# [seqfan] Primes in fibonnaci progression (was: Where are the

Olivier Gerard ogerard at ext.jussieu.fr
Tue May 12 19:21:10 CEST 1998

```At 18:17 +0200 98.05.12, David W. Wilson wrote:
> > I have found an AP of 12 primes with difference 2310 (the least
> > possible for a prime AP of length 12), and the least possible
> > starting value, which is 147692845283.
> >
> > Would some math-funster please verify that this number
> > indeed begins an AP of primes of length 12 and difference 2310?
> >
Well I am no math-funster but I did. (with Mma 3.0 and also with a personal
C code)

>
>The first AP of 13 primes with difference 30030 starts at 14933623
> (confirmation?).
yes ! (same method)

What about primes in Fibonacci progression ?

p
q
p+q+1
p+2q+2
2p+3q+4
3p+5q+7
5p+8q+12
..
F[n] p + F[n+1] q + F[n+2]-1

are primes.
An example with length 2+5 is {29,83}
29, 83, 113, 197, 311, 509, 821  (next term 1331 is composed)

and an example with length 2+6 is {89,359}
89, 359, 449, 809, 1259, 2069, 3329, 5399

I am sure there is much longer.

Olivier

(David: edit and forward to math-fun if appropriate)

```