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	(22*10^87863-1)/3	87864	Robert Price	12/2014
7502	2^291822-2797811	87848	Enzo Doria	04/2016
7503	(2^291730+1614)/2	87820	Stefano Morozzi	01/2020
7504	2^291716-111389	87816	Enzo Doria	05/2014
7505	(782*10^87809-71)/9	87811	Robert Price	06/2017
7506	3^184039+1820	87809	Lelio R Paula	12/2015
7507	12^81356+41	87798	Lelio R Paula	11/2015
7508	21307^13188+13188^21307	87789	Hans Havermann	08/2020
7509	(2527^25801-1)/2526	87788	Serge Batalov	08/2020
7510	(2^291596+1986)/2	87779	Stefano Morozzi	01/2020
7512	6^112792-18983	87770	Enzo Doria	03/2013
7511	(3123^25117-1)/3122	87770	Serge Batalov	08/2020
7513	3*6^112787-5	87766	Lelio R Paula	10/2014
7514	7^103848+82	87762	Lelio R Paula	10/2015
7515	(19*2^291534-1)/178696395	87754	Lelio R Paula	02/2014
7516	(2^291506+918)/2	87752	Stefano Morozzi	01/2020
7517	24411^3932+3932^24411	87749	Hans Havermann	08/2020
7518	(3^183915+5)/128	87748	Lelio R Paula	01/2013
7519	19^68619+24	87747	Lelio R Paula	12/2015
7521	2^291480+1185	87745	Lelio R Paula	10/2013
7520	2^291482+1867369	87745	Enzo Doria	03/2016
7522	2^291467-937	87741	Yves Minet	05/2013
7523	(25*10^87726+161)/3	87727	Robert Price	01/2017
7524	11^84239-2850	87726	Enzo Doria	12/2012
7525	10^87720+215541	87721	Patrick De Geest	01/2011
7526	10^87720-3	87720	Markus Tervooren	07/2010
7527	(2^291383+3078)/2	87715	Stefano Morozzi	01/2020
7529	(5*10^87712-473)/9	87712	Robert Price	12/2017
7528	(2^291373+2946)/2	87712	Stefano Morozzi	01/2020
7530	22591^7630+7630^22591	87711	Hans Havermann	08/2020
7531	22081^9378+9378^22081	87709	Hans Havermann	08/2020
7532	(2^291357+5)/6847	87704	Lelio R Paula	01/2013
7533	(2^291280+462)/2	87684	Stefano Morozzi	01/2020
7534	20749^16816+16816^20749	87680	Hans Havermann	08/2020
7536	93^44541-2	87679	Lelio R Paula	09/2013
7535	2^291261-109561	87679	Enzo Doria	04/2014
7537	(4*10^87669+149)/9	87669	Robert Price	03/2017
7538	2^291217+4257	87666	Lelio R Paula	10/2013
7539	22748^7137+7137^22748	87660	Hans Havermann	08/2020
7540	2*12^81214-5^81214	87645	Mike Oakes	12/2010
7541	(5005^23689-1)/5004	87632	Serge Batalov	08/2020
7542	(5*10^87622-473)/9	87622	Robert Price	12/2017
7543	12^81188+85	87617	Lelio R Paula	11/2015
7544	(2^291030+3462)/2	87609	Stefano Morozzi	01/2020
7545	(21*2^290980-1)/5	87595	Lelio R Paula	02/2014
7546	(2^290980+1150)/2	87594	Stefano Morozzi	01/2020
7547	2^290958+127	87588	Lelio R Paula	09/2012
7548	78531!4-8	87580	Robert Price	11/2019
7549	2^290923-67	87577	Lelio R Paula	09/2012
7550	3*10^87573-97	87574	Robert Price	08/2017
7551	(13*10^87565+11)/3	87566	Robert Price	05/2015
7552	(2^290881+1022)/2	87564	Stefano Morozzi	01/2020
7553	(2^290857-7)/55	87555	Lelio R Paula	01/2013
7554	(2^290808+1498)/2	87542	Stefano Morozzi	01/2020
7555	2^290802+82875	87541	Lelio R Paula	10/2013
7556	(509203*2^290792-1)/7560987	87536	Lelio R Paula	04/2015
7557	3^183441+236	87524	Lelio R Paula	12/2015
7558	2^290618-33	87485	Lelio R Paula	09/2012
7559	(184*10^87473-1)/3	87475	Robert Price	02/2017
7560	2^290534-115151	87460	Enzo Doria	06/2015
7561	2^290512-109757	87453	Enzo Doria	04/2014
7562	(32*10^87448-41)/9	87449	Robert Price	05/2015
7563	(2^290493+3074)/2	87447	Stefano Morozzi	01/2020
