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Message boards : General discussion : A Small Prime Number Question

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Message 78554 - Posted: 6 Aug 2014 | 5:34:24 UTC

Q. Is there an infinite number of primes in the form "p^2+4?"
(Note: 'p' itself is a prime)

Examples.
3^2+4=13, 5^2+4=29, 7^2+4=53, etc.

+The background for this question is the curiosity for
the equation "p^2+q^2=r" where p, q, r are all prime.
Considering the infiniteness of the solution eventually leads to
the question above.

JeppeSN

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Message 78575 - Posted: 6 Aug 2014 | 22:28:28 UTC - in response to Message 78554.

It is very probable (very natural to conjecture) that the answer is "yes".

It is probably hard to prove (see for example Landau's 4th problem).

There is a list of the first 1000 such numbers in the Links section of OEIS: A062324.

/JeppeSN

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Message 78609 - Posted: 8 Aug 2014 | 1:11:49 UTC - in response to Message 78575.