What is the 3300th prime number?
The 3300th prime number is 30559. The next prime is 30577 (a gap of 18) and the one before is 30557.
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 3300th one is 30559.
- 2
30559 is prime because no prime up to ā30559 ā 174.81 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 3300th prime is close to 3300 Ć ln(3300) ā 26736, and here it is 30559.
- 4
30559 is a twin prime: 30557 and 30559 are both prime.
Primes around the 3300th
| Position | Prime | Gap from the previous |
|---|---|---|
| 3297 | 30539 | 10 |
| 3298 | 30553 | 14 |
| 3299 | 30557 | 4 |
| 3300 | 30559 | 2 |
| 3301 | 30577 | 18 |
| 3302 | 30593 | 16 |
| 3303 | 30631 | 38 |
Questions
What is the 3300th prime number?
30559.
Which prime number is 30559?
30559 is the 3300th prime number.
What is the sum of the first 3300 primes?
47,341,329.