A tetradic (or four-way) number is a number that remains unchanged when flipped back to front, mirrored up-down, or flipped up-down. Since the only numbers that remain unchanged which turned up-side-down or mirrored are 0, 1, and 8 (here, the numerals 1 and 8 are assumed to be written as a single stroke and symmetrical pair of loops, respectively), a tetradic number is precisely a palindromic number containing only 0, 1, and 8 as digits. The first few are therefore 1, 8, 11, 88, 101, 111, 181, 808, 818, ... (OEIS A006072).

The first few tetradic primes are 11, 101, 181, 18181, 1008001, 1180811, 1880881, 1881881, ... (OEIS A068188). The largest known tetradic prime as of Apr. 2010 is

where  is a repunit (https://primes.utm.edu/top20/page.php?id=53#records), which has  decimal digits.

REFERENCES:

Sloane, N. J. A. Sequences A006072/M4481 and A068188 in "The On-Line Encyclopedia of Integer Sequences."