Daily Archives: January 21, 2005

Fourth Prime Tree of Depth 22 Discovered — 2p +/- 4,322,175 at 3,406,147

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My seemingly unending quest for a prime tree deeper than 22 generations continues apace.  Today a fourth D22 tree was found.  This one was not revealed through experimentation or pushback analysis on earlier trees like the last one was, and sadly, before you ask, no, the new D22 tree itself will not push back any further…

If you don't remember what a prime tree is, feel free to check the article I wrote the last time a D22 tree was discovered, there's a nice recap there.  If you feel a need for even more details such as “Why do you care?”, you can check the first article I wrote on prime trees.

So this is yet another tie for the deepest tree, and like the others it refuses to push back a generation.  Here's what the new tree looks like:

2p +/- 4,322,175 at 3,406,147 (D22, P32):
 [3406147]   - = [2490119]   .   + = [9302413]   .       + = [22927001]   .           - = [41531827]   .               - = [78741479]   .               .   - = [153160783]   .               .       + = [310643741]   .               .           + = [625609657]   .               .               - = [1246897139]   .               + = [87385829]   .                   + = [179093833]   .                       + = [362509841]   .                           + = [729341857]   .                               - = [1454361539]   .                                   + = [2913045253]   .                                       - = [5821768331]   .                                       + = [5830412681]   .                                           + = [11665147537]   .                                               - = [23325972899]   .                                                   - = [46647623623]   .                                                       + = [93299569421]   .                                                           + = [186603461017]   .                                                               - = [373202599859]   .                                                               + = [373211244209]   .                                                                   - = [746418166243]   .                                                                       - = [1492832010311]   .                                                                           - = [2985659698447]   .                                                                               + = [5971323719069]   + = [11134469]       - = [17946763]       + = [26591113]

Wow, what a monster.  The largest prime churned out by this tree is 5,971,323,719,069.  That's 5.9 trillion, folks.  As I noted earlier, the tree doesn't “push back”.  Which is to say if you try to find a number that you can multiply by this coefficient, and then subtract this offset to get the root of this tree, that number is not prime:

Solve 2p – 4322175 = 3406147.
p = 3864161.
p is not prime.  3864161 = 7 x 23 x 24001.

Dang.  No way to grow this D22 tree into a D23 tree.  Ah well, just have to keep looking.  This tree was found by my coworker Dan, who has been very gracious in letting me use his otherwise unused computer time.  By a strange coincidence, Dan is also the person who found the very first D22 tree!

So the known list of D22 trees is now:

  1. 2p +/- 569,415 at 384,187 (D22, P29)
  2. 2p +/- 2,258,025 at 1,867,823 (D22, P29)
  3. 2p +/- 4,849,845 at 3,337,421 (D22, P41)
  4. 2p +/- 4,322,175 at 3,406,147 (D22, P32)

Note that the offset for the new tree is again one of those offsets that seems to be a series of low sequential primes multiplied together… although this one has some holes.

4,322,175 = 3 x 5^2 x 11 x 13^2 x 31

In other news the number of known D21 trees is now 10 and the number of known D20 trees is now 42 with one more predicted by pushback analysis.  Total number of (inverted) monster trees (D>=16 or P>=30) found to date is 5,983.  In the next few days ShareCal will pass the 6,000 monsters milestone.  At this time, the total number of trees computed by ShareCal is 89,275,088,340 (that's 89.2 billion trees).

ShareCal is going strong in its new screensaver incarnation and is averaging about 36 active clients.  I would really like to push that up to 50 if possible.

Fear of the Virtual

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In the Lifestyle section on USAToday.com, as reported via Yahoo.com, there is an article lamenting the modern trend toward digital cameras.  The article can be summarized like so:

  1. Digital cameras have a delete button.  So now, instead of going into a shoebox with the good photos, photos deemed 'mistakes' are erased forever.
     
  2. Even photos which don't get erased are rarely printed.  Most exist only on the hard drive of the photographer's computer.
     
  3. Hard drives are ultimately unreliable… sooner or later they crash, which could lead to a loss of one's entire digital photo album.
     
  4. Historians often learn a lot from old pictures which are mistakes, but in the future, the mistakes are going to be harder to find.  This may prove misleading to future historians.
     
  5. Children need photographs they can hold to create a sense of emotional well being.  'Proof' they were loved, and all that. “What about the children?”
     
  6. In order to view a digital picture, you have to go through an “unnatural act” to see it, and computer formats change.  Old versions of diskettes with family photos on them may not be readable when your greatgrandkids discover them in your attic.

