What is the 278th prime number?
The 278th prime number is 1789. The next prime is 1801 (a gap of 12) and the one before is 1787.
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 278th one is 1789.
- 2
1789 is prime because no prime up to ā1789 ā 42.30 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 278th prime is close to 278 Ć ln(278) ā 1564, and here it is 1789.
- 4
1789 is a twin prime: 1787 and 1789 are both prime.
Primes around the 278th
| Position | Prime | Gap from the previous |
|---|---|---|
| 275 | 1777 | 18 |
| 276 | 1783 | 6 |
| 277 | 1787 | 4 |
| 278 | 1789 | 2 |
| 279 | 1801 | 12 |
| 280 | 1811 | 10 |
| 281 | 1823 | 12 |
Questions
What is the 278th prime number?
1789.
Which prime number is 1789?
1789 is the 278th prime number.
What is the sum of the first 278 primes?
229,407.