A Multiplication Based Logic Puzzle

101 and Level 6

101 is a prime number. 101 = 1 x 101. Its only factors are 1 and 101. Prime factorization: none.

How do we know that 101 is a prime number? The square root of 101 is an irrational number approximately equal to 10.05. If 101 were not a prime number, then it would be divisible by at least one prime number less than or equal to 10.05. Since 101 is not divisible by 2, 3, 5, or 7, it is a prime number.

101 is never a clue in the FIND THE FACTORS puzzles.

2014-16 Level 6

This week’s puzzles and last week’s solutions: 12 Factors 2014-04-21

2014-16 Level 6 Logic


Comments on: "101 and Level 6" (3)

  1. pingback[…] 101 and Level 6 […]


  2. You know, that’s peculiar. I mean, it’s obvious that 101 is a prime number, but I don’t remember noticing it before, which is funny since it’s the sort of attention-getting number that I’d think I would notice was or wasn’t prime.

    1001, 10001, and so on up to 10^18 + 1 all turn out to be composites, so I wonder if 101 is the last of these powers-of-ten-plus-one numbers to be prime.


    • ivasallay said:

      I’m glad 101 and other numbers get your attention! Thanks for informing us about all of these powers-of-ten-plus-one numbers. If there is an even number of zeros sandwiched between the 1s, the resulting number is always divisible by 11. I don’t know any general rule about these numbers with an odd number of zeros.


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