311 (number)

{{About|the numerical value|other uses|311 (disambiguation)}}

{{Infobox number

| number = 311

| prime = 64th

| lang1 = Hebrew

| lang1 symbol = 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;{{cite web|title=Sloane's A000928 : Irregular primes|url=https://oeis.org/A000928|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-02}} an emirp, an Eisenstein prime with no imaginary part and real part of the form 3n - 1; a Gaussian prime with no imaginary part and real part of the form 4n - 1; 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.{{cite web|title=Sloane's A016038 : Strictly non-palindromic numbers|url=https://oeis.org/A016038|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-02}}

311 is the smallest positive integer d such that the imaginary quadratic field Q({{sqrt|–d}}) has class number = 19.{{cite web|title=Tables of imaginary quadratic fields with small class number|website=numbertheory.org|url=http://www.numbertheory.org/classnos/}}

4311 - 3311 is prime

References

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{{Integers|3}}

Category:Integers