What is the 1305th prime number?
The 1305th prime number is 10709. The next prime is 10711 (a gap of 2) and the one before is 10691.
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 1305th one is 10709.
- 2
10709 is prime because no prime up to ā10709 ā 103.48 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 1305th prime is close to 1305 Ć ln(1305) ā 9362, and here it is 10709.
- 4
10709 is a twin prime: 10709 and 10711 are both prime.
Primes around the 1305th
| Position | Prime | Gap from the previous |
|---|---|---|
| 1302 | 10667 | 4 |
| 1303 | 10687 | 20 |
| 1304 | 10691 | 4 |
| 1305 | 10709 | 18 |
| 1306 | 10711 | 2 |
| 1307 | 10723 | 12 |
| 1308 | 10729 | 6 |
Questions
What is the 1305th prime number?
10709.
Which prime number is 10709?
10709 is the 1305th prime number.
What is the sum of the first 1305 primes?
6,522,914.