What is the 516th prime number?
The 516th prime number is 3697. The next prime is 3701 (a gap of 4) and the one before is 3691.
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 516th one is 3697.
- 2
3697 is prime because no prime up to ā3697 ā 60.80 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 516th prime is close to 516 Ć ln(516) ā 3223, and here it is 3697.
- 4
3697 has no twin: neither 3695 nor 3699 is prime.
Primes around the 516th
| Position | Prime | Gap from the previous |
|---|---|---|
| 513 | 3673 | 2 |
| 514 | 3677 | 4 |
| 515 | 3691 | 14 |
| 516 | 3697 | 6 |
| 517 | 3701 | 4 |
| 518 | 3709 | 8 |
| 519 | 3719 | 10 |
Questions
What is the 516th prime number?
3697.
Which prime number is 3697?
3697 is the 516th prime number.
What is the sum of the first 516 primes?
882,889.