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Is there an even numbers between every pair of consecutive odd numbers?
yes
Why can there never be a pair of consecutive prime numbers that are both prime?
If you mean consecutive numbers that are prime? than the answer is 2,3 are consecutive numbers which are prime. except for this pair it is impossible for consecutive numbers to be prime because every second number is multiple of 2
Why is 2 and 3 the only consecutive prime numbers?
Because every other set of primes has at least one even number between them.
What is the number of non-square numbers between 2 consecutive numbers?
There is no such thing as consecutive numbers because numbers are infinitely dense. Between any two numbers there is another and so there is no such thing as a "next" number.There are no integers (square or non-square) between any two consecutive integers. There are infinitely many numbers between any two consecutive integers and, if the integers are non-negative, every one of these will be a square of some number so the answer is none. If the integers are negative then the infinitely many numbers will have a square root in the complex field but not in real numbers. In this case the answer is either none or infinitely many, depending on the domain.
Other than two and three can two consecutive whole number be prime numbers explain why or why not?
No. Every other pair has at least one even number between them.
