What is the 168th prime number?
The 168th prime number is 997. The next prime is 1009 (a gap of 12) and the one before is 991.
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 168th one is 997.
- 2
997 is prime because no prime up to ā997 ā 31.58 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 168th prime is close to 168 Ć ln(168) ā 861, and here it is 997.
- 4
997 has no twin: neither 995 nor 999 is prime.
Primes around the 168th
| Position | Prime | Gap from the previous |
|---|---|---|
| 165 | 977 | 6 |
| 166 | 983 | 6 |
| 167 | 991 | 8 |
| 168 | 997 | 6 |
| 169 | 1009 | 12 |
| 170 | 1013 | 4 |
| 171 | 1019 | 6 |
Questions
What is the 168th prime number?
997.
Which prime number is 997?
997 is the 168th prime number.
What is the sum of the first 168 primes?
76,127.