What is the 745th prime number?
The 745th prime number is 5657. The next prime is 5659 (a gap of 2) and the one before is 5653.
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 745th one is 5657.
- 2
5657 is prime because no prime up to ā5657 ā 75.21 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 745th prime is close to 745 Ć ln(745) ā 4927, and here it is 5657.
- 4
5657 is a twin prime: 5657 and 5659 are both prime.
Primes around the 745th
| Position | Prime | Gap from the previous |
|---|---|---|
| 742 | 5647 | 6 |
| 743 | 5651 | 4 |
| 744 | 5653 | 2 |
| 745 | 5657 | 4 |
| 746 | 5659 | 2 |
| 747 | 5669 | 10 |
| 748 | 5683 | 14 |
Questions
What is the 745th prime number?
5657.
Which prime number is 5657?
5657 is the 745th prime number.
What is the sum of the first 745 primes?
1,953,714.