What is the 13th prime number?
The 13th prime number is 41. The next prime is 43 (a gap of 2) and the one before is 37.
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 13th one is 41.
- 2
41 is prime because no prime up to ā41 ā 6.40 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 13th prime is close to 13 Ć ln(13) ā 33, and here it is 41.
- 4
41 is a twin prime: 41 and 43 are both prime.
Primes around the 13th
| Position | Prime | Gap from the previous |
|---|---|---|
| 10 | 29 | 6 |
| 11 | 31 | 2 |
| 12 | 37 | 6 |
| 13 | 41 | 4 |
| 14 | 43 | 2 |
| 15 | 47 | 4 |
| 16 | 53 | 6 |
Questions
What is the 13th prime number?
41.
Which prime number is 41?
41 is the 13th prime number.
What is the sum of the first 13 primes?
238.