What is the 45th prime number?
The 45th prime number is 197. The next prime is 199 (a gap of 2) and the one before is 193.
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 45th one is 197.
- 2
197 is prime because no prime up to ā197 ā 14.04 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 45th prime is close to 45 Ć ln(45) ā 171, and here it is 197.
- 4
197 is a twin prime: 197 and 199 are both prime.
Primes around the 45th
| Position | Prime | Gap from the previous |
|---|---|---|
| 42 | 181 | 2 |
| 43 | 191 | 10 |
| 44 | 193 | 2 |
| 45 | 197 | 4 |
| 46 | 199 | 2 |
| 47 | 211 | 12 |
| 48 | 223 | 12 |
Questions
What is the 45th prime number?
197.
Which prime number is 197?
197 is the 45th prime number.
What is the sum of the first 45 primes?
4,028.