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	(21181*2^224570+1)/5	67606	Lelio R Paula	06/2014
7502	89762!6-3	67606	Robert Price	08/2018
7503	2^224578-111041	67605	Enzo Doria	05/2014
7504	2^224569-113233	67603	Enzo Doria	07/2014
7505	2^224562-113171	67600	Enzo Doria	07/2014
7506	2^224556-113129	67599	Enzo Doria	07/2014
7507	6*7^79980-5	67592	Lelio R Paula	09/2014
7508	(6883*2^224523-1)/16031	67588	Lelio R Paula	04/2015
7509	10^67579+164779	67580	Patrick De Geest	07/2017
7511	(52*10^67578-61)/9	67579	Robert Price	09/2015
7510	10^67579-401	67579	Robert Price	06/2017
7512	(17^54919-1)/16	67574	Paul Bourdelais	03/2010
7513	((10^33771-1)10000/9+6389)10^33771+(10^33771-1)/9	67546	Hans Havermann	05/2019
7514	(2^224363-9)/1951	67537	Lelio R Paula	04/2012
7515	(709*10^67517-7)/9	67519	Robert Price	09/2017
7516	47719!3-59049	67516	Robert Price	12/2015
7517	(22^50287+1)/23	67506	Robert Price	06/2013
7518	3*10^67499+67	67500	Robert Price	11/2017
7519	11^64811-5820	67494	Enzo Doria	01/2013
7520	131^31870+31870^131	67478	Serge Batalov	05/2014
7521	9*10^67468+7	67469	Dmitry Domanov	11/2010
7522	(31*2^224115-1)/47723	67463	Lelio R Paula	01/2014
7523	128^32001+32001^128	67433	Serge Batalov	05/2014
7524	(89*10^67431-17)/9	67432	Robert Price	11/2015
7525	2^223912-111059	67405	Enzo Doria	05/2014
7526	2^223913+73697	67405	Enzo Doria	04/2016
7527	(2*10^67405-23)/3	67405	Robert Price	09/2017
7528	(10^67404+179)/9	67404	Serge Batalov	12/2014
7529	18738^3955+3955^18738	67404	Hans Havermann	09/2016
7530	9*7^79728-2	67379	Lelio R Paula	09/2014
7531	(28*10^67378-43)/3	67379	Robert Price	04/2016
7532	(3^141234-7)/430241282	67378	Lelio R Paula	04/2012
7533	211^28988-2	67377	Lelio R Paula	09/2013
7534	4*10^67375+91	67376	Robert Price	11/2017
7535	2^223793-18069	67369	Enzo Doria	05/2013
7536	2^223777-2521	67364	Yves Minet	07/2014
7537	(15185*2^223775-1)/15183	67363	Lelio R Paula	04/2015
7538	(2^223759-lucasV(1,2,223759)+1)/2	67358	Mike Oakes	11/2016
7539	V(340138)	67336	Serge Batalov	03/2015
7540	43125^14528-106	67334	Enzo Doria	07/2012
7541	15275^16086-16086^15275	67304	Norbert Schneider	09/2018
7542	8*10^67302-51	67303	Robert Price	10/2017
7543	17458^7153+7153^17458	67292	Hans Havermann	08/2016
7544	16366^12925+12925^16366	67288	Hans Havermann	08/2016
7545	37^42906-2	67286	Lelio R Paula	08/2013
7546	18^53592-13	67273	Lelio R Paula	08/2013
7547	V(396221)	67256	Serge Batalov	03/2015
7549	(34*10^67245-7)/9/3^4/193/1381537	67236	Makoto Morimoto	04/2016
7548	(14*10^67235-101)/3	67236	Robert Price	04/2017
7550	53^38993-52^38993	67235	Robert Price	01/2013
7551	(2^223349-7)/6485	67231	Lelio R Paula	04/2012
7552	2^223333+315	67230	Lelio R Paula	04/2012
7553	2^223278-111041	67214	Enzo Doria	05/2014
7554	(23472^223281+1)/(351971213*1783)	67208	Jens K. Andersen	09/2007
7555	2^223256-45	67207	Lelio R Paula	02/2012
7556	2^223253-112111	67206	Enzo Doria	06/2014
7557	18407^4474+4474^18407	67199	Hans Havermann	08/2016
7558	47^40182+40182^47	67189	Norbert Schneider	11/2014
7559	13^60309+94	67181	Lelio R Paula	07/2013
7560	11^64503-84	67173	Lelio R Paula	07/2013
7561	3^140781+236	67170	Lelio R Paula	06/2013
7562	2^223107-865057	67162	Paul Bourdelais	03/2013
