In My Primes

Every SSC event involves mathematics. From public outreach to school groups to summer camps, there are numbers and math, often involving division and primes. The challenges are so basic and common that we give them little thought, but they are there nonetheless.

It often begins with bagels or pastries, where whole numbers are less critical if you don’t mind dividing a Danish. Getting equal-size student groups can be more difficult. What size do you make the groups when you have 17 students and 5 volunteers?

Primes are the atoms of arithmetic. — Richard Dedekind, German mathematician, 1872

Primes are more than mathematical meanderings; they leak into life in subtle ways. Schedules can work better on prime intervals: if you belong to two groups and one meets every 7 days while the other meets every 11 days, scheduling conflicts will occur only once every 77 days. In this way, prime numbers can extend patterns to lengthen interference periods.

Similar principles appear in mechanical design. Engineers may choose gears with prime numbers of teeth to reduce repetitive wear—a 47-tooth gear will mesh with the same tooth on its 43-tooth partner only once in every 43 rotations. Even wave phenomena, like those we demonstrate in our exhibits, are influenced by primes: in the ocean, the superposition of random waves can create a more even sea—until several combine to form a rogue wave.

The discussion of degrees in this month’s Science Corner is another example of why primes matter. The 360 degrees we use to divide a circle isn’t arbitrary. 360 is a composite number comprised of six primes. Significantly, it has 23 proper divisors—far more than the average of six for a typical three-digit number. Using 360 degrees makes it easy to divide a circle into halves, thirds, quarters, fifths, and so on*. Indeed, a numbering system’s utility connects closely with how rich it is in prime factors.

It was the Babylonians who put the 360 degrees in our circles 4,400 years ago. The closeness of 360 degrees to the 365 days in a year was also useful for their astronomical interests. 365, which is divisible by only 5 and 73, would have been significantly more difficult to work with. Compared to other three-digit options, 360 stands out as the winning choice to mark our arcs. We should all give a nod to those clever Babylonians for their well-considered choice.

But things often divide unevenly. When that happens, we get remainders—a feeling every leader knows, whether it’s periods, people, or pastries. When remainders appear, someone has to carry the extra. In our case, it often means me, heading home from a school visit with an orphan bagel, buried in a bag. A small price to pay for a day well spent inspiring future sailors and scientists.

*For the curious: the three-digit number with the most proper divisors is 840, which has six prime factors (2 × 2 × 2 × 3 × 5 × 7) and 31 proper divisors (1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420).

If this blog taught you something, gave you new perspectives, or you just enjoyed it, click the ❤. If it failed to perform, drop us a note. Thanks!