Problem 54620. List the Euclid numbers
Euclid proved that the number of primes is infinite with the following argument. Suppose the primes form a finite set , , . Compute . This number N is either prime or composite.
If it is prime, then the original supposition that the primes form a finite set is false. For example, if we assume that the only primes are 2, 3, and 5, then , which is prime. Therefore, 31 should be in the set of primes.
If N is composite, then there must be another prime number because N is not divisible by any of the primes in the original set. For example, if we assume the only primes are 2, 3, 5, and 31, then . Therefore, 7 and 19 should be in the set as well.
Either way, a contradiction is reached, and the set of primes must be infinite. In other words, we can always add another prime to the set.
Write a function to return the nth Euclid number as a character string, where is the nth prime. Take the zeroth Euclid number to be 2.
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