8719

This number is a prime.

Prime 8719 is the smallest prime p for which the continued fraction expansion of 1/sqrt(p) contains each of the first 13 natural numbers. The continued fraction expansion of sqrt(8719) is [93; 2, 1, 1, 1, 26, 18, 1, 1, 1, 3, 6, 1, 1, 1, 4, 7, 3, 1, 11, 1, 2, 4, 9, 1, 1, 2, 30, 1, 2, 1, 2, 3, 1, 3, 1, 2, 12, 10, 1, 9, 2, 6, 1, 2, 2, 2, 3, 1, 1, 3, 1, 1, 2, 2, 2, 13, 1, 19, 1, 4, 1, 1, 5, 1, 2, 8, 1, 1, 5, 2, 61, 1, 3, 1, 4, 8, 1, 2, 5, 1, 7, 3, 1, 1, 1, 1, 4, 1, 2, 1, 1, 1, 3, 37, 13, 3, 5, 93, 5, 3, 13, 37, 3, 1, 1, 1, 2, 1, 4, 1, 1, 1, 1, 3, 7, 1, 5, 2, 1, 8, 4, 1, 3, 1, 61, 2, 5, 1, 1, 8, 2, 1, 5, 1, 1, 4, 1, 19, 1, 13, 2, 2, 2, 1, 1, 3, 1, 1, 3, 2, 2, 2, 1, 6, 2, 9, 1, 10, 12, 2, 1, 3, 1, 3, 2, 1, 2, 1, 30, 2, 1, 1, 9, 4, 2, 1, 11, 1, 3, 7, 4, 1, 1, 1, 6, 3, 1, 1, 1, 18, 26, 1, 1, 1, 2, 186] and has period 196. Its terms contain every integer from 1 to 13, as indicated in bold. [Keith]