What is the 3686th prime number?
The 3686th prime number is 34501. The next prime is 34511 (a gap of 10) and the one before is 34499.
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 3686th one is 34501.
- 2
34501 is prime because no prime up to ā34501 ā 185.74 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 3686th prime is close to 3686 Ć ln(3686) ā 30271, and here it is 34501.
- 4
34501 is a twin prime: 34499 and 34501 are both prime.
Primes around the 3686th
| Position | Prime | Gap from the previous |
|---|---|---|
| 3683 | 34483 | 12 |
| 3684 | 34487 | 4 |
| 3685 | 34499 | 12 |
| 3686 | 34501 | 2 |
| 3687 | 34511 | 10 |
| 3688 | 34513 | 2 |
| 3689 | 34519 | 6 |
Questions
What is the 3686th prime number?
34501.
Which prime number is 34501?
34501 is the 3686th prime number.
What is the sum of the first 3686 primes?
59,907,167.