prime numbers are irrational.
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Prime numbers are by definition integers with certain special properties. An irrational number is not an integer, and so cannot be a prime number. ... The definition of an irrational number is a real number which cannot be written as a fraction ab where a and b are integers.
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All prime numbers are natural numbers. All natural numbers are rational numbers, and are therefore not irrational numbers. Therefore, no prime numbers are irrational.
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