Folly of the Faithful Canine

The College Board, the group that always makes the SAT,
Has rarely copped to errors in an almost century.
One infamous example came in 1982,
When zero of the options then available were true.

This item showed two circles, A and B, where B had thrice
The radius of A (the illustration was precise)
And A would roll around B, so how often, then, would A
Complete a full rotation in its circuit, would you say?

I’d like to note the text said “revolution,” not “rotation”—
Ambiguous, but not the bigger cause of consternation.
The closest given answer to the proper one was three,
But take two circles, try it for yourself, and then you’ll see.

The coin rotation paradox results in one spin more,
So A’s rotation total in the trek ‘round B is four.
Although it rolls but three times its circumference, the path
It travels on is circular, and that explains the math.

Three boys who took that SAT wrote in to tell the board
About its subtle oversight. I’m sure they left it floored.
The problem was discounted, bringing down a lot of scores
And costing takers money for correction (but of course).

Within the decades since, the board’s made many more mistakes.
I’d say its biggest issue’s not a membership of flakes:
Today most U.S. colleges say applicants need not
Take any test that’s standardized to prove what they were taught.

I’ve learned about a number set (a thing I do for fun)
Of 2, 3, 5, 11, 17, and 41.
They’re Euler’s “lucky” numbers, and the formula’s like so:
All positive k integers below these n’s will show
That k^2 – k + n is bound to yield a prime.
(If k were n, the value would be n^2 every time.)
You’ll notice one’s much larger than the others in the set.
It’s now my age. Here’s hoping that my luck increases yet.

You may have heard that one’s not prime.
That’s not been standard all the time.
The notion comes from ancient Greeks,
Who deemed one not a number (freaks).
Some also thought all primes were odd,
Omitting two as well (how flawed).
The Middle Ages saw at last
That one’s a number; then it passed
For prime for several centuries,
Contested seldom (Euler, please),
But after 1956,
Instructors had agreed to fix
Their lists of primes to all exclude
The number one, which now is viewed
To be a “unit.” What’s the deal?
To count it now, we would repeal
The wording of a lot of rules
Most often learned in higher schools.
The sieve of Eratosthenes,
For instance, wouldn’t work with ease.
So every prime must have two factors,
Heedless of the rule’s detractors.