The next four exercises present another example of a system where unique factorization into primes fails. Let Η be the set of all positive integers of the form 4k + 1, where k is a nonnegative integer.
An element h ≠ 1 in H is called a Hilbert prime (named after famous German mathematician David Hilbert) if the only way it can be written as the product of two integers in Η is h = h ·1 = 1 · h. Find the 20 smallest Hilbert primes.
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