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53 (number)

← 52 53 54 →
Cardinalfifty-three
Ordinal53rd
(fifty-third)
Factorizationprime
Prime16th
Divisors1, 53
Greek numeralΝΓ´
Roman numeralLIII
Binary1101012
Ternary12223
Quaternary3114
Quinary2035
Senary1256
Octal658
Duodecimal4512
Hexadecimal3516
Vigesimal2D20
Base 361H36

53 (fifty-three) is the natural number following 52 and preceding 54. It is the 16th prime number.

In mathematics

  • Fifty-three is the 16th prime number. It is also an Eisenstein prime, and a Sophie Germain prime.[1]
  • The sum of the first 53 primes is 5830, which is divisible by 53, a property shared by few other numbers.[2][3]
  • 53 written in hexadecimal is 35, that is, the same characters used in the decimal representation, but reversed. Four additional multiples of 53 share this property: 371 = 17316, 5141 = 141516, 99481 = 1849916, and 8520280 = 082025816. Apart from the trivial case of single-digit decimals, no other number has this property.[4]
  • 53 cannot be expressed as the sum of any integer and its base-10 digits, making 53 a self number.[5]
  • 53 is the smallest prime number that does not divide the order of any sporadic group.

In science

Astronomy

In other fields

Fifty-three is:

A fan-built Herbie

Sports

References

  1. ^ Sloane, N.J.A. (ed.). "Sequence A005384 (Sophie Germain primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
  2. ^ Sloane, N.J.A. (ed.). "Sequence A045345 (Numbers n such that n divides sum of first n primes A007504(n).)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  3. ^ Puzzle 31.- The Average Prime number, APN(k) = S(Pk)/k from The Prime Puzzles & Problems Connection website
  4. ^ "elementary number theory - Decimal/hex palindromes: why multiples of 53?". Mathematics Stack Exchange. June 16, 2015. Retrieved 29 September 2018.
  5. ^ Sloane, N.J.A. (ed.). "Sequence A003052 (Self numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
  6. ^ [www.rosaryworkshop.com]