Fibonacci Primitive Part

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The Prime Pages

GIMPS has discovered a new largest known prime number: 2^82589933-1 (24,862,048 digits)

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

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Record Primes of this Type

rank prime digits who when comment

1 primU(77387) 15319 c77 Mar 2019 Fibonacci primitive part, ECPP
2 primU(67703) 13954 c77 Jul 2018 Fibonacci primitive part, ECPP
3 primU(94551) 13174 c77 Apr 2018 Fibonacci primitive part, ECPP
4 primU(62771) 12791 c77 Apr 2018 Fibonacci primitive part, ECPP
5 primU(73025) 11587 c77 Apr 2015 Fibonacci primitive part, ECPP
6 primU(67781) 11587 c77 Apr 2015 Fibonacci primitive part, ECPP
7 primU(67825) 11336 x23 Feb 2007 Fibonacci primitive part
8 primU(61733) 11058 c77 Mar 2015 Fibonacci primitive part, ECPP
9 primU(55297) 10483 c8 Sep 2014 Fibonacci primitive part, ECPP
10 primU(44113) 8916 c8 Apr 2014 Fibonacci primitive part, ECPP
11 primU(46711) 8367 c8 Oct 2013 Fibonacci primitive part, ECPP
12 primU(62373) 8173 c8 Oct 2013 Fibonacci primitive part, ECPP
13 primU(43121) 7975 c8 Aug 2013 Fibonacci primitive part, ECPP
14 primU(48965) 7012 c8 Apr 2013 Fibonacci primitive part, ECPP
15 primU(58773) 6822 c8 Apr 2013 Fibonacci primitive part, ECPP
16 primU(40295) 6737 p12 Apr 2001 Fibonacci primitive part
17 primU(43653) 6082 CH7 May 2010 Fibonacci primitive part
18 primU(70455) 6019 c8 Mar 2013 Fibonacci primitive part, ECPP
19 primU(43359) 5939 c8 Mar 2013 Fibonacci primitive part, ECPP
20 primU(28667) 5914 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 [From the review: "This remarkable paper answers completely a one century old problem, by proving that, for any integer n>30, the n-th element of any Lucas or Lehmer sequence has a primitive divisor."]
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."]