What is the 564th prime number?
The 564th prime number is 4093. The next prime is 4099 (a gap of 6) and the one before is 4091.
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 564th one is 4093.
- 2
4093 is prime because no prime up to ā4093 ā 63.98 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 564th prime is close to 564 Ć ln(564) ā 3573, and here it is 4093.
- 4
4093 is a twin prime: 4091 and 4093 are both prime.
Primes around the 564th
| Position | Prime | Gap from the previous |
|---|---|---|
| 561 | 4073 | 16 |
| 562 | 4079 | 6 |
| 563 | 4091 | 12 |
| 564 | 4093 | 2 |
| 565 | 4099 | 6 |
| 566 | 4111 | 12 |
| 567 | 4127 | 16 |
Questions
What is the 564th prime number?
4093.
Which prime number is 4093?
4093 is the 564th prime number.
What is the sum of the first 564 primes?
1,070,091.