What is the 585th prime number?
The 585th prime number is 4261. The next prime is 4271 (a gap of 10) and the one before is 4259.
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 585th one is 4261.
- 2
4261 is prime because no prime up to ā4261 ā 65.28 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 585th prime is close to 585 Ć ln(585) ā 3727, and here it is 4261.
- 4
4261 is a twin prime: 4259 and 4261 are both prime.
Primes around the 585th
| Position | Prime | Gap from the previous |
|---|---|---|
| 582 | 4243 | 2 |
| 583 | 4253 | 10 |
| 584 | 4259 | 6 |
| 585 | 4261 | 2 |
| 586 | 4271 | 10 |
| 587 | 4273 | 2 |
| 588 | 4283 | 10 |
Questions
What is the 585th prime number?
4261.
Which prime number is 4261?
4261 is the 585th prime number.
What is the sum of the first 585 primes?
1,158,040.