EmirpPrimes

The emirps $13, 17, 31, 37, 71, …$: primes whose decimal reversal is a DIFFERENT prime ('prime' spelled backwards).

OEISA006567↗

EmirpPrimesthe prime $p$ with $\mathrm{reverse}(p) \ne p$ also prime, an indexed collection of open infinitude.

Domain: Collections

Details

• A lazy indexed collection; infinitude is conjectured but unproven, so $Count(EmirpPrimes) = NaN$. OEIS A006567. Excludes palindromic primes ($\mathrm{reverse}(p)=p$ is disqualified, even though $p$ is trivially 'prime both ways').
• $At(EmirpPrimes, k)$ unranks by scanning forward, testing primality of $n$ and its reversal -- $At(EmirpPrimes, 1) = 13$ ($31$ is prime, and $31 \ne 13$).
• Membership goes through Element: $Element(13, EmirpPrimes)$ is true, $Element(11, EmirpPrimes)$ is false (reversal is itself, a palindrome).

Enumeration

Examples

1 more kept as data, checked against the oracles

About

Examples	1
Crosswalk	OEIS

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