What is the 21st prime number?
The 21st prime number is 73. The next prime is 79 (a gap of 6) and the one before is 71.
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 21st one is 73.
- 2
73 is prime because no prime up to ā73 ā 8.54 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 21st prime is close to 21 Ć ln(21) ā 64, and here it is 73.
- 4
73 is a twin prime: 71 and 73 are both prime.
Primes around the 21st
| Position | Prime | Gap from the previous |
|---|---|---|
| 18 | 61 | 2 |
| 19 | 67 | 6 |
| 20 | 71 | 4 |
| 21 | 73 | 2 |
| 22 | 79 | 6 |
| 23 | 83 | 4 |
| 24 | 89 | 6 |
Questions
What is the 21st prime number?
73.
Which prime number is 73?
73 is the 21st prime number.
What is the sum of the first 21 primes?
712.