Repeat the string 1808010808 1560 times, and tack on a 1 the end:

The resulting 15601-digit number is prime, and because it’s a palindrome made up of the digits 1, 8, and 0, it remains prime when read backward, upside down, or in a mirror.

Unrelated mirror curiosity: Outline the reflection of your head on the glass of a mirror, then back away. At any distance, the image continues to fill the outline (which is half the size of your head).