What is the 3638th prime number?
The 3638th prime number is 33997. The next prime is 34019 (a gap of 22) and the one before is 33967.
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 3638th one is 33997.
- 2
33997 is prime because no prime up to ā33997 ā 184.38 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 3638th prime is close to 3638 Ć ln(3638) ā 29829, and here it is 33997.
- 4
33997 has no twin: neither 33995 nor 33999 is prime.
Primes around the 3638th
| Position | Prime | Gap from the previous |
|---|---|---|
| 3635 | 33941 | 4 |
| 3636 | 33961 | 20 |
| 3637 | 33967 | 6 |
| 3638 | 33997 | 30 |
| 3639 | 34019 | 22 |
| 3640 | 34031 | 12 |
| 3641 | 34033 | 2 |
Questions
What is the 3638th prime number?
33997.
Which prime number is 33997?
33997 is the 3638th prime number.
What is the sum of the first 3638 primes?
58,262,037.