What is the 459th prime number?
The 459th prime number is 3253. The next prime is 3257 (a gap of 4) and the one before is 3251.
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 459th one is 3253.
- 2
3253 is prime because no prime up to ā3253 ā 57.04 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 459th prime is close to 459 Ć ln(459) ā 2813, and here it is 3253.
- 4
3253 is a twin prime: 3251 and 3253 are both prime.
Primes around the 459th
| Position | Prime | Gap from the previous |
|---|---|---|
| 456 | 3221 | 4 |
| 457 | 3229 | 8 |
| 458 | 3251 | 22 |
| 459 | 3253 | 2 |
| 460 | 3257 | 4 |
| 461 | 3259 | 2 |
| 462 | 3271 | 12 |
Questions
What is the 459th prime number?
3253.
Which prime number is 3253?
3253 is the 459th prime number.
What is the sum of the first 459 primes?
684,510.