What is the 506th prime number?
The 506th prime number is 3617. The next prime is 3623 (a gap of 6) and the one before is 3613.
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 506th one is 3617.
- 2
3617 is prime because no prime up to ā3617 ā 60.14 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 506th prime is close to 506 Ć ln(506) ā 3151, and here it is 3617.
- 4
3617 has no twin: neither 3615 nor 3619 is prime.
Primes around the 506th
| Position | Prime | Gap from the previous |
|---|---|---|
| 503 | 3593 | 10 |
| 504 | 3607 | 14 |
| 505 | 3613 | 6 |
| 506 | 3617 | 4 |
| 507 | 3623 | 6 |
| 508 | 3631 | 8 |
| 509 | 3637 | 6 |
Questions
What is the 506th prime number?
3617.
Which prime number is 3617?
3617 is the 506th prime number.
What is the sum of the first 506 primes?
846,287.