What is the 382nd prime number?
The 382nd prime number is 2633. The next prime is 2647 (a gap of 14) and the one before is 2621.
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 382nd one is 2633.
- 2
2633 is prime because no prime up to ā2633 ā 51.31 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 382nd prime is close to 382 Ć ln(382) ā 2271, and here it is 2633.
- 4
2633 has no twin: neither 2631 nor 2635 is prime.
Primes around the 382nd
| Position | Prime | Gap from the previous |
|---|---|---|
| 379 | 2609 | 16 |
| 380 | 2617 | 8 |
| 381 | 2621 | 4 |
| 382 | 2633 | 12 |
| 383 | 2647 | 14 |
| 384 | 2657 | 10 |
| 385 | 2659 | 2 |
Questions
What is the 382nd prime number?
2633.
Which prime number is 2633?
2633 is the 382nd prime number.
What is the sum of the first 382 primes?
459,349.