What is the 450th prime number?
The 450th prime number is 3181. The next prime is 3187 (a gap of 6) and the one before is 3169.
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 450th one is 3181.
- 2
3181 is prime because no prime up to ā3181 ā 56.40 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 450th prime is close to 450 Ć ln(450) ā 2749, and here it is 3181.
- 4
3181 has no twin: neither 3179 nor 3183 is prime.
Primes around the 450th
| Position | Prime | Gap from the previous |
|---|---|---|
| 447 | 3163 | 26 |
| 448 | 3167 | 4 |
| 449 | 3169 | 2 |
| 450 | 3181 | 12 |
| 451 | 3187 | 6 |
| 452 | 3191 | 4 |
| 453 | 3203 | 12 |
Questions
What is the 450th prime number?
3181.
Which prime number is 3181?
3181 is the 450th prime number.
What is the sum of the first 450 primes?
655,549.