19 is a prime number from 1-100. 19 has 2 factors, 1 and 19. It is the last number within the range of 1-20 that ends with the suffix -teen. It is also the smallest prime number that is not an emirp (91 is divisible by 7), and the smallest prime number that becomes divisible by 7 when a 1 is inserted to left of it, as 119 is divisible by 7. The primorial of 19 is 9,699,690.
Proofs[]
— 19 is divisible by 1.
— 19 is not divisible by 2-18.
- — 19 is divisible by 19.
- Therefore, it has 2 factors and is prime.
As an Exponent of Mersenne Number[]
219 - 1, which is the number 524,287, is a prime number. It is the 7th Mersenne prime.
Relationship with other odd numbers[]
The numbers before[]
- 13 is the second previous prime number.
- The difference between 19 and 13 is 6. Therefore, they are sexy primes.
- 15 is not a prime number; it is divisible by 3 and 5.
- The previous odd number, 17, is a prime number.
- There are no odd numbers between 17 and 19. As a result, they are twin primes.
The numbers after[]
- 21 is not a prime number; it is divisible by 3 and 7.
- 23, the odd number following 21, is a prime number.
- The difference between 23 and 19 is 4. Therefore, they are cousin primes.
- 25, the odd number following 23, is not a prime number. It is a square number: 52 = 25.