What is the 261st prime number?
The 261st prime number is 1663. The next prime is 1667 (a gap of 4) and the one before is 1657.
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 261st one is 1663.
- 2
1663 is prime because no prime up to ā1663 ā 40.78 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 261st prime is close to 261 Ć ln(261) ā 1452, and here it is 1663.
- 4
1663 has no twin: neither 1661 nor 1665 is prime.
Primes around the 261st
| Position | Prime | Gap from the previous |
|---|---|---|
| 258 | 1627 | 6 |
| 259 | 1637 | 10 |
| 260 | 1657 | 20 |
| 261 | 1663 | 6 |
| 262 | 1667 | 4 |
| 263 | 1669 | 2 |
| 264 | 1693 | 24 |
Questions
What is the 261st prime number?
1663.
Which prime number is 1663?
1663 is the 261st prime number.
What is the sum of the first 261 primes?
199,960.