What is the 1005th prime number?
The 1005th prime number is 7951. The next prime is 7963 (a gap of 12) and the one before is 7949.
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 1005th one is 7951.
- 2
7951 is prime because no prime up to ā7951 ā 89.17 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 1005th prime is close to 1005 Ć ln(1005) ā 6947, and here it is 7951.
- 4
7951 is a twin prime: 7949 and 7951 are both prime.
Primes around the 1005th
| Position | Prime | Gap from the previous |
|---|---|---|
| 1002 | 7933 | 6 |
| 1003 | 7937 | 4 |
| 1004 | 7949 | 12 |
| 1005 | 7951 | 2 |
| 1006 | 7963 | 12 |
| 1007 | 7993 | 30 |
| 1008 | 8009 | 16 |
Questions
What is the 1005th prime number?
7951.
Which prime number is 7951?
7951 is the 1005th prime number.
What is the sum of the first 1005 primes?
3,722,610.