# Lucas cofactor

This page : Definition(s) | Records | References |
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 Notes

The Lucas numbers can be defined as follows:
v1 = 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

rankprime digitswhowhencomment
1V(52859)/1124137922466041911 11029 c8 Oct 2014 Lucas cofactor, ECPP
2V(52201)/705\
85804042896975505694709575919458733851279868446609
10857 c8 Mar 2015 Lucas cofactor, ECPP
3V(52009)/39772636393178951550299332730909 10838 c8 Mar 2015 Lucas cofactor, ECPP
4V(51941)/28080521576109021\
14547210696868337380250300924116591143641642866931
10789 c8 Jan 2015 Lucas cofactor, ECPP
5V(51349)/224417260052884218046541 10708 c8 Sep 2014 Lucas cofactor, ECPP
6V(50989)/69818796119453411 10640 c8 Aug 2014 Lucas cofactor, ECPP
7V(49391)/298414424560419239 10305 c8 Jun 2013 Lucas cofactor, ECPP
8V(45953)/4561241750239 9591 c56 Mar 2012 Lucas cofactor, ECPP
9V(43987)/175949 9188 c8 May 2014 Lucas cofactor, ECPP
10V(39769)/18139109172816581 8295 c8 Nov 2013 Lucas cofactor, ECPP
11V(39607)/158429 8273 c46 Dec 2011 Lucas cofactor, ECPP
12V(37357)/20210113386303842894568629 7782 c8 Sep 2013 Lucas cofactor, ECPP
13V(35107)/525110138418084707309 7317 c8 Sep 2013 Lucas cofactor, ECPP
14V(34759)/27112021 7257 c33 Jul 2005 Lucas cofactor, ECPP
15V(33353)/279902102741094707003083072429 6941 c8 May 2013 Lucas cofactor, ECPP
16V(31547)/221409808384144085062492986575402586918348866650893130934479823303462\
27824686184228977375762399380559492255026457207263\
13249552565534024996670996378968020508259098756301
6425 c8 Jun 2013 Lucas cofactor, ECPP
17V(27827)/3579579016301 5803 c4 Nov 2011 Lucas cofactor, ECPP
18V(26309)/42316339086094085101 5479 c8 May 2013 Lucas cofactor, ECPP
19V(25873)/34396575615094965590217427573609664640790259 5364 c8 May 2013 Lucas cofactor, ECPP
20V(25763)/92864275685263243511877732271066626563444291249 5338 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.]