What is the 39th prime number?
The 39th prime number is 167. The next prime is 173 (a gap of 6) and the one before is 163.
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 39th one is 167.
- 2
167 is prime because no prime up to ā167 ā 12.92 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 39th prime is close to 39 Ć ln(39) ā 143, and here it is 167.
- 4
167 has no twin: neither 165 nor 169 is prime.
Primes around the 39th
| Position | Prime | Gap from the previous |
|---|---|---|
| 36 | 151 | 2 |
| 37 | 157 | 6 |
| 38 | 163 | 6 |
| 39 | 167 | 4 |
| 40 | 173 | 6 |
| 41 | 179 | 6 |
| 42 | 181 | 2 |
Questions
What is the 39th prime number?
167.
Which prime number is 167?
167 is the 39th prime number.
What is the sum of the first 39 primes?
2,914.