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) !!!

Submit your PRPs

See the Top discoverers
See the Latest PRPs
Search by form


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	(77*10^66237-257)/9	66238	Robert Price	10/2017
7502	29^45285+2	66225	Ray Chandler	08/2011
7503	15^56289+38	66202	Lelio R Paula	08/2013
7504	3^138749+98	66201	Lelio R Paula	06/2013
7505	(21*2^219912-1)/5	66201	Lelio R Paula	01/2014
7506	2^219904-16995	66198	Lelio R Paula	10/2011
7507	(3^138712-2)/5297	66179	Lelio R Paula	04/2012
7508	Phi(198552,10)	66177	Ray Chandler	07/2010
7509	4*6^85041+7	66176	Lelio R Paula	09/2014
7510	2^219812-3149	66171	Yves Minet	10/2009
7511	2^219795-611167	66165	Paul Bourdelais	03/2013
7512	32455!2+512	66162	Robert Price	02/2015
7513	(27*2^219760-1)/227	66154	Lelio R Paula	01/2014
7515	(11^63521-4^63521)/7	66150	Robert Price	03/2013
7514	5*7^78274-6	66150	Lelio R Paula	09/2014
7516	(-lucasV(1,2,439441)-2)/(31192781359)	66134	Mike Oakes	04/2017
7517	2^219679-112015	66130	Enzo Doria	05/2014
7518	2^219653+15015*219653	66123	Henri Lifchitz	04/2005
7519	15445^15782-15782^15445	66108	Norbert Schneider	08/2018
7520	2^219600+76561	66107	Enzo Doria	05/2016
7521	2^219594+255255	66105	Lelio R Paula	10/2011
7522	4*7^78210-3	66096	Lelio R Paula	09/2014
7523	(15185*2^219557-1)/63	66096	Lelio R Paula	04/2015
7524	(19*2^219499-1)/13	66076	Lelio R Paula	01/2014
7525	2^219496+66615	66075	Lelio R Paula	10/2011
7526	(F(79021)^5-F(79020)^5)/F(79019)	66057	Wayne Halsdorf	03/2012
7527	(2^219414+7)/443657	66045	Lelio R Paula	04/2012
7528	(115*10^66043-1)/3	66045	Serge Batalov	12/2014
7529	10^66033+19	66034	Robert Price	01/2011
7530	10^66033-78309	66033	Patrick De Geest	05/2013
7531	(lucasV(1,2,438701)+2)/7599419	66025	Mike Oakes	04/2017
7532	2^219304+454245	66018	Henri Lifchitz	03/2007
7533	(27*2^219293+1)/9145	66012	Lelio R Paula	08/2012
7534	2^219273-112635	66008	Enzo Doria	06/2014
7535	2^219250+25	66001	Lelio R Paula	08/2011
7536	132^31123+131	65999	Norbert Schneider	03/2015
7537	V(319871)	65987	Serge Batalov	03/2015
7538	2^219189-195	65983	Lelio R Paula	08/2011
7539	(7*2^219143-1)/55	65968	Lelio R Paula	01/2014
7540	(73^35401-1)/72	65962	Paul Bourdelais	08/2017
7541	2^219112-17009	65960	Enzo Doria	05/2013
7542	2^219093-111201	65954	Enzo Doria	05/2014
7543	2^219089-112099	65953	Enzo Doria	06/2014
7544	46714!3+81	65950	Robert Price	09/2014
7545	(11*10^65944-131)/3	65945	Robert Price	02/2017
7546	2^219021-3553	65932	Yves Minet	03/2017
7547	Pell-LucasQ(172243)/2	65931	Eric W. Weisstein	01/2007
7548	2^218990+73519	65923	Enzo Doria	04/2016
7549	58^37378-57	65914	Norbert Schneider	09/2014
7551	(2^218945-7)/1675	65906	Lelio R Paula	04/2012
7550	5*10^65905+81	65906	Robert Price	08/2017
7552	3*10^65899-13	65900	Robert Price	11/2017
7553	(-lucasV(1,2,437845)-2)/1679917	65896	Mike Oakes	04/2017
7554	127^31322-2	65896	Lelio R Paula	10/2017
7555	2^218897-111889	65895	Enzo Doria	05/2014
7556	2^218896+1869451	65895	Enzo Doria	05/2016
7557	63^36616+2	65885	Lelio R Paula	05/2013
7558	(3*2^218822-1)/11	65872	Lelio R Paula	01/2014
7559	2^218796-113297	65865	Enzo Doria	07/2014
7560	2^218797+73727	65865	Enzo Doria	04/2016
7561	3^138040-110	65862	Lelio R Paula	06/2013
