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	19^52265+52	66835	Lelio R Paula	08/2013
7502	2*10^66826-27	66827	Robert Price	02/2017
7503	4*6^85867+5	66819	Lelio R Paula	09/2014
7504	11955^16384+2	66807	Matt Stath	12/2018
7505	15^56800+8	66802	Lelio R Paula	08/2013
7506	(2^221891-2^110946+1)/5	66796		11/2006
7507	10^66793+69441	66794	Patrick De Geest	05/2013
7508	10^66793-63	66793	Robert Price	05/2011
7509	35^43256-1704	66791	Enzo Doria	03/2013
7510	3^139976+2^(139976-1)	66786	Robert Price	05/2016
7511	88769!6-48	66786	Robert Price	08/2018
7512	7^79023-54	66783	Lelio R Paula	06/2013
7513	104^33109-103	66782	Norbert Schneider	11/2016
7514	(34*10^66778-7)/9/37/358901	66772	Makoto Morimoto	04/2016
7515	(-lucasV(1,2,443622)+2)/(7281487)	66766	Mike Oakes	04/2017
7516	2^221768+183	66759	Lelio R Paula	02/2012
7517	gcd(V(1197915),5F(239583)(F(239583)+1)+1)	66759	Serge Batalov	04/2015
7518	(154*10^66755-1)/9	66757	Serge Batalov	12/2014
7519	11^64097+48	66751	Lelio R Paula	07/2013
7520	(lucasV(1,2,443547)-2)/(713791327221773)	66749	Mike Oakes	04/2017
7521	(19*10^66748+413)/9	66749	Robert Price	10/2017
7522	(3*2^221696-1)/13	66737	Lelio R Paula	01/2014
7523	8*6^85758-7	66734	Lelio R Paula	09/2014
7524	135^31325+2	66733	Lelio R Paula	05/2013
7525	(49*10^66729+41)/9	66730	Robert Price	07/2015
7526	(349*10^66720-7)/9	66722	Robert Price	03/2017
7527	(-lucasV(1,2,443285)+2)/(3^2*307)	66718	Mike Oakes	04/2017
7528	(25*10^66714+71)/3	66715	Robert Price	01/2017
7529	11^64061-780	66713	Enzo Doria	11/2012
7530	7^78929+4	66703	Lelio R Paula	06/2013
7531	11^64048-930	66700	Enzo Doria	11/2012
7532	120^32079-119	66699	Norbert Schneider	09/2018
7533	2*7^78921+5	66697	Lelio R Paula	09/2014
7534	(25*2^221526+1)/409	66685	Lelio R Paula	08/2012
7535	(2^221509-1)/292391881	66673	Jens K. Andersen	02/2009
7536	2^221479+72953	66672	Enzo Doria	04/2016
7537	10^66666+275403	66667	Patrick De Geest	03/2010
7538	10^66666-115521	66666	Patrick De Geest	03/2010
7539	(18*10^66657-81)/99	66657	Ray Chandler	01/2011
7540	4*10^66653+21	66654	Robert Price	08/2016
7541	(10^66650+149)/3	66650	Serge Batalov	12/2014
7542	9^69842+38^69842-24^69842-3*2^69842	66647	Mike Oakes	12/2010
7543	2^221391-2145	66646	Lelio R Paula	04/2012
7544	(5*10^66613-119)/3	66614	Robert Price	04/2016
7545	2^221273-113233	66610	Enzo Doria	07/2014
7546	3^139571-46	66593	Lelio R Paula	06/2013
7547	(410^(233295)-2*(10^33295)+1)/3	66591	Robert Price	04/2018
7548	2^221181-869688105	66583	Lelio R Paula	02/2016
7549	(61*10^66575-7)/9	66576	Ray Chandler	02/2012
7550	2^221126+133	66566	Lelio R Paula	02/2012
7551	12^61680+91	66564	Lelio R Paula	07/2013
7552	(lucasV(1,2,442258)+2)/103	66564	Mike Oakes	04/2017
7553	(13*10^66551-73)/3	66552	Robert Price	12/2016
7554	11^63901-1590	66547	Enzo Doria	12/2012
7555	11^63901-1500	66547	Enzo Doria	12/2012
7556	6^85517+23	66546	Lelio R Paula	07/2013
7557	17^54069-40	66530	Lelio R Paula	08/2013
7558	(2^110503+4725)^2+(2^110503+4725)+41	66530	Makoto Morimoto	05/2016
7559	(2^110503+8099)^2+(2^110503+8099)+41	66530	Makoto Morimoto	05/2016
7560	(2^221008-1017)/78533	66526	Lelio R Paula	04/2012
7561	3^139432+26	66526	Lelio R Paula	06/2013
