How many prime numbers are there between 200 and 230?

To find the prime numbers between 200 and 230, we examine the odd numbers in this range (excluding those ending in 5) and test for divisibility by prime factors such as 3, 7, 11, 13, and 17:

• 201: 2+0+1 = 3 (divisible by 3)
• 203: 203 ÷ 7 = 29 (divisible by 7)
• 207: 2+0+7 = 9 (divisible by 3)
• 209: 209 ÷ 11 = 19 (divisible by 11)
• 211: No prime factors up to √211 ≈ 14.5 (Prime)
• 213: 2+1+3 = 6 (divisible by 3)
• 217: 217 ÷ 7 = 31 (divisible by 7)
• 219: 2+1+9 = 12 (divisible by 3)
• 221: 221 ÷ 13 = 17 (divisible by 13)
• 223: No prime factors up to √223 ≈ 14.9 (Prime)
• 227: No prime factors up to √227 ≈ 15.06 (Prime)
• 229: No prime factors up to √229 ≈ 15.1 (Prime)

The prime numbers are 211, 223, 227, and 229. Therefore, there are 4 prime numbers in the given range.