What is the 705th prime number?
The 705th prime number is 5323. The next prime is 5333 (a gap of 10) and the one before is 5309.
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 705th one is 5323.
- 2
5323 is prime because no prime up to ā5323 ā 72.96 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 705th prime is close to 705 Ć ln(705) ā 4624, and here it is 5323.
- 4
5323 has no twin: neither 5321 nor 5325 is prime.
Primes around the 705th
| Position | Prime | Gap from the previous |
|---|---|---|
| 702 | 5297 | 16 |
| 703 | 5303 | 6 |
| 704 | 5309 | 6 |
| 705 | 5323 | 14 |
| 706 | 5333 | 10 |
| 707 | 5347 | 14 |
| 708 | 5351 | 4 |
Questions
What is the 705th prime number?
5323.
Which prime number is 5323?
5323 is the 705th prime number.
What is the sum of the first 705 primes?
1,733,802.