What is the 42nd prime number?
The 42nd prime number is 181. The next prime is 191 (a gap of 10) and the one before is 179.
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 42nd one is 181.
- 2
181 is prime because no prime up to ā181 ā 13.45 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 42nd prime is close to 42 Ć ln(42) ā 157, and here it is 181.
- 4
181 is a twin prime: 179 and 181 are both prime.
Primes around the 42nd
| Position | Prime | Gap from the previous |
|---|---|---|
| 39 | 167 | 4 |
| 40 | 173 | 6 |
| 41 | 179 | 6 |
| 42 | 181 | 2 |
| 43 | 191 | 10 |
| 44 | 193 | 2 |
| 45 | 197 | 4 |
Questions
What is the 42nd prime number?
181.
Which prime number is 181?
181 is the 42nd prime number.
What is the sum of the first 42 primes?
3,447.