What is the 1581st prime number?
The 1581st prime number is 13313. The next prime is 13327 (a gap of 14) and the one before is 13309.
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 1581st one is 13313.
- 2
13313 is prime because no prime up to ā13313 ā 115.38 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 1581st prime is close to 1581 Ć ln(1581) ā 11645, and here it is 13313.
- 4
13313 has no twin: neither 13311 nor 13315 is prime.
Primes around the 1581st
| Position | Prime | Gap from the previous |
|---|---|---|
| 1578 | 13291 | 24 |
| 1579 | 13297 | 6 |
| 1580 | 13309 | 12 |
| 1581 | 13313 | 4 |
| 1582 | 13327 | 14 |
| 1583 | 13331 | 4 |
| 1584 | 13337 | 6 |
Questions
What is the 1581st prime number?
13313.
Which prime number is 13313?
13313 is the 1581st prime number.
What is the sum of the first 1581 primes?
9,844,318.