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512 is the natural number following 511 and preceding 513.
512 is a power of two: 29 (2 to the 9th power) and the cube of 8: 83.
Also, it is the eleventh Leyland number.
Special use in computers 
512 bytes is a common sector size and exactly a half of kibibyte.
Internet Relay Chat restricts the size of a message to 510 bytes, which fits to 512-bytes buffer together with message separating CRLF sequence.
512 = 2·256 is the highest number of glyphs, which VGA character generator can use simultaneously.
Most CT scans are 512x512 resolution.