Blum Integer Checker

Blum Integer Checker is a free online tool used to check if the number is a Blum integer.

A natural number n is called a Blum integer if n is a semiprime number that can be represented as a product of two prime numbers p and q. The number n is a Blum integer only if p and q are distinct prime numbers congruent to 3 mod 4. This means that both p and q should be represented as 4 * t + 3, where t is some integer. Blum integer is named after the computer scientist, Manuel Blum.

So, Blum integer n = p * q, where p and q are primes of the form 4 * t + 3 for any integer t.

For example, is 253 a Blum integer?

With the Prime Factorization Calculator, we can get the prime factorization of 253 is

253 = 11 * 23

Here 11 and 23 are prime numbers. Both can be represented as 4 * t + 3.

11 = 4 * 2 + 3

23 = 4 * 5 + 3

So, 253 is a Blum integer.

39 is not a Blum integer because 39 = 3 * 13. Among them, 13 cannot be expressed as 4 * t + 3.

The procedure to use the Blum integer checker is as follows: