What is the smallest positive integer $n$ such that $$\phi_{21209}(n)=\frac{(n^{21209}-1)(n-1)}{(n^{127}-1)(n^{167}-1)}$$ is a prime number ?
I chose the $21209$ th cyclotomic polynomial because the smallest possible prime factor is $$2\ 290\ 573$$ and because of this , I expected to find a prime relatively early.
However, I did not find a prime for $n\le 6\ 500$. If there actually is no prime upto this $n$, a prime of this form must have more than $79\ 000$ digits.
Can anyone doublecheck the range, find a prime or give a reference in the case someone has done this already ?