Lucas cofactor
This page : Definition(s) | Records | References |
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Lucas cofactorThis page : Definition(s) | Records | References |
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The Prime Pages keeps a list of the 5000 largest known primes, plus a few each of certain selected archivable forms and classes. These forms are defined in this collection's home page. This page is about one of those forms. Comments and suggestions requested.
Definitions and Notesv1 = 1, v2 = 3 and vn+1 = vn + vn-1 (n > 2)
It can be shown that, for odd m, vn divides vnm.
In the same way that we defined a Mersenne cofactor, we define a Lucas cofactor to be a proper divisor of a Lucas number with a prime index.
Record Primes of this Type
rank prime digits who when comment 1 V(68213)/7290202116115634431 14237 c77 Aug 2018 Lucas cofactor, ECPP 2 V(66533)/2128184670585621839884209100279 13875 c77 Dec 2018 Lucas cofactor, ECPP 3 V(52859)/1124137922466041911 11029 c8 Oct 2014 Lucas cofactor, ECPP 4 V(52201)/705\
8580404289697550569470957591945873385127986844660910857 c8 Mar 2015 Lucas cofactor, ECPP 5 V(52009)/39772636393178951550299332730909 10838 c8 Mar 2015 Lucas cofactor, ECPP 6 V(51941)/28080521576109021\
1454721069686833738025030092411659114364164286693110789 c8 Jan 2015 Lucas cofactor, ECPP 7 V(51349)/224417260052884218046541 10708 c8 Sep 2014 Lucas cofactor, ECPP 8 V(50989)/69818796119453411 10640 c8 Aug 2014 Lucas cofactor, ECPP 9 V(49391)/298414424560419239 10305 c8 Jun 2013 Lucas cofactor, ECPP 10 V(45953)/4561241750239 9591 c56 Mar 2012 Lucas cofactor, ECPP 11 V(43987)/175949 9188 c8 May 2014 Lucas cofactor, ECPP 12 V(39769)/18139109172816581 8295 c8 Nov 2013 Lucas cofactor, ECPP 13 V(39607)/158429 8273 c46 Dec 2011 Lucas cofactor, ECPP 14 V(37357)/20210113386303842894568629 7782 c8 Sep 2013 Lucas cofactor, ECPP 15 V(35107)/525110138418084707309 7317 c8 Sep 2013 Lucas cofactor, ECPP 16 V(34759)/27112021 7257 c33 Jul 2005 Lucas cofactor, ECPP 17 V(33353)/279902102741094707003083072429 6941 c8 May 2013 Lucas cofactor, ECPP 18 V(31547)/221409808384144085062492986575402586918348866650893130934479823303462\
27824686184228977375762399380559492255026457207263\
132495525655340249966709963789680205082590987563016425 c8 Jun 2013 Lucas cofactor, ECPP 19 V(27827)/3579579016301 5803 c4 Nov 2011 Lucas cofactor, ECPP 20 V(26309)/42316339086094085101 5479 c8 May 2013 Lucas cofactor, ECPP
References
- BMS1988
- J. Brillhart, P. Montgomery and R. Silverman, "Tables of Fibonacci and Lucas factorizations," Math. Comp., 50 (1988) 251--260. MR 89h:11002
- DK1999
- H. Dubner and W. Keller, "New Fibonacci and Lucas primes," Math. Comp., 68 (1999) 417--427. MR 99c:11008 [A supplement gives the complete factorization of Fn and Ln for n>1000 whenever it is known.]