Ok, here’s all you need to know. (And if you giveth not a sh*t about numbers, just click out now; check how many ‘Likes’ Linsey Lohan got today..) I forgive you.
Anyway, I’m done lying in bed factoring 2739 in my head, and equally finished reading all the multi-millenia speculation from math thinkers who would have profited from having a day job.
The Hell wid it! The is NOTHING SPECIAL about prime numbers, save their indivisibility. It’s not even something they should be be proud of; It’s almost akin to a ‘special-interest’ internet group whose members ‘do not collect stamps’, as a common bond.
Ok, here’s the whole picture, so you-uns can sleep at night:
Step One: My Excellent House party.
Where: A room in my Mom’s basement.
What: I sent out invitations to numbers 1-6 for a start, asked them to bring their nifty ‘Divisibility-Lasers’.
OK, 2,3,5, and 7, SMS-ed right away that they’ed be there. ‘4’ said “Two will take care of it for me.” and ‘6’ didn’t get back. No problem.
I set up the room thusly:
Ceiling tiles, one foot square, 10 X 10. A hundred tiles in all. Took me three hours to ‘magic-marker’ the numbers on each one.
I made sure to put a comfy rug in the center of the floor, and ordered pizza for the party. All four of the guests arrived, each in his fav color: 2: bright red, 3: a lovely green, 5: nice utilitarian brown, and 7: a tastefull beige. Their lasers were of the same matching color, of course.
And so, after a good half hour of pizza-munching and Rules-explanation, they were ready! A lovely sight, the four of them in a pile on the rug, kinda like ‘And the Lion shall lie down with the Lamb’
At the signal, 2 started first. Machine-gunning all the even-numbered rows with her red laser.
Oops. forgot ‘The Rules’:
1) If you light up a number you can divide evenly (like, for ‘2’, 32/2=16) it puts a little tag on the tile with your name/number on it.
More rules to follow..
And so ‘2’ ‘hit’ fully half of the numbers, but managed to knock to the floor only one tile: ‘Two’,(herself) which she put in her box, kinda disappointed.
Three went next. Took a little longer since he couldn’t exactly shoot in straight or diagonal lines. He got ‘3’ knocked down for his box, but also ‘6’. Why? Well, Six had already been divided by 2 into a ‘3’, so it fell to the floor, having been completely factored. Not so for ‘9’, which three would need to ‘hit’ twice to knock off the ceiling.
Anyway, I hope you kinda get the rules by now.
“Five” with his brown laser went over the ceiling carefully, hit all the numbers ending with ‘0’ or ‘5’. Ended up, in his box, with ‘5’ (of course) but also ’15’ (since 3’s laser had already turned it into a ‘5’. (oh, and ’10’, same reason.)
Seven’s turn was last, but he had a great time: Got ‘7’ of course, but also ’14’, ’21’ and ’35’ for his box-o-goodies. Thanks to help from the smaller divisors.
Anyway, this party continued for a good two hours: more turns, more pizza, more beer, but hey, who’s counting?
In The End:
And in the end, what was left on the ceiling?
1) First of all, repeated ‘hits’ by ‘2’s red light got her, 4,8,16,32, and ’64’.
Three netted in addition to ‘3’: 9 and 27
Five grabbed ’25, and Seven, likewise netted ’21,and ’49’.
Most of the othe tiles were split in the boxes between the co-contributers to their divisibility:
Like ‘Tile 60’, who ended up in shards in several boxes, namely : 2,3,and 5.
And Then a Knock on the Door!
I opened the front door carefully, so I thought, but not quickly enough to prevent ’11’ and ’13’ from barging right in. They’d heard on FB that a party had happened without them, and were greatly un-happy.
I sat them down in the kitchen, with the last pizza ‘Pepperoni, no anchovies’, and listened to their case:
“What are we… goats!” they spit. “22,33,44,55…” Eleven ran off the list of numbers only he could divide, echoed seconds later by ‘Thirteen’, with “13,26,39,52…”
What could I do as a fair panel-moderator?
I led them to the basement room, where it turned out 2.3.5.and 7 had alreay realized that they may need offshore help to bring down the ceiling. I expected a floor-fight, but the Numbers joined hands in exemplary fashion. Within minutes, the ceiling was much closer to what I’d hoped for when I called the party.
And still.. there were ..um.. hold-outs.. stalwarts. Numbers like ’57’, sitting there overhead, mocking me.
Hmm.. 57=3X19. Nineteen? I scrolled through my phone ‘Contacts’. ‘Not found’ Ditto for, turned out, 17,23,29,31,37,41,47,53, ugh, the list goes on.
I needed to sit and think a second: What exactly was I trying to accomplish??
Ok, un-numbered milligrams of Ritalin and Valium later, it turns out that it’s ridiculously easy to lose track of what one is after. But I now know:
1)The ceiling’ is the set of numbers from 1 to 100 base 10
2) My guests, including the party-crashers 11, 13..etc are the survivors, numbers who themselves have no clean divisors.. ok ‘Primes’.
3 And any tile left on the ceiling after the party , having survived all attempts to divide it by smaller numbers is also a Prime.
So I went out and ordered like, gift-cards, printed-up for the lucky bunch. Wrote on them
“Sub-100 Prime Club!” And I sincerely expected that they’d take it as the compliment I’d intended.
Oy! closest I can get to why they ‘hated it’ is that the name reminded them of their insignificance in the Universe, their puny role in a continuum where even 100 to the 100th power is still a long way from infinity.
Hmm.. my next party was to have been a ‘blow-up’ of the above, but with a ceiling at 500 feet altitude, and 1000X1000 tiles. Woulda been fun, I still say. (setting aside the tactical/budgetary issues of 170 meter towers and 300+ meter steel cables. I do have the space on my property, but $400 a month Israeli social security might not cover the materials.
But, in principle, this ‘party-mood’ can be extended out to Alpha Centauri any way beyond. Numbers never stop, nor do primes, (although primes do grow scarcer. In fact, the percentage of primes per hundred drops as the inverse-logarithm of the ‘number of numbers’.
Main Point here: I don’t care about any of that!
Life is short and I’m thrilled to know and love the primes to 100. Hell, I bought ’em pizza, now they owe me, if I can find a quid-pro-quo./ JS