What is the 451st prime number?
The 451st prime number is 3187. The next prime is 3191 (a gap of 4) and the one before is 3181.
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 451st one is 3187.
- 2
3187 is prime because no prime up to ā3187 ā 56.45 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 451st prime is close to 451 Ć ln(451) ā 2756, and here it is 3187.
- 4
3187 has no twin: neither 3185 nor 3189 is prime.
Primes around the 451st
| Position | Prime | Gap from the previous |
|---|---|---|
| 448 | 3167 | 4 |
| 449 | 3169 | 2 |
| 450 | 3181 | 12 |
| 451 | 3187 | 6 |
| 452 | 3191 | 4 |
| 453 | 3203 | 12 |
| 454 | 3209 | 6 |
Questions
What is the 451st prime number?
3187.
Which prime number is 3187?
3187 is the 451st prime number.
What is the sum of the first 451 primes?
658,736.