What is the 265th prime number?
The 265th prime number is 1697. The next prime is 1699 (a gap of 2) and the one before is 1693.
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 265th one is 1697.
- 2
1697 is prime because no prime up to ā1697 ā 41.19 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 265th prime is close to 265 Ć ln(265) ā 1479, and here it is 1697.
- 4
1697 is a twin prime: 1697 and 1699 are both prime.
Primes around the 265th
| Position | Prime | Gap from the previous |
|---|---|---|
| 262 | 1667 | 4 |
| 263 | 1669 | 2 |
| 264 | 1693 | 24 |
| 265 | 1697 | 4 |
| 266 | 1699 | 2 |
| 267 | 1709 | 10 |
| 268 | 1721 | 12 |
Questions
What is the 265th prime number?
1697.
Which prime number is 1697?
1697 is the 265th prime number.
What is the sum of the first 265 primes?
206,686.