Strobogrammatic
Turn it upside down — same number.
A number that looks identical rotated 180°: 0, 1 and 8 stay put while 6 and 9 mirror each other, like 69, 619 or 8008.
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Strobogrammatic rarity comes from a double lock: every digit must come from the five symbols 0, 1, 6, 8, 9, and positions are pairwise bound — the first digit determines the last, the second the second-to-last. Six-digit strobogrammatic numbers number just 4×5×5 = 100; the whole range holds 199, about 0.02%, roughly one roll in 5,025 — the rarest feature in the symmetry family.
The most famous strobogrammatic number is the year 1961 — flip the calendar and it still reads 1961. The previous such year was 1881, the next is 6009, over four thousand years away. Anyone who lives through even one strobogrammatic year is lucky; two is the lifetime maximum.
Among single digits only 0, 1 and 8 qualify: 6 and 9 alone rotate into each other, which does not count. The old calculator trick of spelling words upside down (5318008 and friends) plays with the same set of rotationally meaningful symbols — except it maps digits to letters, while strobogrammatic demands they map back to digits.