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 (> 30000)	Who ?	When ?
6501	(2^223759-lucasV(1,2,223759)+1)/2	67358	Mike Oakes	11/2016
6502	V(340138)	67336	Serge Batalov	03/2015
6503	43125^14528-106	67334	Enzo Doria	07/2012
6504	8*10^67302-51	67303	Robert Price	10/2017
6505	17458^7153+7153^17458	67292	Hans Havermann	08/2016
6506	16366^12925+12925^16366	67288	Hans Havermann	08/2016
6507	37^42906-2	67286	Lelio R Paula	08/2013
6508	18^53592-13	67273	Lelio R Paula	08/2013
6509	V(396221)	67256	Serge Batalov	03/2015
6511	(34*10^67245-7)/9/3^4/193/1381537	67236	Makoto Morimoto	04/2016
6510	(14*10^67235-101)/3	67236	Robert Price	04/2017
6512	53^38993-52^38993	67235	Robert Price	01/2013
6513	(2^223349-7)/6485	67231	Lelio R Paula	04/2012
6514	2^223333+315	67230	Lelio R Paula	04/2012
6515	2^223278-111041	67214	Enzo Doria	05/2014
6516	(23472^223281+1)/(351971213*1783)	67208	Jens K. Andersen	09/2007
6517	2^223256-45	67207	Lelio R Paula	02/2012
6518	2^223253-112111	67206	Enzo Doria	06/2014
6519	18407^4474+4474^18407	67199	Hans Havermann	08/2016
6520	47^40182+40182^47	67189	Norbert Schneider	11/2014
6521	13^60309+94	67181	Lelio R Paula	07/2013
6522	11^64503-84	67173	Lelio R Paula	07/2013
6523	3^140781+236	67170	Lelio R Paula	06/2013
6524	2^223107-865057	67162	Paul Bourdelais	03/2013
6525	2^223100-59	67160	Lelio R Paula	02/2012
6526	2^223087+71963	67156	Enzo Doria	04/2016
6527	18^53481-3779	67134	Enzo Doria	03/2013
6528	(326^26713-1)/325	67134	Eric Chen	09/2017
6529	4^111473-62573	67114	Mike Oakes	02/2011
6530	2^222943+29	67113	Henri Lifchitz	08/2005
6531	(2^222939-9)/103	67110	Lelio R Paula	04/2012
6532	2^222862-459161	67089	Enzo Doria	05/2015
6533	2^222828+8193	67078	Lelio R Paula	04/2012
6534	3^140570+2660	67069	Lelio R Paula	06/2013
6535	2^222744+855	67053	Lelio R Paula	04/2012
6536	13^60189+84	67048	Lelio R Paula	07/2013
6537	2^222701+577294575	67040	Lelio R Paula	02/2016
6538	(13*10^67038-31)/9	67039	Serge Batalov	11/2008
6539	(151*10^67027-7)/9	67029	Robert Price	07/2017
6540	(58695*2^222620-1)/61	67019	Lelio R Paula	04/2015
6541	2^222614-111041	67014	Enzo Doria	05/2014
6542	2^222520-1907	66986	Yves Minet	03/2013
6543	(4^111231+23)/3	66968	Robert Price	02/2017
6544	2^222408-111275	66952	Enzo Doria	05/2014
6545	10^66949-9^66949	66949	Jean-Louis Charton	12/2005
6546	2^222378-1005	66943	Lelio R Paula	04/2012
6547	(9*2^222366+1)/73	66938	Lelio R Paula	08/2012
6548	7^79202-6^(79202+1)	66934	Robert Price	06/2016
6549	2^222325-112255	66927	Enzo Doria	06/2014
6550	20^51428+33	66910	Lelio R Paula	08/2013
6551	2^222224-18509	66897	Enzo Doria	05/2013
6552	2^222192-869688105	66887	Lelio R Paula	02/2016
6553	11^64219-64	66878	Lelio R Paula	07/2013
6554	2^222151-17295	66875	Lelio R Paula	04/2012
6555	gcd(V(799885),5F(159977)(F(159977)+1)+1)	66867	Serge Batalov	04/2015
6556	2^222085-111031	66855	Enzo Doria	05/2014
6557	8*10^66848-13	66849	Robert Price	05/2017
6558	(3^140087+4)/13	66838	Lelio R Paula	04/2012
6559	(3^140102+4)/8843609437	66836	Lelio R Paula	04/2012
6560	19^52265+52	66835	Lelio R Paula	08/2013
6561	2*10^66826-27	66827	Robert Price	02/2017
6562	4*6^85867+5	66819	Lelio R Paula	09/2014
6563	15^56800+8	66802	Lelio R Paula	08/2013
