What is the 164th prime number?
The 164th prime number is 971. The next prime is 977 (a gap of 6) and the one before is 967.
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 164th one is 971.
- 2
971 is prime because no prime up to ā971 ā 31.16 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 164th prime is close to 164 Ć ln(164) ā 836, and here it is 971.
- 4
971 has no twin: neither 969 nor 973 is prime.
Primes around the 164th
| Position | Prime | Gap from the previous |
|---|---|---|
| 161 | 947 | 6 |
| 162 | 953 | 6 |
| 163 | 967 | 14 |
| 164 | 971 | 4 |
| 165 | 977 | 6 |
| 166 | 983 | 6 |
| 167 | 991 | 8 |
Questions
What is the 164th prime number?
971.
Which prime number is 971?
971 is the 164th prime number.
What is the sum of the first 164 primes?
72,179.