7562	((2^110503+5139)^2+(2^110503+5139)+41)/20865797	66523	Makoto Morimoto	05/2016
7563	((2^110503+6647)^2+(2^110503+6647)+41)/197/17327	66523	Makoto Morimoto	05/2016
7564	6^85481+85481	66518	Henri Lifchitz	08/2014
7565	(9179*2^220913-1)/399	66503	Lelio R Paula	04/2015
7566	13^59687+66	66488	Lelio R Paula	07/2013
7567	(49*10^66485-31)/9	66486	Robert Price	07/2015
7568	(46*10^66469+17)/9	66470	Robert Price	06/2015
7569	2^220790+97	66465	Lelio R Paula	02/2012
7570	(23*2^220790+1)/807	66463	Lelio R Paula	06/2012
7571	40009^14441-102	66460	Enzo Doria	07/2012
7572	2^220736-143	66449	Lelio R Paula	02/2012
7573	(79*10^66447-97)/99	66447	Ray Chandler	01/2011
7574	2^220675+69	66430	Lelio R Paula	02/2012
7575	88323!6-16	66419	Robert Price	08/2018
7576	2^220633-111381	66418	Enzo Doria	05/2014
7577	(2^220625-509203)/4000321	66409	Lelio R Paula	05/2012
7578	2^220596-15813	66407	Enzo Doria	04/2013
7579	(5*10^66394-17)/3	66395	Serge Batalov	05/2009
7580	2^220549-1859173	66392	Enzo Doria	04/2016
7581	2^220478-161	66371	Lelio R Paula	02/2012
7582	5^94938-14636	66359	Enzo Doria	02/2013
7583	(F(67)^4861-F(66)^4861)/F(65)	66353	Wayne Halsdorf	03/2012
7584	15444^15839-15839^15444	66346	Norbert Schneider	08/2018
7585	2^220253-114871	66303	Enzo Doria	05/2015
7586	12^61432+95	66297	Lelio R Paula	07/2013
7587	2^220192-111563	66285	Enzo Doria	05/2014
7588	2^220188-111449	66284	Enzo Doria	05/2014
7589	(4*10^66284+23)/9	66284	Robert Price	11/2014
7590	32501!2+2	66266	Robert Price	01/2015
7591	(8*10^66261-101)/3	66262	Robert Price	10/2017
7592	1530*10^66254+R(66254)	66258	Patrick De Geest	05/2016
7593	(47^39623-1)/46	66252	Robert Price	06/2014
7594	2^220044-97305	66240	Lelio R Paula	04/2012
7595	(77*10^66237-257)/9	66238	Robert Price	10/2017
7596	29^45285+2	66225	Ray Chandler	08/2011
7597	15^56289+38	66202	Lelio R Paula	08/2013
7598	3^138749+98	66201	Lelio R Paula	06/2013
7599	(21*2^219912-1)/5	66201	Lelio R Paula	01/2014
7600	2^219904-16995	66198	Lelio R Paula	10/2011
7601	(3^138712-2)/5297	66179	Lelio R Paula	04/2012
7602	Phi(198552,10)	66177	Ray Chandler	07/2010
7603	4*6^85041+7	66176	Lelio R Paula	09/2014
7604	2^219812-3149	66171	Yves Minet	10/2009
7605	2^219795-611167	66165	Paul Bourdelais	03/2013
7606	32455!2+512	66162	Robert Price	02/2015
7607	(27*2^219760-1)/227	66154	Lelio R Paula	01/2014
7609	(11^63521-4^63521)/7	66150	Robert Price	03/2013
7608	5*7^78274-6	66150	Lelio R Paula	09/2014
7610	(-lucasV(1,2,439441)-2)/(31192781359)	66134	Mike Oakes	04/2017
7611	2^219679-112015	66130	Enzo Doria	05/2014
7612	2^219653+15015*219653	66123	Henri Lifchitz	04/2005
7613	15445^15782-15782^15445	66108	Norbert Schneider	08/2018
7614	2^219600+76561	66107	Enzo Doria	05/2016
7615	2^219594+255255	66105	Lelio R Paula	10/2011
7616	4*7^78210-3	66096	Lelio R Paula	09/2014
7617	(15185*2^219557-1)/63	66096	Lelio R Paula	04/2015
7618	(19*2^219499-1)/13	66076	Lelio R Paula	01/2014
7619	2^219496+66615	66075	Lelio R Paula	10/2011
7620	(F(79021)^5-F(79020)^5)/F(79019)	66057	Wayne Halsdorf	03/2012
7621	(2^219414+7)/443657	66045	Lelio R Paula	04/2012
7622	(115*10^66043-1)/3	66045	Serge Batalov	12/2014
7623	10^66033+19	66034	Robert Price	01/2011
7624	10^66033-78309	66033	Patrick De Geest	05/2013
