CousinPrimes

The (lesser) cousin primes $3, 7, 13, 19, 37, …$: primes $p$ with $p+4$ also prime.

OEISA023200↗

CousinPrimesthe lesser prime $p$ of a cousin pair $(p, p+4)$, an indexed collection of open infinitude.

Domain: Collections

Details

• A lazy indexed collection; open infinitude (a cousin-prime analogue of the twin-prime conjecture), so $Count(CousinPrimes) = NaN$. OEIS A023200 (the lesser member).
• $At(CousinPrimes, k)$ unranks by scanning forward, testing primality of $n$ and $n+4$ -- $At(CousinPrimes, 2) = 7$.
• Membership goes through Element: $Element(7, CousinPrimes)$ is true ($7, 11$ both prime), $Element(11, CousinPrimes)$ is false ($15$ is not).
• $CousinPrimes$ is $PrimePairs(4)$ verbatim.

Enumeration

Examples

Basic #

The first 20 lesser cousin primes, OEIS A023200

live ↗

In$\mathrm{Take}(\mathrm{CousinPrimes}, 20)$Out$\bigl\lbrack3, 7, 13, 19, 37, 43, 67, 79, 97, 103, 109, 127, 163, 193, 223, 229, 277, 307, 313, 349\bigr\rbrack$

About

Examples	1
Crosswalk	OEIS

See also: Count, At, Element, TwinPrimes, SexyPrimes, PrimePairs