311 (number)

From Wikipedia, the free encyclopedia
Jump to navigation Jump to search
← 310 311 312 →
Cardinalthree hundred eleven
Ordinal311th
(three hundred eleventh)
Factorizationprime
Primetwin prime
Greek numeralΤΙΑ´
Roman numeralCCCXI
Binary1001101112
Ternary1021123
Quaternary103134
Quinary22215
Senary12356
Octal4678
Duodecimal21B12
Hexadecimal13716
VigesimalFB20
Base 368N36
Hebrewשיא

311 (three hundred [and] eleven) is the natural number following 310 and preceding 312.

In mathematics[edit]

311 is the 64th prime; 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]

311 is the smallest positive integer d such that the imaginary quadratic field Q(d) has class number = 19.[3]

Notable uses of numerical value[edit]

  • 311 is used in the name of a gang in Las Vegas, known as the 311 Boyz.
  • 311 was formerly the Los Angeles Police Code for an armed robbery. This is sometimes referenced in Hip-Hop/Rap music and films.
  • 3-1-1 is a special phone number used in many large cities such as New York City, Chicago, Houston, and Los Angeles that provides access to non-emergency municipal services.
  • 311 is the name of an American alternative rock band.
  • As "311" or "3/11", typically pronounced "three-eleven" by analogy with "9/11", it is commonly used to refer the calendar dates November 3 or March 11, depending on which date notation is used. The latter usage may refer to the March 11, 2011, Tōhoku earthquake and tsunami in Japan or the March 11, 2004, Madrid train bombings.
  • According to the Anti-Defamation League, 311 is a hate symbol used by some Ku Klux Klan members, referring to three repetitions of the eleventh letter of the Latin alphabet ("K").[4]

References[edit]

  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. ^ "Tables of imaginary quadratic fields with small class number". numbertheory.org.
  4. ^ Hate Number Symbols: 311 - From A Visual Database of Extremist Symbols, Logos and Tattoos Archived 2007-09-26 at the Wayback Machine. 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."