What is the 46th prime number?
The 46th prime number is 199. The next prime is 211 (a gap of 12) and the one before is 197.
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 46th one is 199.
- 2
199 is prime because no prime up to ā199 ā 14.11 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 46th prime is close to 46 Ć ln(46) ā 176, and here it is 199.
- 4
199 is a twin prime: 197 and 199 are both prime.
Primes around the 46th
| Position | Prime | Gap from the previous |
|---|---|---|
| 43 | 191 | 10 |
| 44 | 193 | 2 |
| 45 | 197 | 4 |
| 46 | 199 | 2 |
| 47 | 211 | 12 |
| 48 | 223 | 12 |
| 49 | 227 | 4 |
Questions
What is the 46th prime number?
199.
Which prime number is 199?
199 is the 46th prime number.
What is the sum of the first 46 primes?
4,227.