What is the 165th prime number?
The 165th prime number is 977. The next prime is 983 (a gap of 6) and the one before is 971.
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 165th one is 977.
- 2
977 is prime because no prime up to ā977 ā 31.26 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 165th prime is close to 165 Ć ln(165) ā 842, and here it is 977.
- 4
977 has no twin: neither 975 nor 979 is prime.
Primes around the 165th
| Position | Prime | Gap from the previous |
|---|---|---|
| 162 | 953 | 6 |
| 163 | 967 | 14 |
| 164 | 971 | 4 |
| 165 | 977 | 6 |
| 166 | 983 | 6 |
| 167 | 991 | 8 |
| 168 | 997 | 6 |
Questions
What is the 165th prime number?
977.
Which prime number is 977?
977 is the 165th prime number.
What is the sum of the first 165 primes?
73,156.