Besties Not-Quite-Palindrome

Raira asked her 4 bffs to share their favorite numbers. It just happened that all of the 5 numbers are prime, and Raira's number k k was the smallest one. The other 4 primes were:

  • A: 1 less than a multiple of k k
  • B: 2 more than a multiple of k k
  • C: 3 less than a multiple of k k
  • D: 4 more than a multiple of k k

Out of curiosity, she used a calculator to find the product of the favorite numbers, and then Shayena, the bff who was sitting across her at the table pointed out that the product looks exactly the same (on the calculator) when rotated 180 degrees.

Find the product of these primes.


The answer is 1962961.

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1 solution

Mark Hennings
Dec 8, 2016

The prime numbers are 7 , 11 , 13 , 37 , 53 7,11,13,37,53 , and the product 1962961 \boxed{1962961} .

Thank you, Mark! Actually I asked without checking whether there would be any answers other than my one given as answer. But thankfully you answered after I did my rechecking, that all the other UpDown numbers did not meet the criteria I set for their prime factors. Or maybe I should edit the question to claim the answer as SMALLEST UpDown number?

Saya Suka - 4 years, 6 months ago

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To be honest, I did not prove this was the only one, I just found it...

Mark Hennings - 4 years, 6 months ago

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I know, but I checked for sure after posting the answer if there are others, but found none that fulfill the conditions.

Saya Suka - 6 months, 1 week ago

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