Gaussian primes and Lucas numbers Let $L_{n}$ be the $n$ th Lucas number. For example, $L_{1} = 1, L_{2} = 3, L_{3} = 4$.
Conjecture: there is no Gaussian primes in the sequence $(L_{n-1} + L_{n} i)$ for $n = 2$ to $\infty$.
I hope that this will be proved or disproved.

$L_{n-1}+L_n i= (2+i)(F_n+F_{n-1}i)$.