7562	11^63240-1950	65858	Enzo Doria	12/2012
7563	2^218764-111873	65855	Enzo Doria	05/2014
7564	(34*10^65839-7)/9/37	65839	Makoto Morimoto	04/2016
7565	3^137988+26	65838	Lelio R Paula	06/2013
7566	2^218680-719	65830	Yves Minet	05/2012
7567	18^52424+17	65807	Lelio R Paula	08/2013
7568	(2*15683^15683+1)/732384425	65789	David Broadhurst	09/2010
7569	(23*2^218517+1)/19003	65778	Lelio R Paula	07/2012
7570	(5*10^65773+1)/3	65774	Erik Branger	12/2013
7571	160^29839-159	65769	Norbert Schneider	12/2018
7572	2^218457-17329	65763	Enzo Doria	05/2013
7573	151703#+223381	65759	Nicolas PALAU	10/2016
7574	2^218436+40755	65756	Lelio R Paula	10/2011
7575	(F(44)^7433-F(43)^7433)/F(42)	65744	Wayne Halsdorf	03/2012
7576	157^29934+29934^157	65733	Serge Batalov	05/2014
7577	211^28273-2	65715	Lelio R Paula	09/2013
7578	(59*10^65712+31)/9	65713	Robert Price	09/2015
7579	611^23586+23586^611	65712	Norbert Schneider	08/2016
7580	p(13991)#/2+32	65712	Robert Price	12/2016
7581	2^218282-18485	65710	Enzo Doria	05/2013
7582	2^218274-111251	65708	Enzo Doria	05/2014
7583	2*F(314335)-1	65693	Henri Lifchitz	12/2009
7584	2^218200+427	65685	Henri Lifchitz	01/2005
7585	(10199^16384+10197^16384)/2	65676	Jeppe Stig Nielsen	04/2018
7586	(10199^(2^14)+(10197)^(2^14))/2	65676	Robert Price	05/2018
7587	46532!3+3	65667	Robert Price	10/2014
7588	2^218120-147	65661	Lelio R Paula	08/2011
7589	452^24729+24729^452	65659	Norbert Schneider	09/2016
7590	2^218102-114893	65656	Enzo Doria	05/2015
7591	(15*2^218083-1)/17	65650	Lelio R Paula	01/2014
7592	(15*2^218081+1)/18941	65646	Lelio R Paula	08/2012
7593	(306^26407-1)/305	65638	Eric Chen	09/2017
7595	19^51326+36	65634	Lelio R Paula	08/2013
7594	(21*2^218045-1)/451583	65634	Lelio R Paula	01/2014
7596	2^217989-33	65622	Lelio R Paula	08/2011
7597	(13*2^217961+1)/3	65614	Lelio R Paula	06/2012
7598	4*6^84315-5	65611	Lelio R Paula	09/2014
7599	(315047^11933+1)/315048	65607	Faysal YAtim	06/2008
7600	6^84303+55	65601	Lelio R Paula	07/2013
7601	(-lucasV(1,2,435857)+2)/(1738598017)	65595	Mike Oakes	04/2017
7602	(9787*2^217873-1)/37	65589	Lelio R Paula	04/2015
7603	5*2^217858+3	65583	Lelio R Paula	04/2014
7604	(19*10^65572+119)/3	65573	Robert Price	02/2017
7606	20^50399+51	65571	Lelio R Paula	08/2013
7605	7162^17009+17009^7162	65571	Norbert Schneider	07/2018
7607	11^62946-5670	65552	Enzo Doria	01/2013
7608	2^217742-3911	65547	Yves Minet	08/2009
7609	(19*10^65545+77)/3	65546	Robert Price	08/2016
7610	2^217731+131	65544	Lelio R Paula	08/2011
7611	2^217720-111287	65541	Enzo Doria	05/2014
7612	(365^25579+1)/366	65539	Eric Chen	10/2017
7613	10^65537+27	65538	Robert Price	01/2011
7614	10^65537-76859	65537	Patrick De Geest	05/2013
7615	(28*10^65532+359)/9	65533	Robert Price	11/2017
7616	(10223*2^217676+1)/3	65531	Lelio R Paula	06/2014
7617	PadovanNumber[536485]	65518	Eric W. Weisstein	05/2009
7618	5*10^65509+23	65510	Robert Price	11/2017
7619	(8*10^65507-83)/3	65508	Robert Price	10/2017
7620	7*10^65492-47	65493	Robert Price	02/2017
7621	2^217547-1868407	65489	Enzo Doria	04/2016
7622	2^217531-111769	65484	Enzo Doria	05/2014
7623	7^77484-18	65482	Lelio R Paula	06/2013
7624	2^217488-113285	65471	Enzo Doria	07/2014
7625	151153#/30-30	65468	Henri Lifchitz	12/2011
