The Top Twenty--a Prime Page Collection

Fibonacci cofactor

This page : Definition(s) | Records | References | RSS 2.0 Feed
  View this page in:   language help
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.

(up) Definitions and Notes

The Fibonacci numbers can be defined as follows:
u1 = u2 = 1 and un+1 = un + un-1 (n > 2).
It is easy to show that un divides unm (see primitive part of a Fibonacci number).

In the same way we defined a Mersenne cofactor, we define a Fibonacci cofactor to be a proper divisor of a Fibonacci number with a prime index.

(up) Record Primes of this Type

rankprime digitswhowhencomment
12337 c79 Apr 2015 Fibonacci cofactor, ECPP
2U(54799)/4661437953906084533621577211561 11422 c8 Jan 2015 Fibonacci cofactor, ECPP
3U(54521)/6403194135342743624071073 11370 c8 Jan 2015 Fibonacci cofactor, ECPP
4U(53189)/69431662887136064191105625570683133711989 11075 c8 Dec 2014 Fibonacci cofactor, ECPP
5U(51031)/95846689435051369 10648 c8 Sep 2014 Fibonacci cofactor, ECPP
9010 c8 Sep 2013 Fibonacci cofactor, ECPP
7U(42829)/107130175995197969243646842778153077 8916 c8 Apr 2014 Fibonacci cofactor, ECPP
8U(42043)/1681721 8780 c56 Feb 2012 Fibonacci cofactor, ECPP
9U(40763)/643247084652261620737 8498 c8 Nov 2013 Fibonacci cofactor, ECPP
10U(37987)/(16117960073 · 94533840409 · 1202815961509) 7906 c39 Sep 2012 Fibonacci cofactor, ECPP
11U(37217)/4466041 7771 c46 Dec 2011 Fibonacci cofactor, ECPP
12U(34897)/4599458691503517435329 7272 c8 Aug 2013 Fibonacci cofactor, ECPP
13U(34807)/551750980997908879677508732866536453 7239 c8 Jul 2013 Fibonacci cofactor, ECPP
14U(34607)/13088506284255296513 7213 c8 Jul 2013 Fibonacci cofactor, ECPP
7053 c8 Apr 2013 Fibonacci cofactor, ECPP
16U(32077)/153087505413829037510511957221947361 6669 c8 May 2013 Fibonacci cofactor, ECPP
17U(30727)/2281521813578534245193 6400 c8 May 2013 Fibonacci cofactor, ECPP
18U(30671)/1141737296775689 6395 c41 Dec 2005 Fibonacci cofactor, ECPP
19U(28277)/347428330081374457 5892 c8 May 2013 Fibonacci cofactor, ECPP
20U(26591)/1929661069931436974692472737757606381 5521 c8 May 2013 Fibonacci cofactor, ECPP

(up) References

J. Brillhart, P. Montgomery and R. Silverman, "Tables of Fibonacci and Lucas factorizations," Math. Comp., 50 (1988) 251--260.  MR 89h:11002
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.]
Chris K. Caldwell © 1996-2017 (all rights reserved)