What is the 174th prime number?
The 174th prime number is 1033. The next prime is 1039 (a gap of 6) and the one before is 1031.
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 174th one is 1033.
- 2
1033 is prime because no prime up to ā1033 ā 32.14 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 174th prime is close to 174 Ć ln(174) ā 898, and here it is 1033.
- 4
1033 is a twin prime: 1031 and 1033 are both prime.
Primes around the 174th
| Position | Prime | Gap from the previous |
|---|---|---|
| 171 | 1019 | 6 |
| 172 | 1021 | 2 |
| 173 | 1031 | 10 |
| 174 | 1033 | 2 |
| 175 | 1039 | 6 |
| 176 | 1049 | 10 |
| 177 | 1051 | 2 |
Questions
What is the 174th prime number?
1033.
Which prime number is 1033?
1033 is the 174th prime number.
What is the sum of the first 174 primes?
82,253.