What is the 676th prime number?
The 676th prime number is 5051. The next prime is 5059 (a gap of 8) and the one before is 5039.
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 676th one is 5051.
- 2
5051 is prime because no prime up to ā5051 ā 71.07 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 676th prime is close to 676 Ć ln(676) ā 4405, and here it is 5051.
- 4
5051 has no twin: neither 5049 nor 5053 is prime.
Primes around the 676th
| Position | Prime | Gap from the previous |
|---|---|---|
| 673 | 5021 | 10 |
| 674 | 5023 | 2 |
| 675 | 5039 | 16 |
| 676 | 5051 | 12 |
| 677 | 5059 | 8 |
| 678 | 5077 | 18 |
| 679 | 5081 | 4 |
Questions
What is the 676th prime number?
5051.
Which prime number is 5051?
5051 is the 676th prime number.
What is the sum of the first 676 primes?
1,583,293.