What is the 2538th prime number?
The 2538th prime number is 22717. The next prime is 22721 (a gap of 4) and the one before is 22709.
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 2538th one is 22717.
- 2
22717 is prime because no prime up to ā22717 ā 150.72 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 2538th prime is close to 2538 Ć ln(2538) ā 19896, and here it is 22717.
- 4
22717 has no twin: neither 22715 nor 22719 is prime.
Primes around the 2538th
| Position | Prime | Gap from the previous |
|---|---|---|
| 2535 | 22697 | 6 |
| 2536 | 22699 | 2 |
| 2537 | 22709 | 10 |
| 2538 | 22717 | 8 |
| 2539 | 22721 | 4 |
| 2540 | 22727 | 6 |
| 2541 | 22739 | 12 |
Questions
What is the 2538th prime number?
22717.
Which prime number is 22717?
22717 is the 2538th prime number.
What is the sum of the first 2538 primes?
27,067,409.