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 ?
6501	5*7^89231-6	75410	Lelio R Paula	10/2014
6503	2^250503-16995	75409	Lelio R Paula	05/2013
6502	11^72411-28	75409	Lelio R Paula	02/2015
6504	3*5^107860-8	75392	Lelio R Paula	10/2014
6505	(34*10^75387-403)/9	75388	Robert Price	10/2017
6507	2^250426+29835	75386	Lelio R Paula	05/2013
6506	8*3^157999-7	75386	Lelio R Paula	05/2014
6508	(88*10^75381-43)/9	75382	Robert Price	11/2015
6509	2^250382-111755	75373	Enzo Doria	05/2014
6510	2^250374-2798051	75371	Eric Chen	03/2016
6511	(22*10^75368-1)/3	75369	Robert Price	12/2014
6512	2^250369-4543	75369	Yves Minet	03/2019
6513	(19*10^75338+119)/3	75339	Robert Price	02/2017
6514	2^250223-1859167	75325	Enzo Doria	03/2016
6515	(3^157854-7)/66025282	75308	Lelio R Paula	06/2012
6516	3^157831-98	75305	Lelio R Paula	01/2015
6517	(46^45281+11^45281)/57	75290	Serge Batalov	12/2016
6518	92^38335-91	75282	Norbert Schneider	01/2016
6519	2^250020+18915	75264	Lelio R Paula	05/2013
6520	2^250002+8193	75259	Lelio R Paula	05/2013
6521	(11*2^249977-7)/15	75251	Renaud Lifchitz	02/2011
6522	(2^249968+78557)/63	75247	Lelio R Paula	07/2012
6523	(5*10^75244+91)/3	75245	Robert Price	11/2016
6524	(10489!)^2+Prime(10489)	75242	Robert Price	08/2014
6525	14^65644+67	75237	Lelio R Paula	01/2015
6526	(2^249928-5)/11859059	75229	Lelio R Paula	06/2012
6527	129^35638+2	75218	Lelio R Paula	05/2013
6528	2^249853-110475	75214	Enzo Doria	05/2014
6529	2^249762+75409	75186	Enzo Doria	04/2016
6530	565^27318+27318^565	75181	Norbert Schneider	12/2016
6531	(2^249741-7)/685	75177	Lelio R Paula	06/2012
6532	2^249726-112181	75176	Enzo Doria	06/2014
6533	2^249721+11715	75174	Lelio R Paula	05/2013
6534	(38661^16384+1)/2	75158	Lelio R Paula	11/2011
6535	2^249658-47355	75155	Lelio R Paula	05/2013
6536	155^34311+2	75153	Lelio R Paula	05/2013
6537	(10^87682+1)/(10^12526+1)/990099009901	75145	Maksym Voznyy	06/2015
6538	(23*2^249602+1)/93	75138	Lelio R Paula	08/2012
6539	2^249522+8415	75114	Lelio R Paula	05/2013
6540	2^249489-110911	75104	Enzo Doria	05/2014
6541	(28*10^75078+131)/3	75079	Robert Price	02/2017
6542	(206*10^75073-17)/9	75075	Robert Price	03/2017
6543	2^249368-110573	75068	Enzo Doria	05/2014
6544	NaturalLogarithmOf10(75067)	75067	Eric W. Weisstein	10/2015
6545	(2^249375+78557)/45056125	75062	Lelio R Paula	07/2012
6546	(26*10^75055-173)/3	75056	Robert Price	10/2017
6547	2^249272+193	75039	Lelio R Paula	03/2012
6548	14^65468+43	75035	Lelio R Paula	01/2015
6549	37^47844+36	75030	Norbert Schneider	05/2014
6550	(52*10^75027-7)/9	75028	Robert Price	12/2014
6551	20^57653+89	75009	Lelio R Paula	01/2015
6552	2^249061-1868353	74975	Enzo Doria	04/2016
6553	7^88713+2*3^88713	74972	Mike Oakes	07/2010
6554	2*6^96313+5	74947	Lelio R Paula	10/2014
6555	(8*10^74944+49)/3	74945	Robert Price	03/2016
6556	300^30247+30247^300	74926	Norbert Schneider	11/2014
6557	2^248866-171	74917	Lelio R Paula	03/2012
6558	6*5^107168-7	74908	Lelio R Paula	10/2014
6559	11^71926+78	74904	Lelio R Paula	02/2015
6560	2^248824+1869391	74904	Enzo Doria	05/2016
6561	2^248816+1111	74902	Lelio R Paula	01/2011
6562	V(388219)	74890	Serge Batalov	03/2015
