Английская Википедия:311 (number)

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Версия от 23:23, 25 декабря 2023; EducationBot (обсуждение | вклад) (Новая страница: «{{Английская Википедия/Панель перехода}} {{About|the numerical value|other uses|311 (disambiguation)}} {{Infobox number | number = 311 | prime = 64th | lang1 = Hebrew | lang1 symbol = <span style="font-size:150%;">שיא</span> }} '''311''' ('''three hundred [and] eleven''') is the natural number following 310 and preceding 312. 311 is the 64th prime...»)
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Шаблон:About Шаблон:Infobox number

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>3n - 1</math>; a Gaussian prime with no imaginary part and real part of the form <math>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(Шаблон:Sqrt) has class number = 19.[3]

4311 - 3311 is prime

References

Шаблон:Reflist

Шаблон:Integers