What is the 338th prime number?
The 338th prime number is 2273. The next prime is 2281 (a gap of 8) and the one before is 2269.
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 338th one is 2273.
- 2
2273 is prime because no prime up to ā2273 ā 47.68 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 338th prime is close to 338 Ć ln(338) ā 1968, and here it is 2273.
- 4
2273 has no twin: neither 2271 nor 2275 is prime.
Primes around the 338th
| Position | Prime | Gap from the previous |
|---|---|---|
| 335 | 2251 | 8 |
| 336 | 2267 | 16 |
| 337 | 2269 | 2 |
| 338 | 2273 | 4 |
| 339 | 2281 | 8 |
| 340 | 2287 | 6 |
| 341 | 2293 | 6 |
Questions
What is the 338th prime number?
2273.
Which prime number is 2273?
2273 is the 338th prime number.
What is the sum of the first 338 primes?
351,821.