What is the 746th prime number?
The 746th prime number is 5659. The next prime is 5669 (a gap of 10) and the one before is 5657.
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 746th one is 5659.
- 2
5659 is prime because no prime up to ā5659 ā 75.23 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 746th prime is close to 746 Ć ln(746) ā 4935, and here it is 5659.
- 4
5659 is a twin prime: 5657 and 5659 are both prime.
Primes around the 746th
| Position | Prime | Gap from the previous |
|---|---|---|
| 743 | 5651 | 4 |
| 744 | 5653 | 2 |
| 745 | 5657 | 4 |
| 746 | 5659 | 2 |
| 747 | 5669 | 10 |
| 748 | 5683 | 14 |
| 749 | 5689 | 6 |
Questions
What is the 746th prime number?
5659.
Which prime number is 5659?
5659 is the 746th prime number.
What is the sum of the first 746 primes?
1,959,373.