What is the 33rd prime number?
The 33rd prime number is 137. The next prime is 139 (a gap of 2) and the one before is 131.
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 33rd one is 137.
- 2
137 is prime because no prime up to ā137 ā 11.70 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 33rd prime is close to 33 Ć ln(33) ā 115, and here it is 137.
- 4
137 is a twin prime: 137 and 139 are both prime.
Primes around the 33rd
| Position | Prime | Gap from the previous |
|---|---|---|
| 30 | 113 | 4 |
| 31 | 127 | 14 |
| 32 | 131 | 4 |
| 33 | 137 | 6 |
| 34 | 139 | 2 |
| 35 | 149 | 10 |
| 36 | 151 | 2 |
Questions
What is the 33rd prime number?
137.
Which prime number is 137?
137 is the 33rd prime number.
What is the sum of the first 33 primes?
1,988.