What is the 514th prime number?
The 514th prime number is 3677. The next prime is 3691 (a gap of 14) and the one before is 3673.
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 514th one is 3677.
- 2
3677 is prime because no prime up to ā3677 ā 60.64 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 514th prime is close to 514 Ć ln(514) ā 3209, and here it is 3677.
- 4
3677 has no twin: neither 3675 nor 3679 is prime.
Primes around the 514th
| Position | Prime | Gap from the previous |
|---|---|---|
| 511 | 3659 | 16 |
| 512 | 3671 | 12 |
| 513 | 3673 | 2 |
| 514 | 3677 | 4 |
| 515 | 3691 | 14 |
| 516 | 3697 | 6 |
| 517 | 3701 | 4 |
Questions
What is the 514th prime number?
3677.
Which prime number is 3677?
3677 is the 514th prime number.
What is the sum of the first 514 primes?
875,501.