The smallest prime number greater than 200 is 211.
To understand why 211 is the smallest prime number greater than 200, we need to revisit what a prime number is. A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. In simpler terms, it has only two divisors: 1 and itself.
Starting from 201, we can check consecutive numbers to see if they are prime:
- 201: Divisible by 3 (201 = 3 x 67)
- 202: Even number (divisible by 2)
- 203: Divisible by 7 (203 = 7 x 29)
- 204: Even number (divisible by 2)
- 205: Divisible by 5 (205 = 5 x 41)
- 206: Even number (divisible by 2)
- 207: Divisible by 3 (207 = 3 x 69)
- 208: Even number (divisible by 2)
- 209: Divisible by 11 (209 = 11 x 19)
- 210: Even number (divisible by 2)
- 211: Not divisible by 2, 3, 5, 7, 11, or 13, thus it is prime!
Hence, after evaluating the numbers one by one, we find that 211 is indeed the smallest prime number that is greater than 200.