What is the 40th prime number?
The 40th prime number is 173. The next prime is 179 (a gap of 6) and the one before is 167.
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 40th one is 173.
- 2
173 is prime because no prime up to ā173 ā 13.15 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 40th prime is close to 40 Ć ln(40) ā 148, and here it is 173.
- 4
173 has no twin: neither 171 nor 175 is prime.
Primes around the 40th
| Position | Prime | Gap from the previous |
|---|---|---|
| 37 | 157 | 6 |
| 38 | 163 | 6 |
| 39 | 167 | 4 |
| 40 | 173 | 6 |
| 41 | 179 | 6 |
| 42 | 181 | 2 |
| 43 | 191 | 10 |
Questions
What is the 40th prime number?
173.
Which prime number is 173?
173 is the 40th prime number.
What is the sum of the first 40 primes?
3,087.