1089

Number

$1089$ (one thousand and eighty-nine) is:

$3^2 \times 11^2$

The $1$st number which is reversed when multiplied by $9$:

$1089 \times 9 = 9801$

The $1$st of only $2$ numbers with $4$ digits or fewer which has a multiple which is its reversal:

$1089 \times 9 = 9801$

The $29$th positive integer which cannot be expressed as the sum of a square and a prime:

$1$, $10$, $25$, $34$, $58$, $64$, $85$, $\ldots$, $400$, $526$, $529$, $625$, $676$, $706$, $730$, $771$, $784$, $841$, $1024$, $1089$, $\ldots$

The $33$rd square number after $1$, $4$, $9$, $16$, $25$, $36$, $\ldots$, $625$, $676$, $729$, $784$, $841$, $900$, $961$, $1024$:

$1089 = 33 \times 33$

Take a $3$-digit number, reverse it and subtract the smaller from the larger, reverse that and add it to itself, and you end up with $1089$.

The only square of a $2$-digit number which has this property:

$33^2 = 65^2 - 56^2$