7626	2^217466+4257	65464	Lelio R Paula	10/2011
7627	46396!3-81	65455	Robert Price	09/2014
7628	2^217421-113185	65451	Enzo Doria	07/2014
7629	(6883*2^217440-1)/1061193295893	65448	Lelio R Paula	04/2015
7630	2^217408-2145	65447	Lelio R Paula	10/2011
7631	2^217398-16947	65444	Enzo Doria	05/2013
7632	8*5^93613+3	65434	Lelio R Paula	09/2014
7633	11^62828-5310	65429	Enzo Doria	01/2013
7634	10^65426+13	65427	Robert Price	01/2011
7635	2^217341-6555	65427	Lelio R Paula	10/2011
7636	10^65426-54849	65426	Patrick De Geest	05/2013
7637	(21*2^217363-1)/56003626667	65424	Lelio R Paula	01/2014
7638	30011^14608-108	65405	Enzo Doria	07/2012
7639	119^31504-2	65389	Lelio R Paula	10/2017
7640	(43^40031-1)/42	65388	Robert Price	04/2014
7641	2^217190+94395	65381	Henri Lifchitz	02/2005
7642	15^55587+46	65376	Lelio R Paula	08/2013
7643	2^217088-111833	65350	Enzo Doria	05/2014
7644	(13*2^217069-1)/1682945	65340	Lelio R Paula	01/2014
7645	(10^65340+47)/3	65340	Robert Price	11/2017
7646	(62*10^65331+1)/9	65332	Serge Batalov	11/2010
7647	2^216947-111351	65308	Enzo Doria	05/2014
7648	-E(18022)/775201845682685322943949235068359	65307	Thomas Ritschel	02/2017
7649	(13*10^65297+83)/3	65298	Robert Price	09/2016
7650	5^93400-8	65284	Lelio R Paula	06/2013
7651	2^216802-165	65264	Lelio R Paula	08/2011
7652	2^216799-28635	65264	Lelio R Paula	10/2011
7653	5*10^65255+51	65256	Robert Price	01/2017
7654	2^216762-167	65252	Lelio R Paula	08/2011
7655	11^62657-5790	65251	Enzo Doria	01/2013
7656	3^136756-112880	65250	Enzo Doria	06/2014
7657	2^216752+21	65249	Lelio R Paula	08/2011
7658	3*10^65247+11	65248	Robert Price	11/2017
7659	11^62651-2700	65245	Enzo Doria	12/2012
7660	15130^15609-15609^15130	65244	Norbert Schneider	07/2018
7662	Pell-LucasQ(170413)/2	65230	Eric W. Weisstein	12/2006
7661	gcd(V(790525),5F(158105)(F(158105)+1)+1)	65230	Serge Batalov	04/2015
7663	(2^216676-1017)/637	65224	Lelio R Paula	04/2012
7664	2^216652-2327	65219	Yves Minet	10/2013
7665	(9179*2^216648-1)/4667	65218	Lelio R Paula	04/2015
7666	(5*10^65203-119)/3	65204	Robert Price	04/2016
7667	2^216555-113269	65190	Enzo Doria	07/2014
7668	(9513^16384+1)/2	65181	Henri Lifchitz	02/2007
7669	2^216474+12915	65166	Lelio R Paula	02/2013
7670	19^50958-32	65163	Lelio R Paula	08/2013
7671	2^216442-112133	65156	Enzo Doria	06/2014
7672	2^216437-112213	65155	Enzo Doria	06/2014
7673	2^216435-112767	65154	Enzo Doria	06/2014
7674	2^216420+12705	65149	Lelio R Paula	02/2013
7675	8*3^136507-7	65132	Lelio R Paula	04/2014
7676	(-lucasV(1,2,432719)-2)/(5*461)	65128	Mike Oakes	03/2017
7677	15132^15575-15575^15132	65102	Norbert Schneider	07/2018
7678	5*10^65086-51	65087	Robert Price	10/2017
7679	2^216197-111769	65082	Enzo Doria	05/2014
7680	6^83631-79	65078	Lelio R Paula	07/2013
7681	572^23601+23601^572	65078	Norbert Schneider	08/2016
7682	(3^136399-7)/544220	65074	Lelio R Paula	04/2012
7683	2^216154-1421	65069	Yves Minet	01/2013
7684	2^216145-112663	65067	Enzo Doria	06/2014
7685	(7*10^65064+53)/3	65065	Robert Price	10/2017
7686	132013*10^65050+2^216091-1	65056	Gilbert Mozzo	01/2014
7687	132019*10^65050+2^216091-1	65056	Gilbert Mozzo	01/2014
7688	148918*10^65050+2^216091-1	65056	Gilbert Mozzo	02/2014
7689	194014*10^65050+2^216091-1	65056	Gilbert Mozzo	02/2014
