What is the 686th prime number?
The 686th prime number is 5147. The next prime is 5153 (a gap of 6) and the one before is 5119.
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 686th one is 5147.
- 2
5147 is prime because no prime up to ā5147 ā 71.74 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 686th prime is close to 686 Ć ln(686) ā 4480, and here it is 5147.
- 4
5147 has no twin: neither 5145 nor 5149 is prime.
Primes around the 686th
| Position | Prime | Gap from the previous |
|---|---|---|
| 683 | 5107 | 6 |
| 684 | 5113 | 6 |
| 685 | 5119 | 6 |
| 686 | 5147 | 28 |
| 687 | 5153 | 6 |
| 688 | 5167 | 14 |
| 689 | 5171 | 4 |
Questions
What is the 686th prime number?
5147.
Which prime number is 5147?
5147 is the 686th prime number.
What is the sum of the first 686 primes?
1,634,283.