What is the 478th prime number?
The 478th prime number is 3391. The next prime is 3407 (a gap of 16) and the one before is 3389.
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 478th one is 3391.
- 2
3391 is prime because no prime up to ā3391 ā 58.23 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 478th prime is close to 478 Ć ln(478) ā 2949, and here it is 3391.
- 4
3391 is a twin prime: 3389 and 3391 are both prime.
Primes around the 478th
| Position | Prime | Gap from the previous |
|---|---|---|
| 475 | 3371 | 10 |
| 476 | 3373 | 2 |
| 477 | 3389 | 16 |
| 478 | 3391 | 2 |
| 479 | 3407 | 16 |
| 480 | 3413 | 6 |
| 481 | 3433 | 20 |
Questions
What is the 478th prime number?
3391.
Which prime number is 3391?
3391 is the 478th prime number.
What is the sum of the first 478 primes?
747,753.