No, they are not. You can add two composite numbers, 15 and 14 for example, and get a sum, 29, that is prime.
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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..
Yes.
Addition.
no
Yes. They are closed under addition, subtraction, multiplication. The rational numbers WITHOUT ZERO are closed under division.