Blum Integer is the number which only haves 2 factors suppose p and q (i.e. n = p * q), both are Semi-prime and also they(p and q) are of the form 4t + 3, where t is some integer.
First few Blum Integers are 21, 33, 57, 69, 77, 93, 129, 133, 141, 161, 177, …
Note: Because of the condition that both the factors should be semi-primes, even numbers can not be Blum integers neither can be the numbers below 20,
So we have to check only for an odd integer greater than 20 that if it is a Blum Integer or not.
Explanation: 33 = 3 * 11, 3 and 11 are both
semi-primes as well as of the form 4t + 3
for t = 0, 2
Explanation: 77 = 7 * 11, 7 and 11 both are
semi-prime as well as of the form 4t + 3
for t = 1, 2
Explanation: 25 = 5*5, 5 and 5 are both
semi-prime but are not of the form 4t
+ 3, Hence 25 is not a Blum integer.
Approach: For a given odd integer greater than 20, we calculate the prime numbers from 1 to that odd integer. If we find any prime number that divides that odd integer and its quotient both are prime and follow the form 4t + 3 for some integer, then the given odd integer is Blum Integer.
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