7564	(2^290491+9)/3179	87444	Lelio R Paula	01/2013
7565	(25*2^290489-1)/51809	87443	Lelio R Paula	02/2014
7566	2^290426+82875	87427	Lelio R Paula	11/2013
7567	3*2^290415-7	87425	Lelio R Paula	08/2014
7570	10^87408+57	87409	Robert Price	03/2011
7569	2^290366+74779	87409	Enzo Doria	04/2016
7568	22284^8365+8365^22284	87409	Hans Havermann	08/2020
7571	10^87408-123569	87408	Patrick De Geest	07/2013
7572	21517^11536+11536^21517	87404	Hans Havermann	08/2020
7573	6*10^87396+77	87397	Robert Price	06/2020
7574	(2^290268+3882)/2	87380	Stefano Morozzi	01/2020
7575	2^290265+58905	87379	Lelio R Paula	10/2013
7576	7^103391+16	87376	Lelio R Paula	10/2015
7577	(115*10^87368-7)/9	87370	Robert Price	11/2017
7578	(92^44491-1)/91	87369	Paul Bourdelais	08/2017
7579	8*7^103379+3	87367	Lelio R Paula	10/2014
7580	(2^290226+7)/71	87365	Lelio R Paula	01/2013
7581	(3216^24907-1)/3215	87354	Serge Batalov	08/2020
7582	(2^290160+2686)/2	87347	Stefano Morozzi	01/2020
7583	13^78407-30	87341	Lelio R Paula	11/2015
7584	4*10^87337-99	87338	Robert Price	12/2016
7585	7*10^87319+39	87320	Robert Price	07/2016
7586	3*5^124921+2	87317	Lelio R Paula	10/2014
7587	78315!4-16	87316	Robert Price	11/2019
7588	3^182984+88	87306	Lelio R Paula	12/2015
7589	(10^87323-1)/(9*33909262597306826117)	87303	Alfred Reich	02/2019
7590	(10^87323-1)/305183363375761435053	87303	Anonymous	10/2020
7591	(2^290008+958)/2	87301	Stefano Morozzi	01/2020
7592	(10536^21701-1)/10535	87293	Serge Batalov	08/2020
7593	4*10^87287-99	87288	Robert Price	12/2016
7595	11^83813-1860	87283	Enzo Doria	12/2012
7594	(3068^25033-1)/3067	87283	Serge Batalov	08/2020
7596	734^30453+30453^734	87270	Norbert Schneider	04/2017
7597	12^80855+29	87258	Lelio R Paula	11/2015
7598	22209^8482+8482^22209	87249	Hans Havermann	08/2020
7599	3*6^112119-5	87247	Lelio R Paula	10/2014
7600	12^80806+79	87205	Lelio R Paula	11/2015
7601	91382^9+9^91382	87201	Andrey Kulsha	11/2004
7602	(21181*2^289657+1)/81	87198	Lelio R Paula	06/2014
7603	6^112054-47	87195	Lelio R Paula	12/2015
7604	(55459*2^289632+1)/55	87191	Lelio R Paula	06/2014
7605	15^74131-68	87185	Lelio R Paula	11/2015
7606	2^289583-741	87174	Lelio R Paula	10/2013
7607	7^103146+12	87169	Lelio R Paula	10/2015
7608	(2^289562+2182)/2	87167	Stefano Morozzi	01/2020
7609	5*2^289556-3	87166	Lelio R Paula	08/2014
7610	2^289543-112735	87162	Enzo Doria	06/2014
7611	20204^20243-20243^20204	87155	Norbert Schneider	04/2020
7612	8*3^182655-7	87150	Lelio R Paula	08/2014
7613	2*10^87144+81	87145	Robert Price	01/2017
7614	20541^17468+17468^20541	87140	Hans Havermann	07/2020
7616	7^103106+2*3^103106	87135	Mike Oakes	08/2010
7615	(65*10^87134-29)/9	87135	Robert Price	01/2021
7617	8*3^182614+7	87130	Lelio R Paula	08/2014
7618	3*10^87121-73	87122	Robert Price	02/2021
7619	(4982^23563-1)/4981	87119	Serge Batalov	08/2020
7620	(2^289368-509203)/9	87108	Lelio R Paula	01/2013
7621	3^182566+14	87107	Robert Price	09/2013
7622	1738^26881+26881^1738	87096	Norbert Schneider	04/2020
7623	24290^3849+3849^24290	87089	Hans Havermann	08/2020
7624	(3^182385-5)/2	87020	Lelio R Paula	01/2013
7625	11^83534-8	86992	Lelio R Paula	11/2015
7626	4^144479-14267	86986	Mike Oakes	03/2011
7627	(145*10^86982-1)/9	86984	Serge Batalov	12/2014
