Hello all !
Let p = 3141592003181
Let N = Phi(6,p^20) = (p^60+1)/(p^20+1) (500 digits)
Then N = 2161.43505714401.F.C with C unfactored and :
F = 94885153006797735097780355737459994238807138067170/
35705930587000916137586283228108163045885559189521 (100 digits)
with F prime ! (proved by Titanix)
This factor F=2.k.p+1, which has no specific form (take a look at F-1 and F+1),
was found by my own special version of CarmiKiller in less than 10 minutes (no,
that's not a joke !!!).
This is a first result : others will follow...
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