Fibonacci Primitive Part 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

Record Primes of this Type

rank prime digits who when comment 1 primU(131481) 15695 c77 Mar 2019 Fibonacci primitive part, ECPP 2 primU(77387) 15319 c77 Mar 2019 Fibonacci primitive part, ECPP 3 primU(67703) 13954 c77 Jul 2018 Fibonacci primitive part, ECPP 4 primU(94551) 13174 c77 Apr 2018 Fibonacci primitive part, ECPP 5 primU(62771) 12791 c77 Apr 2018 Fibonacci primitive part, ECPP 6 primU(73025) 11587 c77 Apr 2015 Fibonacci primitive part, ECPP 7 primU(67781) 11587 c77 Apr 2015 Fibonacci primitive part, ECPP 8 primU(67825) 11336 x23 Feb 2007 Fibonacci primitive part 9 primU(61733) 11058 c77 Mar 2015 Fibonacci primitive part, ECPP 10 primU(55297) 10483 c8 Sep 2014 Fibonacci primitive part, ECPP 11 primU(44113) 8916 c8 Apr 2014 Fibonacci primitive part, ECPP 12 primU(46711) 8367 c8 Oct 2013 Fibonacci primitive part, ECPP 13 primU(62373) 8173 c8 Oct 2013 Fibonacci primitive part, ECPP 14 primU(43121) 7975 c8 Aug 2013 Fibonacci primitive part, ECPP 15 primU(48965) 7012 c8 Apr 2013 Fibonacci primitive part, ECPP 16 primU(58773) 6822 c8 Apr 2013 Fibonacci primitive part, ECPP 17 primU(40295) 6737 p12 Apr 2001 Fibonacci primitive part 18 primU(43653) 6082 CH7 May 2010 Fibonacci primitive part 19 primU(70455) 6019 c8 Mar 2013 Fibonacci primitive part, ECPP 20 primU(43359) 5939 c8 Mar 2013 Fibonacci primitive part, ECPP

References

BHV2002

Bilu, Yu., Hanrot, G. and Voutier, P. M., "Existence of primitive divisors of Lucas and Lehmer numbers," J. Reine Angew. Math., 539 (2001) 75--122.  With an appendix by M. Mignotte.  MR1863855 (Annotation available)

Carmichael1913

R. D. Carmichael, "On the numerical factors of the arithmetic forms αⁿ ± βⁿ," Ann. Math., 15 (1913) 30--70.

Jarden1958

Jarden, Dov, "Supplementary remarks to the paper: Linear forms of primitive prime divisors of Fibonacci numbers," Riveon Lematematika, 12 (1958) 31--32.  MR 0101206

Voutier1995

Voutier, P. M., "Primitive divisors of Lucas and Lehmer sequences," Math. Comp., 64:210 (1995) 869--888.  MR1284673 (Annotation available)

Voutier1996

Voutier, P. M., "Primitive divisors of Lucas and Lehmer sequences. II," J. Th\'eor. Nombres Bordeaux, 8:2 (1996) 251--274.  MR1438469

Voutier1998

Voutier, P. M., "Primitive divisors of Lucas and Lehmer sequences. III," Math. Proc. Cambridge Philos. Soc., 123:3 (1998) 407--419.  MR1607969 [From the review: "The main result of this paper is that for any integer n>30 030, the nth element of any Lucas or Lehmer sequence has a primitive divisor."]