6563	159^34017+158	74885	Norbert Schneider	12/2018
6564	2*F(358297)-1	74880	Henri Lifchitz	12/2009
6565	(22*10^74874-31)/9	74875	Robert Price	04/2015
6566	11^71892-76800000	74868	Enzo Doria	01/2013
6567	9*5^107107-4	74866	Lelio R Paula	10/2014
6568	2^248678-710111	74860	Paul Bourdelais	03/2013
6569	(14*10^74858+211)/9	74859	Robert Price	11/2017
6570	13^67194+12	74851	Lelio R Paula	01/2015
6571	(7*2^248634+1)/71	74846	Lelio R Paula	08/2012
6572	11^71867-3090	74842	Enzo Doria	12/2012
6573	2^248609+262145	74839	Lelio R Paula	05/2013
6574	3^156852+50	74838	Lelio R Paula	01/2015
6575	18^59607-11	74824	Lelio R Paula	01/2015
6576	2^248556-110507	74823	Enzo Doria	05/2014
6577	7^88531-36	74818	Lelio R Paula	01/2015
6578	p(15738)#/2+1024	74814	Robert Price	07/2017
6579	4*3^156740-5	74785	Lelio R Paula	05/2014
6580	(32*10^74773-41)/9	74774	Robert Price	05/2015
6581	(29*2^248384-1)/13	74772	Lelio R Paula	01/2014
6582	19401!+19401#+1	74765	D. Gazzoni Filho & Lucas Teixeira	06/2005
6583	2^248357-12797413	74763	Enzo Doria	03/2016
6584	42^46057+41	74762	Lelio R Paula	07/2012
6585	11^71784-3000	74756	Enzo Doria	12/2012
6586	19^58458+18	74754	Lelio R Paula	01/2015
6587	12^69265-35	74750	Lelio R Paula	02/2015
6588	11^71771-48000	74742	Enzo Doria	12/2012
6589	(7*10^74741+197)/3	74742	Robert Price	07/2017
6590	(2^248282-5)/50129	74736	Lelio R Paula	06/2012
6591	2^248252-110105	74732	Enzo Doria	04/2014
6592	(7*10^74729+71)/3	74730	Robert Price	03/2016
6593	3^156614-50	74724	Lelio R Paula	01/2015
6594	(7*2^248213+1)/135	74719	Lelio R Paula	07/2012
6595	(2^248173+78557)/767	74705	Lelio R Paula	07/2012
6596	125^35622+124	74697	Norbert Schneider	02/2015
6597	(19*2^248099-1)/29	74686	Lelio R Paula	01/2014
6598	(86*10^74676-41)/9	74677	Robert Price	11/2015
6599	(p(15711)#-4)/2	74672	Robert Price	09/2017
6600	10^74670+31	74671	Robert Price	01/2011
6601	10^74670-122463	74670	Patrick De Geest	05/2013
6602	2^248036-69	74667	Lelio R Paula	03/2012
6603	11^71698-6000	74666	Enzo Doria	12/2012
6604	58(10^(324887)-1)/111-1	74661	Robert Price	10/2014
6605	14^65139-45	74658	Lelio R Paula	01/2015
6606	6^95921-133	74642	Lelio R Paula	01/2015
6607	11^71675+78	74642	Lelio R Paula	02/2015
6608	18^59449-91	74625	Lelio R Paula	01/2015
6609	6^95864-16043	74597	Enzo Doria	02/2013
6610	5*7^88261+6	74590	Lelio R Paula	10/2014
6611	9*5^106710+4	74589	Lelio R Paula	10/2014
6612	(7772^247788+1)/(11754121)	74588	Jens K. Andersen	09/2007
6613	(265*10^74579+17)/3	74581	Robert Price	05/2016
6614	(2^247759-1017)/3318311717	74574	Lelio R Paula	07/2012
6615	5^106682-24	74568	Lelio R Paula	08/2014
6616	474^27863+27863^474	74556	Norbert Schneider	01/2017
6617	(14*10^74540+79)/3	74541	Robert Price	11/2017
6618	(35365^16384+1)/2	74524	Lelio R Paula	11/2011
6619	3^156161+2660	74508	Lelio R Paula	01/2015
6620	2^247474-58695	74498	Lelio R Paula	05/2013
6621	11^71519-90	74480	Enzo Doria	07/2012
6622	(19*2^247419-1)/23202983	74475	Lelio R Paula	01/2014
6624	(2^247394-7)/3	74473	Lelio R Paula	06/2012
6623	18^59328+17	74473	Lelio R Paula	01/2015
6625	2^247379-181	74469	Lelio R Paula	03/2012
6626	(15*2^247370-1)/479	74465	Lelio R Paula	01/2014
