What is the 513th prime number?
The 513th prime number is 3673. The next prime is 3677 (a gap of 4) and the one before is 3671.
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 513th one is 3673.
- 2
3673 is prime because no prime up to ā3673 ā 60.61 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 513th prime is close to 513 Ć ln(513) ā 3201, and here it is 3673.
- 4
3673 is a twin prime: 3671 and 3673 are both prime.
Primes around the 513th
| Position | Prime | Gap from the previous |
|---|---|---|
| 510 | 3643 | 6 |
| 511 | 3659 | 16 |
| 512 | 3671 | 12 |
| 513 | 3673 | 2 |
| 514 | 3677 | 4 |
| 515 | 3691 | 14 |
| 516 | 3697 | 6 |
Questions
What is the 513th prime number?
3673.
Which prime number is 3673?
3673 is the 513th prime number.
What is the sum of the first 513 primes?
871,824.