What is the 266th prime number?
The 266th prime number is 1699. The next prime is 1709 (a gap of 10) and the one before is 1697.
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 266th one is 1699.
- 2
1699 is prime because no prime up to ā1699 ā 41.22 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 266th prime is close to 266 Ć ln(266) ā 1485, and here it is 1699.
- 4
1699 is a twin prime: 1697 and 1699 are both prime.
Primes around the 266th
| Position | Prime | Gap from the previous |
|---|---|---|
| 263 | 1669 | 2 |
| 264 | 1693 | 24 |
| 265 | 1697 | 4 |
| 266 | 1699 | 2 |
| 267 | 1709 | 10 |
| 268 | 1721 | 12 |
| 269 | 1723 | 2 |
Questions
What is the 266th prime number?
1699.
Which prime number is 1699?
1699 is the 266th prime number.
What is the sum of the first 266 primes?
208,385.