What is the 496th prime number?
The 496th prime number is 3541. The next prime is 3547 (a gap of 6) and the one before is 3539.
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 496th one is 3541.
- 2
3541 is prime because no prime up to ā3541 ā 59.51 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 496th prime is close to 496 Ć ln(496) ā 3078, and here it is 3541.
- 4
3541 is a twin prime: 3539 and 3541 are both prime.
Primes around the 496th
| Position | Prime | Gap from the previous |
|---|---|---|
| 493 | 3529 | 2 |
| 494 | 3533 | 4 |
| 495 | 3539 | 6 |
| 496 | 3541 | 2 |
| 497 | 3547 | 6 |
| 498 | 3557 | 10 |
| 499 | 3559 | 2 |
Questions
What is the 496th prime number?
3541.
Which prime number is 3541?
3541 is the 496th prime number.
What is the sum of the first 496 primes?
810,459.