What is the 491st prime number?
The 491st prime number is 3517. The next prime is 3527 (a gap of 10) and the one before is 3511.
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 491st one is 3517.
- 2
3517 is prime because no prime up to ā3517 ā 59.30 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 491st prime is close to 491 Ć ln(491) ā 3042, and here it is 3517.
- 4
3517 has no twin: neither 3515 nor 3519 is prime.
Primes around the 491st
| Position | Prime | Gap from the previous |
|---|---|---|
| 488 | 3491 | 22 |
| 489 | 3499 | 8 |
| 490 | 3511 | 12 |
| 491 | 3517 | 6 |
| 492 | 3527 | 10 |
| 493 | 3529 | 2 |
| 494 | 3533 | 4 |
Questions
What is the 491st prime number?
3517.
Which prime number is 3517?
3517 is the 491st prime number.
What is the sum of the first 491 primes?
792,790.