What is the 30th prime number?
The 30th prime number is 113. The next prime is 127 (a gap of 14) and the one before is 109.
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 30th one is 113.
- 2
113 is prime because no prime up to ā113 ā 10.63 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 30th prime is close to 30 Ć ln(30) ā 102, and here it is 113.
- 4
113 has no twin: neither 111 nor 115 is prime.
Primes around the 30th
| Position | Prime | Gap from the previous |
|---|---|---|
| 27 | 103 | 2 |
| 28 | 107 | 4 |
| 29 | 109 | 2 |
| 30 | 113 | 4 |
| 31 | 127 | 14 |
| 32 | 131 | 4 |
| 33 | 137 | 6 |
Questions
What is the 30th prime number?
113.
Which prime number is 113?
113 is the 30th prime number.
What is the sum of the first 30 primes?
1,593.