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	(2^252335+2394)/2	75961	Stefano Morozzi	01/2020
7502	(2^252294+47)/6549	75945	Lelio R Paula	07/2012
7503	2^252261-110595	75939	Enzo Doria	05/2014
7504	7^89853+76	75935	Lelio R Paula	01/2015
7505	3^159132+56	75926	Lelio R Paula	01/2015
7506	730^26513+26513^730	75916	Norbert Schneider	11/2016
7507	(27*2^252163-1)/1945	75907	Lelio R Paula	01/2014
7508	5^108596-14846	75906	Enzo Doria	02/2013
7509	(2^252082+2734)/2	75884	Stefano Morozzi	01/2020
7510	5^108560-14846	75881	Enzo Doria	02/2013
7511	2^252051-110359	75875	Enzo Doria	05/2014
7512	2^251971-110509	75851	Enzo Doria	05/2014
7513	(42457^16384+1)/327682	75819	Lelio R Paula	11/2011
7514	2^251842-4715	75812	Yves Minet	05/2019
7515	99655!6-2	75811	Robert Price	07/2017
7516	(2^251823+3290)/2	75806	Stefano Morozzi	01/2020
7517	14*10^75798+1089	75800	Jens K. Andersen	11/2007
7518	2^251784-455	75795	Yves Minet	03/2012
7519	2^251780-1289	75794	Yves Minet	01/2013
7520	2^251760-215609	75788	Paul Bourdelais	03/2013
7521	21947^2838+2838^21947	75784	Hans Havermann	01/2020
7522	99^37973+2	75781	Lelio R Paula	05/2013
7523	(185*10^75777+7)/3	75779	Robert Price	02/2017
7524	5*2^251690+3	75767	Lelio R Paula	06/2014
7525	6^97366+95	75766	Lelio R Paula	01/2015
7526	s(23010)	75760	Hans Havermann	11/2017
7527	(2^251666+1882)/2	75759	Stefano Morozzi	01/2020
7528	8*6^97337-7	75744	Lelio R Paula	10/2014
7529	24045^1412+1412^24045	75738	Hans Havermann	01/2020
7530	2^251588-111677	75736	Enzo Doria	05/2014
7531	(2^251580+2086)/2	75733	Stefano Morozzi	01/2020
7532	5^108346-13256	75731	Enzo Doria	02/2013
7533	(2^251570+1182)/2	75730	Stefano Morozzi	01/2020
7534	(31^50777+1)/32	75726	Robert Price	07/2013
7535	(10^75707+77)/3	75707	Robert Price	01/2017
7536	(174907#+1673)/(723915467899)	75700	Makoto Morimoto	10/2017
7537	2^251466+193	75699	Lelio R Paula	03/2012
7538	(2^251463+1338)/2	75698	Stefano Morozzi	01/2020
7539	(5*2^251464+1)/9423	75695	Lelio R Paula	07/2012
7540	2^251422-109991	75686	Enzo Doria	04/2014
7541	91(10^23+1)(10^1721+1)*(10^118749+1)/(10^69+1)/(10^5163+1)/(10^39583+1)	75680	Makoto Kamada	03/2019
7542	(2^251355+3806)/2	75666	Stefano Morozzi	01/2020
7543	(2^251347+1278)/2	75663	Stefano Morozzi	01/2020
7544	4*5^108245-3	75661	Lelio R Paula	10/2014
7545	(2^251261+846)/2	75637	Stefano Morozzi	01/2020
7546	(2^251195+3770)/2	75617	Stefano Morozzi	01/2020
7547	12^70067-11^70067	75615	Jean-Louis Charton	11/2006
7548	12^70066+95	75614	Lelio R Paula	02/2015
7549	(2^251181+1130)/2	75613	Stefano Morozzi	01/2020
7550	-E20534/2063	75607	Thomas Ritschel	02/2017
7551	19^59120-50	75600	Lelio R Paula	01/2015
7552	18^60222-4697	75596	Enzo Doria	03/2013
7553	18^60211-4355	75582	Enzo Doria	03/2013
7554	7*2^251014-9	75564	Lelio R Paula	06/2014
7555	6^97101-25	75560	Lelio R Paula	01/2015
7556	8^83663-7^83663	75556	Jean-Louis Charton	01/2004
7557	(2^250974+3838)/2	75551	Stefano Morozzi	01/2020
7558	3^158331-140	75544	Lelio R Paula	01/2015
7561	(37^48157-1)/36	75519	Robert Price	03/2012
7559	(19*10^75518-43)/3	75519	Robert Price	10/2017
7560	2^250868-4229	75519	Yves Minet	08/2018
7562	10^75516+31467	75517	Patrick De Geest	03/2016
