What is the 167th prime number?
The 167th prime number is 991. The next prime is 997 (a gap of 6) and the one before is 983.
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 167th one is 991.
- 2
991 is prime because no prime up to ā991 ā 31.48 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 167th prime is close to 167 Ć ln(167) ā 855, and here it is 991.
- 4
991 has no twin: neither 989 nor 993 is prime.
Primes around the 167th
| Position | Prime | Gap from the previous |
|---|---|---|
| 164 | 971 | 4 |
| 165 | 977 | 6 |
| 166 | 983 | 6 |
| 167 | 991 | 8 |
| 168 | 997 | 6 |
| 169 | 1009 | 12 |
| 170 | 1013 | 4 |
Questions
What is the 167th prime number?
991.
Which prime number is 991?
991 is the 167th prime number.
What is the sum of the first 167 primes?
75,130.