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Pretty primes (Posted on 2017-04-10) Difficulty: 1 of 5
How any primes p exist such that
p4+1 is a prime number as well?

See The Solution Submitted by Ady TZIDON    
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solution | Comment 1 of 2
if p=2 then
p^4+1=2^4+1=17
so it works for p=2

if p>2
then p is either 1 or 3 mod 4

if p=1 mod 4 then
p^4+1=1^4+1 mod 4 = 2 mod 4
and thus is divisible by 2 and not prime

if p=3 mod 4 then
p^4+1=3^4+1 mod 4=2 mod 4
and thus is divisible by 2 and not prime


Thus the only prime p for which p^4+1 is also prime is p=2.

  Posted by Daniel on 2017-04-10 14:43:02
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