What is the 521st prime number?
The 521st prime number is 3733. The next prime is 3739 (a gap of 6) and the one before is 3727.
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 521st one is 3733.
- 2
3733 is prime because no prime up to ā3733 ā 61.10 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 521st prime is close to 521 Ć ln(521) ā 3259, and here it is 3733.
- 4
3733 has no twin: neither 3731 nor 3735 is prime.
Primes around the 521st
| Position | Prime | Gap from the previous |
|---|---|---|
| 518 | 3709 | 8 |
| 519 | 3719 | 10 |
| 520 | 3727 | 8 |
| 521 | 3733 | 6 |
| 522 | 3739 | 6 |
| 523 | 3761 | 22 |
| 524 | 3767 | 6 |
Questions
What is the 521st prime number?
3733.
Which prime number is 3733?
3733 is the 521st prime number.
What is the sum of the first 521 primes?
901,478.