7564	10^75516-10^2256-1	75516	Serge Batalov	01/2011
7563	10^75516-66591	75516	Patrick De Geest	03/2016
7565	2^250851-187	75514	Lelio R Paula	03/2012
7566	(2^250836+466)/2	75509	Stefano Morozzi	01/2020
7567	22273^2454+2454^22273	75503	Hans Havermann	01/2020
7568	(43*10^75498-7)/9	75499	Robert Price	12/2014
7569	(3^158244-5)/247916	75497	Lelio R Paula	06/2012
7570	4*5^107971-3	75470	Lelio R Paula	10/2014
7571	(25*10^75465+71)/3	75466	Robert Price	01/2017
7572	(2^250690+1222)/2	75465	Stefano Morozzi	01/2020
7574	(5*2^250681-1)/999	75461	Lelio R Paula	01/2014
7573	(2^250674+1354)/2	75461	Stefano Morozzi	01/2020
7575	(2^250670+1878)/2	75459	Stefano Morozzi	01/2020
7576	(182*10^75456+1)/3	75458	Robert Price	02/2017
7577	(2^250669-9)/98897729	75451	Lelio R Paula	07/2012
7578	10^75441+13	75442	Robert Price	01/2011
7579	10^75441-9923	75441	Patrick De Geest	05/2013
7580	(27*2^250546-1)/6457	75420	Lelio R Paula	01/2014
7581	5*7^89231-6	75410	Lelio R Paula	10/2014
7583	2^250503-16995	75409	Lelio R Paula	05/2013
7582	11^72411-28	75409	Lelio R Paula	02/2015
7584	3*5^107860-8	75392	Lelio R Paula	10/2014
7585	(34*10^75387-403)/9	75388	Robert Price	10/2017
7587	2^250426+29835	75386	Lelio R Paula	05/2013
7586	8*3^157999-7	75386	Lelio R Paula	05/2014
7588	(2^250417+2642)/2	75383	Stefano Morozzi	01/2020
7589	(88*10^75381-43)/9	75382	Robert Price	11/2015
7590	(2^250394+2902)/2	75376	Stefano Morozzi	01/2020
7591	2^250382-111755	75373	Enzo Doria	05/2014
7592	2^250374-2798051	75371	Eric Chen	03/2016
7594	(22*10^75368-1)/3	75369	Robert Price	12/2014
7593	2^250369-4543	75369	Yves Minet	03/2019
7595	20078^5667+5667^20078	75360	Hans Havermann	02/2020
7596	(2^250318+2242)/2	75353	Stefano Morozzi	01/2020
7598	(19*10^75338+119)/3	75339	Robert Price	02/2017
7597	21517^3172+3172^21517	75339	Hans Havermann	01/2020
7599	2^250223-1859167	75325	Enzo Doria	03/2016
7600	(3^157854-7)/66025282	75308	Lelio R Paula	06/2012
7601	(2^250164+1578)/2	75307	Stefano Morozzi	01/2020
7602	3^157831-98	75305	Lelio R Paula	01/2015
7603	(46^45281+11^45281)/57	75290	Serge Batalov	12/2016
7604	92^38335-91	75282	Norbert Schneider	01/2016
7605	(2^250026+2398)/2	75266	Stefano Morozzi	01/2020
7606	2^250020+18915	75264	Lelio R Paula	05/2013
7607	2^250002+8193	75259	Lelio R Paula	05/2013
7608	(2^249996+1678)/2	75256	Stefano Morozzi	01/2020
7609	(11*2^249977-7)/15	75251	Renaud Lifchitz	02/2011
7610	(2^249968+78557)/63	75247	Lelio R Paula	07/2012
7611	(5*10^75244+91)/3	75245	Robert Price	11/2016
7612	(10489!)^2+Prime(10489)	75242	Robert Price	08/2014
7613	14^65644+67	75237	Lelio R Paula	01/2015
7614	68383!4+32	75236	Robert Price	09/2019
7615	(2^249928-5)/11859059	75229	Lelio R Paula	06/2012
7616	129^35638+2	75218	Lelio R Paula	05/2013
7617	2^249853-110475	75214	Enzo Doria	05/2014
7618	20574^4517+4517^20574	75195	Hans Havermann	01/2020
7619	2^249762+75409	75186	Enzo Doria	04/2016
7620	565^27318+27318^565	75181	Norbert Schneider	12/2016
7621	(2^249741-7)/685	75177	Lelio R Paula	06/2012
7622	2^249726-112181	75176	Enzo Doria	06/2014
7623	2^249721+11715	75174	Lelio R Paula	05/2013
7624	(2^249705+654)/2	75169	Stefano Morozzi	01/2020
7625	(38661^16384+1)/2	75158	Lelio R Paula	11/2011
