What is the 333rd prime number?
The 333rd prime number is 2239. The next prime is 2243 (a gap of 4) and the one before is 2237.
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 333rd one is 2239.
- 2
2239 is prime because no prime up to ā2239 ā 47.32 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 333rd prime is close to 333 Ć ln(333) ā 1934, and here it is 2239.
- 4
2239 is a twin prime: 2237 and 2239 are both prime.
Primes around the 333rd
| Position | Prime | Gap from the previous |
|---|---|---|
| 330 | 2213 | 6 |
| 331 | 2221 | 8 |
| 332 | 2237 | 16 |
| 333 | 2239 | 2 |
| 334 | 2243 | 4 |
| 335 | 2251 | 8 |
| 336 | 2267 | 16 |
Questions
What is the 333rd prime number?
2239.
Which prime number is 2239?
2239 is the 333rd prime number.
What is the sum of the first 333 primes?
340,518.