What is the 223rd prime number?
The 223rd prime number is 1409. The next prime is 1423 (a gap of 14) and the one before is 1399.
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 223rd one is 1409.
- 2
1409 is prime because no prime up to ā1409 ā 37.54 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 223rd prime is close to 223 Ć ln(223) ā 1206, and here it is 1409.
- 4
1409 has no twin: neither 1407 nor 1411 is prime.
Primes around the 223rd
| Position | Prime | Gap from the previous |
|---|---|---|
| 220 | 1373 | 6 |
| 221 | 1381 | 8 |
| 222 | 1399 | 18 |
| 223 | 1409 | 10 |
| 224 | 1423 | 14 |
| 225 | 1427 | 4 |
| 226 | 1429 | 2 |
Questions
What is the 223rd prime number?
1409.
Which prime number is 1409?
1409 is the 223rd prime number.
What is the sum of the first 223 primes?
141,676.