What is the 687th prime number?
The 687th prime number is 5153. The next prime is 5167 (a gap of 14) and the one before is 5147.
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 687th one is 5153.
- 2
5153 is prime because no prime up to ā5153 ā 71.78 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 687th prime is close to 687 Ć ln(687) ā 4488, and here it is 5153.
- 4
5153 has no twin: neither 5151 nor 5155 is prime.
Primes around the 687th
| Position | Prime | Gap from the previous |
|---|---|---|
| 684 | 5113 | 6 |
| 685 | 5119 | 6 |
| 686 | 5147 | 28 |
| 687 | 5153 | 6 |
| 688 | 5167 | 14 |
| 689 | 5171 | 4 |
| 690 | 5179 | 8 |
Questions
What is the 687th prime number?
5153.
Which prime number is 5153?
5153 is the 687th prime number.
What is the sum of the first 687 primes?
1,639,436.