What is the 689th prime number?
The 689th prime number is 5171. The next prime is 5179 (a gap of 8) and the one before is 5167.
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 689th one is 5171.
- 2
5171 is prime because no prime up to ā5171 ā 71.91 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 689th prime is close to 689 Ć ln(689) ā 4503, and here it is 5171.
- 4
5171 has no twin: neither 5169 nor 5173 is prime.
Primes around the 689th
| Position | Prime | Gap from the previous |
|---|---|---|
| 686 | 5147 | 28 |
| 687 | 5153 | 6 |
| 688 | 5167 | 14 |
| 689 | 5171 | 4 |
| 690 | 5179 | 8 |
| 691 | 5189 | 10 |
| 692 | 5197 | 8 |
Questions
What is the 689th prime number?
5171.
Which prime number is 5171?
5171 is the 689th prime number.
What is the sum of the first 689 primes?
1,649,774.