What is the 335th prime number?
The 335th prime number is 2251. The next prime is 2267 (a gap of 16) and the one before is 2243.
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 335th one is 2251.
- 2
2251 is prime because no prime up to ā2251 ā 47.44 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 335th prime is close to 335 Ć ln(335) ā 1948, and here it is 2251.
- 4
2251 has no twin: neither 2249 nor 2253 is prime.
Primes around the 335th
| Position | Prime | Gap from the previous |
|---|---|---|
| 332 | 2237 | 16 |
| 333 | 2239 | 2 |
| 334 | 2243 | 4 |
| 335 | 2251 | 8 |
| 336 | 2267 | 16 |
| 337 | 2269 | 2 |
| 338 | 2273 | 4 |
Questions
What is the 335th prime number?
2251.
Which prime number is 2251?
2251 is the 335th prime number.
What is the sum of the first 335 primes?
345,012.