What is the 586th prime number?
The 586th prime number is 4271. The next prime is 4273 (a gap of 2) and the one before is 4261.
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 586th one is 4271.
- 2
4271 is prime because no prime up to ā4271 ā 65.35 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 586th prime is close to 586 Ć ln(586) ā 3735, and here it is 4271.
- 4
4271 is a twin prime: 4271 and 4273 are both prime.
Primes around the 586th
| Position | Prime | Gap from the previous |
|---|---|---|
| 583 | 4253 | 10 |
| 584 | 4259 | 6 |
| 585 | 4261 | 2 |
| 586 | 4271 | 10 |
| 587 | 4273 | 2 |
| 588 | 4283 | 10 |
| 589 | 4289 | 6 |
Questions
What is the 586th prime number?
4271.
Which prime number is 4271?
4271 is the 586th prime number.
What is the sum of the first 586 primes?
1,162,311.