What is the 34th prime number?
The 34th prime number is 139. The next prime is 149 (a gap of 10) and the one before is 137.
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 34th one is 139.
- 2
139 is prime because no prime up to ā139 ā 11.79 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 34th prime is close to 34 Ć ln(34) ā 120, and here it is 139.
- 4
139 is a twin prime: 137 and 139 are both prime.
Primes around the 34th
| Position | Prime | Gap from the previous |
|---|---|---|
| 31 | 127 | 14 |
| 32 | 131 | 4 |
| 33 | 137 | 6 |
| 34 | 139 | 2 |
| 35 | 149 | 10 |
| 36 | 151 | 2 |
| 37 | 157 | 6 |
Questions
What is the 34th prime number?
139.
Which prime number is 139?
139 is the 34th prime number.
What is the sum of the first 34 primes?
2,127.