311 (number)

Short description: Natural number

| <- 310  | 311 |  312 ->

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List of numbers — Integers

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Cardinal| three hundred eleven
Ordinal| 311th
(three hundred eleventh)
Factorization| prime
Prime| 64th
Greek numeral| ΤΙΑ´
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 (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 [math]\displaystyle{ 3n - 1 }[/math]; a Gaussian prime with no imaginary part and real part of the form [math]\displaystyle{ 4n - 1 }[/math]; 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

## References

1. ↑ "Sloane's A000928 : Irregular primes". OEIS Foundation. https://oeis.org/A000928.
2. ↑ "Sloane's A016038 : Strictly non-palindromic numbers". OEIS Foundation. https://oeis.org/A016038.
3. ↑ "Tables of imaginary quadratic fields with small class number". http://www.numbertheory.org/classnos/.

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