# 79

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## Number

$79$ (seventy-nine) is:

The $22$nd prime number.

The $1$st 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 $6$th of $29$ primes of the form $2 x^2 + 29$:
$2 \times 5^2 + 29 = 79$ (Previous  ... Next)

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 $13$th prime $p$ after $11$, $23$, $29$, $37$, $41$, $43$, $47$, $53$, $59$, $67$, $71$, $73$ such that the Mersenne number $2^p - 1$ is composite

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 $15$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

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 $30$th of $35$ integers less than $91$ to which $91$ itself is a Fermat pseudoprime:
$3$, $4$, $9$, $10$, $12$, $16$, $17$, $22$, $23$, $25$, $27$, $29$, $30$, $36$, $38$, $40$, $43$, $48$, $51$, $53$, $55$, $61$, $62$, $64$, $66$, $68$, $69$, $74$, $75$, $79$, $\ldots$