What is the 259th prime number?
The 259th prime number is 1637. The next prime is 1657 (a gap of 20) and the one before is 1627.
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 259th one is 1637.
- 2
1637 is prime because no prime up to ā1637 ā 40.46 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 259th prime is close to 259 Ć ln(259) ā 1439, and here it is 1637.
- 4
1637 has no twin: neither 1635 nor 1639 is prime.
Primes around the 259th
| Position | Prime | Gap from the previous |
|---|---|---|
| 256 | 1619 | 6 |
| 257 | 1621 | 2 |
| 258 | 1627 | 6 |
| 259 | 1637 | 10 |
| 260 | 1657 | 20 |
| 261 | 1663 | 6 |
| 262 | 1667 | 4 |
Questions
What is the 259th prime number?
1637.
Which prime number is 1637?
1637 is the 259th prime number.
What is the sum of the first 259 primes?
196,640.