What is the 1538th prime number?
The 1538th prime number is 12917. The next prime is 12919 (a gap of 2) and the one before is 12911.
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 1538th one is 12917.
- 2
12917 is prime because no prime up to ā12917 ā 113.65 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 1538th prime is close to 1538 Ć ln(1538) ā 11286, and here it is 12917.
- 4
12917 is a twin prime: 12917 and 12919 are both prime.
Primes around the 1538th
| Position | Prime | Gap from the previous |
|---|---|---|
| 1535 | 12899 | 6 |
| 1536 | 12907 | 8 |
| 1537 | 12911 | 4 |
| 1538 | 12917 | 6 |
| 1539 | 12919 | 2 |
| 1540 | 12923 | 4 |
| 1541 | 12941 | 18 |
Questions
What is the 1538th prime number?
12917.
Which prime number is 12917?
12917 is the 1538th prime number.
What is the sum of the first 1538 primes?
9,280,595.