What is the 255th prime number?
The 255th prime number is 1613. The next prime is 1619 (a gap of 6) and the one before is 1609.
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 255th one is 1613.
- 2
1613 is prime because no prime up to ā1613 ā 40.16 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 255th prime is close to 255 Ć ln(255) ā 1413, and here it is 1613.
- 4
1613 has no twin: neither 1611 nor 1615 is prime.
Primes around the 255th
| Position | Prime | Gap from the previous |
|---|---|---|
| 252 | 1601 | 4 |
| 253 | 1607 | 6 |
| 254 | 1609 | 2 |
| 255 | 1613 | 4 |
| 256 | 1619 | 6 |
| 257 | 1621 | 2 |
| 258 | 1627 | 6 |
Questions
What is the 255th prime number?
1613.
Which prime number is 1613?
1613 is the 255th prime number.
What is the sum of the first 255 primes?
190,136.