What is the 458th prime number?
The 458th prime number is 3251. The next prime is 3253 (a gap of 2) and the one before is 3229.
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 458th one is 3251.
- 2
3251 is prime because no prime up to ā3251 ā 57.02 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 458th prime is close to 458 Ć ln(458) ā 2806, and here it is 3251.
- 4
3251 is a twin prime: 3251 and 3253 are both prime.
Primes around the 458th
| Position | Prime | Gap from the previous |
|---|---|---|
| 455 | 3217 | 8 |
| 456 | 3221 | 4 |
| 457 | 3229 | 8 |
| 458 | 3251 | 22 |
| 459 | 3253 | 2 |
| 460 | 3257 | 4 |
| 461 | 3259 | 2 |
Questions
What is the 458th prime number?
3251.
Which prime number is 3251?
3251 is the 458th prime number.
What is the sum of the first 458 primes?
681,257.