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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
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Is it true that the sum of two prime numbers is always an even number?
Not quite.When two prime numbers of 3 and higher are added together, the result is always even, because all such prime numbers are odd numbers, and when two odd numbers are added together, the result is always an even number.However 2 is a prime number, and 2 is also an even number. Adding 2 (an even number) to a different prime number (an odd number) will always yield an odd number.Only if you don't include "2".
Is it possible for two numbers that are both even to be relatively prime?
No. Two numbers are relatively prime if they have no prime factors in common. Two even numbers will have 2 as a prime factor in common.
Can the sum of 2 odd prime numbers ever be prime?
No. The sum of two odd numbers is always even, and no prime is even (apart from 2, but it is the lowest prime, so no primes can be added to form it).
When you add two prime numbers together why do you get an even number?
You don't always. 2 + 5 = 7, for example. But all prime numbers other than 2 are odd and two odd numbers always equal an even number when added together.
Can the sum of two prime numbers be a prime number?
Yes, but since 2 is the only even prime number and the sum of two odd numbers is always even, one of the two prime numbers being added will always be a 2. So, for example: 3 + 2 = 5 11 + 2 = 13 71 + 2 = 73
