What is the 113th prime number?
The 113th prime number is 617. The next prime is 619 (a gap of 2) and the one before is 613.
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 113th one is 617.
- 2
617 is prime because no prime up to ā617 ā 24.84 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 113th prime is close to 113 Ć ln(113) ā 534, and here it is 617.
- 4
617 is a twin prime: 617 and 619 are both prime.
Primes around the 113th
| Position | Prime | Gap from the previous |
|---|---|---|
| 110 | 601 | 2 |
| 111 | 607 | 6 |
| 112 | 613 | 6 |
| 113 | 617 | 4 |
| 114 | 619 | 2 |
| 115 | 631 | 12 |
| 116 | 641 | 10 |
Questions
What is the 113th prime number?
617.
Which prime number is 617?
617 is the 113th prime number.
What is the sum of the first 113 primes?
31,734.