What is the 480th prime number?
The 480th prime number is 3413. The next prime is 3433 (a gap of 20) and the one before is 3407.
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 480th one is 3413.
- 2
3413 is prime because no prime up to ā3413 ā 58.42 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 480th prime is close to 480 Ć ln(480) ā 2963, and here it is 3413.
- 4
3413 has no twin: neither 3411 nor 3415 is prime.
Primes around the 480th
| Position | Prime | Gap from the previous |
|---|---|---|
| 477 | 3389 | 16 |
| 478 | 3391 | 2 |
| 479 | 3407 | 16 |
| 480 | 3413 | 6 |
| 481 | 3433 | 20 |
| 482 | 3449 | 16 |
| 483 | 3457 | 8 |
Questions
What is the 480th prime number?
3413.
Which prime number is 3413?
3413 is the 480th prime number.
What is the sum of the first 480 primes?
754,573.