What is the 522nd prime number?
The 522nd prime number is 3739. The next prime is 3761 (a gap of 22) and the one before is 3733.
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 522nd one is 3739.
- 2
3739 is prime because no prime up to ā3739 ā 61.15 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 522nd prime is close to 522 Ć ln(522) ā 3267, and here it is 3739.
- 4
3739 has no twin: neither 3737 nor 3741 is prime.
Primes around the 522nd
| Position | Prime | Gap from the previous |
|---|---|---|
| 519 | 3719 | 10 |
| 520 | 3727 | 8 |
| 521 | 3733 | 6 |
| 522 | 3739 | 6 |
| 523 | 3761 | 22 |
| 524 | 3767 | 6 |
| 525 | 3769 | 2 |
Questions
What is the 522nd prime number?
3739.
Which prime number is 3739?
3739 is the 522nd prime number.
What is the sum of the first 522 primes?
905,217.