What is the 688th prime number?
The 688th prime number is 5167. The next prime is 5171 (a gap of 4) and the one before is 5153.
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 688th one is 5167.
- 2
5167 is prime because no prime up to ā5167 ā 71.88 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 688th prime is close to 688 Ć ln(688) ā 4495, and here it is 5167.
- 4
5167 has no twin: neither 5165 nor 5169 is prime.
Primes around the 688th
| Position | Prime | Gap from the previous |
|---|---|---|
| 685 | 5119 | 6 |
| 686 | 5147 | 28 |
| 687 | 5153 | 6 |
| 688 | 5167 | 14 |
| 689 | 5171 | 4 |
| 690 | 5179 | 8 |
| 691 | 5189 | 10 |
Questions
What is the 688th prime number?
5167.
Which prime number is 5167?
5167 is the 688th prime number.
What is the sum of the first 688 primes?
1,644,603.