What is the 456th prime number?
The 456th prime number is 3221. The next prime is 3229 (a gap of 8) and the one before is 3217.
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 456th one is 3221.
- 2
3221 is prime because no prime up to ā3221 ā 56.75 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 456th prime is close to 456 Ć ln(456) ā 2792, and here it is 3221.
- 4
3221 has no twin: neither 3219 nor 3223 is prime.
Primes around the 456th
| Position | Prime | Gap from the previous |
|---|---|---|
| 453 | 3203 | 12 |
| 454 | 3209 | 6 |
| 455 | 3217 | 8 |
| 456 | 3221 | 4 |
| 457 | 3229 | 8 |
| 458 | 3251 | 22 |
| 459 | 3253 | 2 |
Questions
What is the 456th prime number?
3221.
Which prime number is 3221?
3221 is the 456th prime number.
What is the sum of the first 456 primes?
674,777.