What is the 114th prime number?
The 114th prime number is 619. The next prime is 631 (a gap of 12) and the one before is 617.
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 114th one is 619.
- 2
619 is prime because no prime up to ā619 ā 24.88 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 114th prime is close to 114 Ć ln(114) ā 540, and here it is 619.
- 4
619 is a twin prime: 617 and 619 are both prime.
Primes around the 114th
| Position | Prime | Gap from the previous |
|---|---|---|
| 111 | 607 | 6 |
| 112 | 613 | 6 |
| 113 | 617 | 4 |
| 114 | 619 | 2 |
| 115 | 631 | 12 |
| 116 | 641 | 10 |
| 117 | 643 | 2 |
Questions
What is the 114th prime number?
619.
Which prime number is 619?
619 is the 114th prime number.
What is the sum of the first 114 primes?
32,353.