What is the 465th prime number?
The 465th prime number is 3307. The next prime is 3313 (a gap of 6) and the one before is 3301.
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 465th one is 3307.
- 2
3307 is prime because no prime up to ā3307 ā 57.51 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 465th prime is close to 465 Ć ln(465) ā 2856, and here it is 3307.
- 4
3307 has no twin: neither 3305 nor 3309 is prime.
Primes around the 465th
| Position | Prime | Gap from the previous |
|---|---|---|
| 462 | 3271 | 12 |
| 463 | 3299 | 28 |
| 464 | 3301 | 2 |
| 465 | 3307 | 6 |
| 466 | 3313 | 6 |
| 467 | 3319 | 6 |
| 468 | 3323 | 4 |
Questions
What is the 465th prime number?
3307.
Which prime number is 3307?
3307 is the 465th prime number.
What is the sum of the first 465 primes?
704,204.