Redundant Primality Test?

Number Theory Level 2

Given that 4999 is a prime number , determine which of these numbers has less positive divisors than the other.

5000 4999

Pi Han Goh by Pi Han Goh , 30, Malaysia

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1 solution

Zee Ell
Sep 29, 2016

Prime numbers (like 4999) have exactly 2 divisors. 5000 is not a prime number (since it is even, 2 is an additional prime number), hence our answer is: 4999 \boxed {4999}

The number of divisors of 5000:

5000 = 2 3 × 5 4 5000 = 2^3 × 5^4

ϕ ( 5000 ) = ( 3 + 1 ) ( 4 + 1 ) = 4 × 5 = 20 \phi (5000) = (3+1)(4+1) = 4×5 = 20

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