7563	2^223100-59	67160	Lelio R Paula	02/2012
7564	2^223087+71963	67156	Enzo Doria	04/2016
7565	18^53481-3779	67134	Enzo Doria	03/2013
7566	(326^26713-1)/325	67134	Eric Chen	09/2017
7567	4^111473-62573	67114	Mike Oakes	02/2011
7568	2^222943+29	67113	Henri Lifchitz	08/2005
7569	(2^222939-9)/103	67110	Lelio R Paula	04/2012
7570	2^222862-459161	67089	Enzo Doria	05/2015
7571	2^222828+8193	67078	Lelio R Paula	04/2012
7572	3^140570+2660	67069	Lelio R Paula	06/2013
7573	2^222744+855	67053	Lelio R Paula	04/2012
7574	13^60189+84	67048	Lelio R Paula	07/2013
7575	2*10^67043-51	67044	Robert Price	11/2017
7576	2^222701+577294575	67040	Lelio R Paula	02/2016
7577	(13*10^67038-31)/9	67039	Serge Batalov	11/2008
7578	(151*10^67027-7)/9	67029	Robert Price	07/2017
7579	(58695*2^222620-1)/61	67019	Lelio R Paula	04/2015
7580	2^222614-111041	67014	Enzo Doria	05/2014
7581	118^32333-117	66991	Norbert Schneider	08/2018
7582	2^222520-1907	66986	Yves Minet	03/2013
7583	(4^111231+23)/3	66968	Robert Price	02/2017
7584	2^222408-111275	66952	Enzo Doria	05/2014
7585	10^66949-9^66949	66949	Jean-Louis Charton	12/2005
7586	2^222378-1005	66943	Lelio R Paula	04/2012
7587	(9*2^222366+1)/73	66938	Lelio R Paula	08/2012
7588	7^79202-6^(79202+1)	66934	Robert Price	06/2016
7589	2^222325-112255	66927	Enzo Doria	06/2014
7590	20^51428+33	66910	Lelio R Paula	08/2013
7591	2^222224-18509	66897	Enzo Doria	05/2013
7592	(38*10^66896+187)/9	66897	Robert Price	11/2017
7593	2^222192-869688105	66887	Lelio R Paula	02/2016
7594	(19*10^66878-43)/3	66879	Robert Price	10/2017
7595	11^64219-64	66878	Lelio R Paula	07/2013
7596	2^222151-17295	66875	Lelio R Paula	04/2012
7597	gcd(V(799885),5F(159977)(F(159977)+1)+1)	66867	Serge Batalov	04/2015
7598	2^222085-111031	66855	Enzo Doria	05/2014
7599	8*10^66848-13	66849	Robert Price	05/2017
7600	(3^140087+4)/13	66838	Lelio R Paula	04/2012
7601	(3^140102+4)/8843609437	66836	Lelio R Paula	04/2012
7602	19^52265+52	66835	Lelio R Paula	08/2013
7603	2*10^66826-27	66827	Robert Price	02/2017
7604	4*6^85867+5	66819	Lelio R Paula	09/2014
7605	11955^16384+2	66807	Matt Stath	12/2018
7606	15^56800+8	66802	Lelio R Paula	08/2013
7607	(2^221891-2^110946+1)/5	66796		11/2006
7608	10^66793+69441	66794	Patrick De Geest	05/2013
7609	10^66793-63	66793	Robert Price	05/2011
7610	35^43256-1704	66791	Enzo Doria	03/2013
7611	3^139976+2^(139976-1)	66786	Robert Price	05/2016
7612	88769!6-48	66786	Robert Price	08/2018
7613	7^79023-54	66783	Lelio R Paula	06/2013
7614	104^33109-103	66782	Norbert Schneider	11/2016
7615	(34*10^66778-7)/9/37/358901	66772	Makoto Morimoto	04/2016
7616	(-lucasV(1,2,443622)+2)/(7281487)	66766	Mike Oakes	04/2017
7617	2^221768+183	66759	Lelio R Paula	02/2012
7618	gcd(V(1197915),5F(239583)(F(239583)+1)+1)	66759	Serge Batalov	04/2015
7619	(154*10^66755-1)/9	66757	Serge Batalov	12/2014
7620	11^64097+48	66751	Lelio R Paula	07/2013
7621	(lucasV(1,2,443547)-2)/(713791327221773)	66749	Mike Oakes	04/2017
7622	(19*10^66748+413)/9	66749	Robert Price	10/2017
7623	(3*2^221696-1)/13	66737	Lelio R Paula	01/2014
7624	8*6^85758-7	66734	Lelio R Paula	09/2014
7625	135^31325+2	66733	Lelio R Paula	05/2013
7626	(49*10^66729+41)/9	66730	Robert Price	07/2015
7627	(349*10^66720-7)/9	66722	Robert Price	03/2017
