What is the 556th prime number?
The 556th prime number is 4021. The next prime is 4027 (a gap of 6) and the one before is 4019.
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 556th one is 4021.
- 2
4021 is prime because no prime up to ā4021 ā 63.41 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 556th prime is close to 556 Ć ln(556) ā 3514, and here it is 4021.
- 4
4021 is a twin prime: 4019 and 4021 are both prime.
Primes around the 556th
| Position | Prime | Gap from the previous |
|---|---|---|
| 553 | 4007 | 4 |
| 554 | 4013 | 6 |
| 555 | 4019 | 6 |
| 556 | 4021 | 2 |
| 557 | 4027 | 6 |
| 558 | 4049 | 22 |
| 559 | 4051 | 2 |
Questions
What is the 556th prime number?
4021.
Which prime number is 4021?
4021 is the 556th prime number.
What is the sum of the first 556 primes?
1,037,571.