What is the 558th prime number?
The 558th prime number is 4049. The next prime is 4051 (a gap of 2) and the one before is 4027.
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 558th one is 4049.
- 2
4049 is prime because no prime up to ā4049 ā 63.63 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 558th prime is close to 558 Ć ln(558) ā 3529, and here it is 4049.
- 4
4049 is a twin prime: 4049 and 4051 are both prime.
Primes around the 558th
| Position | Prime | Gap from the previous |
|---|---|---|
| 555 | 4019 | 6 |
| 556 | 4021 | 2 |
| 557 | 4027 | 6 |
| 558 | 4049 | 22 |
| 559 | 4051 | 2 |
| 560 | 4057 | 6 |
| 561 | 4073 | 16 |
Questions
What is the 558th prime number?
4049.
Which prime number is 4049?
4049 is the 558th prime number.
What is the sum of the first 558 primes?
1,045,647.