What is the 838th prime number?
The 838th prime number is 6451. The next prime is 6469 (a gap of 18) and the one before is 6449.
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 838th one is 6451.
- 2
6451 is prime because no prime up to ā6451 ā 80.32 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 838th prime is close to 838 Ć ln(838) ā 5641, and here it is 6451.
- 4
6451 is a twin prime: 6449 and 6451 are both prime.
Primes around the 838th
| Position | Prime | Gap from the previous |
|---|---|---|
| 835 | 6421 | 24 |
| 836 | 6427 | 6 |
| 837 | 6449 | 22 |
| 838 | 6451 | 2 |
| 839 | 6469 | 18 |
| 840 | 6473 | 4 |
| 841 | 6481 | 8 |
Questions
What is the 838th prime number?
6451.
Which prime number is 6451?
6451 is the 838th prime number.
What is the sum of the first 838 primes?
2,517,223.