1. **State the problem:** We need to find two prime numbers that add up to 30. 2. **Recall the definition of prime numbers:** A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. 3. **Find pairs of primes that sum to 30:** We check pairs of primes less than 30: - 2 + 28 (28 is not prime) - 3 + 27 (27 is not prime) - 5 + 25 (25 is not prime) - 7 + 23 (23 is prime) ✔ - 11 + 19 (19 is prime) ✔ - 13 + 17 (17 is prime) ✔ So possible pairs are (7, 23), (11, 19), and (13, 17). 4. **Choose one pair:** Let's pick (13, 17). 5. **Verify the sum:** $$13 + 17 = 30$$ --- 1. **State the problem:** Choose an even number greater than 50 and find two primes that add to it. 2. **Choose an even number:** Let's pick 56. 3. **Find pairs of primes that sum to 56:** Check primes less than 56: - 3 + 53 (53 prime) ✔ - 5 + 51 (51 not prime) - 7 + 49 (49 not prime) - 13 + 43 (43 prime) ✔ - 17 + 39 (39 not prime) - 19 + 37 (37 prime) ✔ 4. **Choose one pair:** Let's pick (19, 37). 5. **Verify the sum:** $$19 + 37 = 56$$ **Final answers:** - a) Two primes that add to 30: 13 and 17 - b) Two primes that add to 56: 19 and 37