263 (number)
| ||||
|---|---|---|---|---|
| Cardinal | two hundred sixty-three | |||
| Ordinal | 263rd (two hundred sixty-third) | |||
| Factorization | prime | |||
| Prime | 56th | |||
| Greek numeral | ΣΞΓ´ | |||
| Roman numeral | CCLXIII, cclxiii | |||
| Binary | 1000001112 | |||
| Ternary | 1002023 | |||
| Senary | 11156 | |||
| Octal | 4078 | |||
| Duodecimal | 19B12 | |||
| Hexadecimal | 10716 | |||
263 (two hundred [and] sixty-three) is the natural number between 262 and 264. It is also a honaker prime number.
In mathematics
[edit]263 is the smallest prime number in base 10 whose expansion in any smaller base is never prime when interpreted in base 10:[1]
| Base | Expansion of 263 | Factorisation of expansion in base 10 |
|---|---|---|
| 2 | 1000001112 | 467 × 214133 |
| 3 | 1002023 | 2 × 50101 |
| 4 | 100134 | 17 × 19 × 31 |
| 5 | 20235 | 7 × 17 × 17 |
| 6 | 11156 | 5 × 223 |
| 7 | 5247 | 2 × 2 × 131 |
| 8 | 4078 | 11 × 37 |
| 9 | 3229 | 2 × 7 × 23 |
It is also:
- a balanced prime,[2]
- an irregular prime,[3]
- a Ramanujan prime,[4]
- a Chen prime,[5] and
- a safe prime.[6]
It is also a strictly non-palindromic number and a happy number.[7]
References
[edit]- ^ Sloane, N. J. A. (ed.). "Sequence A052033 (Primes base 10 that are never primes in any smaller base b, 2<=b<10, expansions interpreted as decimal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A006562 (Balanced primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000928 (Irregular primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A104272 (Ramanujan primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A109611 (Chen primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A005385 (Safe primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "Sloane's A007770 : Happy numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-04-21.
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