TMUA 2019 Paper 2 Q4 — Worked Solution

P2·Number Theory & Divisibility, Logic & Quantifiers·6.0Official · 2019 · Q4

counterexampleconjectureprimality

Consider the following conjecture: If

N

is a positive integer that consists of the digit 1 followed by an odd number of 0 digits and then a final digit 1, then

N

is a prime number. Here are three candidate numbers.

N = 101

(which is a prime number)

N = 1001

(which equals

7 \times 11 \times 13

)

III

N = 10001

(which equals

73 \times 137

)

Which of these provide(s) a counterexample to the conjecture?

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