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	(21*2^234772-1)/2095	70672	Lelio R Paula	01/2014
7502	(29*2^234686-1)/21145	70645	Lelio R Paula	01/2014
7503	(15*2^234688-1)/5278141	70643	Lelio R Paula	01/2014
7505	2^234655-67	70639	Lelio R Paula	02/2012
7504	(79*10^70638-61)/9	70639	Robert Price	10/2015
7506	2^234652-173	70638	Lelio R Paula	02/2012
7507	2^234618-3645	70628	Lelio R Paula	05/2012
7508	(2^234610-5)/19	70624	Lelio R Paula	05/2012
7509	4*5^101038+9	70624	Lelio R Paula	10/2014
7510	2^234603+71963	70623	Enzo Doria	04/2016
7511	2^234600-113129	70622	Enzo Doria	07/2014
7512	2^234586+9	70618	Lelio R Paula	02/2012
7513	3^148008+26	70618	Robert Price	11/2013
7514	(7*10^70616-151)/9	70616	Robert Price	09/2017
7515	65^38947+32	70608	Lelio R Paula	01/2016
7516	18363^6988+6988^18363	70594	Hans Havermann	10/2019
7517	(2^234488-3)/11	70587	Lelio R Paula	05/2012
7518	(3*2^234451+1)/35	70576	Lelio R Paula	08/2012
7519	Phi(159495,10)	70560	Maksym Voznyy	09/2015
7520	2^234383-4035	70557	Lelio R Paula	05/2012
7521	2^234315-111241	70536	Enzo Doria	05/2014
7522	14^61526+97	70517	Lelio R Paula	01/2015
7523	14742^16915+16915^14742	70512	Norbert Schneider	10/2019
7524	(3*2^234170+1)/13	70492	Lelio R Paula	08/2012
7525	51^41281-50^41281	70491	Robert Price	02/2013
7526	2^234141-112123	70484	Enzo Doria	06/2014
7527	2^234139+12285	70483	Lelio R Paula	04/2012
7528	2^234133-3163	70482	Yves Minet	04/2009
7529	2^234115+83	70476	Lelio R Paula	02/2012
7530	2^234114-1595	70476	Lelio R Paula	05/2012
7531	24^51061-23^51061	70475	Robert Price	07/2012
7532	19471^16428-2	70467	Faysal YAtim	09/2005
7533	7^83381+12	70466	Robert Price	01/2014
7534	2^234067-111427	70462	Enzo Doria	05/2014
7535	(266*10^70457+1)/3	70459	Robert Price	02/2016
7536	(31*2^234041-1)/97	70453	Lelio R Paula	01/2014
7537	2^234026+12909	70449	Lelio R Paula	04/2012
7538	2^233965-19	70431	Lelio R Paula	02/2012
7539	(5*2^233932-1)/179	70419	Lelio R Paula	01/2014
7540	2^233908-17109	70414	Enzo Doria	05/2013
7541	695^24772+24772^695	70402	Norbert Schneider	09/2016
7542	3*5^100719-2	70401	Lelio R Paula	10/2014
7543	2^233829-111355	70390	Enzo Doria	05/2014
7544	(19775^16384+1)/2	70388	Henri Lifchitz	03/2007
7545	7*3^147519+8	70386	Lelio R Paula	04/2014
7546	141^32749-2	70385	Lelio R Paula	10/2017
7547	5*7^83265+2	70368	Lelio R Paula	10/2014
7548	(23*10^70363+97)/3	70364	Robert Price	02/2017
7549	(23*2^233749-1)/35325	70363	Lelio R Paula	01/2014
7550	5^100652-13916	70353	Enzo Doria	02/2013
7551	45^42555-2	70353	Lelio R Paula	08/2013
7552	2^233661-61	70339	Lelio R Paula	02/2012
7553	2^233523-112249	70298	Enzo Doria	06/2014
7554	5*3^147324-8	70293	Lelio R Paula	04/2014
7555	2^233488-13065	70287	Enzo Doria	11/2012
7556	(3^147322+8)/42851	70286	Lelio R Paula	06/2012
7557	(22*10^70259+161)/3	70260	Robert Price	02/2017
7559	2^233388+465	70257	Lelio R Paula	11/2012
7558	14^61299+59	70257	Lelio R Paula	01/2015
7560	2^233383+94065	70256	Lelio R Paula	04/2012
7561	49471!3-6561	70253	Robert Price	11/2015
7562	7^83121+6^(83121-1)	70246	Robert Price	03/2016
7563	(197*10^70241-11)/3	70243	Robert Price	10/2017
7564	23*10^70240-7	70242	Robert Price	03/2016
