What is the 163rd prime number?
The 163rd prime number is 967. The next prime is 971 (a gap of 4) and the one before is 953.
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 163rd one is 967.
- 2
967 is prime because no prime up to ā967 ā 31.10 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 163rd prime is close to 163 Ć ln(163) ā 830, and here it is 967.
- 4
967 has no twin: neither 965 nor 969 is prime.
Primes around the 163rd
| Position | Prime | Gap from the previous |
|---|---|---|
| 160 | 941 | 4 |
| 161 | 947 | 6 |
| 162 | 953 | 6 |
| 163 | 967 | 14 |
| 164 | 971 | 4 |
| 165 | 977 | 6 |
| 166 | 983 | 6 |
Questions
What is the 163rd prime number?
967.
Which prime number is 967?
967 is the 163rd prime number.
What is the sum of the first 163 primes?
71,208.