What is the 501st prime number?
The 501st prime number is 3581. The next prime is 3583 (a gap of 2) and the one before is 3571.
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 501st one is 3581.
- 2
3581 is prime because no prime up to ā3581 ā 59.84 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 501st prime is close to 501 Ć ln(501) ā 3115, and here it is 3581.
- 4
3581 is a twin prime: 3581 and 3583 are both prime.
Primes around the 501st
| Position | Prime | Gap from the previous |
|---|---|---|
| 498 | 3557 | 10 |
| 499 | 3559 | 2 |
| 500 | 3571 | 12 |
| 501 | 3581 | 10 |
| 502 | 3583 | 2 |
| 503 | 3593 | 10 |
| 504 | 3607 | 14 |
Questions
What is the 501st prime number?
3581.
Which prime number is 3581?
3581 is the 501st prime number.
What is the sum of the first 501 primes?
828,274.