What is the 5003rd prime number?
The 5003rd prime number is 48647. The next prime is 48649 (a gap of 2) and the one before is 48623.
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 5003rd one is 48647.
- 2
48647 is prime because no prime up to ā48647 ā 220.56 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 5003rd prime is close to 5003 Ć ln(5003) ā 42615, and here it is 48647.
- 4
48647 is a twin prime: 48647 and 48649 are both prime.
Primes around the 5003rd
| Position | Prime | Gap from the previous |
|---|---|---|
| 5000 | 48611 | 18 |
| 5001 | 48619 | 8 |
| 5002 | 48623 | 4 |
| 5003 | 48647 | 24 |
| 5004 | 48649 | 2 |
| 5005 | 48661 | 12 |
| 5006 | 48673 | 12 |
Questions
What is the 5003rd prime number?
48647.
Which prime number is 48647?
48647 is the 5003rd prime number.
What is the sum of the first 5003 primes?
114,601,148.