What is the 173rd prime number?
The 173rd prime number is 1031. The next prime is 1033 (a gap of 2) and the one before is 1021.
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 173rd one is 1031.
- 2
1031 is prime because no prime up to ā1031 ā 32.11 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 173rd prime is close to 173 Ć ln(173) ā 892, and here it is 1031.
- 4
1031 is a twin prime: 1031 and 1033 are both prime.
Primes around the 173rd
| Position | Prime | Gap from the previous |
|---|---|---|
| 170 | 1013 | 4 |
| 171 | 1019 | 6 |
| 172 | 1021 | 2 |
| 173 | 1031 | 10 |
| 174 | 1033 | 2 |
| 175 | 1039 | 6 |
| 176 | 1049 | 10 |
Questions
What is the 173rd prime number?
1031.
Which prime number is 1031?
1031 is the 173rd prime number.
What is the sum of the first 173 primes?
81,220.