What is the 123rd prime number?
The 123rd prime number is 677. The next prime is 683 (a gap of 6) and the one before is 673.
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 123rd one is 677.
- 2
677 is prime because no prime up to ā677 ā 26.02 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 123rd prime is close to 123 Ć ln(123) ā 592, and here it is 677.
- 4
677 has no twin: neither 675 nor 679 is prime.
Primes around the 123rd
| Position | Prime | Gap from the previous |
|---|---|---|
| 120 | 659 | 6 |
| 121 | 661 | 2 |
| 122 | 673 | 12 |
| 123 | 677 | 4 |
| 124 | 683 | 6 |
| 125 | 691 | 8 |
| 126 | 701 | 10 |
Questions
What is the 123rd prime number?
677.
Which prime number is 677?
677 is the 123rd prime number.
What is the sum of the first 123 primes?
38,238.