What is the 497th prime number?
The 497th prime number is 3547. The next prime is 3557 (a gap of 10) and the one before is 3541.
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 497th one is 3547.
- 2
3547 is prime because no prime up to ā3547 ā 59.56 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 497th prime is close to 497 Ć ln(497) ā 3086, and here it is 3547.
- 4
3547 has no twin: neither 3545 nor 3549 is prime.
Primes around the 497th
| Position | Prime | Gap from the previous |
|---|---|---|
| 494 | 3533 | 4 |
| 495 | 3539 | 6 |
| 496 | 3541 | 2 |
| 497 | 3547 | 6 |
| 498 | 3557 | 10 |
| 499 | 3559 | 2 |
| 500 | 3571 | 12 |
Questions
What is the 497th prime number?
3547.
Which prime number is 3547?
3547 is the 497th prime number.
What is the sum of the first 497 primes?
814,006.