The list is infinite. Here are the first few: 23 29 31 37 41 43 47 53 59 61 67 71 73 . . .
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The squares of prime numbers greater than 10.
Look up a list of prime numbers (a Google search for "prime numbers" or "list of prime numbers" should do); every number (greater than 1) that is NOT a prime number is composite.
Searching in Google for "list of prime numbers" should help you get a listing. From there you can pick the prime numbers that satisfy your criteria.
There are infinitely many prime numbers which are greater than 30.
There are no prime numbers greater than 10 that add up to 29. Since all prime numbers greater than 2 are odd numbers, no two prime numbers greater than 2 can have an even number for their sum.