What is the 2000th prime number?
The 2000th prime number is 17389. The next prime is 17393 (a gap of 4) and the one before is 17387.
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 2000th one is 17389.
- 2
17389 is prime because no prime up to ā17389 ā 131.87 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 2000th prime is close to 2000 Ć ln(2000) ā 15202, and here it is 17389.
- 4
17389 is a twin prime: 17387 and 17389 are both prime.
Primes around the 2000th
| Position | Prime | Gap from the previous |
|---|---|---|
| 1997 | 17377 | 18 |
| 1998 | 17383 | 6 |
| 1999 | 17387 | 4 |
| 2000 | 17389 | 2 |
| 2001 | 17393 | 4 |
| 2002 | 17401 | 8 |
| 2003 | 17417 | 16 |
Questions
What is the 2000th prime number?
17389.
Which prime number is 17389?
17389 is the 2000th prime number.
What is the sum of the first 2000 primes?
16,274,627.