What is the 559th prime number?
The 559th prime number is 4051. The next prime is 4057 (a gap of 6) and the one before is 4049.
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 559th one is 4051.
- 2
4051 is prime because no prime up to ā4051 ā 63.65 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 559th prime is close to 559 Ć ln(559) ā 3536, and here it is 4051.
- 4
4051 is a twin prime: 4049 and 4051 are both prime.
Primes around the 559th
| Position | Prime | Gap from the previous |
|---|---|---|
| 556 | 4021 | 2 |
| 557 | 4027 | 6 |
| 558 | 4049 | 22 |
| 559 | 4051 | 2 |
| 560 | 4057 | 6 |
| 561 | 4073 | 16 |
| 562 | 4079 | 6 |
Questions
What is the 559th prime number?
4051.
Which prime number is 4051?
4051 is the 559th prime number.
What is the sum of the first 559 primes?
1,049,698.