What is the 1585th prime number?
The 1585th prime number is 13339. The next prime is 13367 (a gap of 28) and the one before is 13337.
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 1585th one is 13339.
- 2
13339 is prime because no prime up to ā13339 ā 115.49 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 1585th prime is close to 1585 Ć ln(1585) ā 11679, and here it is 13339.
- 4
13339 is a twin prime: 13337 and 13339 are both prime.
Primes around the 1585th
| Position | Prime | Gap from the previous |
|---|---|---|
| 1582 | 13327 | 14 |
| 1583 | 13331 | 4 |
| 1584 | 13337 | 6 |
| 1585 | 13339 | 2 |
| 1586 | 13367 | 28 |
| 1587 | 13381 | 14 |
| 1588 | 13397 | 16 |
Questions
What is the 1585th prime number?
13339.
Which prime number is 13339?
13339 is the 1585th prime number.
What is the sum of the first 1585 primes?
9,897,652.