What is the 638th prime number?
The 638th prime number is 4729. The next prime is 4733 (a gap of 4) and the one before is 4723.
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 638th one is 4729.
- 2
4729 is prime because no prime up to ā4729 ā 68.77 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 638th prime is close to 638 Ć ln(638) ā 4120, and here it is 4729.
- 4
4729 has no twin: neither 4727 nor 4731 is prime.
Primes around the 638th
| Position | Prime | Gap from the previous |
|---|---|---|
| 635 | 4703 | 12 |
| 636 | 4721 | 18 |
| 637 | 4723 | 2 |
| 638 | 4729 | 6 |
| 639 | 4733 | 4 |
| 640 | 4751 | 18 |
| 641 | 4759 | 8 |
Questions
What is the 638th prime number?
4729.
Which prime number is 4729?
4729 is the 638th prime number.
What is the sum of the first 638 primes?
1,396,911.