What is the 2140th prime number?
The 2140th prime number is 18749. The next prime is 18757 (a gap of 8) and the one before is 18743.
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 2140th one is 18749.
- 2
18749 is prime because no prime up to ā18749 ā 136.93 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 2140th prime is close to 2140 Ć ln(2140) ā 16411, and here it is 18749.
- 4
18749 has no twin: neither 18747 nor 18751 is prime.
Primes around the 2140th
| Position | Prime | Gap from the previous |
|---|---|---|
| 2137 | 18719 | 6 |
| 2138 | 18731 | 12 |
| 2139 | 18743 | 12 |
| 2140 | 18749 | 6 |
| 2141 | 18757 | 8 |
| 2142 | 18773 | 16 |
| 2143 | 18787 | 14 |
Questions
What is the 2140th prime number?
18749.
Which prime number is 18749?
18749 is the 2140th prime number.
What is the sum of the first 2140 primes?
18,802,735.