53 (number)

In mathematics

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, and the ninth Eisenstein prime.

The sum of the first 53 primes is 5830, which is divisible by 53, a property shared by only a few other numbers.

53 cannot be expressed as the sum of any integer and its decimal digits, making 53 the ninth self number in decimal.

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}.

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 = , 5141 = , 99,481 = , and 8,520,280 = 0. Aside from the trivial single digit numbers, these are the only numbers that share this property.

References

References

1. {{Cite OEIS. A005384. sophie germain primes
2. {{Cite OEIS
3. {{Cite OEIS
4. [http://www.primepuzzles.net/puzzles/puzz_031.htm Puzzle 31.- The Average Prime number, APN(k) = S(Pk)/k] from The Prime Puzzles & Problems Connection website
5. {{Cite OEIS
6. {{Cite OEIS. A154363. Numbers from Bhargava's prime-universality criterion theorem
7. {{Cite OEIS. A133377. Complete list of decimal numbers that when converted to hexadecimal produce the mirror image of the original number.