What is the 505th prime number?
The 505th prime number is 3613. The next prime is 3617 (a gap of 4) and the one before is 3607.
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 505th one is 3613.
- 2
3613 is prime because no prime up to ā3613 ā 60.11 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 505th prime is close to 505 Ć ln(505) ā 3143, and here it is 3613.
- 4
3613 has no twin: neither 3611 nor 3615 is prime.
Primes around the 505th
| Position | Prime | Gap from the previous |
|---|---|---|
| 502 | 3583 | 2 |
| 503 | 3593 | 10 |
| 504 | 3607 | 14 |
| 505 | 3613 | 6 |
| 506 | 3617 | 4 |
| 507 | 3623 | 6 |
| 508 | 3631 | 8 |
Questions
What is the 505th prime number?
3613.
Which prime number is 3613?
3613 is the 505th prime number.
What is the sum of the first 505 primes?
842,670.