What is the 685th prime number?
The 685th prime number is 5119. The next prime is 5147 (a gap of 28) and the one before is 5113.
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 685th one is 5119.
- 2
5119 is prime because no prime up to ā5119 ā 71.55 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 685th prime is close to 685 Ć ln(685) ā 4473, and here it is 5119.
- 4
5119 has no twin: neither 5117 nor 5121 is prime.
Primes around the 685th
| Position | Prime | Gap from the previous |
|---|---|---|
| 682 | 5101 | 2 |
| 683 | 5107 | 6 |
| 684 | 5113 | 6 |
| 685 | 5119 | 6 |
| 686 | 5147 | 28 |
| 687 | 5153 | 6 |
| 688 | 5167 | 14 |
Questions
What is the 685th prime number?
5119.
Which prime number is 5119?
5119 is the 685th prime number.
What is the sum of the first 685 primes?
1,629,136.