What is the 38th prime number?
The 38th prime number is 163. The next prime is 167 (a gap of 4) and the one before is 157.
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 38th one is 163.
- 2
163 is prime because no prime up to ā163 ā 12.77 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 38th prime is close to 38 Ć ln(38) ā 138, and here it is 163.
- 4
163 has no twin: neither 161 nor 165 is prime.
Primes around the 38th
| Position | Prime | Gap from the previous |
|---|---|---|
| 35 | 149 | 10 |
| 36 | 151 | 2 |
| 37 | 157 | 6 |
| 38 | 163 | 6 |
| 39 | 167 | 4 |
| 40 | 173 | 6 |
| 41 | 179 | 6 |
Questions
What is the 38th prime number?
163.
Which prime number is 163?
163 is the 38th prime number.
What is the sum of the first 38 primes?
2,747.