What is the 681st prime number?
The 681st prime number is 5099. The next prime is 5101 (a gap of 2) and the one before is 5087.
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 681st one is 5099.
- 2
5099 is prime because no prime up to ā5099 ā 71.41 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 681st prime is close to 681 Ć ln(681) ā 4443, and here it is 5099.
- 4
5099 is a twin prime: 5099 and 5101 are both prime.
Primes around the 681st
| Position | Prime | Gap from the previous |
|---|---|---|
| 678 | 5077 | 18 |
| 679 | 5081 | 4 |
| 680 | 5087 | 6 |
| 681 | 5099 | 12 |
| 682 | 5101 | 2 |
| 683 | 5107 | 6 |
| 684 | 5113 | 6 |
Questions
What is the 681st prime number?
5099.
Which prime number is 5099?
5099 is the 681st prime number.
What is the sum of the first 681 primes?
1,608,696.