What is the 2138th prime number?
The 2138th prime number is 18731. The next prime is 18743 (a gap of 12) and the one before is 18719.
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 2138th one is 18731.
- 2
18731 is prime because no prime up to ā18731 ā 136.86 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 2138th prime is close to 2138 Ć ln(2138) ā 16393, and here it is 18731.
- 4
18731 has no twin: neither 18729 nor 18733 is prime.
Primes around the 2138th
| Position | Prime | Gap from the previous |
|---|---|---|
| 2135 | 18701 | 10 |
| 2136 | 18713 | 12 |
| 2137 | 18719 | 6 |
| 2138 | 18731 | 12 |
| 2139 | 18743 | 12 |
| 2140 | 18749 | 6 |
| 2141 | 18757 | 8 |
Questions
What is the 2138th prime number?
18731.
Which prime number is 18731?
18731 is the 2138th prime number.
What is the sum of the first 2138 primes?
18,765,243.