What is the 680th prime number?
The 680th prime number is 5087. The next prime is 5099 (a gap of 12) and the one before is 5081.
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 680th one is 5087.
- 2
5087 is prime because no prime up to ā5087 ā 71.32 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 680th prime is close to 680 Ć ln(680) ā 4435, and here it is 5087.
- 4
5087 has no twin: neither 5085 nor 5089 is prime.
Primes around the 680th
| Position | Prime | Gap from the previous |
|---|---|---|
| 677 | 5059 | 8 |
| 678 | 5077 | 18 |
| 679 | 5081 | 4 |
| 680 | 5087 | 6 |
| 681 | 5099 | 12 |
| 682 | 5101 | 2 |
| 683 | 5107 | 6 |
Questions
What is the 680th prime number?
5087.
Which prime number is 5087?
5087 is the 680th prime number.
What is the sum of the first 680 primes?
1,603,597.