“Eeek Alors!” as my high school friend Shears used to say. This is it. We’re at the very start of the build. And I, for one, am squirming around in my seat in excitement.
What’s that? Well, yes, “Shears” is an unusual name. His given name was Mark Burkinshaw. Over time, he became known as Billy Burkinshaw. Eventually, this evolved into Billy Shears as sung about in Sgt Pepper’s Lonely Hearts Club Band by the Beatles. Later, people dropped the “Billy” and we just called him Shears (apart from my dear old dad, who called him “scissors”).
As you may recall from Day 0 of this mini-mega-series-saga, my chum John is building a LEGO Ultimate Collector Series version of the A-Wing Starfighter from Star Wars: Return of the Jedi. In order to develop the drama and excitement, John has divided the 570 instructions into 30 days of 19 instructions each.
Today’s photo shows the result of the first 19 instructions, which form the heart of the beast. As John said in his accompanying email, “Strange start to the build because it doesn’t feel like LEGO. So many linking pieces that, ultimately, will make it a very strong build, but not much in the way of traditional LEGO blocks yet. I’ve seen this system used for building outwards but not so intense. It will be interesting to see how many internal cavities are formed. Anyways, here’s the result from the first 19 instructions.”
As an aside, I’m sure that when you first saw the number 19 in my previous column, you thought “prime number” (as did I) and immediately moved on with your life (as did I).
Well, strange to relate, my chum Jay Dowling just sent me an email that has forever changed my view of prime 19 and its companions. If I change either of this number’s two digits, I may end up with another prime or with a composite (non-prime) value. For example, 29, 59, 79, and 89 are prime, while 39, 49, 69, and 99 are composite. Similarly, 17, 13, and 11 are prime, while 18, 16, 15, 14, 12, and 10 are composite.
Well, it turns out that, since 1978, mathematicians have known about a special class of prime numbers they call “digitally delicate primes” that they somehow failed to share with the rest of us. They may protest their innocence, but I know for sure that these little rascals (the mathematicians) never called me to tell me about these little rascals (the digitally delicate primes), which makes me wonder what other nuggets of knowledge and tidbits of trivia they’ve been keeping from us.
As we read in this column, a digitally delicate prime is a prime number in which the changing of any digit results in a composite value. As the aforementioned column says, “Change the 1 in 294,001 to a 7, for instance, and the resulting number is divisible by 7; change it to a 9, and it’s divisible by 3.”
But wait, there’s more, because – not content to leave well enough alone – those little scamps (the mathematicians) subsequently postulated a class of numbers they call the “widely digitally delicate primes.” This involves a subset of digitally delicate prime numbers that – if you prepend them with an infinite number of leading zeros – then changing any of those leading zeros would result in a composite.
Returning to the original column, we read, “Not surprisingly, the added condition makes such numbers harder to find. “294,001 is digitally delicate, but not widely digitally delicate […] since if we change …000,294,001 to …010,294,001, we get 10,294,001,” which is another prime number.
I tell you, we have to give mathematicians credit, because they hammered away at this problem using their esoteric mathematical tools – such as “covering congruences” and “sieves” – eventually proving the existence and extensiveness of widely digitally delicate prime numbers.
What use is all this? I don’t have a clue. Why am I waffling on about it here? Once again, I don’t have a clue. All I can offer is that it’s yet another thread in life’s rich tapestry. How about you? Is there anything you would care to share regarding anything you’ve read here?