53 (number)
Template:Infobox number 53 (fifty-three) is the natural number following 52 and preceding 54. It is the 16th prime number.
In mathematicsEdit
Fifty-three is the 16th prime number. It is the second balanced prime, and fifth isolated prime.
53 is a sexy prime with 47 and 59. It is the eighth Sophie Germain prime, <ref>Template:Cite OEIS</ref> and the ninth Eisenstein prime.<ref>Template:Cite OEIS</ref>
The sum of the first 53 primes is 5830, which is divisible by 53, a property shared by only a few other numbers.<ref>Template:Cite OEIS</ref><ref>Puzzle 31.- The Average Prime number, APN(k) = S(Pk)/k from The Prime Puzzles & Problems Connection website</ref>
53 cannot be expressed as the sum of any integer and its decimal digits, making 53 the ninth self number in decimal.<ref>Template:Cite OEIS</ref>
53 is the smallest prime number that does not divide the order of any sporadic group, inclusive of the six pariahs; it is also the first prime number that is not a member of Bhargava's prime-universality criterion theorem (followed by the next prime number 59), an integer-matrix quadratic form that represents all prime numbers when it represents the sequence of seventeen integers {2, ..., 47, 67, 73}.<ref>Template:Cite OEIS</ref>
In hexadecimal, 53 is 35, that is, the same characters used in the decimal representation, but reversed. Four additional multiples of 53 share this property: 371 = Template:Hexadecimal, 5141 = Template:Hexadecimal, 99,481 = Template:Hexadecimal, and 8,520,280 = 0Template:Hexadecimal. Aside from the trivial single digit numbers, these are the only numbers that share this property.<ref>Template:Cite OEIS</ref>