What is the 463rd prime number?
The 463rd prime number is 3299. The next prime is 3301 (a gap of 2) and the one before is 3271.
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 463rd one is 3299.
- 2
3299 is prime because no prime up to ā3299 ā 57.44 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 463rd prime is close to 463 Ć ln(463) ā 2842, and here it is 3299.
- 4
3299 is a twin prime: 3299 and 3301 are both prime.
Primes around the 463rd
| Position | Prime | Gap from the previous |
|---|---|---|
| 460 | 3257 | 4 |
| 461 | 3259 | 2 |
| 462 | 3271 | 12 |
| 463 | 3299 | 28 |
| 464 | 3301 | 2 |
| 465 | 3307 | 6 |
| 466 | 3313 | 6 |
Questions
What is the 463rd prime number?
3299.
Which prime number is 3299?
3299 is the 463rd prime number.
What is the sum of the first 463 primes?
697,596.