What is the 67th prime number?
The 67th prime number is 331. The next prime is 337 (a gap of 6) and the one before is 317.
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 67th one is 331.
- 2
331 is prime because no prime up to ā331 ā 18.19 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 67th prime is close to 67 Ć ln(67) ā 282, and here it is 331.
- 4
331 has no twin: neither 329 nor 333 is prime.
Primes around the 67th
| Position | Prime | Gap from the previous |
|---|---|---|
| 64 | 311 | 4 |
| 65 | 313 | 2 |
| 66 | 317 | 4 |
| 67 | 331 | 14 |
| 68 | 337 | 6 |
| 69 | 347 | 10 |
| 70 | 349 | 2 |
Questions
What is the 67th prime number?
331.
Which prime number is 331?
331 is the 67th prime number.
What is the sum of the first 67 primes?
9,854.