1027

Number
$1027$ (one thousand and twenty-seven) is:
 * $13 \times 79$


 * The $8$th after $4$, $13$, $38$, $87$, $208$, $377$, $666$ in the sequence formed by adding the squares of the first $n$ primes:
 * $1027 = \ds \sum_{i \mathop = 1}^8 {p_i}^2 = 2^2 + 3^2 + 5^2 + 7^2 + 11^2 + 13^2 + 17^2 + 19^2$


 * The $19$th centered hexagonal number after $1$, $7$, $19$, $37$, $61$, $91$, $127$, $169$, $217$, $271$, $331$, $397$, $469$, $547$, $631$, $721$, $817$, $919$:
 * $1027 = \ds 1 + \sum_{k \mathop = 1}^{19 - 1} 6 k = 19^3 - 18^3$


 * The $26$th second pentagonal number after $2$, $7$, $15$, $26$, $\ldots$, $610$, $672$, $737$, $805$, $876$, $950$:
 * $1027 = \dfrac {26 \paren {3 \times 26 + 1} } 2$


 * The $52$nd generalized pentagonal number after $1$, $2$, $5$, $7$, $12$, $15$, $\ldots$, $610$, $651$, $672$, $715$, $737$, $782$, $805$, $852$, $876$, $925$, $950$, $1001$:
 * $1027 = \dfrac {26 \paren {3 \times 26 + 1} } 2$