What is the 175th prime number?
The 175th prime number is 1039. The next prime is 1049 (a gap of 10) and the one before is 1033.
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 175th one is 1039.
- 2
1039 is prime because no prime up to ā1039 ā 32.23 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 175th prime is close to 175 Ć ln(175) ā 904, and here it is 1039.
- 4
1039 has no twin: neither 1037 nor 1041 is prime.
Primes around the 175th
| Position | Prime | Gap from the previous |
|---|---|---|
| 172 | 1021 | 2 |
| 173 | 1031 | 10 |
| 174 | 1033 | 2 |
| 175 | 1039 | 6 |
| 176 | 1049 | 10 |
| 177 | 1051 | 2 |
| 178 | 1061 | 10 |
Questions
What is the 175th prime number?
1039.
Which prime number is 1039?
1039 is the 175th prime number.
What is the sum of the first 175 primes?
83,292.