7625	(lucasV(1,2,438701)+2)/7599419	66025	Mike Oakes	04/2017
7626	2^219304+454245	66018	Henri Lifchitz	03/2007
7627	(27*2^219293+1)/9145	66012	Lelio R Paula	08/2012
7628	2^219273-112635	66008	Enzo Doria	06/2014
7629	2^219250+25	66001	Lelio R Paula	08/2011
7630	132^31123+131	65999	Norbert Schneider	03/2015
7631	V(319871)	65987	Serge Batalov	03/2015
7632	2^219189-195	65983	Lelio R Paula	08/2011
7633	(7*2^219143-1)/55	65968	Lelio R Paula	01/2014
7634	(73^35401-1)/72	65962	Paul Bourdelais	08/2017
7635	2^219112-17009	65960	Enzo Doria	05/2013
7636	2^219093-111201	65954	Enzo Doria	05/2014
7637	2^219089-112099	65953	Enzo Doria	06/2014
7638	46714!3+81	65950	Robert Price	09/2014
7639	(11*10^65944-131)/3	65945	Robert Price	02/2017
7640	2^219021-3553	65932	Yves Minet	03/2017
7641	Pell-LucasQ(172243)/2	65931	Eric W. Weisstein	01/2007
7642	2^218990+73519	65923	Enzo Doria	04/2016
7643	58^37378-57	65914	Norbert Schneider	09/2014
7645	(2^218945-7)/1675	65906	Lelio R Paula	04/2012
7644	5*10^65905+81	65906	Robert Price	08/2017
7646	3*10^65899-13	65900	Robert Price	11/2017
7647	(-lucasV(1,2,437845)-2)/1679917	65896	Mike Oakes	04/2017
7648	127^31322-2	65896	Lelio R Paula	10/2017
7649	2^218897-111889	65895	Enzo Doria	05/2014
7650	2^218896+1869451	65895	Enzo Doria	05/2016
7651	63^36616+2	65885	Lelio R Paula	05/2013
7652	(3*2^218822-1)/11	65872	Lelio R Paula	01/2014
7653	2^218796-113297	65865	Enzo Doria	07/2014
7654	2^218797+73727	65865	Enzo Doria	04/2016
7655	3^138040-110	65862	Lelio R Paula	06/2013
7656	11^63240-1950	65858	Enzo Doria	12/2012
7657	2^218764-111873	65855	Enzo Doria	05/2014
7658	(34*10^65839-7)/9/37	65839	Makoto Morimoto	04/2016
7659	3^137988+26	65838	Lelio R Paula	06/2013
7660	2^218680-719	65830	Yves Minet	05/2012
7661	18^52424+17	65807	Lelio R Paula	08/2013
7662	(2*15683^15683+1)/732384425	65789	David Broadhurst	09/2010
7663	(23*2^218517+1)/19003	65778	Lelio R Paula	07/2012
7664	(5*10^65773+1)/3	65774	Erik Branger	12/2013
7665	160^29839-159	65769	Norbert Schneider	12/2018
7666	2^218457-17329	65763	Enzo Doria	05/2013
7667	151703#+223381	65759	Nicolas PALAU	10/2016
7668	2^218436+40755	65756	Lelio R Paula	10/2011
7669	(F(44)^7433-F(43)^7433)/F(42)	65744	Wayne Halsdorf	03/2012
7670	157^29934+29934^157	65733	Serge Batalov	05/2014
7671	211^28273-2	65715	Lelio R Paula	09/2013
7672	(59*10^65712+31)/9	65713	Robert Price	09/2015
7673	611^23586+23586^611	65712	Norbert Schneider	08/2016
7674	p(13991)#/2+32	65712	Robert Price	12/2016
7675	2^218282-18485	65710	Enzo Doria	05/2013
7676	2^218274-111251	65708	Enzo Doria	05/2014
7677	2*F(314335)-1	65693	Henri Lifchitz	12/2009
7678	2^218200+427	65685	Henri Lifchitz	01/2005
7679	(10199^16384+10197^16384)/2	65676	Jeppe Stig Nielsen	04/2018
7680	(10199^(2^14)+(10197)^(2^14))/2	65676	Robert Price	05/2018
7681	46532!3+3	65667	Robert Price	10/2014
7682	2^218120-147	65661	Lelio R Paula	08/2011
7683	452^24729+24729^452	65659	Norbert Schneider	09/2016
7684	2^218102-114893	65656	Enzo Doria	05/2015
7685	(15*2^218083-1)/17	65650	Lelio R Paula	01/2014
7686	(15*2^218081+1)/18941	65646	Lelio R Paula	08/2012
7687	(306^26407-1)/305	65638	Eric Chen	09/2017
7689	19^51326+36	65634	Lelio R Paula	08/2013
