What is the 748th prime number?
The 748th prime number is 5683. The next prime is 5689 (a gap of 6) and the one before is 5669.
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 748th one is 5683.
- 2
5683 is prime because no prime up to ā5683 ā 75.39 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 748th prime is close to 748 Ć ln(748) ā 4950, and here it is 5683.
- 4
5683 has no twin: neither 5681 nor 5685 is prime.
Primes around the 748th
| Position | Prime | Gap from the previous |
|---|---|---|
| 745 | 5657 | 4 |
| 746 | 5659 | 2 |
| 747 | 5669 | 10 |
| 748 | 5683 | 14 |
| 749 | 5689 | 6 |
| 750 | 5693 | 4 |
| 751 | 5701 | 8 |
Questions
What is the 748th prime number?
5683.
Which prime number is 5683?
5683 is the 748th prime number.
What is the sum of the first 748 primes?
1,970,725.