7565	(71*10^70227-53)/9	70228	Robert Price	10/2015
7566	19825^3486+3486^19825	70227	Hans Havermann	10/2019
7567	10815^17408+17408^10815	70225	Norbert Schneider	05/2019
7568	(2^233247-9)/17	70214	Lelio R Paula	05/2012
7569	(11^67421-2^67421)/9	70211	Robert Price	01/2013
7570	(23*10^70209-41)/9	70210	Robert Price	03/2015
7571	(29*10^70194-11)/9	70195	Robert Price	04/2015
7572	3^147109+196	70189	Lelio R Paula	05/2014
7573	(34*10^70191-7)/9/3/40583/573047	70181	Makoto Morimoto	05/2016
7574	9^73538+8^(73538+1)	70174	Robert Price	06/2016
7575	2*5^100391+7	70171	Lelio R Paula	10/2014
7576	99^35156-2	70159	Lelio R Paula	08/2013
7577	(68*10^70148+7)/3	70150	Robert Price	03/2016
7578	11^67360-6030	70149	Enzo Doria	01/2013
7579	(35*10^70130-377)/9	70131	Robert Price	12/2017
7580	49391!3+3^49391	70128	Robert Price	09/2015
7581	(229*10^70122-1)/3	70124	Robert Price	12/2016
7582	7^82975-92	70123	Lelio R Paula	07/2014
7583	20294^2853+2853^20294	70122	Hans Havermann	10/2019
7584	65^38670+58	70106	Lelio R Paula	01/2016
7585	105^34684+34684^105	70103	Serge Batalov	05/2014
7586	18597^5882+5882^18597	70102	Hans Havermann	10/2019
7587	134^32955-133	70099	Norbert Schneider	03/2015
7590	2^232836-227903	70091	Enzo Doria	12/2012
7589	2^232837-1859173	70091	Enzo Doria	03/2016
7588	17778^8761+8761^17778	70091	Hans Havermann	10/2019
7591	3*2^232820+5	70087	Lelio R Paula	04/2014
7593	2^232799+90195	70080	Lelio R Paula	02/2013
7592	2^232799-112237	70080	Enzo Doria	06/2014
7594	17894^8247+8247^17894	70079	Hans Havermann	09/2019
7595	2^232759+262145	70068	Lelio R Paula	04/2012
7596	16817^14670+14670^16817	70067	Hans Havermann	09/2019
7597	3*2^232750+7	70066	Lelio R Paula	04/2014
7598	12^64918-11	70059	Lelio R Paula	01/2015
7599	7^82899-12	70058	Lelio R Paula	09/2013
7600	(22*10^70051-13)/9	70052	Robert Price	03/2015
7601	16428^16615-16615^16428	70042	Norbert Schneider	11/2019
7602	(2^232685-7)/2514625	70039	Lelio R Paula	04/2012
7603	18^55786-5363	70027	Enzo Doria	03/2013
7604	(2^(77537*3+1)+243)/7	70023	Kevin Acres	11/2013
7605	2^232602+169	70021	Lelio R Paula	02/2012
7606	(137^32768+29^32768)/2	70016	Jeppe Stig Nielsen	04/2018
7607	2^232580+72133	70014	Enzo Doria	04/2016
7608	4*6^89958-7	70002	Lelio R Paula	09/2014
7609	10^70000+80487	70001	Milton L. Brown	05/2006
7610	10^69999+134857	70000	Patrick De Geest	02/2007
7611	10^70000-9273	70000	Patrick De Geest	08/2009
7612	(79*10^69999-7)/9	70000	Robert Price	01/2015
7615	((2^43112609)/10^38420)%10^70000	70000	Michael Vang	10/2016
7613	(2^756839/10^36014)%10^70000	70000	Michael Vang	12/2016
7614	(2^74207281/10^32641)%10^70000	70000	Michael Vang	12/2016
7616	10^69999-88251	69999	Patrick De Geest	08/2009
7617	2^232507+1089	69992	Lelio R Paula	04/2012
7618	(17*2^232445+1)/5	69974	Lelio R Paula	08/2012
7619	(529^25693+1)/530	69972	Richard Fischer	12/2017
7620	7^82778+48	69956	Lelio R Paula	09/2013
7621	7*2^232381+3	69955	Lelio R Paula	04/2014
7622	19305^4204+4204^19305	69955	Hans Havermann	10/2019
7623	2^232362-110541	69948	Enzo Doria	05/2014
7624	19442^3957+3957^19442	69940	Hans Havermann	09/2019
7625	2^232326-112391	69938	Enzo Doria	06/2014
7626	3^146575+236	69935	Lelio R Paula	09/2013
