What is the 204th prime number?
The 204th prime number is 1249. The next prime is 1259 (a gap of 10) and the one before is 1237.
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 204th one is 1249.
- 2
1249 is prime because no prime up to ā1249 ā 35.34 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 204th prime is close to 204 Ć ln(204) ā 1085, and here it is 1249.
- 4
1249 has no twin: neither 1247 nor 1251 is prime.
Primes around the 204th
| Position | Prime | Gap from the previous |
|---|---|---|
| 201 | 1229 | 6 |
| 202 | 1231 | 2 |
| 203 | 1237 | 6 |
| 204 | 1249 | 12 |
| 205 | 1259 | 10 |
| 206 | 1277 | 18 |
| 207 | 1279 | 2 |
Questions
What is the 204th prime number?
1249.
Which prime number is 1249?
1249 is the 204th prime number.
What is the sum of the first 204 primes?
116,533.