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311 (number)

From Wikipedia, the free encyclopedia
This article is about the numerical value. For other uses, see311 (disambiguation).
Natural number
← 310311 312 →
Cardinalthree hundred eleven
Ordinal311th
(three hundred eleventh)
Factorizationprime
Prime64th
Greek numeralΤΙΑ´
Roman numeralCCCXI,cccxi
Binary1001101112
Ternary1021123
Senary12356
Octal4678
Duodecimal21B12
Hexadecimal13716
Hebrewשיא

311 (three hundred [and] eleven) is thenatural number following310 and preceding312.

311 is the 64thprime; atwin prime with313; anirregular prime;[1] anemirp, anEisenstein prime with noimaginary part andreal part of the form3n1{\displaystyle 3n-1}; aGaussian prime with no imaginary part and real part of the form4n1{\displaystyle 4n-1}; and apermutable prime with113 and131.

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 integerd such that the imaginaryquadratic fieldQ(d) hasclass number = 19.[3]

4311 - 3311 is prime

References

[edit]
  1. ^"Sloane's A000928 : Irregular primes".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-02.
  2. ^"Sloane's A016038 : Strictly non-palindromic numbers".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-02.
  3. ^"Tables of imaginary quadratic fields with small class number".numbertheory.org.
0 to 199
200 to 399
400 to 999
1000s and 10,000s
1000s
10,000s
100,000s to 10,000,000,000,000s
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