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Thursday, 31 May 2007

# Why Seventeen Years?

I heard on the news yet again about the cicadas in the Middle West coming out, as cicadas will do, for a month every seventeen years. Why seventeen years?  I wanted to know.

I looked in Wikipedia. Here is what I found, sensibly abridged:

Seventeen is the 7th prime number. The next prime is nineteen, with which it forms a twin prime. 17 is the sum of the first four primes. 17 is the sixth Mersenne prime exponent, yielding 131071. 17 is an Eisenstein prime with no imaginary part and real part of the form 3n − 1.

17 is the third Fermat prime. Since 17 is a Fermat prime, heptadecagons can be drawn with compass and ruler. This was proved by Carl Friedrich Gauss. Another consequence of 17 being a Fermat prime is that it is not a Higgs prime for squares or cubes.

17 is the only positive Genocchi prime, the only negative one being -3. It is also the third Stern prime.

There are exactly seventeen two-dimensional space (plane symmetry) groups. These are sometimes called wallpaper groups, as they represent the seventeen possible symmetry types that can be used for wallpaper.

Like 41, the number 17 is a prime that yields primes in the polynomial n2 + n + p, for all positive n < p - 1.

Consider a sequence of real numbers between 0 and 1 such that the first two lie in different halves of this interval, the first three in different thirds, and so forth. The maximum possible length of such a sequence is 17 (Berlekamp & Graham, 1970, example 63).

16 and 18 unit squares can each be formed into rectangles with perimeter equal to the area; and they are the only solutions. The Platonists regarded this as a sign of their peculiar propriety; and Plutarch explains that 17 is therefore an unlucky number.

17 is the tenth Perrin number, preceded in the sequence by 7, 10, 12.

In base 9, the smallest prime with a composite sum of digits is 17.

17 is known as the Feller number, after the famous mathematician William Feller who taught at Princeton University for many years. Feller would say, when discussing an unsolved mathematical problem, that if it could be proved for the case n = 17 then it could be proved for all positive integers n. He would also say in lectures, "Let's try this for an arbitrary value of n, say n=17." There is an unproved conjecture that 17 is the value most likely to be picked as a "random" number when such is needed in journalism which is derived from the Feller number.[1]

17! = 355687428096000

It is a repunit prime in hexadecimal (11).

It is believed that the minimum possible number of givens for a sudoku puzzle with a unique solution is 17, but this has yet to be proven.

There are 17 orthogonal curvilinear coordinate systems (to within a conformal symmetry) in which the 3-variable Laplace equation can be solved using the separation of variables technique.

• Described at MIT as 'the most random number', according to hackers' lore. This is supposedly because in a study where respondents were asked to choose a random number from 1 to 20, 17 was the most common choice.
• The numbet of the raka'ahs that muslim perform in Salah on daily basis.
• A mild swear word in Swedish. The origin is debated, and is commonly used as "sjutton också!" ("seventeen, too!"). It can roughly be translated to "Darn!". It is of course also used for the number 17.
• The maximum number of strokes of a Chinese radical.
• The number of syllables in a haiku (5+7+5).
• The number of trees Dostoevsky could see out of the window of his cell while he was in prison.
• In Italian culture, the number 17 is considered unlucky. When viewed as the Roman numeral, XVII, it is then changed anagramtically to VIXI, which in the Latin language it translates to "I have lived", the perfect tense implying "My life is over." (c.f. "Vixerunt", Cicero's famous announcement of an execution.) The Italian airline carrier, Alitalia, does not have a seat 17. Renault sold its "R17" model in Italy as "R177."
• Some species of cicadas have a life cycle of 17 years (ie they are buried in the ground for 17 years between every mating season).

So at the very end "some species of cicadas have a life cycle of 17 years" -- they are born, they go underground, they emerge -- or do they, or is it other cicadas, born undreground, who emerge? -- and mate and take brief roles in summer-stock plays based on "Le Cigale et Le Fourmi" or possibly Dickens's "The Cricket on the Hearth" and then, tired of being type-cast, disappear as suddenly as they had come, for another 17 years.

But why? Why not sixteen? Why not eighteen? Why not ten or twenty-two? Why seventeen?

Possibly Mother Nature couldn't count, or at least count in a way that would make sense for her proudest creation, man.

But then I realized that the number 17 is at the heart of one of the greatest mysteries in American constitutional history. Senior parties at Fish and Richardson, and winners of the Lemelson Prize at MIT, will know at once what I mean.

Why is it, in not only recognizing (hell, all kinds of countries do that) but in enshrining in the Constitution itself, the length of time that patents may be awarded, did the Framers decide on making the patent term not ten years, or twenty, or thirty, or life plus fifty, but "seventeen years." Why, why, why? I've read Jefferson. I've read George Mason and James Madison, I've looked at the Papers of Count Rumford and even went to visit his house, I've tried to find out but no one seems to have the answer. "No one knows why" is not a satisfactory answer.

Why "17 years" for the length of a patent term? Why? Why?

Perhaps I should mention that I have come up with a new solar energy invention that will revolutionize the entire field and save the world. I am ready with my claims. I have written up the thing so that it will withstand every challenge. But I won't make a move to submit a patent application, much less tell anyone a thing about it, until someone can satisfactorily answer this question.

Posted on 05/31/2007 10:10 PM by Hugh Fitzgerald
1 Jun 2007
Mary Jackson
I am sixteen going on seventeen
Innocent as a rose
Bachelor dandies, drinkers of brandies
What do I know of those

Totally unprepared am I
To face a world of men
Timid and shy and scared am I
Of things beyond my ken

I need someone older and wiser
Telling me what to do
You are seventeen going on eighteen
I'll depend on you

A bit of googling reveals that it used to be fourteen years, which was, way back when, two apprenticeship terms of seven years each. Then (1861)it was lengthened to seventeen years.

Could it have anything to do with the age of majority being eighteen? Probably not.

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