What is the 457th prime number?
The 457th prime number is 3229. The next prime is 3251 (a gap of 22) and the one before is 3221.
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 457th one is 3229.
- 2
3229 is prime because no prime up to ā3229 ā 56.82 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 457th prime is close to 457 Ć ln(457) ā 2799, and here it is 3229.
- 4
3229 has no twin: neither 3227 nor 3231 is prime.
Primes around the 457th
| Position | Prime | Gap from the previous |
|---|---|---|
| 454 | 3209 | 6 |
| 455 | 3217 | 8 |
| 456 | 3221 | 4 |
| 457 | 3229 | 8 |
| 458 | 3251 | 22 |
| 459 | 3253 | 2 |
| 460 | 3257 | 4 |
Questions
What is the 457th prime number?
3229.
Which prime number is 3229?
3229 is the 457th prime number.
What is the sum of the first 457 primes?
678,006.