What is the 461st prime number?
The 461st prime number is 3259. The next prime is 3271 (a gap of 12) and the one before is 3257.
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 461st one is 3259.
- 2
3259 is prime because no prime up to ā3259 ā 57.09 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 461st prime is close to 461 Ć ln(461) ā 2827, and here it is 3259.
- 4
3259 is a twin prime: 3257 and 3259 are both prime.
Primes around the 461st
| Position | Prime | Gap from the previous |
|---|---|---|
| 458 | 3251 | 22 |
| 459 | 3253 | 2 |
| 460 | 3257 | 4 |
| 461 | 3259 | 2 |
| 462 | 3271 | 12 |
| 463 | 3299 | 28 |
| 464 | 3301 | 2 |
Questions
What is the 461st prime number?
3259.
Which prime number is 3259?
3259 is the 461st prime number.
What is the sum of the first 461 primes?
691,026.