Fibonacci prime
Known Fibonacci primes
2, 3, 5, 13, 89, 233, 1597, 28657, 514229, 433494437, 2971215073, .... It is not known whether there are infinitely many Fibonacci primes. With the indexing starting with F1 = F2 = 1, the first 34 are Fn for the n values (sequence A001605 in the OEIS):
Fibonacci prime-3