What is the 267th prime number?
The 267th prime number is 1709. The next prime is 1721 (a gap of 12) and the one before is 1699.
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 267th one is 1709.
- 2
1709 is prime because no prime up to ā1709 ā 41.34 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 267th prime is close to 267 Ć ln(267) ā 1492, and here it is 1709.
- 4
1709 has no twin: neither 1707 nor 1711 is prime.
Primes around the 267th
| Position | Prime | Gap from the previous |
|---|---|---|
| 264 | 1693 | 24 |
| 265 | 1697 | 4 |
| 266 | 1699 | 2 |
| 267 | 1709 | 10 |
| 268 | 1721 | 12 |
| 269 | 1723 | 2 |
| 270 | 1733 | 10 |
Questions
What is the 267th prime number?
1709.
Which prime number is 1709?
1709 is the 267th prime number.
What is the sum of the first 267 primes?
210,094.