What is the 1638th prime number?
The 1638th prime number is 13873. The next prime is 13877 (a gap of 4) and the one before is 13859.
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 1638th one is 13873.
- 2
13873 is prime because no prime up to ā13873 ā 117.78 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 1638th prime is close to 1638 Ć ln(1638) ā 12123, and here it is 13873.
- 4
13873 has no twin: neither 13871 nor 13875 is prime.
Primes around the 1638th
| Position | Prime | Gap from the previous |
|---|---|---|
| 1635 | 13831 | 2 |
| 1636 | 13841 | 10 |
| 1637 | 13859 | 18 |
| 1638 | 13873 | 14 |
| 1639 | 13877 | 4 |
| 1640 | 13879 | 2 |
| 1641 | 13883 | 4 |
Questions
What is the 1638th prime number?
13873.
Which prime number is 13873?
13873 is the 1638th prime number.
What is the sum of the first 1638 primes?
10,619,617.