6627	2^247344+2047	74458	Lelio R Paula	05/2013
6628	2^247311-1017	74449	Lelio R Paula	05/2013
6629	2^247280+7	74439	Lelio R Paula	03/2012
6630	(68*10^74434+13)/9	74435	Ray Chandler	11/2010
6631	3^156004-62	74433	Lelio R Paula	01/2015
6632	36095!2-64	74416	Robert Price	06/2015
6633	2^247165-3	74405	M. Frind & P. Underwood	07/2002
6634	2^247150+32769	74400	Lelio R Paula	05/2013
6635	12^68911+73	74368	Lelio R Paula	01/2015
6636	2^246999+74903	74355	Enzo Doria	04/2016
6637	2^246989-110643	74352	Enzo Doria	05/2014
6638	10^74350+279439	74351	Patrick De Geest	07/2017
6641	(10^74350+11)/3	74350	Robert Price	11/2014
6639	10^74350-400000001	74350	Robert Price	07/2017
6640	10^74350-716241	74350	Patrick De Geest	07/2017
6642	10^74335+13659	74336	Patrick De Geest	05/2013
6643	10^74335-53	74335	Robert Price	05/2011
6644	2^246906-1215	74327	Lelio R Paula	05/2013
6645	2^246848+111	74309	Lelio R Paula	03/2012
6646	6^95490-18443	74306	Enzo Doria	03/2013
6647	18^59188-2369	74298	Enzo Doria	03/2013
6648	(13632^246767+1)/(35713^2*743)	74281	Jens K. Andersen	09/2007
6649	2^246744+40755	74278	Lelio R Paula	05/2013
6650	(29*10^74276+91)/3	74277	Robert Price	03/2016
6651	6^95441+163	74268	Lelio R Paula	01/2015
6652	V(390863)	74258	Serge Batalov	03/2015
6653	10^74254+91	74255	Robert Price	03/2011
6655	(19*10^74253-1)/9	74254	Ray Chandler	02/2012
6654	10^74254-130569	74254	Patrick De Geest	05/2013
6656	771^25718+25718^771	74250	Norbert Schneider	10/2016
6657	2^246618+427	74240	Henri Lifchitz	02/2005
6658	88*10^74234+3	74236	Robert Price	11/2016
6659	8*10^74234-49	74235	Robert Price	04/2016
6660	2^246578+12285	74228	Lelio R Paula	05/2013
6661	(3^155569-5)/2	74225	Lelio R Paula	06/2012
6662	13^66628+46	74220	Lelio R Paula	01/2015
6663	2^246476-17295	74197	Lelio R Paula	05/2013
6664	(61*10^74189-1)/3	74191	Robert Price	11/2017
6665	(15185*2^246432-1)/13	74187	Lelio R Paula	04/2015
6666	5*2^246413-3	74179	Lelio R Paula	05/2014
6667	2^246386-28635	74170	Lelio R Paula	05/2013
6668	2^246334-111245	74154	Enzo Doria	05/2014
6669	39^77708+7^77708-24^77708-3	74153	Mike Oakes	12/2010
6670	15^63045+82	74147	Lelio R Paula	01/2015
6671	19255!+19255#+1	74140	D. Gazzoni Filho & Lucas Teixeira	06/2005
6672	2^246268-110507	74135	Enzo Doria	05/2014
6673	3^155328+2660	74111	Lelio R Paula	01/2015
6674	2^246148-2786249	74098	Enzo Doria	03/2016
6675	(16*10^74092-19)/3	74093	Robert Price	03/2016
6676	2^246115-110767	74088	Enzo Doria	05/2014
6677	7^87666-68	74087	Lelio R Paula	08/2014
6678	10^74079+1145141919	74080	Marisa Kirisame	03/2015
6679	10^74079+6219	74080	Patrick De Geest	03/2016
6680	10^74079-282707	74079	Patrick De Geest	03/2016
6681	129^35098+2	74078	Lelio R Paula	05/2013
6682	2^246025-112123	74061	Enzo Doria	06/2014
6683	(67*10^74045+17)/3	74047	Robert Price	02/2017
6684	2^245823+66831	74001	Marek Hubal	02/2017
6685	5^105869+42	74000	Lelio R Paula	08/2014
6686	(21*2^245806+1)/634555	73991	Lelio R Paula	08/2012
6687	(22699*2^245762+1)/119	73985	Lelio R Paula	06/2014
6688	(3^155048-7)/262	73975	Lelio R Paula	06/2012
6689	9998*2^245696+3	73966	Donovan Johnson	10/2004
