What is the 1584th prime number?
The 1584th prime number is 13337. The next prime is 13339 (a gap of 2) and the one before is 13331.
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 1584th one is 13337.
- 2
13337 is prime because no prime up to ā13337 ā 115.49 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 1584th prime is close to 1584 Ć ln(1584) ā 11670, and here it is 13337.
- 4
13337 is a twin prime: 13337 and 13339 are both prime.
Primes around the 1584th
| Position | Prime | Gap from the previous |
|---|---|---|
| 1581 | 13313 | 4 |
| 1582 | 13327 | 14 |
| 1583 | 13331 | 4 |
| 1584 | 13337 | 6 |
| 1585 | 13339 | 2 |
| 1586 | 13367 | 28 |
| 1587 | 13381 | 14 |
Questions
What is the 1584th prime number?
13337.
Which prime number is 13337?
13337 is the 1584th prime number.
What is the sum of the first 1584 primes?
9,884,313.