79

Number
$79$ (seventy-nine) is:


 * The $22$nd prime number.


 * The $7$th emirp after $13, 17, 31, 37, 71, 73$.


 * The $12$th permutable prime after $2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73$.


 * The $19$th lucky number:
 * $1, 3, 7, 9, 13, 15, 21, 25, 31, 33, 37, 43, 49, 51, 63, 67, 73, 75, 79, \ldots$


 * The $14$th happy number after $1, 7, 10, 13, 19, 23, 28, 31, 32, 44, 49, 68, 70$:
 * $79 \to 7^2 + 9^2 = 49 + 81 = 130 \to 1^2 + 3^2 + 0^2 = 1 + 9 + 0 = 10 \to 1^2 + 0^2 = 1$


 * The $6$th of $29$ primes of the form $2 x^2 + 29$:
 * $2 \times 5^2 + 29 = 79$


 * The smallest positive integer which cannot be expressed as the sum of fewer than $19$ fourth powers:
 * $79 = 15 \times 1^4 + 4 \times 2^4$


 * The $15$th positive integer $n$ after $5, 11, 17, 23, 29, 30, 36, 42, 48, 54, 60, 61, 67, 73$ such that no factorial of an integer can end with $n$ zeroes.

Also see

 * Smallest Number not Expressible as Sum of Fewer than 19 Fourth Powers