What is the 264th prime number?
The 264th prime number is 1693. The next prime is 1697 (a gap of 4) and the one before is 1669.
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 264th one is 1693.
- 2
1693 is prime because no prime up to ā1693 ā 41.15 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 264th prime is close to 264 Ć ln(264) ā 1472, and here it is 1693.
- 4
1693 has no twin: neither 1691 nor 1695 is prime.
Primes around the 264th
| Position | Prime | Gap from the previous |
|---|---|---|
| 261 | 1663 | 6 |
| 262 | 1667 | 4 |
| 263 | 1669 | 2 |
| 264 | 1693 | 24 |
| 265 | 1697 | 4 |
| 266 | 1699 | 2 |
| 267 | 1709 | 10 |
Questions
What is the 264th prime number?
1693.
Which prime number is 1693?
1693 is the 264th prime number.
What is the sum of the first 264 primes?
204,989.