What is the 460th prime number?
The 460th prime number is 3257. The next prime is 3259 (a gap of 2) and the one before is 3253.
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 460th one is 3257.
- 2
3257 is prime because no prime up to ā3257 ā 57.07 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 460th prime is close to 460 Ć ln(460) ā 2820, and here it is 3257.
- 4
3257 is a twin prime: 3257 and 3259 are both prime.
Primes around the 460th
| Position | Prime | Gap from the previous |
|---|---|---|
| 457 | 3229 | 8 |
| 458 | 3251 | 22 |
| 459 | 3253 | 2 |
| 460 | 3257 | 4 |
| 461 | 3259 | 2 |
| 462 | 3271 | 12 |
| 463 | 3299 | 28 |
Questions
What is the 460th prime number?
3257.
Which prime number is 3257?
3257 is the 460th prime number.
What is the sum of the first 460 primes?
687,767.