What is the 584th prime number?
The 584th prime number is 4259. The next prime is 4261 (a gap of 2) and the one before is 4253.
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 584th one is 4259.
- 2
4259 is prime because no prime up to ā4259 ā 65.26 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 584th prime is close to 584 Ć ln(584) ā 3720, and here it is 4259.
- 4
4259 is a twin prime: 4259 and 4261 are both prime.
Primes around the 584th
| Position | Prime | Gap from the previous |
|---|---|---|
| 581 | 4241 | 10 |
| 582 | 4243 | 2 |
| 583 | 4253 | 10 |
| 584 | 4259 | 6 |
| 585 | 4261 | 2 |
| 586 | 4271 | 10 |
| 587 | 4273 | 2 |
Questions
What is the 584th prime number?
4259.
Which prime number is 4259?
4259 is the 584th prime number.
What is the sum of the first 584 primes?
1,153,779.