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What number would be a counter example to the following conjecture. Prime numbers are odd?
The number 2 is even as well as prime.
When multiplying an odd number by an odd number why is the result odd?
The product of multiplication results in a number that has all of the factors of the two numbers being multiplied. All even numbers have the prime factor 2. Since no odd number has the factor 2, no product of those numbers can have it. So: - Odd numbers times odd numbers produce odd numbers. - Odd numbers times even numbers produce even numbers. - Even numbers times even numbers produce even numbers.
Is the product of any two prime numbers is always odd?
No, because 2 is prime. Otherwise the product of two odds is odd, and all primes are odd except 2.
Is the prduct of two prime numbers always even?
No, as 2 is a prime number, the product of 2 prime numbers can be even But all other prime numbers (except 2) are odd then their product is odd (2 x n1+1) x (2 x n2+1) = 2 x (2 x n1 x n2 + n1+ n2) +1
The sum of two consecutive odd numbers is the square of the product of the first and fourth prime numbers what are the two odd numbers?
Let n = smallest of the odd numbers, then let n+2 = the larger of the two numbers (Remember, 1 is not a prime number.) n+ n+2 = {(2)(7)}2 2n +2 = 142 2n = 196 -2 2n = 194 n = 97 n + 2 = 99
