Fibonacci Primitive Part

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.

Definitions and Notes

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Record Primes of this Type

rank prime digits who when comment

1 primU(183537) 25571 E1 Oct 2024 Fibonacci primitive part, ECPP
2 primU(118319) 24553 E1 Oct 2024 Fibonacci primitive part, ECPP
3 primU(115373) 23875 E1 Oct 2024 Fibonacci primitive part, ECPP
4 primU(135421) 23725 E1 Oct 2024 Fibonacci primitive part, ECPP
5 primU(164185) 23524 E1 Oct 2024 Fibonacci primitive part, ECPP
6 primU(166737) 23231 E1 Oct 2024 Fibonacci primitive part, ECPP
7 primU(102689) 20715 E1 Sep 2024 Fibonacci primitive part, ECPP
8 primU(105821) 20598 E1 Sep 2022 Fibonacci primitive part, ECPP
9 primU(172179) 20540 E1 Sep 2022 Fibonacci primitive part, ECPP
10 primU(137439) 19148 E1 Jun 2022 Fibonacci primitive part, ECPP
11 primU(107779) 18980 E1 May 2022 Fibonacci primitive part, ECPP
12 primU(131481) 15695 c77 Mar 2019 Fibonacci primitive part, ECPP
13 primU(77387) 15319 c77 Mar 2019 Fibonacci primitive part, ECPP
14 primU(67703) 13954 c77 Jul 2018 Fibonacci primitive part, ECPP
15 primU(94551) 13174 c77 Apr 2018 Fibonacci primitive part, ECPP
16 primU(62771) 12791 c77 Apr 2018 Fibonacci primitive part, ECPP
17 primU(73025) 11587 c77 Apr 2015 Fibonacci primitive part, ECPP
18 primU(67781) 11587 c77 Apr 2015 Fibonacci primitive part, ECPP
19 primU(67825) 11336 x23 Feb 2007 Fibonacci primitive part
20 primU(61733) 11058 c77 Mar 2015 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."]