SOLUTION: can the sum of two prime mubers be a prime number?

Question 98948: can the sum of two prime mubers be a prime number?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
There is only one case where this would happen

Add 2 and 3 (which are both prime) to get 5 (which is prime also). Otherwise, you would always add to an nonprime number. Remember every prime is odd (except 2). Also when two odd numbers are added up, they result in an even number (which is never prime). So the only time when 2 prime numbers add to get a prime number is when the two numbers are 2 and 3.

Update: Someone messaged me and helped point out that there are other cases. So I apologize. It turns out that we have cases like this

5+2 = 7
2+29 = 31
17+2 = 19

which are cases of Twin Primes
RELATED QUESTIONS
the sum of the digits of a two-digit prime number is subtracted from the number. Prove... (answered by solver91311)

I'm a two digit number less than 40. I'm divisible by only one prime number. The sum of... (answered by Alan3354)

Can you please help me with this question? Two dice are rolled. What is the probability... (answered by stanbon,JeeJa)

two dice are rolled. what is the probability the sum of the two dice will be a prime... (answered by )

which of the 10 digits can be the ones digit of a prime... (answered by Alan3354)

The sum of two mubers is 36. Their difference is 12. What are the two... (answered by dr2400,TP)

"I'm a product of four prime numbers. My three digits are all prime and different. The... (answered by Edwin McCravy)

the numbers 2 and 3 are prime numbers and their sum 5 is also a prime number, fine five... (answered by Alan3354)

If you add a prime number to itself,is the sum composite or prime?... (answered by solver91311)