6564	(2^221891-2^110946+1)/5	66796		11/2006
6565	10^66793+69441	66794	Patrick De Geest	05/2013
6566	10^66793-63	66793	Robert Price	05/2011
6567	35^43256-1704	66791	Enzo Doria	03/2013
6568	3^139976+2^(139976-1)	66786	Robert Price	05/2016
6569	7^79023-54	66783	Lelio R Paula	06/2013
6570	104^33109-103	66782	Norbert Schneider	11/2016
6571	(34*10^66778-7)/9/37/358901	66772	Makoto Morimoto	04/2016
6572	(-lucasV(1,2,443622)+2)/(7281487)	66766	Mike Oakes	04/2017
6574	2^221768+183	66759	Lelio R Paula	02/2012
6573	gcd(V(1197915),5F(239583)(F(239583)+1)+1)	66759	Serge Batalov	04/2015
6575	(154*10^66755-1)/9	66757	Serge Batalov	12/2014
6576	11^64097+48	66751	Lelio R Paula	07/2013
6577	(lucasV(1,2,443547)-2)/(713791327221773)	66749	Mike Oakes	04/2017
6578	(19*10^66748+413)/9	66749	Robert Price	10/2017
6579	(3*2^221696-1)/13	66737	Lelio R Paula	01/2014
6580	8*6^85758-7	66734	Lelio R Paula	09/2014
6581	135^31325+2	66733	Lelio R Paula	05/2013
6582	(49*10^66729+41)/9	66730	Robert Price	07/2015
6583	(349*10^66720-7)/9	66722	Robert Price	03/2017
6584	(-lucasV(1,2,443285)+2)/(3^2*307)	66718	Mike Oakes	04/2017
6585	(25*10^66714+71)/3	66715	Robert Price	01/2017
6586	11^64061-780	66713	Enzo Doria	11/2012
6587	7^78929+4	66703	Lelio R Paula	06/2013
6588	11^64048-930	66700	Enzo Doria	11/2012
6589	2*7^78921+5	66697	Lelio R Paula	09/2014
6590	(25*2^221526+1)/409	66685	Lelio R Paula	08/2012
6591	(2^221509-1)/292391881	66673	Jens K. Andersen	02/2009
6592	2^221479+72953	66672	Enzo Doria	04/2016
6593	10^66666+275403	66667	Patrick De Geest	03/2010
6594	10^66666-115521	66666	Patrick De Geest	03/2010
6595	(18*10^66657-81)/99	66657	Ray Chandler	01/2011
6596	4*10^66653+21	66654	Robert Price	08/2016
6597	(10^66650+149)/3	66650	Serge Batalov	12/2014
6598	9^69842+38^69842-24^69842-3*2^69842	66647	Mike Oakes	12/2010
6599	2^221391-2145	66646	Lelio R Paula	04/2012
6600	(5*10^66613-119)/3	66614	Robert Price	04/2016
6601	2^221273-113233	66610	Enzo Doria	07/2014
6602	3^139571-46	66593	Lelio R Paula	06/2013
6603	2^221181-869688105	66583	Lelio R Paula	02/2016
6604	(61*10^66575-7)/9	66576	Ray Chandler	02/2012
6605	2^221126+133	66566	Lelio R Paula	02/2012
6607	12^61680+91	66564	Lelio R Paula	07/2013
6606	(lucasV(1,2,442258)+2)/103	66564	Mike Oakes	04/2017
6608	(13*10^66551-73)/3	66552	Robert Price	12/2016
6609	11^63901-1590	66547	Enzo Doria	12/2012
6610	11^63901-1500	66547	Enzo Doria	12/2012
6611	6^85517+23	66546	Lelio R Paula	07/2013
6612	17^54069-40	66530	Lelio R Paula	08/2013
6613	(2^110503+4725)^2+(2^110503+4725)+41	66530	Makoto Morimoto	05/2016
6614	(2^110503+8099)^2+(2^110503+8099)+41	66530	Makoto Morimoto	05/2016
6615	(2^221008-1017)/78533	66526	Lelio R Paula	04/2012
6616	3^139432+26	66526	Lelio R Paula	06/2013
6617	((2^110503+5139)^2+(2^110503+5139)+41)/20865797	66523	Makoto Morimoto	05/2016
6618	((2^110503+6647)^2+(2^110503+6647)+41)/197/17327	66523	Makoto Morimoto	05/2016
6619	6^85481+85481	66518	Henri Lifchitz	08/2014
6620	(9179*2^220913-1)/399	66503	Lelio R Paula	04/2015
6621	13^59687+66	66488	Lelio R Paula	07/2013
6622	(49*10^66485-31)/9	66486	Robert Price	07/2015
6623	(46*10^66469+17)/9	66470	Robert Price	06/2015