7690	223864*10^65050+2^216091-1	65056	Gilbert Mozzo	04/2014
7693	82090*10^65050+2^216091-1	65055	Gilbert Mozzo	07/2012
7692	95133*10^65050+2^216091-1	65055	Gilbert Mozzo	12/2013
7691	98142*10^65050+2^216091-1	65055	Gilbert Mozzo	12/2013
7694	((2^216091-1)*34009-48)/25	65054	Serge Batalov	01/2012
7695	5977*10^65050+2^216091-1	65054	Gilbert Mozzo	03/2012
7696	7*2^216091+2^298-13	65051	Peter Lesala	03/2007
7697	2^216091+2*29208-1	65050	Makoto Morimoto	10/2013
7698	(10^(232521+1)-610^32521-1)/3	65043	Robert Price	02/2016
7699	p(13861)#/2+256	65039	Robert Price	05/2017
7700	(2^216091-2096)/(2^432918437*5220283)	65036	Makoto Morimoto	10/2017
7701	11^62439-4380	65024	Enzo Doria	01/2013
7702	3^136244+2	65005	Mike Oakes	11/2009
7703	13^58343-50	64991	Lelio R Paula	07/2013
7704	331^25791-10002	64989	Enzo Doria	07/2012
7705	2^215877+131	64986	Lelio R Paula	08/2011
7706	4*5^92959+9	64977	Lelio R Paula	09/2014
7707	2^215789-18825	64959	Lelio R Paula	09/2011
7708	(2^215801-509203)/41327	64958	Lelio R Paula	05/2012
7709	U(315311)	64954	Serge Batalov	03/2015
7710	46072!3-59049	64951	Robert Price	12/2015
7711	2^215750-5955	64948	Lelio R Paula	09/2011
7712	13^58281+46	64922	Lelio R Paula	07/2013
7713	2^215623+183	64909	Lelio R Paula	08/2011
7714	(46*10^64904+521)/9	64905	Robert Price	08/2017
7715	(3^136043-2^136043)/(19862279*33466579)	64895	Mike Oakes	12/2016
7716	5*2^215554+3	64889	Lelio R Paula	04/2014
7717	2^215541-112075	64885	Enzo Doria	06/2014
7718	2*10^64882-3	64883	Dmitry Domanov	11/2010
7719	10^64862+342339	64863	Patrick De Geest	05/2013
7720	10^64862-47	64862	Robert Price	05/2011
7721	19^50718-84	64856	Lelio R Paula	08/2013
7722	(30452^215471-1)/(17115127067173473)	64853	Jens K. Andersen	09/2007
7723	86413!6-12	64846	Robert Price	08/2018
7725	10^64843+4278697839	64844	Robert Price	05/2015
7724	10^64843+21967	64844	Patrick De Geest	03/2016
7726	10^64843-340073	64843	Patrick De Geest	03/2016
7727	11^62254+70	64831	Lelio R Paula	07/2013
7728	2^215351-111925	64828	Enzo Doria	05/2014
7729	2^215310-117	64815	Lelio R Paula	08/2011
7730	124^30958-123	64809	Norbert Schneider	02/2015
7731	(7*10^64807+17)/3	64808	Erik Branger	03/2014
7732	(710^(232400+1)-27*10^32400-7)/9	64801	Robert Price	11/2015
7733	2^215243-15949	64795	Enzo Doria	04/2013
7734	23^47581-22^47581	64793	Robert Price	08/2012
7735	(62*10^64783-17)/9	64784	Robert Price	09/2015
7736	5*3^135747-4	64769	Lelio R Paula	04/2014
7737	(59*10^64767-41)/9	64768	Robert Price	09/2015
7738	(2^215140+3)/19	64763	Lelio R Paula	04/2012
7739	2^215135-17169	64763	Enzo Doria	05/2013
7740	2^215115-111277	64757	Enzo Doria	05/2014
7741	9*5^92641+2	64755	Lelio R Paula	09/2014
7742	(lucasV(1,2,430086)-2)/(7*1033)	64731	Mike Oakes	03/2017
7743	5791^17200+17200^5791	64720	Norbert Schneider	12/2018
7744	(5*10^64715-23)/9	64715	Robert Price	11/2014
7745	2^214938-1781	64703	Yves Minet	03/2013
7746	11^62111-420	64682	Enzo Doria	08/2012
7747	5^92525+42	64673	Lelio R Paula	06/2013
7748	2^214824+71893	64669	Enzo Doria	04/2016
7749	2^214799-2221	64661	Yves Minet	08/2013
7750	5939^17128+17128^5939	64637	Norbert Schneider	10/2018

Find by discoverer :

PRP Records

Probable Primes Top 10000

(252538 PRPs in the top)