Integers are whole numbers, therefore they are not irrational
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No. Prime numbers are positive integers, and integers are not irrational.
They can be integers, rational numbers or even approximations for irrational numbers.
Any of the numbers which cannot be expressed as a ratio of two integers is irrational.
Because that is the definition of irrational numbers: They are the numbers that cannot be written as a ratio of two integers! A fraction is a ratio of two integers.
A number that cannot be expressed as a quotient of two integers is called an irrational number. Some common irrational numbers are pi (3.14159....) and the square root of two.