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53 (number)
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| 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.
In mathematics
[edit]53 is a balanced prime, an isolated prime, the eighth Sophie Germain prime,[1] and the ninth Eisenstein prime.[2] It is a sexy prime with 47 and 59.
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}.[3]
53 is the smallest prime number with primitive roots 2, 3, and 5.[4]
References
[edit]- ^ Sloane, N. J. A. (ed.). "Sequence A005384 (sophie germain primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A005384 (Sophie Germain primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
- ^ Sloane, N. J. A. (ed.). "Sequence A154363 (Numbers from Bhargava's prime-universality criterion theorem)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-04-22.
- ^ Sloane, N. J. A. (ed.). "Sequence A213052 (Increasing sequence of primes p such that all of 2,3,5,...,prime(n) are primitive roots mod p)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2026-05-28.
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