What is the 3688th prime number?
The 3688th prime number is 34513. The next prime is 34519 (a gap of 6) and the one before is 34511.
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 3688th one is 34513.
- 2
34513 is prime because no prime up to ā34513 ā 185.78 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 3688th prime is close to 3688 Ć ln(3688) ā 30289, and here it is 34513.
- 4
34513 is a twin prime: 34511 and 34513 are both prime.
Primes around the 3688th
| Position | Prime | Gap from the previous |
|---|---|---|
| 3685 | 34499 | 12 |
| 3686 | 34501 | 2 |
| 3687 | 34511 | 10 |
| 3688 | 34513 | 2 |
| 3689 | 34519 | 6 |
| 3690 | 34537 | 18 |
| 3691 | 34543 | 6 |
Questions
What is the 3688th prime number?
34513.
Which prime number is 34513?
34513 is the 3688th prime number.
What is the sum of the first 3688 primes?
59,976,191.