no, not all prime numbers are closed under addition. why? because, when you add 2 prime numbers you will not always get a prime number. example: 5+3= 8 5 and 3 are prime numbers but their sum is 8 which is a composite number..
No, they are not. You can add two composite numbers, 15 and 14 for example, and get a sum, 29, that is prime.
The answer depends on how the numbers are combined: addition, subtraction or multiplication.
No.
No.
No.
Sometimes.
prime numbers, co-prime numbers
Always
No. The product of two primes cannot, by definition, be a prime.
It is, and always is relatively prime.
Combining prime numbers other than 2, whether through addition or multiplication, will result in a composite number.