What is the 268th prime number?
The 268th prime number is 1721. The next prime is 1723 (a gap of 2) and the one before is 1709.
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 268th one is 1721.
- 2
1721 is prime because no prime up to ā1721 ā 41.48 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 268th prime is close to 268 Ć ln(268) ā 1498, and here it is 1721.
- 4
1721 is a twin prime: 1721 and 1723 are both prime.
Primes around the 268th
| Position | Prime | Gap from the previous |
|---|---|---|
| 265 | 1697 | 4 |
| 266 | 1699 | 2 |
| 267 | 1709 | 10 |
| 268 | 1721 | 12 |
| 269 | 1723 | 2 |
| 270 | 1733 | 10 |
| 271 | 1741 | 8 |
Questions
What is the 268th prime number?
1721.
Which prime number is 1721?
1721 is the 268th prime number.
What is the sum of the first 268 primes?
211,815.