What is the 464th prime number?
The 464th prime number is 3301. The next prime is 3307 (a gap of 6) and the one before is 3299.
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 464th one is 3301.
- 2
3301 is prime because no prime up to ā3301 ā 57.45 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 464th prime is close to 464 Ć ln(464) ā 2849, and here it is 3301.
- 4
3301 is a twin prime: 3299 and 3301 are both prime.
Primes around the 464th
| Position | Prime | Gap from the previous |
|---|---|---|
| 461 | 3259 | 2 |
| 462 | 3271 | 12 |
| 463 | 3299 | 28 |
| 464 | 3301 | 2 |
| 465 | 3307 | 6 |
| 466 | 3313 | 6 |
| 467 | 3319 | 6 |
Questions
What is the 464th prime number?
3301.
Which prime number is 3301?
3301 is the 464th prime number.
What is the sum of the first 464 primes?
700,897.