Mursalin's Magnificent Mustache and his Magical Razor

Number Theory Level 3

After many years of "No shave New Years resolutions," Mursalin finally decides to shave his magnificent mustache of 2014 hairs. Each hair is randomly assigned a number from 1 to 2014 such that no two have the same number.

However, he just so happens to have a magical razor with an infinite amount of blades. Each blade is assigned a number from 1 to \(\aleph_0\) such that each blade cuts every hair which is a multiple of that razor's number. The first blade is defective and only cuts the first hair then breaks.

What is the number on the blade that cuts the last hair?

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Trevor Arashiro by Trevor Arashiro
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