What is the 677th prime number?
The 677th prime number is 5059. The next prime is 5077 (a gap of 18) and the one before is 5051.
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 677th one is 5059.
- 2
5059 is prime because no prime up to ā5059 ā 71.13 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 677th prime is close to 677 Ć ln(677) ā 4412, and here it is 5059.
- 4
5059 has no twin: neither 5057 nor 5061 is prime.
Primes around the 677th
| Position | Prime | Gap from the previous |
|---|---|---|
| 674 | 5023 | 2 |
| 675 | 5039 | 16 |
| 676 | 5051 | 12 |
| 677 | 5059 | 8 |
| 678 | 5077 | 18 |
| 679 | 5081 | 4 |
| 680 | 5087 | 6 |
Questions
What is the 677th prime number?
5059.
Which prime number is 5059?
5059 is the 677th prime number.
What is the sum of the first 677 primes?
1,588,352.