What is the 1582nd prime number?
The 1582nd prime number is 13327. The next prime is 13331 (a gap of 4) and the one before is 13313.
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 1582nd one is 13327.
- 2
13327 is prime because no prime up to ā13327 ā 115.44 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 1582nd prime is close to 1582 Ć ln(1582) ā 11654, and here it is 13327.
- 4
13327 has no twin: neither 13325 nor 13329 is prime.
Primes around the 1582nd
| Position | Prime | Gap from the previous |
|---|---|---|
| 1579 | 13297 | 6 |
| 1580 | 13309 | 12 |
| 1581 | 13313 | 4 |
| 1582 | 13327 | 14 |
| 1583 | 13331 | 4 |
| 1584 | 13337 | 6 |
| 1585 | 13339 | 2 |
Questions
What is the 1582nd prime number?
13327.
Which prime number is 13327?
13327 is the 1582nd prime number.
What is the sum of the first 1582 primes?
9,857,645.