number.wiki
Term

Circular Prime

Primes that stay prime under every cyclic rotation of their digits (197 → 971 → 719; 1193, 3779, 11939, …).

43 numbers tagged.

A circular prime remains prime through every cyclic rotation of its digits. 197 is one: rotating gives 971 and 719, both prime. The circular primes (counting each cycle once by its smallest member) include 2, 3, 5, 7, 11, 13, 17, 37, 79, 113, 197, 199, 337, and the repunit-based giants R₁₉ and R₂₃.

Any circular prime with two or more digits can only use the digits 1, 3, 7, and 9 — because a 0, 2, 4, 5, 6, or 8 would eventually rotate into the last place and make a rotation divisible by 2 or 5. It's conjectured that beyond a point all circular primes are repunits (numbers like 11, 1111111111111111111), but this is unproven.

← all tags