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This can be an extension to the proof that there are infinitely many prime numbers. If there are infinitely many prime numbers, then there are also infinitely many PRODUCTS of prime numbers. Those numbers that are the product of 2 or more prime numbers are not prime numbers.
There are infinitely many numbers in each system, however base 10 uses 10 digits {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} and binary uses 2 digits {0, 1}. The maximum digit is one less than the base.
Numbers are infinite.
There are an infinite number of numbers.