Pierre CAMI wrote:

> I found that n^14-n^7+1 is never prime

n^14-n^7+1 = (n^2-n+1)*(n^12+n^11-n^9-n^8+n^6-n^4-n^3+n+1)

> When using pfgw -q729^^14-729^^7+1 I have the answer it is PRP

> but pfgw -t -q729^^14-729^^7+1 give the answer composite with the

> factor found ! What is the bug for PRP answer ?

729^14-729^7+1 is indeed 3-PRP. Note that 729 = 3^6.

Some number forms involving powers of b are b-PRP.

Base 3 is default in pfgw. Here is base 2:

C:\Users\Jens>pfgw -b2 -q729^^14-729^^7+1

PFGW Version 1.2.0 for Windows [FFT v23.8]

Switching to Exponentiating using GMP

729^14-729^7+1 is composite: [D66D28B9C614392] (0.0004s+0.0003s)

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Jens Kruse Andersen