What is the 2013th prime number?
The 2013th prime number is 17491. The next prime is 17497 (a gap of 6) and the one before is 17489.
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 2013th one is 17491.
- 2
17491 is prime because no prime up to ā17491 ā 132.25 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 2013th prime is close to 2013 Ć ln(2013) ā 15314, and here it is 17491.
- 4
17491 is a twin prime: 17489 and 17491 are both prime.
Primes around the 2013th
| Position | Prime | Gap from the previous |
|---|---|---|
| 2010 | 17477 | 6 |
| 2011 | 17483 | 6 |
| 2012 | 17489 | 6 |
| 2013 | 17491 | 2 |
| 2014 | 17497 | 6 |
| 2015 | 17509 | 12 |
| 2016 | 17519 | 10 |
Questions
What is the 2013th prime number?
17491.
Which prime number is 17491?
17491 is the 2013th prime number.
What is the sum of the first 2013 primes?
16,501,458.