7626	2^249658-47355	75155	Lelio R Paula	05/2013
7627	155^34311+2	75153	Lelio R Paula	05/2013
7628	(10^87682+1)/(10^12526+1)/990099009901	75145	Maksym Voznyy	06/2015
7629	(23*2^249602+1)/93	75138	Lelio R Paula	08/2012
7630	2^249522+8415	75114	Lelio R Paula	05/2013
7631	2^249489-110911	75104	Enzo Doria	05/2014
7632	(28*10^75078+131)/3	75079	Robert Price	02/2017
7633	(206*10^75073-17)/9	75075	Robert Price	03/2017
7634	(2^249384+3330)/2	75072	Stefano Morozzi	01/2020
7635	2^249368-110573	75068	Enzo Doria	05/2014
7636	NaturalLogarithmOf10(75067)	75067	Eric W. Weisstein	10/2015
7637	19167^8248+8248^19167	75065	Hans Havermann	02/2020
7638	(2^249375+78557)/45056125	75062	Lelio R Paula	07/2012
7639	(26*10^75055-173)/3	75056	Robert Price	10/2017
7641	2^249272+193	75039	Lelio R Paula	03/2012
7640	17433^17692-17692^17433	75039	Norbert Schneider	11/2019
7642	14^65468+43	75035	Lelio R Paula	01/2015
7643	37^47844+36	75030	Norbert Schneider	05/2014
7644	(52*10^75027-7)/9	75028	Robert Price	12/2014
7645	17943^15178+15178^17943	75024	Hans Havermann	02/2020
7646	(2^249219+494)/2	75023	Stefano Morozzi	01/2020
7647	20^57653+89	75009	Lelio R Paula	01/2015
7648	(2^249084+2682)/2	74982	Stefano Morozzi	01/2020
7649	2^249061-1868353	74975	Enzo Doria	04/2016
7650	(2^249056+1006)/2	74974	Stefano Morozzi	01/2020
7651	7^88713+2*3^88713	74972	Mike Oakes	07/2010
7652	18325^12334+12334^18325	74970	Hans Havermann	02/2020
7653	2*6^96313+5	74947	Lelio R Paula	10/2014
7654	(8*10^74944+49)/3	74945	Robert Price	03/2016
7655	300^30247+30247^300	74926	Norbert Schneider	11/2014
7656	2^248866-171	74917	Lelio R Paula	03/2012
7657	6*5^107168-7	74908	Lelio R Paula	10/2014
7658	11^71926+78	74904	Lelio R Paula	02/2015
7659	2^248824+1869391	74904	Enzo Doria	05/2016
7660	2^248816+1111	74902	Lelio R Paula	01/2011
7661	V(388219)	74890	Serge Batalov	03/2015
7662	159^34017+158	74885	Norbert Schneider	12/2018
7663	2*F(358297)-1	74880	Henri Lifchitz	12/2009
7664	(22*10^74874-31)/9	74875	Robert Price	04/2015
7665	11^71892-76800000	74868	Enzo Doria	01/2013
7666	9*5^107107-4	74866	Lelio R Paula	10/2014
7667	2^248678-710111	74860	Paul Bourdelais	03/2013
7668	(14*10^74858+211)/9	74859	Robert Price	11/2017
7669	13^67194+12	74851	Lelio R Paula	01/2015
7670	(7*2^248634+1)/71	74846	Lelio R Paula	08/2012
7671	11^71867-3090	74842	Enzo Doria	12/2012
7672	68057!4-16	74841	Robert Price	11/2019
7673	2^248609+262145	74839	Lelio R Paula	05/2013
7674	3^156852+50	74838	Lelio R Paula	01/2015
7675	18^59607-11	74824	Lelio R Paula	01/2015
7676	2^248556-110507	74823	Enzo Doria	05/2014
7677	7^88531-36	74818	Lelio R Paula	01/2015
7678	p(15738)#/2+1024	74814	Robert Price	07/2017
7679	(2^248505+422)/2	74808	Stefano Morozzi	01/2020
7680	(2^248507+1938)/2	74808	Stefano Morozzi	01/2020
7681	21137^3454+3454^21137	74790	Hans Havermann	11/2019
7682	4*3^156740-5	74785	Lelio R Paula	05/2014
7683	17918^14907+14907^17918	74779	Hans Havermann	12/2019
7684	(32*10^74773-41)/9	74774	Robert Price	05/2015
7685	(29*2^248384-1)/13	74772	Lelio R Paula	01/2014
7686	19401!+19401#+1	74765	D. Gazzoni Filho & Lucas Teixeira	06/2005
7687	2^248357-12797413	74763	Enzo Doria	03/2016
7688	42^46057+41	74762	Lelio R Paula	07/2012
