What is the 120th prime number?
The 120th prime number is 659. The next prime is 661 (a gap of 2) and the one before is 653.
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 120th one is 659.
- 2
659 is prime because no prime up to ā659 ā 25.67 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 120th prime is close to 120 Ć ln(120) ā 574, and here it is 659.
- 4
659 is a twin prime: 659 and 661 are both prime.
Primes around the 120th
| Position | Prime | Gap from the previous |
|---|---|---|
| 117 | 643 | 2 |
| 118 | 647 | 4 |
| 119 | 653 | 6 |
| 120 | 659 | 6 |
| 121 | 661 | 2 |
| 122 | 673 | 12 |
| 123 | 677 | 4 |
Questions
What is the 120th prime number?
659.
Which prime number is 659?
659 is the 120th prime number.
What is the sum of the first 120 primes?
36,227.