7627	30^47341-29	69929	Norbert Schneider	02/2014
7628	5^100040-68	69925	Lelio R Paula	09/2013
7629	9946^17491+17491^9946	69923	Norbert Schneider	07/2019
7630	16351^16592-16592^16351	69912	Norbert Schneider	11/2019
7631	(35*10^69866-593)/9	69867	Robert Price	08/2017
7632	2^232045-17295	69853	Lelio R Paula	04/2012
7633	(2^231987+78557)/95	69834	Lelio R Paula	05/2012
7634	2^231955+74243	69826	Yves Minet	03/2011
7635	2^231946-15873	69823	Enzo Doria	04/2013
7636	18^55618+95	69816	Lelio R Paula	09/2013
7637	6^89712+5^(89712-1)	69810	Robert Price	02/2016
7638	2^231870+135	69800	Lelio R Paula	02/2012
7639	(23*2^231827-1)/4179	69785	Lelio R Paula	01/2014
7640	2^231778+54615	69773	Lelio R Paula	04/2012
7641	(19*2^231780+1)/235	69772	Lelio R Paula	08/2012
7642	14^60866+27	69761	Lelio R Paula	09/2013
7643	13^62619-44	69755	Lelio R Paula	09/2013
7644	(2^231715-509203)/35	69752	Lelio R Paula	05/2012
7645	2^231711-110467	69752	Enzo Doria	05/2014
7646	(19^54547+18^54547)/37	69751	Robert Price	08/2013
7647	(23*2^231697-1)/45	69748	Lelio R Paula	01/2014
7648	2^231696-1861499	69748	Enzo Doria	03/2016
7649	2^231684-147	69744	Lelio R Paula	02/2012
7650	(23*2^231686-1)/1183	69743	Lelio R Paula	01/2014
7651	2^231591-477397	69716	Paul Bourdelais	03/2013
7652	16916^13209+13209^16916	69709	Hans Havermann	09/2019
7653	16568^16095+16095^16568	69697	Hans Havermann	09/2019
7654	11^66916-420	69686	Enzo Doria	08/2012
7655	5^99680-13706	69674	Enzo Doria	02/2013
7656	(8*10^69674-53)/9	69674	Robert Price	11/2014
7657	(44*10^69663-413)/9	69664	Robert Price	10/2017
7658	18950^4743+4743^18950	69662	Hans Havermann	10/2019
7659	(77*10^69656-23)/9	69657	Robert Price	10/2015
7660	6^89509+131	69652	Lelio R Paula	09/2013
7661	(78557*2^231349+1)/35	69647	Lelio R Paula	06/2014
7662	(11*10^69645+19)/3	69646	Robert Price	03/2016
7663	11^66875-28	69644	Lelio R Paula	09/2013
7664	2^231347+71483	69643	Enzo Doria	04/2016
7665	(14^60763+3^60763)/17	69641	Robert Price	04/2013
7666	(4*10^69626+173)/3	69627	Robert Price	01/2017
7667	2^231289+255	69625	Lelio R Paula	04/2012
7668	19794^3287+3287^19794	69612	Hans Havermann	09/2019
7669	2^231234-112913	69609	Enzo Doria	06/2014
7670	(265*10^69602-7)/3	69604	Robert Price	07/2016
7671	2^231182-112841	69593	Enzo Doria	06/2014
7672	(15*2^231129+1)/23	69577	Lelio R Paula	08/2012
7673	3^145806-28	69568	Lelio R Paula	09/2013
7674	(265*10^69554-7)/3	69556	Robert Price	07/2016
7675	2^231052-113159	69554	Enzo Doria	07/2014
7676	(10^9+1)(10^129+1)(10^831+1)*(10^107199+1)/1001/(10^387+1)/(10^2493+1)/(10^35733+1)	69552	Makoto Kamada	03/2019
7677	11^66784-8	69549	Lelio R Paula	09/2013
7678	Phi(104409,10)/2296999	69546	Maksym Voznyy	07/2015
7679	2^231016-110523	69543	Enzo Doria	05/2014
7680	2^231014+577294575	69543	Lelio R Paula	02/2016
7681	14^60658+67	69522	Lelio R Paula	09/2013
7682	5^99418+36	69491	Lelio R Paula	06/2013
7683	7^82203-30	69470	Lelio R Paula	09/2013
7684	(63^38609-1)/62	69469	Paul Bourdelais	08/2017
7685	5^99359-2^99360	69449	Mike Oakes	12/2010
7686	(29*2^230684+1)/1395	69442	Lelio R Paula	08/2012
7687	17692^8411+8411^17692	69439	Hans Havermann	09/2019
7688	(19*10^69424+77)/3	69425	Robert Price	08/2016