6624	2^220790+97	66465	Lelio R Paula	02/2012
6625	(23*2^220790+1)/807	66463	Lelio R Paula	06/2012
6626	40009^14441-102	66460	Enzo Doria	07/2012
6627	2^220736-143	66449	Lelio R Paula	02/2012
6628	(79*10^66447-97)/99	66447	Ray Chandler	01/2011
6629	2^220675+69	66430	Lelio R Paula	02/2012
6630	2^220633-111381	66418	Enzo Doria	05/2014
6631	(2^220625-509203)/4000321	66409	Lelio R Paula	05/2012
6632	2^220596-15813	66407	Enzo Doria	04/2013
6633	(5*10^66394-17)/3	66395	Serge Batalov	05/2009
6634	2^220549-1859173	66392	Enzo Doria	04/2016
6635	2^220478-161	66371	Lelio R Paula	02/2012
6636	5^94938-14636	66359	Enzo Doria	02/2013
6637	(F(67)^4861-F(66)^4861)/F(65)	66353	Wayne Halsdorf	03/2012
6638	2^220253-114871	66303	Enzo Doria	05/2015
6639	12^61432+95	66297	Lelio R Paula	07/2013
6640	2^220192-111563	66285	Enzo Doria	05/2014
6641	2^220188-111449	66284	Enzo Doria	05/2014
6642	(4*10^66284+23)/9	66284	Robert Price	11/2014
6643	32501!2+2	66266	Robert Price	01/2015
6644	1530*10^66254+R(66254)	66258	Patrick De Geest	05/2016
6645	(47^39623-1)/46	66252	Robert Price	06/2014
6646	2^220044-97305	66240	Lelio R Paula	04/2012
6647	(77*10^66237-257)/9	66238	Robert Price	10/2017
6648	29^45285+2	66225	Ray Chandler	08/2011
6649	15^56289+38	66202	Lelio R Paula	08/2013
6650	3^138749+98	66201	Lelio R Paula	06/2013
6651	(21*2^219912-1)/5	66201	Lelio R Paula	01/2014
6652	2^219904-16995	66198	Lelio R Paula	10/2011
6653	(3^138712-2)/5297	66179	Lelio R Paula	04/2012
6654	Phi(198552,10)	66177	Ray Chandler	07/2010
6655	4*6^85041+7	66176	Lelio R Paula	09/2014
6656	2^219812-3149	66171	Yves Minet	10/2009
6657	2^219795-611167	66165	Paul Bourdelais	03/2013
6658	32455!2+512	66162	Robert Price	02/2015
6659	(27*2^219760-1)/227	66154	Lelio R Paula	01/2014
6661	(11^63521-4^63521)/7	66150	Robert Price	03/2013
6660	5*7^78274-6	66150	Lelio R Paula	09/2014
6662	(-lucasV(1,2,439441)-2)/(31192781359)	66134	Mike Oakes	04/2017
6663	2^219679-112015	66130	Enzo Doria	05/2014
6664	2^219653+15015*219653	66123	Henri Lifchitz	04/2005
6665	2^219600+76561	66107	Enzo Doria	05/2016
6666	2^219594+255255	66105	Lelio R Paula	10/2011
6667	4*7^78210-3	66096	Lelio R Paula	09/2014
6668	(15185*2^219557-1)/63	66096	Lelio R Paula	04/2015
6669	(19*2^219499-1)/13	66076	Lelio R Paula	01/2014
6670	2^219496+66615	66075	Lelio R Paula	10/2011
6671	(F(79021)^5-F(79020)^5)/F(79019)	66057	Wayne Halsdorf	03/2012
6672	(2^219414+7)/443657	66045	Lelio R Paula	04/2012
6673	(115*10^66043-1)/3	66045	Serge Batalov	12/2014
6674	10^66033+19	66034	Robert Price	01/2011
6675	10^66033-78309	66033	Patrick De Geest	05/2013
6676	(lucasV(1,2,438701)+2)/7599419	66025	Mike Oakes	04/2017
6677	2^219304+454245	66018	Henri Lifchitz	03/2007
6678	(27*2^219293+1)/9145	66012	Lelio R Paula	08/2012
6679	2^219273-112635	66008	Enzo Doria	06/2014
6680	2^219250+25	66001	Lelio R Paula	08/2011
6681	132^31123+131	65999	Norbert Schneider	03/2015
6682	V(319871)	65987	Serge Batalov	03/2015
6683	2^219189-195	65983	Lelio R Paula	08/2011
6684	(7*2^219143-1)/55	65968	Lelio R Paula	01/2014
6685	(73^35401-1)/72	65962	Paul Bourdelais	08/2017
6686	2^219112-17009	65960	Enzo Doria	05/2013
6687	2^219093-111201	65954	Enzo Doria	05/2014
