What is the 675th prime number?
The 675th prime number is 5039. The next prime is 5051 (a gap of 12) and the one before is 5023.
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 675th one is 5039.
- 2
5039 is prime because no prime up to ā5039 ā 70.99 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 675th prime is close to 675 Ć ln(675) ā 4397, and here it is 5039.
- 4
5039 has no twin: neither 5037 nor 5041 is prime.
Primes around the 675th
| Position | Prime | Gap from the previous |
|---|---|---|
| 672 | 5011 | 2 |
| 673 | 5021 | 10 |
| 674 | 5023 | 2 |
| 675 | 5039 | 16 |
| 676 | 5051 | 12 |
| 677 | 5059 | 8 |
| 678 | 5077 | 18 |
Questions
What is the 675th prime number?
5039.
Which prime number is 5039?
5039 is the 675th prime number.
What is the sum of the first 675 primes?
1,578,242.