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How many prime numbers are theree?
There are an infinite number of prime numbers. The first to have proven this was Euclid. Here are the general lines of his proof:Suppose there are n prime numbers overall.Let N be a common multiple of all these primes.Is N+1 prime? If it is, we have found a new prime.Suppose N+1 is not prime. Thus, there exists a prime number p which divides N+1 evenly. If p is one of the primes dividing N, it also divides 1 evenly, which is impossible. Thus, p is not one of the n primes, and we found a new prime.(see the related link for a list of the first 500 prime numbers)
Do perfect numbers have to be prime numbers?
Perfect numbers cannot be prime numbers. Here's why:A number N is perfect if σ(N) = 2N (σ is the sum of divisors function). If there is a prime p that is a perfect number, then σ(p) = 2p. However, the only factors of p are 1 and p, so σ(p) is also equal to p+1. If 2p = p+1, then p=1, which is not prime, and 1 is defined to have only one factor, 1.
Twin prime numbers?
These are prime numbers of the form p and p+2.
How do you find the multiplicative inverse of a number mod a number?
Formally, a number n, has an inverse mod p only if p is prime. The inverse of n, mod p, is one of the numbers {0, 1, 2, ... , k-1} such that n*(p-1) = 1 mod p If p is not a prime then: if n is a factor of p then there is no such "inverse"; and if n is not a factor of p then there may be several possible "inverses".
What is m plus N plus p equals p plus n plus m?
It would be the same number either way because its addition.
