What is the 260th prime number?
The 260th prime number is 1657. The next prime is 1663 (a gap of 6) and the one before is 1637.
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 260th one is 1657.
- 2
1657 is prime because no prime up to ā1657 ā 40.71 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 260th prime is close to 260 Ć ln(260) ā 1446, and here it is 1657.
- 4
1657 has no twin: neither 1655 nor 1659 is prime.
Primes around the 260th
| Position | Prime | Gap from the previous |
|---|---|---|
| 257 | 1621 | 2 |
| 258 | 1627 | 6 |
| 259 | 1637 | 10 |
| 260 | 1657 | 20 |
| 261 | 1663 | 6 |
| 262 | 1667 | 4 |
| 263 | 1669 | 2 |
Questions
What is the 260th prime number?
1657.
Which prime number is 1657?
1657 is the 260th prime number.
What is the sum of the first 260 primes?
198,297.