7628	(-lucasV(1,2,443285)+2)/(3^2*307)	66718	Mike Oakes	04/2017
7629	(25*10^66714+71)/3	66715	Robert Price	01/2017
7630	11^64061-780	66713	Enzo Doria	11/2012
7631	7^78929+4	66703	Lelio R Paula	06/2013
7632	11^64048-930	66700	Enzo Doria	11/2012
7633	120^32079-119	66699	Norbert Schneider	09/2018
7634	2*7^78921+5	66697	Lelio R Paula	09/2014
7635	(25*2^221526+1)/409	66685	Lelio R Paula	08/2012
7636	(2^221509-1)/292391881	66673	Jens K. Andersen	02/2009
7637	2^221479+72953	66672	Enzo Doria	04/2016
7638	10^66666+275403	66667	Patrick De Geest	03/2010
7639	10^66666-115521	66666	Patrick De Geest	03/2010
7640	(18*10^66657-81)/99	66657	Ray Chandler	01/2011
7641	4*10^66653+21	66654	Robert Price	08/2016
7642	(10^66650+149)/3	66650	Serge Batalov	12/2014
7643	9^69842+38^69842-24^69842-3*2^69842	66647	Mike Oakes	12/2010
7644	2^221391-2145	66646	Lelio R Paula	04/2012
7645	(5*10^66613-119)/3	66614	Robert Price	04/2016
7646	2^221273-113233	66610	Enzo Doria	07/2014
7647	3^139571-46	66593	Lelio R Paula	06/2013
7648	(410^(233295)-2*(10^33295)+1)/3	66591	Robert Price	04/2018
7649	2^221181-869688105	66583	Lelio R Paula	02/2016
7650	(61*10^66575-7)/9	66576	Ray Chandler	02/2012
7651	2^221126+133	66566	Lelio R Paula	02/2012
7652	12^61680+91	66564	Lelio R Paula	07/2013
7653	(lucasV(1,2,442258)+2)/103	66564	Mike Oakes	04/2017
7654	(13*10^66551-73)/3	66552	Robert Price	12/2016
7655	11^63901-1590	66547	Enzo Doria	12/2012
7656	11^63901-1500	66547	Enzo Doria	12/2012
7657	6^85517+23	66546	Lelio R Paula	07/2013
7658	17^54069-40	66530	Lelio R Paula	08/2013
7659	(2^110503+4725)^2+(2^110503+4725)+41	66530	Makoto Morimoto	05/2016
7660	(2^110503+8099)^2+(2^110503+8099)+41	66530	Makoto Morimoto	05/2016
7661	(2^221008-1017)/78533	66526	Lelio R Paula	04/2012
7662	3^139432+26	66526	Lelio R Paula	06/2013
7663	((2^110503+5139)^2+(2^110503+5139)+41)/20865797	66523	Makoto Morimoto	05/2016
7664	((2^110503+6647)^2+(2^110503+6647)+41)/197/17327	66523	Makoto Morimoto	05/2016
7665	6^85481+85481	66518	Henri Lifchitz	08/2014
7666	(9179*2^220913-1)/399	66503	Lelio R Paula	04/2015
7667	13^59687+66	66488	Lelio R Paula	07/2013
7668	(49*10^66485-31)/9	66486	Robert Price	07/2015
7669	(46*10^66469+17)/9	66470	Robert Price	06/2015
7670	2^220790+97	66465	Lelio R Paula	02/2012
7671	(23*2^220790+1)/807	66463	Lelio R Paula	06/2012
7672	40009^14441-102	66460	Enzo Doria	07/2012
7673	2^220736-143	66449	Lelio R Paula	02/2012
7674	(79*10^66447-97)/99	66447	Ray Chandler	01/2011
7675	2^220675+69	66430	Lelio R Paula	02/2012
7676	88323!6-16	66419	Robert Price	08/2018
7677	2^220633-111381	66418	Enzo Doria	05/2014
7678	(2^220625-509203)/4000321	66409	Lelio R Paula	05/2012
7679	2^220596-15813	66407	Enzo Doria	04/2013
7680	(5*10^66394-17)/3	66395	Serge Batalov	05/2009
7681	2^220549-1859173	66392	Enzo Doria	04/2016
7682	2^220478-161	66371	Lelio R Paula	02/2012
7683	5^94938-14636	66359	Enzo Doria	02/2013
7684	(F(67)^4861-F(66)^4861)/F(65)	66353	Wayne Halsdorf	03/2012
7685	15444^15839-15839^15444	66346	Norbert Schneider	08/2018
7686	2^220253-114871	66303	Enzo Doria	05/2015
7687	12^61432+95	66297	Lelio R Paula	07/2013
7688	2^220192-111563	66285	Enzo Doria	05/2014
7689	2^220188-111449	66284	Enzo Doria	05/2014