7629	(151*10^86963-1)/3	86965	Robert Price	04/2017
7628	(2^288892+826)/2	86965	Stefano Morozzi	01/2020
7630	15^73940-58	86961	Lelio R Paula	11/2015
7631	2^288761-113143	86926	Enzo Doria	07/2014
7632	24440^3603+3603^24440	86925	Hans Havermann	08/2020
7634	2^288747+3083	86922	Yves Minet	03/2011
7633	(2^288749+3102)/2	86922	Stefano Morozzi	01/2020
7635	30^58842+29	86917	Norbert Schneider	03/2017
7636	(2^288705+2186)/2	86909	Stefano Morozzi	01/2020
7637	(10^86906-13)/3	86906	Robert Price	02/2017
7638	2^288692-110027	86905	Enzo Doria	04/2014
7639	(2^288682+7)/259895449	86894	Lelio R Paula	01/2013
7640	(26*10^86885+79)/3	86886	Robert Price	09/2020
7641	(2^288636+47)/1293	86885	Lelio R Paula	01/2013
7642	3^182089-34	86879	Robert Price	11/2013
7643	(2^288571+1698)/2	86869	Stefano Morozzi	01/2020
7644	2^288543-109801	86861	Enzo Doria	04/2014
7645	60^48847-59	86858	Norbert Schneider	10/2014
7646	(2^288484+3186)/2	86843	Stefano Morozzi	01/2020
7647	2^288470-64875	86839	Lelio R Paula	10/2013
7648	10^86816+32997	86817	Patrick De Geest	07/2013
7649	10^86816-99	86816	Robert Price	05/2011
7650	(89*10^86802-539)/9	86803	Robert Price	11/2017
7651	20272^19123+19123^20272	86796	Hans Havermann	07/2020
7652	(2^288316+1530)/2	86792	Stefano Morozzi	01/2020
7653	(2^288316+2218)/2	86792	Stefano Morozzi	01/2020
7654	41487!2+256	86786	Robert Price	01/2015
7655	(5*2^288301-1)/999	86785	Lelio R Paula	02/2014
7656	(2^288278+1750)/2	86781	Stefano Morozzi	01/2020
7657	2^288243+76043	86770	Enzo Doria	04/2016
7658	(29*2^288232+1)/15	86767	Lelio R Paula	01/2013
7659	9*6^111495+5	86761	Lelio R Paula	10/2014
7660	(5*2^288202+1)/81	86757	Lelio R Paula	01/2013
7661	9*7^102654-2	86754	Lelio R Paula	10/2014
7662	(2^288155+1154)/2	86743	Stefano Morozzi	01/2020
7663	2^288122-112841	86734	Enzo Doria	06/2014
7664	5^124062-68	86716	Lelio R Paula	10/2015
7665	(2^288007-3)/125	86697	Lelio R Paula	01/2013
7666	379*10^86691+9	86694	Arkadiusz Wesolowski	10/2011
7667	7^102555+48	86670	Lelio R Paula	10/2015
7668	2^287902-4961	86668	Yves Minet	05/2019
7669	77779!4+2	86660	Robert Price	08/2017
7670	(2^287842+3250)/2	86649	Stefano Morozzi	01/2020
7671	2^287809-111355	86640	Enzo Doria	05/2014
7672	(47*2^287795+1)/7	86636	Lelio R Paula	04/2015
7673	9*7^102504+8	86627	Lelio R Paula	10/2014
7674	3^181551+32	86622	Robert Price	11/2013
7675	2^287735-521347	86617	Paul Bourdelais	05/2013
7676	21912^8953+8953^21912	86596	Hans Havermann	08/2020
7677	(1017*2^287600-1)/91	86578	Lelio R Paula	04/2015
7678	(2^287552+1302)/2	86562	Stefano Morozzi	01/2020
7679	2^287540-112967	86559	Enzo Doria	06/2014
7680	3^181407+20	86554	Robert Price	10/2013
7681	(28*10^86550+101)/3	86551	Robert Price	09/2020
7683	(13*10^86546+83)/3	86547	Robert Price	09/2016
7682	(2^287502+2238)/2	86547	Stefano Morozzi	01/2020
7684	2^287482-4715	86541	Yves Minet	05/2019
7685	3^181378-2^(181378-1)	86540	Robert Price	01/2016
7686	24588^3305+3305^24588	86530	Hans Havermann	08/2020
7687	83^45080-2	86513	Lelio R Paula	08/2013
7688	(2^287367+2570)/2	86506	Stefano Morozzi	01/2020
7690	(78557*2^287351+1)/611	86504	Lelio R Paula	06/2014
7689	(2^287360+1006)/2	86504	Stefano Morozzi	01/2020
7691	25*29^59147+20936	86498	Curtis Bright	05/2015
