What is the 380th prime number?
The 380th prime number is 2617. The next prime is 2621 (a gap of 4) and the one before is 2609.
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 380th one is 2617.
- 2
2617 is prime because no prime up to ā2617 ā 51.16 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 380th prime is close to 380 Ć ln(380) ā 2257, and here it is 2617.
- 4
2617 has no twin: neither 2615 nor 2619 is prime.
Primes around the 380th
| Position | Prime | Gap from the previous |
|---|---|---|
| 377 | 2591 | 12 |
| 378 | 2593 | 2 |
| 379 | 2609 | 16 |
| 380 | 2617 | 8 |
| 381 | 2621 | 4 |
| 382 | 2633 | 12 |
| 383 | 2647 | 14 |
Questions
What is the 380th prime number?
2617.
Which prime number is 2617?
2617 is the 380th prime number.
What is the sum of the first 380 primes?
454,095.