What is the 742nd prime number?
The 742nd prime number is 5647. The next prime is 5651 (a gap of 4) and the one before is 5641.
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 742nd one is 5647.
- 2
5647 is prime because no prime up to ā5647 ā 75.15 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 742nd prime is close to 742 Ć ln(742) ā 4904, and here it is 5647.
- 4
5647 has no twin: neither 5645 nor 5649 is prime.
Primes around the 742nd
| Position | Prime | Gap from the previous |
|---|---|---|
| 739 | 5623 | 32 |
| 740 | 5639 | 16 |
| 741 | 5641 | 2 |
| 742 | 5647 | 6 |
| 743 | 5651 | 4 |
| 744 | 5653 | 2 |
| 745 | 5657 | 4 |
Questions
What is the 742nd prime number?
5647.
Which prime number is 5647?
5647 is the 742nd prime number.
What is the sum of the first 742 primes?
1,936,753.