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Pretty primes (Posted on 2017-04-10)

How any primes p exist such that
p⁴+1 is a prime number as well?

See The Solution Submitted by Ady TZIDON

Rating: 2.0000 (1 votes)

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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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