What is the 35th prime number?
The 35th prime number is 149. The next prime is 151 (a gap of 2) and the one before is 139.
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 35th one is 149.
- 2
149 is prime because no prime up to ā149 ā 12.21 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 35th prime is close to 35 Ć ln(35) ā 124, and here it is 149.
- 4
149 is a twin prime: 149 and 151 are both prime.
Primes around the 35th
| Position | Prime | Gap from the previous |
|---|---|---|
| 32 | 131 | 4 |
| 33 | 137 | 6 |
| 34 | 139 | 2 |
| 35 | 149 | 10 |
| 36 | 151 | 2 |
| 37 | 157 | 6 |
| 38 | 163 | 6 |
Questions
What is the 35th prime number?
149.
Which prime number is 149?
149 is the 35th prime number.
What is the sum of the first 35 primes?
2,276.