SophieGermainPrimes

The Sophie Germain primes $2, 3, 5, 11, 23, …$: primes $p$ with $2p+1$ also prime.

OEISA005384↗

SophieGermainPrimesthe prime $p$ with $2p+1$ also prime, an indexed collection of open infinitude.

Domain: Collections

Details

• A lazy indexed collection; whether there are infinitely many is open, so $Count(SophieGermainPrimes) = NaN$. OEIS A005384.
• $At(SophieGermainPrimes, k)$ unranks by scanning forward, testing primality of $n$ and $2n+1$ -- $At(SophieGermainPrimes, 4) = 11$ ($23$ is prime).
• Membership goes through Element: $Element(11, SophieGermainPrimes)$ is true, $Element(7, SophieGermainPrimes)$ is false ($15$ is not prime).

Enumeration

Examples

1 more kept as data, checked against the oracles

About

Examples	1
Crosswalk	OEIS

See also: Count, At, Element, SafePrimes, PrimeNumbers