311 (number)

This article is about the numerical value. For other uses, see 311 (disambiguation).
310 311 312
Cardinal three hundred eleven
Ordinal 311th
(three hundred and eleventh)
Factorization 311
Prime twin prime
Roman numeral CCCXI
Binary 1001101112
Ternary 1021123
Quaternary 103134
Quinary 22215
Senary 12356
Octal 4678
Duodecimal 21B12
Hexadecimal 13716
Vigesimal FB20
Base 36 8N36
Hebrew שיא

311 is the natural number after 310 and before 312.

In mathematics

311 is a twin prime with 313; an irregular prime;[1] 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]

Notable uses of numerical value

References

  1. "Sloane's A000928 : Irregular primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-02.
  2. "Sloane's A016038 : Strictly non-palindromic numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-02.
  3. Hate Number Symbols: 311 - From A Visual Database of Extremist Symbols, Logos and Tattoos. Anti-Defamation League. Accessed 2008-08-21. "The eleventh letter of the alphabet is the letter "K"; thus 3 times 11 equals "KKK," or Ku Klux Klan."
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