What is the 381st prime number?
The 381st prime number is 2621. The next prime is 2633 (a gap of 12) and the one before is 2617.
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 381st one is 2621.
- 2
2621 is prime because no prime up to ā2621 ā 51.20 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 381st prime is close to 381 Ć ln(381) ā 2264, and here it is 2621.
- 4
2621 has no twin: neither 2619 nor 2623 is prime.
Primes around the 381st
| Position | Prime | Gap from the previous |
|---|---|---|
| 378 | 2593 | 2 |
| 379 | 2609 | 16 |
| 380 | 2617 | 8 |
| 381 | 2621 | 4 |
| 382 | 2633 | 12 |
| 383 | 2647 | 14 |
| 384 | 2657 | 10 |
Questions
What is the 381st prime number?
2621.
Which prime number is 2621?
2621 is the 381st prime number.
What is the sum of the first 381 primes?
456,716.