7688	(21*2^218045-1)/451583	65634	Lelio R Paula	01/2014
7690	2^217989-33	65622	Lelio R Paula	08/2011
7691	(13*2^217961+1)/3	65614	Lelio R Paula	06/2012
7692	4*6^84315-5	65611	Lelio R Paula	09/2014
7693	(315047^11933+1)/315048	65607	Faysal YAtim	06/2008
7694	6^84303+55	65601	Lelio R Paula	07/2013
7695	(-lucasV(1,2,435857)+2)/(1738598017)	65595	Mike Oakes	04/2017
7696	(9787*2^217873-1)/37	65589	Lelio R Paula	04/2015
7697	5*2^217858+3	65583	Lelio R Paula	04/2014
7698	(19*10^65572+119)/3	65573	Robert Price	02/2017
7700	20^50399+51	65571	Lelio R Paula	08/2013
7699	7162^17009+17009^7162	65571	Norbert Schneider	07/2018
7701	11^62946-5670	65552	Enzo Doria	01/2013
7702	2^217742-3911	65547	Yves Minet	08/2009
7703	(19*10^65545+77)/3	65546	Robert Price	08/2016
7704	2^217731+131	65544	Lelio R Paula	08/2011
7705	2^217720-111287	65541	Enzo Doria	05/2014
7706	(365^25579+1)/366	65539	Eric Chen	10/2017
7707	10^65537+27	65538	Robert Price	01/2011
7708	10^65537-76859	65537	Patrick De Geest	05/2013
7709	(28*10^65532+359)/9	65533	Robert Price	11/2017
7710	(10223*2^217676+1)/3	65531	Lelio R Paula	06/2014
7711	PadovanNumber[536485]	65518	Eric W. Weisstein	05/2009
7712	5*10^65509+23	65510	Robert Price	11/2017
7713	(8*10^65507-83)/3	65508	Robert Price	10/2017
7714	7*10^65492-47	65493	Robert Price	02/2017
7715	2^217547-1868407	65489	Enzo Doria	04/2016
7716	2^217531-111769	65484	Enzo Doria	05/2014
7717	7^77484-18	65482	Lelio R Paula	06/2013
7718	2^217488-113285	65471	Enzo Doria	07/2014
7719	151153#/30-30	65468	Henri Lifchitz	12/2011
7720	2^217466+4257	65464	Lelio R Paula	10/2011
7721	46396!3-81	65455	Robert Price	09/2014
7722	2^217421-113185	65451	Enzo Doria	07/2014
7723	(6883*2^217440-1)/1061193295893	65448	Lelio R Paula	04/2015
7724	2^217408-2145	65447	Lelio R Paula	10/2011
7725	2^217398-16947	65444	Enzo Doria	05/2013
7726	8*5^93613+3	65434	Lelio R Paula	09/2014
7727	11^62828-5310	65429	Enzo Doria	01/2013
7728	10^65426+13	65427	Robert Price	01/2011
7729	2^217341-6555	65427	Lelio R Paula	10/2011
7730	10^65426-54849	65426	Patrick De Geest	05/2013
7731	(21*2^217363-1)/56003626667	65424	Lelio R Paula	01/2014
7732	30011^14608-108	65405	Enzo Doria	07/2012
7733	119^31504-2	65389	Lelio R Paula	10/2017
7734	(43^40031-1)/42	65388	Robert Price	04/2014
7735	2^217190+94395	65381	Henri Lifchitz	02/2005
7736	15^55587+46	65376	Lelio R Paula	08/2013
7737	2^217088-111833	65350	Enzo Doria	05/2014
7738	(13*2^217069-1)/1682945	65340	Lelio R Paula	01/2014
7739	(10^65340+47)/3	65340	Robert Price	11/2017
7740	(62*10^65331+1)/9	65332	Serge Batalov	11/2010
7741	2^216947-111351	65308	Enzo Doria	05/2014
7742	-E(18022)/775201845682685322943949235068359	65307	Thomas Ritschel	02/2017
7743	(13*10^65297+83)/3	65298	Robert Price	09/2016
7744	5^93400-8	65284	Lelio R Paula	06/2013
7745	2^216802-165	65264	Lelio R Paula	08/2011
7746	2^216799-28635	65264	Lelio R Paula	10/2011
7747	5*10^65255+51	65256	Robert Price	01/2017
7748	2^216762-167	65252	Lelio R Paula	08/2011
7749	11^62657-5790	65251	Enzo Doria	01/2013
7750	3^136756-112880	65250	Enzo Doria	06/2014

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Probable Primes Top 10000

(252675 PRPs in the top)