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Sum of two prime numbers

Can the sum of two prime numbers be a prime number? Is the sum of two prime numbers always even? Is the sum of two prime numbers always a prime number?

Let us consider the sum of two prime numbers.

Can the sum of two prime numbers be a prime number?

Yes, the sum of two prime numbers can be a prime number.

Examples of the sum of two prime numbers:

2 + 3 = 5
2 + 5 = 7
2 + 29 = 31

Is the sum of 2 prime numbers always even?

No, the sum of 2 prime numbers can be odd but it can be also even.

Examples:

2 + 3 = 5
the sum is odd

3 + 7 = 10
the sum is even.

So we cannot state that the sum of two prime numbers is always an even number.

Does the sum of two prime numbers equal a prime number?

It can be so but not always.

Examples:

2 + 3 = 5
5 is a prime number

3 + 11 = 14
14 is not a prime number.

Can the difference between two prime numbers be a prime number?

Yes, the difference between two prime numbers can be a prime number.

Examples:

5 - 3 = 2
823 - 821 = 2

Can the sum of two prime numbers be odd?

Yes, the sum of two prime numbers can be odd.

Examples:

2 + 3 = 5
311 + 2 = 313

Can the sum of two odd prime numbers ever be prime?

No, the sum of two odd prime numbers can't be prime.

Because the sum of two odd prime numbers is always even and greater then two.

There is only one even prime number, it is two.

Can the sum of two prime numbers be odd?

Yes, the sum of two prime numbers can be odd.

Examples:

2 + 3 = 5
311 + 2 = 313
2 + 17 = 19
2 + 9 = 11

Can the sum of two odd prime numbers ever be even?

No, the sum of two odd prime numbers can't be even.

Because the sum of two odd prime numbers is always even and greater then two. There is only one even prime number, it is two.