53 (number)

← 52 53 54 →
← 50 51 52 53 54 55 56 57 58 59 → List of numbers Integers ← 0 10 20 30 40 50 60 70 80 90 →
Cardinal	fifty-three
Ordinal	53rd (fifty-third)
Factorization	prime
Prime	16th
Divisors	1, 53
Greek numeral	ΝΓ´
Roman numeral	LIII, liii
Binary	1101012
Ternary	12223
Senary	1256
Octal	658
Duodecimal	4512
Hexadecimal	3516

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 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. ^[1]

The sum of the first 53 primes is 5830, which is divisible by 53, a property shared by only a few other numbers. ^{[2] [3]}

53 cannot be expressed as the sum of any integer and its decimal digits, making 53 the ninth self number in decimal. ^[4]

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}. ^[5]

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 = 173₁₆, 5141 = 1415₁₆, 99,481 = 18499₁₆, and 8,520,280 = 0820258₁₆. Aside from the trivial single digit numbers, these are the only numbers that share this property. ^[6]

References

1. Sloane, N. J. A. (ed.). "SequenceA005384(Sophie Germain primes)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-05-30.
2. Sloane, N. J. A. (ed.). "SequenceA045345(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. Sloane, N. J. A. (ed.). "SequenceA003052(Self numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-05-30.
5. Sloane, N. J. A. (ed.). "SequenceA154363(Numbers from Bhargava's prime-universality criterion theorem)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-04-22.
6. Sloane, N. J. A. (ed.). "SequenceA133377(Complete list of decimal numbers that when converted to hexadecimal produce the mirror image of the original number.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-10-23.