What is the 36th prime number?
The 36th prime number is 151. The next prime is 157 (a gap of 6) and the one before is 149.
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 36th one is 151.
- 2
151 is prime because no prime up to ā151 ā 12.29 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 36th prime is close to 36 Ć ln(36) ā 129, and here it is 151.
- 4
151 is a twin prime: 149 and 151 are both prime.
Primes around the 36th
| Position | Prime | Gap from the previous |
|---|---|---|
| 33 | 137 | 6 |
| 34 | 139 | 2 |
| 35 | 149 | 10 |
| 36 | 151 | 2 |
| 37 | 157 | 6 |
| 38 | 163 | 6 |
| 39 | 167 | 4 |
Questions
What is the 36th prime number?
151.
Which prime number is 151?
151 is the 36th prime number.
What is the sum of the first 36 primes?
2,427.