What is the 467th prime number?
The 467th prime number is 3319. The next prime is 3323 (a gap of 4) and the one before is 3313.
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 467th one is 3319.
- 2
3319 is prime because no prime up to ā3319 ā 57.61 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 467th prime is close to 467 Ć ln(467) ā 2870, and here it is 3319.
- 4
3319 has no twin: neither 3317 nor 3321 is prime.
Primes around the 467th
| Position | Prime | Gap from the previous |
|---|---|---|
| 464 | 3301 | 2 |
| 465 | 3307 | 6 |
| 466 | 3313 | 6 |
| 467 | 3319 | 6 |
| 468 | 3323 | 4 |
| 469 | 3329 | 6 |
| 470 | 3331 | 2 |
Questions
What is the 467th prime number?
3319.
Which prime number is 3319?
3319 is the 467th prime number.
What is the sum of the first 467 primes?
710,836.