Problem of the Day
A new programming or logic puzzle every Mon-Fri

Three Primes

Happy Friday!

Today's goal is to come up with 3 prime numbers that all multiply to a prime number. In addition to this the second and first numbers are equal to the difference between the third and second numbers. What 3 numbers fit this criteria?

Permalink: http://problemotd.com/problem/three-primes/

Comments:

  • Bob - 9 years, 10 months ago

    Maybe its me but if you multiply three primes (as in a * b * c) you will never get a prime, right? Since a prime has no divisors? Would make this problem kind of pointless xd

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  • Andre Scholtz - 9 years, 10 months ago

    Unless I am not understanding this problem correctly, it doesn't seem possible. 3 prime numbers, say x, y and z, such that x * y * z is also a prime, a. by definition, that isn't possible because a would be divisible by x, y and z.

    The second part also states that z - y = x = y. That would imply that z is 0, which is not a prime number.

    Is there something I am missing here?

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  • Derek - 9 years, 10 months ago

    I think the numbers you're looking for are 1, 1 and 2.

    They satisfy the first criteria, 1*1*2 = 2, which is prime.

    They satisfy the second criteria, 1 = 1 = 2-1 = 1.

    But 1 is NOT a prime number.

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  • Gasfire - 9 years, 10 months ago

    WTF! 3 prime numbers that multiply to a prime number... The definition of prime numbers means that impossible.

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  • D - 9 years, 10 months ago

    Haha I read the comments here and immediately thought: they are right. But how did I find this solution then?

    3*26813*53623=18413201

    All numbers are primes, however after further inspection 18413201 is a overflow of 4313380497. Which is not a prime. Perhaps the author made the same mistake?

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  • Max Burstein - 9 years, 10 months ago

    Sorry for not responding to this sooner. The problem is indeed a bit confusing. The trick is that the numbers can be negative. -3, -1, and 1 fit the criteria for this problem.

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  • Anonymous - 9 years, 10 months ago

    1 is not a prime number. Negative numbers are also not prime numbers.

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