What is the 565th prime number?
The 565th prime number is 4099. The next prime is 4111 (a gap of 12) and the one before is 4093.
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 565th one is 4099.
- 2
4099 is prime because no prime up to ā4099 ā 64.02 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 565th prime is close to 565 Ć ln(565) ā 3580, and here it is 4099.
- 4
4099 has no twin: neither 4097 nor 4101 is prime.
Primes around the 565th
| Position | Prime | Gap from the previous |
|---|---|---|
| 562 | 4079 | 6 |
| 563 | 4091 | 12 |
| 564 | 4093 | 2 |
| 565 | 4099 | 6 |
| 566 | 4111 | 12 |
| 567 | 4127 | 16 |
| 568 | 4129 | 2 |
Questions
What is the 565th prime number?
4099.
Which prime number is 4099?
4099 is the 565th prime number.
What is the sum of the first 565 primes?
1,074,190.