A prime p 4 + 5 p^{4}+5

How many primes p p exist between 1 and 7 ! 7! inclusive for which p 4 + 5 p^{4}+5 is prime?


The answer is 0.

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1 solution

Ron Lauterbach
Sep 17, 2017

An odd number to any power (greater than 0) is odd, as it does not have the factor 2. An odd number added to an odd number is even. Each even number has the factor 2 and is therefore except for 2 itself, not prime. 2 4 + 5 = 21 = 7 × 3 2^{4}+5=21=7 \times 3 Therefore there exists no such number.

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