What is the 170th prime number?
The 170th prime number is 1013. The next prime is 1019 (a gap of 6) and the one before is 1009.
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 170th one is 1013.
- 2
1013 is prime because no prime up to ā1013 ā 31.83 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 170th prime is close to 170 Ć ln(170) ā 873, and here it is 1013.
- 4
1013 has no twin: neither 1011 nor 1015 is prime.
Primes around the 170th
| Position | Prime | Gap from the previous |
|---|---|---|
| 167 | 991 | 8 |
| 168 | 997 | 6 |
| 169 | 1009 | 12 |
| 170 | 1013 | 4 |
| 171 | 1019 | 6 |
| 172 | 1021 | 2 |
| 173 | 1031 | 10 |
Questions
What is the 170th prime number?
1013.
Which prime number is 1013?
1013 is the 170th prime number.
What is the sum of the first 170 primes?
78,149.