What is the 1000th prime number?
The 1000th prime number is 7919. The next prime is 7927 (a gap of 8) and the one before is 7907.
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 1000th one is 7919.
- 2
7919 is prime because no prime up to ā7919 ā 88.99 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 1000th prime is close to 1000 Ć ln(1000) ā 6908, and here it is 7919.
- 4
7919 has no twin: neither 7917 nor 7921 is prime.
Primes around the 1000th
| Position | Prime | Gap from the previous |
|---|---|---|
| 997 | 7883 | 4 |
| 998 | 7901 | 18 |
| 999 | 7907 | 6 |
| 1000 | 7919 | 12 |
| 1001 | 7927 | 8 |
| 1002 | 7933 | 6 |
| 1003 | 7937 | 4 |
Questions
What is the 1000th prime number?
7919.
Which prime number is 7919?
7919 is the 1000th prime number.
What is the sum of the first 1000 primes?
3,682,913.