What is the 393rd prime number?
The 393rd prime number is 2699. The next prime is 2707 (a gap of 8) and the one before is 2693.
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 393rd one is 2699.
- 2
2699 is prime because no prime up to ā2699 ā 51.95 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 393rd prime is close to 393 Ć ln(393) ā 2348, and here it is 2699.
- 4
2699 has no twin: neither 2697 nor 2701 is prime.
Primes around the 393rd
| Position | Prime | Gap from the previous |
|---|---|---|
| 390 | 2687 | 4 |
| 391 | 2689 | 2 |
| 392 | 2693 | 4 |
| 393 | 2699 | 6 |
| 394 | 2707 | 8 |
| 395 | 2711 | 4 |
| 396 | 2713 | 2 |
Questions
What is the 393rd prime number?
2699.
Which prime number is 2699?
2699 is the 393rd prime number.
What is the sum of the first 393 primes?
488,774.