# Fibonacci cofactor

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 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.

### Record Primes of this Type

rankprime digitswhowhencomment
1U(66947)/12485272838388758877279873712131648167413 13951 c77 Apr 2017 Fibonacci cofactor, ECPP
2U(59369)/244242366914846603945\
83037561699885688092693836440759407570209763004757
12337 c79 Apr 2015 Fibonacci cofactor, ECPP
3U(54799)/4661437953906084533621577211561 11422 c8 Jan 2015 Fibonacci cofactor, ECPP
4U(54521)/6403194135342743624071073 11370 c8 Jan 2015 Fibonacci cofactor, ECPP
5U(53189)/69431662887136064191105625570683133711989 11075 c8 Dec 2014 Fibonacci cofactor, ECPP
6U(51031)/95846689435051369 10648 c8 Sep 2014 Fibonacci cofactor, ECPP
7U(43399)/4704006095\
75881344601538056264109423291827366228494341196421
9010 c8 Sep 2013 Fibonacci cofactor, ECPP
8U(42829)/107130175995197969243646842778153077 8916 c8 Apr 2014 Fibonacci cofactor, ECPP
9U(42043)/1681721 8780 c56 Feb 2012 Fibonacci cofactor, ECPP
10U(40763)/643247084652261620737 8498 c8 Nov 2013 Fibonacci cofactor, ECPP
11U(37987)/(16117960073 · 94533840409 · 1202815961509) 7906 c39 Sep 2012 Fibonacci cofactor, ECPP
12U(37217)/4466041 7771 c46 Dec 2011 Fibonacci cofactor, ECPP
13U(34897)/4599458691503517435329 7272 c8 Aug 2013 Fibonacci cofactor, ECPP
14U(34807)/551750980997908879677508732866536453 7239 c8 Jul 2013 Fibonacci cofactor, ECPP
15U(34607)/13088506284255296513 7213 c8 Jul 2013 Fibonacci cofactor, ECPP
16U(33997)/81\
19544695419968014626314520991088099382355441843013
7053 c8 Apr 2013 Fibonacci cofactor, ECPP
17U(32077)/153087505413829037510511957221947361 6669 c8 May 2013 Fibonacci cofactor, ECPP
18U(30727)/2281521813578534245193 6400 c8 May 2013 Fibonacci cofactor, ECPP
19U(30671)/1141737296775689 6395 c41 Dec 2005 Fibonacci cofactor, ECPP
20U(28277)/347428330081374457 5892 c8 May 2013 Fibonacci 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.]