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How many of the prime numbers between 10 and 20 can be written as the sum of two primes?
All prime numbers greater than 2 are odd numbers. For an odd prime to be written as the sum of two primes, one of the primes must be 2 because two odd primes will produce an even sum. 11 cannot be written as the sum of two primes. 13 = 2 + 11. 17 cannot be written as the sum of two primes. 19 = 2 + 17.
Is the sum of two prime numbers always a prime numer?
It is not. Of the infinitely many primes only one (the number 2) is even, the rest are all odd. The sum of any two primes other than 2 is even and therefore not a prime. If one of the primes in the sum is 2 then the sum is a prime only if the other is the lower of a pair of twin primes. So, while it is possible, it is certainly more likely that the sum is a composite.
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).
Can every odd number greater than 3 be written as the sum of two prime numbers?
No.Consider that every prime number except 2 is an odd number.Consider also that the sum of two odd numbers is always an even number.Thus, the only case in which an odd number can be expressed as the sum of two primes is when it is 2 greater than a prime number, since it can take advantage of the only even prime number, 2.For example, 21 can be expressed as 2+19, both of which are primes. However, 27 has no such two primes, since 25 is not prime (5x5=25).
What two prime numbers added together equals 97?
No two prime numbers added together have a sum of 97. All primes except the number 2 are odd numbers, and two odd numbers added together always produce an even sum.