7692	2^287298+1871359	86486	Enzo Doria	05/2016
7693	118^41740-117	86481	Norbert Schneider	08/2018
7694	3*10^86478+89	86479	Robert Price	03/2017
7695	2^287272-79049	86478	Paul Bourdelais	02/2012
7696	(2^287259+2846)/2	86474	Stefano Morozzi	01/2020
7697	9067052((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
7698	8118242((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
7699	7790642((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
7700	7683852((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
7701	7008912((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
7702	6523202((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
7703	3779202((10^86453-1)/9)+1	86458	Danilo Nitsche	01/2016
7704	2550602((10^86453-1)/9)+1	86458	Danilo Nitsche	01/2016
7705	1871112((10^86453-1)/9)+1	86458	Danilo Nitsche	01/2016
7706	(10^86453-1)/9	86453	Lew Baxter	10/2000
7707	(2^287172+658)/2	86448	Stefano Morozzi	01/2020
7708	(2^287146+2542)/2	86440	Stefano Morozzi	01/2020
7709	(2^287136+1726)/2	86437	Stefano Morozzi	01/2020
7710	(2^287128+958)/2	86434	Stefano Morozzi	01/2020
7711	87^44563-86^44563	86431	Robert Price	05/2015
7712	6^111057+61	86420	Lelio R Paula	12/2015
7713	2^287057-109909	86413	Enzo Doria	04/2014
7714	5^123608+22	86399	Lelio R Paula	10/2015
7715	(2^286970+618)/2	86387	Stefano Morozzi	01/2020
7716	(2^286916+2646)/2	86371	Stefano Morozzi	01/2020
7717	(2^286907+3690)/2	86368	Stefano Morozzi	01/2020
7718	(31*10^86364-121)/9	86365	Robert Price	06/2016
7719	(2^286868+2686)/2	86356	Stefano Morozzi	01/2020
7720	2^286859+71663	86354	Enzo Doria	04/2016
7721	(2^286845+1866)/2	86349	Stefano Morozzi	01/2020
7722	2^286740+29835	86318	Lelio R Paula	10/2013
7723	2*10^86310+9^86310	86311	Mike Oakes	05/2011
7724	11^82878-1860	86309	Enzo Doria	12/2012
7725	2223^25780+25780^2223	86285	Norbert Schneider	12/2019
7726	2^286547+16095	86260	Lelio R Paula	10/2013
7727	(58*10^86242+329)/9	86243	Robert Price	11/2017
7728	2^286455-110427	86232	Enzo Doria	05/2014
7729	(37*10^86230+53)/9	86231	Robert Price	05/2015
7730	8*3^180700+5	86217	Lelio R Paula	08/2014
7731	3^180697-40	86215	Lelio R Paula	12/2015
7732	(2^286383+3386)/2	86210	Stefano Morozzi	01/2020
7733	(13*2^286318-1)/13257	86188	Lelio R Paula	02/2014
7734	(2^286295+1934)/2	86184	Stefano Morozzi	01/2020
7735	(2^286251+3974)/2	86170	Stefano Morozzi	01/2020
7736	2^286165+77	86145	Lelio R Paula	08/2012
7737	9*2^286140+7	86138	Lelio R Paula	08/2014
7738	(2^286128+1762)/2	86133	Stefano Morozzi	01/2020
7739	(29*2^286108-1)/2002367	86123	Lelio R Paula	02/2014
7740	(2^286077+1122)/2	86118	Stefano Morozzi	01/2020
7741	10^86110+161113	86111	Patrick De Geest	07/2013
7742	10^86110-69	86110	Robert Price	05/2011
7743	2^286036-869688105	86106	Lelio R Paula	07/2016
7744	(2^285946+2358)/2	86079	Stefano Morozzi	01/2020
7746	(77*10^86072+31)/9	86073	Robert Price	10/2015
7745	(2^285926+3382)/2	86073	Stefano Morozzi	01/2020
7747	2^285923+345	86072	Lelio R Paula	09/2013
7748	13^77266-90	86070	Lelio R Paula	11/2015
7749	2^285910-458903	86068	Enzo Doria	04/2015
7750	2^285904-125	86066	Lelio R Paula	08/2012

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Probable Primes Top 10000

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