What is the 258th prime number?
The 258th prime number is 1627. The next prime is 1637 (a gap of 10) and the one before is 1621.
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 258th one is 1627.
- 2
1627 is prime because no prime up to ā1627 ā 40.34 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 258th prime is close to 258 Ć ln(258) ā 1433, and here it is 1627.
- 4
1627 has no twin: neither 1625 nor 1629 is prime.
Primes around the 258th
| Position | Prime | Gap from the previous |
|---|---|---|
| 255 | 1613 | 4 |
| 256 | 1619 | 6 |
| 257 | 1621 | 2 |
| 258 | 1627 | 6 |
| 259 | 1637 | 10 |
| 260 | 1657 | 20 |
| 261 | 1663 | 6 |
Questions
What is the 258th prime number?
1627.
Which prime number is 1627?
1627 is the 258th prime number.
What is the sum of the first 258 primes?
195,003.