What is the 118th prime number?
The 118th prime number is 647. The next prime is 653 (a gap of 6) and the one before is 643.
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 118th one is 647.
- 2
647 is prime because no prime up to ā647 ā 25.44 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 118th prime is close to 118 Ć ln(118) ā 563, and here it is 647.
- 4
647 has no twin: neither 645 nor 649 is prime.
Primes around the 118th
| Position | Prime | Gap from the previous |
|---|---|---|
| 115 | 631 | 12 |
| 116 | 641 | 10 |
| 117 | 643 | 2 |
| 118 | 647 | 4 |
| 119 | 653 | 6 |
| 120 | 659 | 6 |
| 121 | 661 | 2 |
Questions
What is the 118th prime number?
647.
Which prime number is 647?
647 is the 118th prime number.
What is the sum of the first 118 primes?
34,915.