FibonacciPrimes

The Fibonacci primes $2, 3, 5, 13, 89, 233, …$ : Fibonacci numbers that are themselves prime.

FibonacciPrimesthe Fibonacci number

F(n)

that is prime, an indexed collection of open infinitude -- only finitely many are known at any time.

Domain: Collections

Details

A lazy indexed collection; whether there are infinitely many is open, so $Count(FibonacciPrimes) = NaN$ . OEIS A005478.
$At(FibonacciPrimes, k)$ unranks from a table of Fibonacci indices verified prime by exact bigint primality testing, not a search -- past the point a term exceeds what a numeric collection element can represent exactly ( $2^{53}-1$ ), $At$ answers $NaN$ rather than hang: $At(FibonacciPrimes, 4) = 13$ ( $F(7)$ ), $At(FibonacciPrimes, 12)$ is $NaN$ .
Membership goes through Element: $Element(89, FibonacciPrimes)$ is true ( $F(11)$ , prime), $Element(21, FibonacciPrimes)$ is false ( $F(8)=21=3\times7$ ).

Enumeration

1 more kept as data, checked against the oracles

About

Examples	1
Crosswalk	OEIS