1024
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Number
$1024$ (one thousand and twenty-four) is:
- $2^{10}$
- The $1$st number with at least $10$ prime factors:
- $1024 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2$
- The $4$th fifth power after $1$, $32$, $243$:
- $1024 = 4 \times 4 \times 4 \times 4 \times 4$
- The $5$th power of $4$ after $(1)$, $4$, $16$, $64$, $256$:
- $1024 = 4^5$
- The $10$th power of $2$ after $(1)$, $2$, $4$, $8$, $16$, $32$, $64$, $128$, $256$, $512$:
- $1024 = 2^{10}$
- The $11$th almost perfect number after $1$, $2$, $4$, $8$, $16$, $32$, $64$, $128$, $256$, $512$:
- $\map {\sigma_1} {1024} = 2047 = 2 \times 1024 - 1$
- The $13$th square number after $1$, $4$, $36$, $121$, $144$, $256$, $324$, $400$, $576$, $784$, $900$, $961$ to be the divisor sum value of some (strictly) positive integer:
- $1024 = \map {\sigma_1} {651} = \map {\sigma_1} {889}$
- The $28$th positive integer which cannot be expressed as the sum of a square and a prime:
- $1$, $10$, $25$, $34$, $58$, $64$, $85$, $\ldots$, $400$, $526$, $529$, $625$, $676$, $706$, $730$, $771$, $784$, $841$, $1024$, $\ldots$
- The $32$nd square number after $1$, $4$, $9$, $16$, $25$, $36$, $\ldots$, $625$, $676$, $729$, $784$, $841$, $900$, $961$:
- $1024 = 32 \times 32$
Also see
- Previous ... Next: Fifth Power
Historical Note
While the metric scaling prefix $\mathrm k$ is generally used to denote a scale factor of $1000$, in the field of computer science it is used to mean a scale factor of $1024$.
In order to distinguish the two in case of confusion, the $1024$ multiplier can be denoted by an uppercase $\mathrm K$.
Thus $1 \, \mathrm K$ of memory conventionally means $1024$ bytes.
It is of course purely coincidental that $2^{10}$ is very close in value to $10^3$.
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $1024$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $1024$