What is the 8003rd prime number?
The 8003rd prime number is 81847. The next prime is 81853 (a gap of 6) and the one before is 81839.
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 8003rd one is 81847.
- 2
81847 is prime because no prime up to ā81847 ā 286.09 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 8003rd prime is close to 8003 Ć ln(8003) ā 71928, and here it is 81847.
- 4
81847 has no twin: neither 81845 nor 81849 is prime.
Primes around the 8003rd
| Position | Prime | Gap from the previous |
|---|---|---|
| 8000 | 81799 | 26 |
| 8001 | 81817 | 18 |
| 8002 | 81839 | 22 |
| 8003 | 81847 | 8 |
| 8004 | 81853 | 6 |
| 8005 | 81869 | 16 |
| 8006 | 81883 | 14 |
Questions
What is the 8003rd prime number?
81847.
Which prime number is 81847?
81847 is the 8003rd prime number.
What is the sum of the first 8003 primes?
309,922,844.