What is the 1586th prime number?
The 1586th prime number is 13367. The next prime is 13381 (a gap of 14) and the one before is 13339.
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 1586th one is 13367.
- 2
13367 is prime because no prime up to ā13367 ā 115.62 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 1586th prime is close to 1586 Ć ln(1586) ā 11687, and here it is 13367.
- 4
13367 has no twin: neither 13365 nor 13369 is prime.
Primes around the 1586th
| Position | Prime | Gap from the previous |
|---|---|---|
| 1583 | 13331 | 4 |
| 1584 | 13337 | 6 |
| 1585 | 13339 | 2 |
| 1586 | 13367 | 28 |
| 1587 | 13381 | 14 |
| 1588 | 13397 | 16 |
| 1589 | 13399 | 2 |
Questions
What is the 1586th prime number?
13367.
Which prime number is 13367?
13367 is the 1586th prime number.
What is the sum of the first 1586 primes?
9,911,019.