SafePrimes

The safe primes $5, 7, 11, 23, 47, …$ : primes $q$ with $(q-1)/2$ also prime.

SafePrimesthe prime

q

with

(q-1)/2

also prime, an indexed collection of open infinitude.

Domain: Collections

Details

A lazy indexed collection, and the mirror image of SophieGermainPrimes ( $q$ is safe iff $(q-1)/2$ is Sophie Germain); infinitude is equally open, so $Count(SafePrimes) = NaN$ . OEIS A005385.
$At(SafePrimes, k)$ unranks by scanning forward, testing primality of $n$ and $(n-1)/2$ -- $At(SafePrimes, 1) = 5$ ( $2$ is prime).
Membership goes through Element: $Element(23, SafePrimes)$ is true ( $11$ is prime), $Element(13, SafePrimes)$ is false ( $6$ is not prime).

Enumeration

1 more kept as data, checked against the oracles

About

Examples	1
Crosswalk	OEIS