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The prime counting function is the function giving the number of primes less than or equal to a given number (Shanks 1993, p. 15). For example, there are no primes , so . There is a single prime (2) , so . There are two primes (2 and 3) , so . And so on.

The notation for the prime counting function is slightly unfortunate because it has nothing whatsoever to do with the constant . This notation was introduced by number theorist Edmund Landau in 1909 and has now become standard. In the words of Derbyshire (2004, p. 38), "I am sorry about this; it's not my fault. You'll just have to put up with it."

Q: Is counting number a prime number?

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The is no last prime number - unless you are counting down, in which case, it is 2.

1

The number 1.

Take any counting number greater than one. 2, 3, 4, 5 and so on. Double it. Between the number and twice the number, there will be at least one prime number. 3, a prime number, is in between 2 and 4.

Yes. All prime numbers and composite numbers are positive integers, or whole counting numbers. That leaves infinitely many numbers that are neither prime nor composite. If you intended to narrow the scope of your question to the whole counting numbers or to the positive integers, then there are NO such numbers that are neither. A counting number, however large, will be either prime or composite.

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1 is the counting number that is neither a prime number nor a composite number.

ANSWER: 1 is the only counting number that is not prime nor composite.

None, everything is either prime or composite.

The is no last prime number - unless you are counting down, in which case, it is 2.

1.

The number 1.

1

The number 1.

No. In fact, every number counting by 90, including 90 itself, is composite.

A composite number.

It is just an integer/real/counting number.

That's a prime number.