Unfortunately, there is no evidence of someone called "Keaghan" (or something similar) who proposed a Prime number theory. I suggest you check your spelling and resubmit the question.
To prove that 61 is a prime number.
540 + 219 = 759 759 is evenly divisible by 3, 11, and 23, so it is not a prime number.
Because 3 is a prime number and as such its square root is irrational
By performing experiments whose goal is to prove that such theory is a mistaken theory.
57 = 3 x 19 111 = 3 x 37 Thus they are not prime numbers
prove the intersction for crisp set theory
Show that only itself and one divide into it. Seriously how old are you? this is easy ...
Newton explained his theory
You create a theory. Prove the theory to be true by testing it. If it works, it is true. If it does not work, it is not true.
yes it can prove ....
Einstein didn't prove the theory of relativity. It is a theory, a possible explanation, it is generally accepted because it explains a lot of things but that doesn't "prove" the theory, at least not to physicists. See related questions for the country of discovery.
Yes. To prove it, you can take the square root of 2011 (about 44.8), and divide 2011 by all the prime numbers under this number. You'll see none of them divide, so it's prime.