# 2701

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## Number

$2701$ (two thousand, seven hundred and one) is:

$37 \times 73$

The $10$th Poulet number after $341$, $561$, $645$, $1105$, $1387$, $1729$, $1905$, $2047$, $2465$:
$2^{2701} \equiv 2 \pmod {2701}$: $2701 = 37 \times 73$

The $13$th Fermat pseudoprime to base $3$ after $91$, $121$, $286$, $671$, $703$, $949$, $1105$, $1541$, $1729$, $1891$, $2465$, $2665$:
$3^{2701} \equiv 3 \pmod {2701}$

The $37$th hexagonal number after $1$, $6$, $15$, $28$, $45$, $66$, $91$, $\ldots$, $1431$, $1540$, $1653$, $1770$, $1891$, $2016$, $2145$, $2278$, $2415$, $2556$:
$2701 = \ds \sum_{k \mathop = 1}^{37} \paren {4 k - 3} = 37 \paren {2 \times 37 - 1}$

The $73$rd triangular number after $1$, $3$, $6$, $10$, $15$, $\ldots$, $2211$, $2278$, $2346$, $2415$, $2485$, $2556$, $2628$:
$2701 = \ds \sum_{k \mathop = 1}^{73} k = \dfrac {73 \times \paren {73 + 1} } 2$

Hence $2701 = 37 \times 73$ is both the $37$th hexagonal number, and the $73$rd triangular number.