What is the 678th prime number?
The 678th prime number is 5077. The next prime is 5081 (a gap of 4) and the one before is 5059.
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 678th one is 5077.
- 2
5077 is prime because no prime up to ā5077 ā 71.25 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 678th prime is close to 678 Ć ln(678) ā 4420, and here it is 5077.
- 4
5077 has no twin: neither 5075 nor 5079 is prime.
Primes around the 678th
| Position | Prime | Gap from the previous |
|---|---|---|
| 675 | 5039 | 16 |
| 676 | 5051 | 12 |
| 677 | 5059 | 8 |
| 678 | 5077 | 18 |
| 679 | 5081 | 4 |
| 680 | 5087 | 6 |
| 681 | 5099 | 12 |
Questions
What is the 678th prime number?
5077.
Which prime number is 5077?
5077 is the 678th prime number.
What is the sum of the first 678 primes?
1,593,429.