7690	(4*10^66284+23)/9	66284	Robert Price	11/2014
7691	32501!2+2	66266	Robert Price	01/2015
7692	(8*10^66261-101)/3	66262	Robert Price	10/2017
7693	1530*10^66254+R(66254)	66258	Patrick De Geest	05/2016
7694	(47^39623-1)/46	66252	Robert Price	06/2014
7695	2^220044-97305	66240	Lelio R Paula	04/2012
7696	(77*10^66237-257)/9	66238	Robert Price	10/2017
7697	29^45285+2	66225	Ray Chandler	08/2011
7698	15^56289+38	66202	Lelio R Paula	08/2013
7699	3^138749+98	66201	Lelio R Paula	06/2013
7700	(21*2^219912-1)/5	66201	Lelio R Paula	01/2014
7701	2^219904-16995	66198	Lelio R Paula	10/2011
7702	2^219903-4615	66198	Yves Minet	05/2019
7703	(3^138712-2)/5297	66179	Lelio R Paula	04/2012
7704	Phi(198552,10)	66177	Ray Chandler	07/2010
7705	4*6^85041+7	66176	Lelio R Paula	09/2014
7706	2^219812-3149	66171	Yves Minet	10/2009
7707	2^219795-611167	66165	Paul Bourdelais	03/2013
7708	32455!2+512	66162	Robert Price	02/2015
7709	(27*2^219760-1)/227	66154	Lelio R Paula	01/2014
7711	(11^63521-4^63521)/7	66150	Robert Price	03/2013
7710	5*7^78274-6	66150	Lelio R Paula	09/2014
7712	(-lucasV(1,2,439441)-2)/(31192781359)	66134	Mike Oakes	04/2017
7713	2^219679-112015	66130	Enzo Doria	05/2014
7714	2^219653+15015*219653	66123	Henri Lifchitz	04/2005
7715	15445^15782-15782^15445	66108	Norbert Schneider	08/2018
7716	2^219600+76561	66107	Enzo Doria	05/2016
7717	2^219594+255255	66105	Lelio R Paula	10/2011
7718	4*7^78210-3	66096	Lelio R Paula	09/2014
7719	(15185*2^219557-1)/63	66096	Lelio R Paula	04/2015
7720	(19*2^219499-1)/13	66076	Lelio R Paula	01/2014
7721	2^219496+66615	66075	Lelio R Paula	10/2011
7722	(F(79021)^5-F(79020)^5)/F(79019)	66057	Wayne Halsdorf	03/2012
7723	(2^219414+7)/443657	66045	Lelio R Paula	04/2012
7724	(115*10^66043-1)/3	66045	Serge Batalov	12/2014
7725	10^66033+19	66034	Robert Price	01/2011
7726	10^66033-78309	66033	Patrick De Geest	05/2013
7727	(lucasV(1,2,438701)+2)/7599419	66025	Mike Oakes	04/2017
7728	2^219304+454245	66018	Henri Lifchitz	03/2007
7729	(27*2^219293+1)/9145	66012	Lelio R Paula	08/2012
7730	2^219273-112635	66008	Enzo Doria	06/2014
7731	2^219250+25	66001	Lelio R Paula	08/2011
7732	132^31123+131	65999	Norbert Schneider	03/2015
7733	V(319871)	65987	Serge Batalov	03/2015
7734	2^219189-195	65983	Lelio R Paula	08/2011
7735	(7*2^219143-1)/55	65968	Lelio R Paula	01/2014
7736	(73^35401-1)/72	65962	Paul Bourdelais	08/2017
7737	2^219112-17009	65960	Enzo Doria	05/2013
7738	2^219093-111201	65954	Enzo Doria	05/2014
7739	2^219089-112099	65953	Enzo Doria	06/2014
7740	46714!3+81	65950	Robert Price	09/2014
7741	(11*10^65944-131)/3	65945	Robert Price	02/2017
7742	2^219021-3553	65932	Yves Minet	03/2017
7743	Pell-LucasQ(172243)/2	65931	Eric W. Weisstein	01/2007
7744	2^218990+73519	65923	Enzo Doria	04/2016
7745	58^37378-57	65914	Norbert Schneider	09/2014
7747	(2^218945-7)/1675	65906	Lelio R Paula	04/2012
7746	5*10^65905+81	65906	Robert Price	08/2017
7748	3*10^65899-13	65900	Robert Price	11/2017
7749	(-lucasV(1,2,437845)-2)/1679917	65896	Mike Oakes	04/2017
7750	127^31322-2	65896	Lelio R Paula	10/2017

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Probable Primes Top 10000

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