6688	2^219089-112099	65953	Enzo Doria	06/2014
6689	46714!3+81	65950	Robert Price	09/2014
6690	(11*10^65944-131)/3	65945	Robert Price	02/2017
6691	2^219021-3553	65932	Yves Minet	03/2017
6692	Pell-LucasQ(172243)/2	65931	Eric W. Weisstein	01/2007
6693	2^218990+73519	65923	Enzo Doria	04/2016
6694	58^37378-57	65914	Norbert Schneider	09/2014
6695	(2^218945-7)/1675	65906	Lelio R Paula	04/2012
6696	5*10^65905+81	65906	Robert Price	08/2017
6697	(-lucasV(1,2,437845)-2)/1679917	65896	Mike Oakes	04/2017
6698	127^31322-2	65896	Lelio R Paula	10/2017
6699	2^218897-111889	65895	Enzo Doria	05/2014
6700	2^218896+1869451	65895	Enzo Doria	05/2016
6701	63^36616+2	65885	Lelio R Paula	05/2013
6702	(3*2^218822-1)/11	65872	Lelio R Paula	01/2014
6703	2^218796-113297	65865	Enzo Doria	07/2014
6704	2^218797+73727	65865	Enzo Doria	04/2016
6705	3^138040-110	65862	Lelio R Paula	06/2013
6706	11^63240-1950	65858	Enzo Doria	12/2012
6707	2^218764-111873	65855	Enzo Doria	05/2014
6708	(34*10^65839-7)/9/37	65839	Makoto Morimoto	04/2016
6709	3^137988+26	65838	Lelio R Paula	06/2013
6710	2^218680-719	65830	Yves Minet	05/2012
6711	18^52424+17	65807	Lelio R Paula	08/2013
6712	(2*15683^15683+1)/732384425	65789	David Broadhurst	09/2010
6713	(23*2^218517+1)/19003	65778	Lelio R Paula	07/2012
6714	(5*10^65773+1)/3	65774	Erik Branger	12/2013
6715	2^218457-17329	65763	Enzo Doria	05/2013
6716	151703#+223381	65759	Nicolas PALAU	10/2016
6717	2^218436+40755	65756	Lelio R Paula	10/2011
6718	(F(44)^7433-F(43)^7433)/F(42)	65744	Wayne Halsdorf	03/2012
6719	157^29934+29934^157	65733	Serge Batalov	05/2014
6720	211^28273-2	65715	Lelio R Paula	09/2013
6721	(59*10^65712+31)/9	65713	Robert Price	09/2015
6723	611^23586+23586^611	65712	Norbert Schneider	08/2016
6722	p(13991)#/2+32	65712	Robert Price	12/2016
6724	2^218282-18485	65710	Enzo Doria	05/2013
6725	2^218274-111251	65708	Enzo Doria	05/2014
6726	2*F(314335)-1	65693	Henri Lifchitz	12/2009
6727	2^218200+427	65685	Henri Lifchitz	01/2005
6728	46532!3+3	65667	Robert Price	10/2014
6729	2^218120-147	65661	Lelio R Paula	08/2011
6730	452^24729+24729^452	65659	Norbert Schneider	09/2016
6731	2^218102-114893	65656	Enzo Doria	05/2015
6732	(15*2^218083-1)/17	65650	Lelio R Paula	01/2014
6733	(15*2^218081+1)/18941	65646	Lelio R Paula	08/2012
6734	(306^26407-1)/305	65638	Eric Chen	09/2017
6736	19^51326+36	65634	Lelio R Paula	08/2013
6735	(21*2^218045-1)/451583	65634	Lelio R Paula	01/2014
6737	2^217989-33	65622	Lelio R Paula	08/2011
6738	(13*2^217961+1)/3	65614	Lelio R Paula	06/2012
6739	4*6^84315-5	65611	Lelio R Paula	09/2014
6740	(315047^11933+1)/315048	65607	Faysal YAtim	06/2008
6741	6^84303+55	65601	Lelio R Paula	07/2013
6742	(-lucasV(1,2,435857)+2)/(1738598017)	65595	Mike Oakes	04/2017
6743	(9787*2^217873-1)/37	65589	Lelio R Paula	04/2015
6744	5*2^217858+3	65583	Lelio R Paula	04/2014
6745	(19*10^65572+119)/3	65573	Robert Price	02/2017
6746	20^50399+51	65571	Lelio R Paula	08/2013
6747	11^62946-5670	65552	Enzo Doria	01/2013
6748	2^217742-3911	65547	Yves Minet	08/2009
6749	(19*10^65545+77)/3	65546	Robert Price	08/2016
6750	2^217731+131	65544	Lelio R Paula	08/2011

Find by discoverer :

PRP Records

Probable Primes Top 10000

(183432 PRPs in the top)