First two digits.

Number Theory Level 2

a b 37 ‾ \overline{ab37} is a prime number. Which of the following could be a b ‾ \overline{ab} ?

15 None of these 30 25 41

Munem Shahriar by Munem Shahriar , 18, Bangladesh

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2 solutions

Edwin Gray
Sep 10, 2018

2537 = 43 59, 1537 = 29 53, 4137 = 3*1379, 3037 has no factors less than sqrt(3037), and is therefore a prime. Ed Gray

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Munem Shahriar
Dec 25, 2017

  • 2537 is not a prime number because 2537 ÷ 43 = 59 2537 \div 43 =59

  • 1537 is not a prime number because 1537 ÷ 29 = 53 1537 \div 29 = 53

  • 4137 is not a prime number because 4137 ÷ 3 = 1379 4137 \div 3 = 1379

  • 3037 \boxed{3037} has only two divisors, 1 and itself. Hence it is a prime number.

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