6690	13^66400-80	73966	Lelio R Paula	01/2015
6691	(2^245704+9)/25	73963	Lelio R Paula	07/2012
6693	11^71023-7170	73963	Enzo Doria	01/2013
6692	3*10^73962+13	73963	Robert Price	08/2017
6694	(31*2^245660-1)/114195	73948	Lelio R Paula	01/2014
6695	2^245629-2797813	73942	Eric Chen	03/2016
6696	2^245557-153	73921	Lelio R Paula	03/2012
6697	(77*10^73917-59)/9	73918	Robert Price	11/2017
6698	2^245525+1869881	73911	Enzo Doria	06/2016
6699	2^245522+159	73910	Lelio R Paula	03/2012
6700	(13*10^73891-43)/3	73892	Robert Price	08/2017
6701	19^57783-56	73891	Lelio R Paula	01/2015
6702	7*10^73888+79	73889	Robert Price	02/2017
6703	6^94948+174281	73884	Mike Oakes	02/2011
6704	11^70939-4860	73876	Enzo Doria	01/2013
6705	2^245372+54615	73865	Lelio R Paula	05/2013
6706	2^245362-143	73862	Lelio R Paula	03/2012
6707	7^87396+6^(87396-1)	73859	Robert Price	03/2016
6708	(22*10^73853-37)/3	73854	Robert Price	05/2017
6709	5^105646-14246	73844	Enzo Doria	02/2013
6711	2^245290-41	73840	Lelio R Paula	03/2012
6710	2^245290-94395	73840	Lelio R Paula	05/2013
6712	8*5^105600-7	73813	Lelio R Paula	10/2014
6713	7*5^105573-4	73794	Lelio R Paula	10/2014
6714	18^58742-4805	73738	Enzo Doria	03/2013
6715	13^66179+66	73720	Lelio R Paula	01/2015
6716	(82*10^73714-1)/9	73715	Robert Price	12/2014
6717	(29*2^244856-1)/186121	73706	Lelio R Paula	01/2014
6718	(13*2^244840-1)/2799	73702	Lelio R Paula	01/2014
6719	(13*10^73701+17)/3	73702	Robert Price	06/2015
6720	(2^244787-1017)/28411	73684	Lelio R Paula	07/2012
6721	(3^154421-4)/23	73677	Lelio R Paula	06/2012
6722	8*7^87170+5	73669	Lelio R Paula	10/2014
6723	(29*10^73659-113)/3	73660	Robert Price	11/2017
6724	Phi(40100,-40100)	73651	Henri Lifchitz	06/2013
6725	(4*10^73647-19)/3	73648	Robert Price	06/2017
6726	2^244618-2297	73638	Yves Minet	10/2009
6727	3*5^105344+8	73633	Lelio R Paula	10/2014
6728	5^105334-14096	73626	Enzo Doria	02/2013
6729	(2^244584-7)/13237074243033	73614	Lelio R Paula	07/2012
6730	2^244465-110185	73592	Enzo Doria	05/2014
6731	2^244443+40755	73585	Lelio R Paula	05/2013
6732	2^244404+3841	73573	Yves Minet	03/2011
6733	2^244372-110627	73564	Enzo Doria	05/2014
6734	(3*2^244255+1)/245	73527	Lelio R Paula	08/2012
6735	(11*2^244245+1)/23	73525	Lelio R Paula	08/2012
6736	(15185*2^244187-1)/6111	73509	Lelio R Paula	04/2015
6737	17063^17362+17362^17063	73477	Norbert Schneider	04/2019
6738	(91^37507+1)/92	73476	Paul Bourdelais	08/2017
6739	18^58521+65	73460	Lelio R Paula	01/2015
6740	13^65940+36	73454	Lelio R Paula	01/2015
6741	(625^26267+1)/626	73437	Richard Fischer	12/2017
6742	5^105050-14	73427	Lelio R Paula	08/2014
6743	(((((((((((((30201^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2	73401	Serge Batalov	07/2016
6744	15^62410-46	73400	Lelio R Paula	01/2015
6745	2^243733+1869707	73371	Enzo Doria	05/2016
6746	11^70439-5430	73355	Enzo Doria	01/2013
6747	2^243676-87	73354	Lelio R Paula	03/2012
6748	(101*10^73346-17)/3	73348	Robert Price	08/2016
6749	2^243621-113185	73338	Enzo Doria	07/2014
6750	(5*2^243610-1)/1669	73332	Lelio R Paula	01/2014

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Probable Primes Top 10000

(252932 PRPs in the top)