7689	19^54287-96	69420	Lelio R Paula	09/2013
7690	20739^2222+2222^20739	69409	Hans Havermann	09/2019
7691	2^230541+58905	69400	Lelio R Paula	04/2012
7692	2^230506+12705	69390	Lelio R Paula	02/2013
7693	8*6^89156-5	69378	Lelio R Paula	09/2014
7694	2^230438-111347	69369	Enzo Doria	05/2014
7695	2^230428-99	69366	Lelio R Paula	02/2012
7696	(62^38699+1)/63	69362	Paul Bourdelais	08/2017
7697	3*10^69354+17	69355	Robert Price	03/2017
7698	(493*10^69340-7)/9	69342	Robert Price	07/2016
7699	(41*10^69321+373)/9	69322	Robert Price	04/2017
7700	6^89072+53	69312	Lelio R Paula	09/2013
7701	155^31639+2	69300	Lelio R Paula	05/2013
7702	3*7^81965-4	69269	Lelio R Paula	09/2014
7703	(16*10^69265+41)/3	69266	Robert Price	10/2017
7704	(86*10^69260-77)/9	69261	Robert Price	05/2016
7705	9*5^99087+4	69260	Lelio R Paula	09/2014
7706	3^145145+2660	69252	Lelio R Paula	09/2013
7707	11^66492-1140	69245	Enzo Doria	11/2012
7708	5*3^145129-4	69245	Lelio R Paula	04/2014
7709	7*3^145126+8	69244	Lelio R Paula	04/2014
7710	11^66480-2370	69232	Enzo Doria	12/2012
7711	2^229962-65	69226	Lelio R Paula	02/2012
7712	2^229958-110733	69225	Enzo Doria	05/2014
7713	V(332407)	69225	Serge Batalov	03/2015
7714	6^88959+7	69224	Lelio R Paula	09/2013
7715	15^58855-94	69219	Lelio R Paula	09/2013
7716	159773#-p(159773)	69212	Henri Lifchitz	12/2018
7717	20223^2638+2638^20223	69189	Hans Havermann	09/2019
7718	(2^229838+47)/12081	69185	Lelio R Paula	04/2012
7719	3^144952+98	69160	Lelio R Paula	09/2013
7720	5^98941-72	69157	Lelio R Paula	06/2013
7721	63329!4+256	69147	Robert Price	09/2019
7722	16422^16229+16229^16422	69142	Hans Havermann	09/2019
7723	(17*2^229604-1)/229	69117	Lelio R Paula	01/2014
7724	2^229585-1063	69112	Yves Minet	11/2012
7725	(13*2^229567-1)/19	69107	Lelio R Paula	01/2014
7726	(13*2^229393-1)/5	69055	Lelio R Paula	01/2014
7727	(53*10^69050-17)/9	69051	Robert Price	09/2015
7728	(43*10^69048+47)/9	69049	Robert Price	12/2017
7729	2^229305-1868533	69028	Enzo Doria	04/2016
7730	2^229297+1385	69026	Lelio R Paula	04/2012
7731	18^54986-2441	69023	Enzo Doria	03/2013
7732	(34*10^69021-7)/9/3/67	69020	Makoto Morimoto	04/2016
7733	5^98736-14636	69014	Enzo Doria	02/2013
7734	(13^61949-5^61949)/8	69007	Robert Price	03/2013
7735	(2^229227+5)/611	69002	Lelio R Paula	04/2012
7736	2^229216-113279	69001	Enzo Doria	07/2014
7737	10^68994+51913	68995	Patrick De Geest	03/2016
7739	10^68994-10^5814-1	68994	Serge Batalov	01/2011
7738	10^68994-82947	68994	Patrick De Geest	03/2016
7740	(17*2^229136-1)/2381	68975	Lelio R Paula	01/2014
7741	2^229113+107	68970	Lelio R Paula	02/2012
7742	16877^12198+12198^16877	68965	Hans Havermann	09/2019
7743	11^66202-4410	68943	Enzo Doria	01/2013
7744	12^63883+5	68942	Lelio R Paula	07/2013
7745	(9913*2^229002-1)/399903	68935	Lelio R Paula	04/2015
7746	2^228962-111581	68925	Enzo Doria	05/2014
7747	2^228944+81	68920	Henri Lifchitz	01/2007
7748	11^66174-54	68914	Lelio R Paula	09/2013
7749	16756^12959+12959^16756	68911	Hans Havermann	09/2019
7750	2^228913-111265	68910	Enzo Doria	05/2014

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PRP Records

Probable Primes Top 10000

(255312 PRPs in the top)