What is the 226th prime number?
The 226th prime number is 1429. The next prime is 1433 (a gap of 4) and the one before is 1427.
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 226th one is 1429.
- 2
1429 is prime because no prime up to ā1429 ā 37.80 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 226th prime is close to 226 Ć ln(226) ā 1225, and here it is 1429.
- 4
1429 is a twin prime: 1427 and 1429 are both prime.
Primes around the 226th
| Position | Prime | Gap from the previous |
|---|---|---|
| 223 | 1409 | 10 |
| 224 | 1423 | 14 |
| 225 | 1427 | 4 |
| 226 | 1429 | 2 |
| 227 | 1433 | 4 |
| 228 | 1439 | 6 |
| 229 | 1447 | 8 |
Questions
What is the 226th prime number?
1429.
Which prime number is 1429?
1429 is the 226th prime number.
What is the sum of the first 226 primes?
145,955.