97830	Enzo Doria	02/2013
8653	(73640^20101-1)/73639	97829	Serge Batalov	06/2022
8654	2^324972-2069	97827	Yves Minet	05/2013
8655	2^324958-4691	97823	Yves Minet	05/2019
8656	(8087^25033-1)/8086	97820	Serge Batalov	06/2022
8657	2^324944-2788319	97818	Enzo Doria	03/2016
8658	22845^19112+19112^22845	97807	Hans Havermann	10/2019
8659	(2^324898+1270)/2	97804	Stefano Morozzi	09/2020
8661	4*10^97799-9	97800	Erik Branger	11/2013
8660	2^324882+577294575	97800	Lelio R Paula	09/2016
8662	2^324863-1867921	97794	Enzo Doria	04/2016
8663	6^125662-18473	97785	Enzo Doria	03/2013
8664	12^90604+11	97779	Lelio R Paula	07/2016
8665	(29*10^97751+49)/3	97752	Robert Price	09/2021
8666	(37108^21391-1)/37107	97741	Serge Batalov	06/2022
8667	5^139830+24	97737	Lelio R Paula	04/2016
8668	(2^324672+1198)/2	97736	Stefano Morozzi	09/2020
8669	(101*10^97724+7)/9	97726	Robert Price	02/2022
8670	2^324612+1155	97718	Lelio R Paula	07/2016
8671	(2^324597+3542)/2	97714	Stefano Morozzi	09/2020
8672	19^76404-44	97702	Lelio R Paula	07/2016
8673	(5939^25889-1)/5938	97694	Serge Batalov	06/2022
8675	2^324505-2983	97686	Yves Minet	04/2011
8674	(7740^25121-1)/7739	97686	Serge Batalov	06/2022
8676	(144^45259+1)/145	97684	Paul Bourdelais	08/2019
8677	(31*2^324496-1)/45	97683	Lelio R Paula	02/2014
8678	(11234^24109-1)/11233	97651	Serge Batalov	06/2022
8679	6^125488-17843	97649	Enzo Doria	02/2013
8680	(2^324350+3198)/2	97639	Stefano Morozzi	09/2020
8681	(75638^20011-1)/75637	97624	Serge Batalov	06/2022
8682	7^115515-2	97622	Lelio R Paula	09/2013
8683	(15672^23269-1)/15671	97613	Serge Batalov	06/2022
8684	(89^50069-1)/88	97603	Paul Bourdelais	08/2017
8685	6^125418-5	97595	Lelio R Paula	11/2014
8686	(2^324193+3522)/2	97592	Stefano Morozzi	09/2020
8687	(2422^28837-1)/2421	97587	Serge Batalov	06/2022
8688	(2^324172+666)/2	97586	Stefano Morozzi	09/2020
8689	2^324091+111546435	97562	Paul Bourdelais	10/2021
8690	2^324076+1155	97557	Lelio R Paula	07/2016
8691	(2^324074+9)/13	97555	Lelio R Paula	10/2013
8692	(11*10^97539-71)/3	97540	Robert Price	04/2022
8693	(55459*2^323993+1)/21	97536	Lelio R Paula	07/2014
8694	13^87557-12^87557	97534	Jean-Louis Charton	12/2008
8695	2^323946+73939	97518	Enzo Doria	04/2016
8696	2^323937+1866947	97515	Enzo Doria	03/2016
8697	(98339^19531-1)/98338	97508	Serge Batalov	06/2022
8699	6^125290-18533	97495	Enzo Doria	03/2013
8698	(2^323870+1650)/2	97495	Stefano Morozzi	09/2020
8700	2^323845+101	97488	Lelio R Paula	12/2012
8701	18^77662+65	97487	Lelio R Paula	07/2016
8702	22634^20265+20265^22634	97479	Hans Havermann	04/2020
8703	(5533^26041-1)/5532	97467	Serge Batalov	06/2022
8704	2^323772+76771	97466	Enzo Doria	05/2016
8705	2^323765-112213	97463	Enzo Doria	06/2014
8706	22730^19389+19389^22730	97457	Hans Havermann	02/2020
8707	2^323720-6555	97450	Lelio R Paula	07/2016
8708	2^323694-1860401	97442	Enzo Doria	03/2016
8709	20^74886+3	97429	Lelio R Paula	06/2016
8710	24476^9561+9561^24476	97427	Hans Havermann	01/2020
8711	(2^323623+1766)/2	97420	Stefano Morozzi	09/2020
8712	(3250^27739-1)/3249	97413	Serge Batalov	06/2022
8714	3*10^97399+73	97400	Robert Price	04/2016
8713	7^115252-50	97400	Lelio R Paula	07/2016
8715	(4715^26513-1)/4714	97392	Serge Batalov	06/2022
8716	224737#+393581	97389	Nicolas PALAU	12/2016
8717	(2^323468+3186)/2	97374	Stefano Morozzi	09/2020
8718	(2^323456+538)/2	97370	Stefano Morozzi	09/2020
8719	23277^15236+15236^23277	97365	Hans Havermann	07/2020
8721	(26*10^97353+31)/3	97354	Robert Price	07/2016
8720	(2^323403+3510)/2	97354	Stefano Morozzi	09/2020
8722	23756^12519+12519^23756	97342	Hans Havermann	07/2020
8723	10^97335+271641	97336	Patrick De Geest	09/2022
8725	10^97335-4000001	97335	Robert Price	07/2021
8724	10^97335-98193	97335	Patrick De Geest	09/2022
8726	(637*10^97331+11)/9	97333	Robert Price	10/2021
8727	23991^11402+11402^23991	97332	Hans Havermann	07/2020
8728	61^54517-60^54517	97331	Jean-Louis Charton	09/2005
8729	(38*10^97329+187)/9	97330	Robert Price	11/2017
8730	(31147^21661-1)/31146	97328	Serge Batalov	06/2022
8731	86455!4+8	97319	Robert Price	09/2019
8732	22591^20310+20310^22591	97316	Hans Havermann	06/2020
8733	2^323261-431173	97312	Harrison Mesh	06/2022
8734	(3996^27017-1)/3995	97302	Serge Batalov	06/2022
8735	25101^7520+7520^25101	97297	Hans Havermann	05/2020
8736	(233*10^97294+7)/3	97296	Robert Price	03/2022
8737	p(19982)#/2-1024	97293	Robert Price	09/2017
8738	(65*10^97288+277)/9	97289	Robert Price	08/2021
8739	6^125021-85	97286	Lelio R Paula	08/2016
8740	2^323164-47355	97283	Lelio R Paula	07/2016
8741	(3^203902+4)/36051015157	97276	Lelio R Paula	09/2013
8742	2^323054-6555	97249	Lelio R Paula	07/2016
8743	22822^18247+18247^22822	97249	Hans Havermann	02/2020
8744	9*10^97247-29	97248	Robert Price	05/2017
8745	24382^9735+9735^24382	97244	Hans Havermann	02/2020
8746	(31*10^97242+41)/9	97243	Robert Price	04/2015
8747	GoldenRatioPrime[97241]	97241	Eric W. Weisstein	06/2009
8748	12^90098-41	97233	Lelio R Paula	07/2016
8749	2^322928-216929	97212	Enzo Doria	05/2014
8750	(16731^23017-1)/16730	97209	Serge Batalov	06/2022

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