none
Chat with our AI personalities
If you multiply two prime numbers, the product (result) will be a composite number, not a prime number. A prime number has exactly two factors, 1 and itself. The product of two prime numbers will have those two numbers as factors, as well. The sum of two prime numbers might be prime if one of those two numbers is 2, the only even prime number, but otherwise it will not be a prime because two odd numbers will have an even sum, which means it is divisible by 2. Examples: 2 + 3 = 5 (prime) 3 + 7 = 10 (not prime) 13 + 17 = 30 (not prime) If you multiply two prime numbers, the sum of the digits of the product might or might not be prime. Examples: 2 x 7 = 14, sum of digits is 5 (prime) 2 x 11 = 22, sum of digits is 4 (not prime) 3 x 5 = 15, sum of digits is 6 (not prime) 3 x 7 = 21, sum of digits is 3 (prime) 5 x 7 = 35, sum of digits is 8 (prime)
Since one number is twice the other, the smaller number must be the greatest common factor. Since the greatest common factor is 7, that would make the other number 14. But, 7 is a prime number and has only one prime factor. However, the larger number, 14, has two prime factors. Also, the sum of the two numbers is 21, not 105. So, the information in the problem does not have a solution. Let us ignore the greatest common factor information. Let the smaller number be x. That means the larger number is 2x. x + 2x = 105 => 3x = 105 => x = 35. The two numbers are 35 and 70. The greatest common factor is 35. The smaller number, 35, has only two prime factors.
There are six prime numbers between 12 and 35: 13,17,19,23,29,31
There are 3 prime numbers from 21 to 35:23, 29 and 31
The only prime numbers between 25 and 35 are: 29 31.