What is the 103rd prime number?
The 103rd prime number is 563. The next prime is 569 (a gap of 6) and the one before is 557.
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 103rd one is 563.
- 2
563 is prime because no prime up to ā563 ā 23.73 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 103rd prime is close to 103 Ć ln(103) ā 477, and here it is 563.
- 4
563 has no twin: neither 561 nor 565 is prime.
Primes around the 103rd
| Position | Prime | Gap from the previous |
|---|---|---|
| 100 | 541 | 18 |
| 101 | 547 | 6 |
| 102 | 557 | 10 |
| 103 | 563 | 6 |
| 104 | 569 | 6 |
| 105 | 571 | 2 |
| 106 | 577 | 6 |
Questions
What is the 103rd prime number?
563.
Which prime number is 563?
563 is the 103rd prime number.
What is the sum of the first 103 primes?
25,800.