**Quote:**

I know that *x*, *x* + 1, *x* + 2 are consecutive, but are *x*, *x* + 2, *x* + 4 consecutive as well by definition?

The term "consecutive" depends on the set of numbers we are considering. If nothing else is specified then it defines consecutive integers.

Three consecutive integers will be

*x*,

*x* + 1,

*x* + 2, where

*x* is an integer.

In many cases the set of numbers we are considering is specified.

For example "consecutive even integers" defines that we are considering consecutive numbers in the set of (among) even integers.

{..., -4, -2, 0, 2, 4, 6, 8, ...}

Three consecutive

**even** integers will be

*x*,

*x* + 2,

*x* + 4, where

*x* is an even integer.

"Consecutive prime numbers" defines that we are considering consecutive numbers in the set of (among) prime numbers.

{2, 3, 5, 7, 11, 13, ...}

Three consecutive prime numbers are 2, 3, 5; or 5, 7, 11 etc.

There can be many other specific sets with term consecutive: "consecutive multiples of 5", "consecutive months", etc.