What is the 3500th prime number?
The 3500th prime number is 32609. The next prime is 32611 (a gap of 2) and the one before is 32603.
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 3500th one is 32609.
- 2
32609 is prime because no prime up to ā32609 ā 180.58 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 3500th prime is close to 3500 Ć ln(3500) ā 28562, and here it is 32609.
- 4
32609 is a twin prime: 32609 and 32611 are both prime.
Primes around the 3500th
| Position | Prime | Gap from the previous |
|---|---|---|
| 3497 | 32579 | 6 |
| 3498 | 32587 | 8 |
| 3499 | 32603 | 16 |
| 3500 | 32609 | 6 |
| 3501 | 32611 | 2 |
| 3502 | 32621 | 10 |
| 3503 | 32633 | 12 |
Questions
What is the 3500th prime number?
32609.
Which prime number is 32609?
32609 is the 3500th prime number.
What is the sum of the first 3500 primes?
53,664,613.