What is the 117th prime number?
The 117th prime number is 643. The next prime is 647 (a gap of 4) and the one before is 641.
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 117th one is 643.
- 2
643 is prime because no prime up to ā643 ā 25.36 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 117th prime is close to 117 Ć ln(117) ā 557, and here it is 643.
- 4
643 is a twin prime: 641 and 643 are both prime.
Primes around the 117th
| Position | Prime | Gap from the previous |
|---|---|---|
| 114 | 619 | 2 |
| 115 | 631 | 12 |
| 116 | 641 | 10 |
| 117 | 643 | 2 |
| 118 | 647 | 4 |
| 119 | 653 | 6 |
| 120 | 659 | 6 |
Questions
What is the 117th prime number?
643.
Which prime number is 643?
643 is the 117th prime number.
What is the sum of the first 117 primes?
34,268.