I have to admit, I have serious trouble taking any of this seriously.  First of all, I think people are taking far more photos than ever before.  Now that I have a digital camera I take pictures practically *every day*.  I take pictures of things I might not have bothered with before.  Like this one:

It's a picture of snow encrusting the skylight over my cube at one of my employer's offices.  Film costs money, developing costs money, and photoalbums cost money too.  By contrast digital pictures almost seem free… people take scads of them.  Sure some of them get deleted but I think if you were to take the number of digital pics in a year that do not get deleted, and compare it to the number of physical pictures taken in the same timeperiod, there'd be no contest.

The fact that a lot of photos aren't printed is probably a *good* thing.  There's less waste involved.  I will probably get a photoprinter at some point.  When I do, I'm quite certain that my pictures of cat food cans and the like will probably not make it to print.

I agree on the point about hard drives.  Many computer owners don't back up their treasured photos.  That is a shame really.  I'm as guilty as the next guy… some of my family pictures are not backed up too.  But I plan on rectifying that situation when my new computer arrives next week.

As far as an absence of mistakes misleading historians?  Yeah I don't buy it.  Any historian worth his salt had better be well aware that this particular age saw the dawn of digital photography.  If anything, to historians who primarily study photographs, this age will be very interesting and important.  Change is always interesting.

Do kids need photos?  Probably.  Do they need photos they can hold?  Ermm.  I don't really think so.  Sounds like someone romanticizing the idea of photo memories as opposed to anything based in hard fact.  It may well be that when most of us who are adults now were children, we loved looking through hardcopy photos.  If such photos were not available and digital photos were, how do we know we wouldn't love them every bit as much?  Neya loves looking at pictures in our digital family album.  She loves using the digital camera and taking pictures of her own, like this one:

If a picture like that doesn't capture what it is to be a child of a technological age, I don't know what does.  Can you hear her thinking “I'm squishing your heaaaaad!”?  I think pictures taken by digicam and placed on a computer are every bit as real to Neya as old Poloroids.  In fact the old poloroids might not seem quite normal to her.

Finally the matter of “unnatural acts” to view digital pictures pretty much seals it for me that this is simply modern prejudice resisting change.  I'm sure that 100 years ago people said the same when comparing driving horses to driving automobiles.  Yeah whatever bub, this too shall pass.

I was appalled by this:

…But are they really pictures if they exist only in the online ether? John Wells, a San Francisco lawyer, thinks not. Ten years ago, after Wells' father died, he was going through his things, including a pile of floppy disks that no longer fit into any functioning computer. So into the trash they went. Then he found a real treasure: a dusty box in the garage rafters filled with thousands of slides that chronicled nearly 40 years of his family's history. He could hold them up to the light and see his half-remembered past – kids' birthday parties, Christmas mornings and long-dead loved ones full of life again…

“Here's a pile of disks Dad used to store information that was important to him.  Gee I don't have a 5.25″ disk drive.  Pitch 'em.”

I have to say that if you call yourself a historian, and you don't have any antiquated computing equipment which you keep maintained and running for inspecting old media, or haven't tried to locate any such service providers, you're not much of a historian.  I would be quite surprised if someone doesn't already have a company which offers just that service.  Bring us your old media, and we'll put it on new media, etc.

Further, I have to argue that ancient family photos can be largely a mystery.  Modern digital photos are more likely to become parts of virtual scrapbooks or websites that include text with the photo explaining its significance and indicating who is depicted, etc.  Old photos?  Better hope somebody wrote on  the back.

I'll conclude with the two oldest photos in my digital library to date, pictures taken around easter of 1998, when my daughter was 1 year old.  Click the thumbnails to see information about the pictures.

Easter 1998: Natalie, Nana, and Neya

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Here's a picture taken when Lynnea was a little over 1 year old.  Each year my parents get a big kick out of having an easter egg hunt for their grandkids and the neighbor's kids.  On the left is Natalie, Lynnea's cousin, then my mom, Lois (lovingly referred to as 'Nana'), and finally Lynnea herself.  At this young age I think Neya found the basket of eggs somewhat awkward to carry.

But When I Got There, the Cupboard was Bare…

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Our company is pretty cool.  Usually the lunchroom is stocked with free/low cost snacks such as candy, cookies, crackers, pretzels, fresh bread, bagels, and fruit.

I say usually because when I walked in there today, this is what I saw.  The bread bins (on the right) were empty, and the snack trays held nothing but a packet of oatmeal, and an open and half-eaten pack of skittles.

So I grabbed an apple juice and had that instead.  When I returned later to discard the apple juice bottle… the half-pack of skittles was gone.

I guess someone was even hungrier than I.

Hungry programmers will eat anything.  I bet the oatmeal is gone by tomorrow.