Is 4^2007 + 2007^4 a Prime Number?

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Discussion Overview

The discussion centers around the question of whether the expression 4^2007 + 2007^4 is a prime number. Participants explore various methods to determine the primality of this expression, including computational approaches and mathematical techniques.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant asks how to determine if 4^2007 + 2007^4 is prime.
  • Another participant questions whether the inquiry is a straightforward question or more of a puzzle.
  • A suggestion is made to write a program to compute the result, implying a computational approach may be effective.
  • One participant asserts that the expression is not prime but does not elaborate further.
  • Another participant proposes using modular arithmetic as a method to investigate the primality, indicating that if a prime p divides the expression, it should be congruent to 0 mod p.

Areas of Agreement / Disagreement

There is no consensus on whether 4^2007 + 2007^4 is prime, as participants present differing views and methods without reaching a definitive conclusion.

muna580
How do I find out if 4^2007 + 2007^4 is a prime number or not?
 
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Is that a question or a puzzle?
 
Write a program and let the computer figure it out. :biggrin:
 
I will tell you, it's not prime; I don't want to say more.
 
Last edited:
try using modular arithmetic. i.e. p divides N if N is congruent to 0 modp.

this is not speculation, this is a hint.
 
Last edited:

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