Why-the-Fermat-formula-about-prime-numbers-is-for-n-5-and-n-6-fail-f-n-2-2-n-1-

Question Number 119094 by syamil last updated on 22/Oct/20

W h y t h e F e r m a t f o r m u l a a b o u t p r i m e n u m b e r s i s f o r n = 5 a n d n = 6 f a i l ?

f (n) = 2^{2^{n}} + 1

Answered by 1549442205PVT last updated on 22/Oct/20

n = 5 \Rightarrow f (5) = 2^{32} + 1 = 641 \times 6700417

n = 6 \Rightarrow f (6) = (1071 . 2^{8} + 1) (2^{8} . 262 814 145 745 + 1)

= 274 177 \times 67 280 421 310 721