What is the 200th prime number?
The 200th prime number is 1223. The next prime is 1229 (a gap of 6) and the one before is 1217.
Position
Pick any whole number from 1 to 10,000.
How to work it out
- 1
List the primes in order: 2, 3, 5, 7, 11, 13, ā¦ The 200th one is 1223.
- 2
1223 is prime because no prime up to ā1223 ā 34.97 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 200th prime is close to 200 Ć ln(200) ā 1060, and here it is 1223.
- 4
1223 has no twin: neither 1221 nor 1225 is prime.
Primes around the 200th
| Position | Prime | Gap from the previous |
|---|---|---|
| 197 | 1201 | 8 |
| 198 | 1213 | 12 |
| 199 | 1217 | 4 |
| 200 | 1223 | 6 |
| 201 | 1229 | 6 |
| 202 | 1231 | 2 |
| 203 | 1237 | 6 |
Questions
What is the 200th prime number?
1223.
Which prime number is 1223?
1223 is the 200th prime number.
What is the sum of the first 200 primes?
111,587.