311 (number)

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← 310 311 312 →
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]

4311 - 3311 is prime

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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. ↑ "Tables of imaginary quadratic fields with small class number". numbertheory.org.
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