7689	(2^248339+1686)/2	74758	Stefano Morozzi	01/2020
7690	11^71784-3000	74756	Enzo Doria	12/2012
7691	19^58458+18	74754	Lelio R Paula	01/2015
7692	12^69265-35	74750	Lelio R Paula	02/2015
7693	(2^248291+830)/2	74743	Stefano Morozzi	01/2020
7695	11^71771-48000	74742	Enzo Doria	12/2012
7694	(7*10^74741+197)/3	74742	Robert Price	07/2017
7696	(2^248282-5)/50129	74736	Lelio R Paula	06/2012
7697	2^248252-110105	74732	Enzo Doria	04/2014
7698	(7*10^74729+71)/3	74730	Robert Price	03/2016
7699	3^156614-50	74724	Lelio R Paula	01/2015
7700	(7*2^248213+1)/135	74719	Lelio R Paula	07/2012
7701	(2^248193+870)/2	74714	Stefano Morozzi	01/2020
7702	(2^248167+1178)/2	74706	Stefano Morozzi	01/2020
7703	(2^248173+78557)/767	74705	Lelio R Paula	07/2012
7704	(2^248145+3866)/2	74699	Stefano Morozzi	01/2020
7705	125^35622+124	74697	Norbert Schneider	02/2015
7706	(2^248114+994)/2	74690	Stefano Morozzi	01/2020
7707	(19*2^248099-1)/29	74686	Lelio R Paula	01/2014
7708	20780^3927+3927^20780	74685	Hans Havermann	12/2019
7709	(86*10^74676-41)/9	74677	Robert Price	11/2015
7710	(2^248065+3650)/2	74675	Stefano Morozzi	01/2020
7711	(p(15711)#-4)/2	74672	Robert Price	09/2017
7712	10^74670+31	74671	Robert Price	01/2011
7713	10^74670-122463	74670	Patrick De Geest	05/2013
7714	2^248036-69	74667	Lelio R Paula	03/2012
7715	11^71698-6000	74666	Enzo Doria	12/2012
7716	(2^248032+406)/2	74665	Stefano Morozzi	01/2020
7717	58(10^(324887)-1)/111-1	74661	Robert Price	10/2014
7718	14^65139-45	74658	Lelio R Paula	01/2015
7719	17967^14288+14288^17967	74653	Hans Havermann	11/2019
7720	6^95921-133	74642	Lelio R Paula	01/2015
7721	11^71675+78	74642	Lelio R Paula	02/2015
7722	17875^14986+14986^17875	74641	Hans Havermann	12/2019
7723	(2^247931+1458)/2	74635	Stefano Morozzi	01/2020
7724	18^59449-91	74625	Lelio R Paula	01/2015
7725	6^95864-16043	74597	Enzo Doria	02/2013
7726	5*7^88261+6	74590	Lelio R Paula	10/2014
7727	9*5^106710+4	74589	Lelio R Paula	10/2014
7728	(7772^247788+1)/(11754121)	74588	Jens K. Andersen	09/2007
7729	21157^3352+3352^21157	74585	Hans Havermann	12/2019
7730	(265*10^74579+17)/3	74581	Robert Price	05/2016
7731	17798^15489+15489^17798	74575	Hans Havermann	11/2019
7732	(2^247759-1017)/3318311717	74574	Lelio R Paula	07/2012
7733	5^106682-24	74568	Lelio R Paula	08/2014
7734	(2^247686+1450)/2	74561	Stefano Morozzi	01/2020
7735	474^27863+27863^474	74556	Norbert Schneider	01/2017
7736	(14*10^74540+79)/3	74541	Robert Price	11/2017
7737	(2^247582+1630)/2	74530	Stefano Morozzi	01/2020
7738	(35365^16384+1)/2	74524	Lelio R Paula	11/2011
7739	3^156161+2660	74508	Lelio R Paula	01/2015
7741	2^247474-58695	74498	Lelio R Paula	05/2013
7740	(2^247476+886)/2	74498	Stefano Morozzi	01/2020
7742	11^71519-90	74480	Enzo Doria	07/2012
7743	(19*2^247419-1)/23202983	74475	Lelio R Paula	01/2014
7745	(2^247394-7)/3	74473	Lelio R Paula	06/2012
7744	18^59328+17	74473	Lelio R Paula	01/2015
7746	2^247379-181	74469	Lelio R Paula	03/2012
7747	(15*2^247370-1)/479	74465	Lelio R Paula	01/2014
7748	18860^8877+8877^18860	74465	Hans Havermann	12/2019
7749	17355^17564-17564^17355	74462	Norbert Schneider	11/2019
7750	2^247344+2047	74458	Lelio R Paula	05/2013

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