What is the 684th prime number?
The 684th prime number is 5113. The next prime is 5119 (a gap of 6) and the one before is 5107.
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 684th one is 5113.
- 2
5113 is prime because no prime up to ā5113 ā 71.51 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 684th prime is close to 684 Ć ln(684) ā 4465, and here it is 5113.
- 4
5113 has no twin: neither 5111 nor 5115 is prime.
Primes around the 684th
| Position | Prime | Gap from the previous |
|---|---|---|
| 681 | 5099 | 12 |
| 682 | 5101 | 2 |
| 683 | 5107 | 6 |
| 684 | 5113 | 6 |
| 685 | 5119 | 6 |
| 686 | 5147 | 28 |
| 687 | 5153 | 6 |
Questions
What is the 684th prime number?
5113.
Which prime number is 5113?
5113 is the 684th prime number.
What is the sum of the first 684 primes?
1,624,017.