What is the 466th prime number?
The 466th prime number is 3313. The next prime is 3319 (a gap of 6) and the one before is 3307.
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 466th one is 3313.
- 2
3313 is prime because no prime up to ā3313 ā 57.56 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 466th prime is close to 466 Ć ln(466) ā 2863, and here it is 3313.
- 4
3313 has no twin: neither 3311 nor 3315 is prime.
Primes around the 466th
| Position | Prime | Gap from the previous |
|---|---|---|
| 463 | 3299 | 28 |
| 464 | 3301 | 2 |
| 465 | 3307 | 6 |
| 466 | 3313 | 6 |
| 467 | 3319 | 6 |
| 468 | 3323 | 4 |
| 469 | 3329 | 6 |
Questions
What is the 466th prime number?
3313.
Which prime number is 3313?
3313 is the 466th prime number.
What is the sum of the first 466 primes?
707,517.