What is the 2038th prime number?
The 2038th prime number is 17749. The next prime is 17761 (a gap of 12) and the one before is 17747.
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 2038th one is 17749.
- 2
17749 is prime because no prime up to ā17749 ā 133.23 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 2038th prime is close to 2038 Ć ln(2038) ā 15529, and here it is 17749.
- 4
17749 is a twin prime: 17747 and 17749 are both prime.
Primes around the 2038th
| Position | Prime | Gap from the previous |
|---|---|---|
| 2035 | 17729 | 16 |
| 2036 | 17737 | 8 |
| 2037 | 17747 | 10 |
| 2038 | 17749 | 2 |
| 2039 | 17761 | 12 |
| 2040 | 17783 | 22 |
| 2041 | 17789 | 6 |
Questions
What is the 2038th prime number?
17749.
Which prime number is 17749?
17749 is the 2038th prime number.
What is the sum of the first 2038 primes?
16,942,161.