Function that reveals primes... NOT

AlbenWeeks · 2020-02-11, 06:43

I've probably only found something that already existed, but am posting here to find out.

Let ((2^n)-2)/n = x

for any positive integer n, if x is a whole number, n is prime. if x is not a whole number, n is not prime.

Is this something basic that's been found before? If so can someone let me know what this is called or why it works if there's a basic reason I'm missing?

Nick · 2020-02-11, 08:59

It's Fermat's little theorem.
x can be whole without n being prime however - for example, try n=341.
Then look up Carmichael numbers.

CRGreathouse · 2020-02-12, 06:23

What a fantastic re-discovery! As Nick said, this is Fermat's "little" theorem in base 2, a wonderful result that is very commonly used. Its counterexamples are the base-2 pseudoprimes. You've found a new world to explore.

2020-02-11, 06:43	#1
AlbenWeeks Feb 2020 1 Posts	Function that reveals primes... NOT I've probably only found something that already existed, but am posting here to find out. Let ((2^n)-2)/n = x for any positive integer n, if x is a whole number, n is prime. if x is not a whole number, n is not prime. Is this something basic that's been found before? If so can someone let me know what this is called or why it works if there's a basic reason I'm missing?

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2020-02-11, 08:59	#2
Nick Dec 2012 The Netherlands 1811₁₀ Posts	It's Fermat's little theorem. x can be whole without n being prime however - for example, try n=341. Then look up Carmichael numbers.

2020-02-12, 06:23	#3
CRGreathouse Aug 2006 5,987 Posts	What a fantastic re-discovery! As Nick said, this is Fermat's "little" theorem in base 2, a wonderful result that is very commonly used. Its counterexamples are the base-2 pseudoprimes. You've found a new world to explore.