| ||||
|---|---|---|---|---|
| Cardinal | three hundred eleven | |||
| Ordinal | 311th (three hundred eleventh) | |||
| Factorization | prime | |||
| Prime | 64th | |||
| Greek numeral | ΤΙΑ´ | |||
| Roman numeral | CCCXI | |||
| Binary | 1001101112 | |||
| Ternary | 1021123 | |||
| Senary | 12356 | |||
| Octal | 4678 | |||
| Duodecimal | 21B12 | |||
| Hexadecimal | 13716 | |||
| Hebrew | שיא | |||
311 (three hundred [and] eleven) is the natural number following 310 and preceding 312.
311 is the 64th prime; a twin prime with 313; an irregular prime;[1] an emirp, an Eisenstein prime with no imaginary part and real part of the form ; a Gaussian prime with no imaginary part and real part of the form ; and a permutable prime with 113 and 131.
It can be expressed as a sum of consecutive primes in four different ways: as a sum of three consecutive primes (101 + 103 + 107), as a sum of five consecutive primes (53 + 59 + 61 + 67 + 71), as a sum of seven consecutive primes (31 + 37 + 41 + 43 + 47 + 53 + 59), and as a sum of eleven consecutive primes (11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47).
311 is a strictly non-palindromic number, as it is not palindromic in any base between base 2 and base 309.[2]
311 is the smallest positive integer d such that the imaginary quadratic field Q(√–d) has class number = 19.[3]
References
[edit]- ^ "Sloane's A000928 : Irregular primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-02.
- ^ "Sloane's A016038 : Strictly non-palindromic numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-02.
- ^ "Tables of imaginary quadratic fields with small class number". numbertheory.org.
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