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Q: Are prime numbers always closed under addition?

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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

Prime numbers have two factors. The sum of their proper divisors is always 1.

Factors are just numbers. Some numbers are positive, some negative. Some numbers are prime, some composite. A prime factor is always positive, but a positive factor is not always 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.

The product of two prime numbers is always a composite number, and it never is a prime number.

There is only one even prime number: 2. All other even numbers have 2 as a factor, in addition to 1 and themselves, so they cannot be prime numbers.

In fact, they can. 2 and 3 are consecutive prime numbers.For larger numbers, one of two consecutive numbers will always be even, and therefore, not a prime.In fact, they can. 2 and 3 are consecutive prime numbers.For larger numbers, one of two consecutive numbers will always be even, and therefore, not a prime.In fact, they can. 2 and 3 are consecutive prime numbers.For larger numbers, one of two consecutive numbers will always be even, and therefore, not a prime.In fact, they can. 2 and 3 are consecutive prime numbers.For larger numbers, one of two consecutive numbers will always be even, and therefore, not a prime.

No.

341 is not a prime number. Prime numbers are defined as numbers which can be divided by 1 and themselves. 341 can be divided by 11 and 31 in addition to 1 and iteslf. Hence, 341 is not a prime number.

Always

No. The product of two primes cannot, by definition, be a prime.

Prime numbers are whole numbers that are not divisible by anything but one and itself. Examples of prime numbers include 1;2;3;5;7;9... etc. Prime numbers must always be odd (except for 2) but not all odd numbers are prime. For example, 21 is odd, but it is divisible by 3 and 7. Therefore, it is not prime.

Yes, the greatest common factor of two different prime numbers is always 1

All prime numbers have only 2 factors which are themselves and one. Al prime numbers are odd numbers except for 2 which is the only even prime number.

No, they do not. If one of the prime numbers is 2, you will have an odd number.

The product of all pairs of prime numbers is always the least common multiple of the two prime numbers.