No. 2 is even and cannot be written as a sum of 2 prime numbers.
For even numbers greater than 2, this is the Goldbach conjecture, one of the best known conjectures. It has been shown to hold true up to 4*10^18 but has not been proved.
There are not three odd primes with the sum of 14. The sum of three odd primes will be an odd number.
Given an arbitrary odd natural number greater than five, x, let y = x - 3, then y is an even number greater than 2. By assumption we have that y is the sum of two primes, say y1 and y2, but then x = y1 + y2 + 3 (which is the sum of three 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.
That is known as the Goldbach conjecture.
2 + 3 = 5
Yes it is called the fundamental theorem of arithmeticand it says that every whole number greater than one, the natural numbers, can be written as a unique product of primes. Dr. Chuck Mathdoc
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).
Goldbach's conjecture says that every even number greater than two can be expressed as the sum of 2 primes. If 30 could not be expressed as the sum of two primes, then this would disprove the conjecture. As it is, 30 can be expressed as the sum of two primes. You can express it as 11+19. Thus, Goldbach's conjecture holds in this case.
The sum of two odd primes is always an even answer or number.
57
According to the Goldbach conjecture, every even prime number greater than 2 can be expressed as a sum of two primes. It has not yet been proven so it is possible that there is an even number that meets your requirements. See related link below for source
This question cannot be answered because three odd primes always have an odd number for their sum.