CircularPrimes

The circular primes $2, 3, 5, 7, 11, 13, 17, 31, …$: primes whose every base-10 digit rotation is also prime.

OEISA068652↗

CircularPrimesthe prime $p$ (no digit 0) with every cyclic rotation of its decimal digits also prime, an indexed collection of open infinitude.

Domain: Collections

Details

• A lazy indexed collection; conjectured but unproven that only finitely many beyond the repunit primes $R_n$ (all-1s) exist at all, and separately whether infinitely many repunit primes exist is itself open, so $Count(CircularPrimes) = NaN$. OEIS A068652. A digit-0 prime is excluded (a rotation would start with a leading zero).
• $At(CircularPrimes, k)$ unranks by scanning forward, testing every rotation's primality -- $At(CircularPrimes, 8) = 31$ ($31$ and $13$ both prime).
• Membership goes through Element: $Element(13, CircularPrimes)$ is true ($13, 31$ both prime), $Element(19, CircularPrimes)$ is false ($91 = 7 \times 13$, its only other rotation, isn't prime).

Enumeration

Examples

1 more kept as data, checked against the oracles

About

Examples	1
Crosswalk	OEIS

See also: Count, At, Element, PalindromicPrimes, EmirpPrimes