What is the 448th prime number?
The 448th prime number is 3167. The next prime is 3169 (a gap of 2) and the one before is 3163.
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 448th one is 3167.
- 2
3167 is prime because no prime up to ā3167 ā 56.28 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 448th prime is close to 448 Ć ln(448) ā 2735, and here it is 3167.
- 4
3167 is a twin prime: 3167 and 3169 are both prime.
Primes around the 448th
| Position | Prime | Gap from the previous |
|---|---|---|
| 445 | 3121 | 2 |
| 446 | 3137 | 16 |
| 447 | 3163 | 26 |
| 448 | 3167 | 4 |
| 449 | 3169 | 2 |
| 450 | 3181 | 12 |
| 451 | 3187 | 6 |
Questions
What is the 448th prime number?
3167.
Which prime number is 3167?
3167 is the 448th prime number.
What is the sum of the first 448 primes?
649,199.