Avi's Number

"... suppose we define f(X) over integers as taking the 1st digit from the left, then the 2nd, then the 4th, then the 8th, etc, so f(12345)=124 and f(12345678)=1248

Set y=f(f(f(f(f(…f(Graham’s number))))) such that there are the fewest number of fs such that y has less than a million digits." [1]

y is Avi's number.  Is Avi's number a prime or composite number?

Because we know the last digits of Graham's number, it seems to me that there might be a way to determine if the last digits of Avi's number is definitely not a prime.

[1] - http://www.scottaaronson.com/blog/?p=2673#comment-1013711

Pistils at dawn

A man with a beard is being harassed by a man in a top hat.  He has had enough and stands up forcefully, “That does it!  Pistols at dawn!”

Cut to black and the sounding of a rooster crowing.  We slowly fade from black and the man in the top hat is revealed holding a .50 caliber desert eagle.  He looks confident and handles the weapon like an expert. 

The camera jumps to the man with the beard.  He’s holding a single petunia.  The camera jumps back to the top hat man who shows a look of incredulity and superiority.  He knows how this duel is going to end. 

Another rooster crows and the bearded man begins to sprint forward.  The top hat man seems somewhat surprised and opens fire.  The bearded man makes a dramatic gesture with the petunia and successfully deflects the incoming bullet with a shower of sparks.  The top hat man begins to panic and fires repeatedly.  The bearded man expertly waves the petunia to deflect each incoming round.  Sparks shower his path as each bullet collides with the petunia and is propelled harmlessly away.  We see one more panicked look of horror on the face of the top hat man and the bearded man has reached him.  An enormous stroke of the petunia cleaves the top hat man in two.  The duel is over.

Cut to the bearded man on a bicycle leaving the scene of the duel.  A quick camera jump down to his feet reveal that they are resting not on normal bicycle pedals, but instead this bicycle uses large rose petals to turn the wheels.

Always a good decision

So the opening shot is a man sitting in his car; it’s dark outside.  The glass on the windows are kind of fogged up and the overall atmosphere is one of heat and wetness and dirt.  His eyes betray his debauchery; he’s had a lot of alcohol tonight.  He’s looking into the rear view mirror and we can see behind his shoulder; there’s flashing police lights.  However, he seems to be looking more at himself than at the flashing lights.

Next shot is uniformed legs in boots walking surely and fully of confidence.  The legs are in no hurry, but they carry an air of speed and certainty.  These legs belong to a man whose face we never see.  A man who knows his job.  A man who knows that his job saves lives.  A man who knows exactly what he’s going to find when he gets to his destination.  The camera pans upward as we get to a car.  All we see of the man is his back.  This is a police officer and he’s about to knock on a car door to deliver a DUI.

We’re back in the first car and the police man is knocking on the window.  The first man rolls down the window with dread and inevitability written on his face.  A shadowed face moves toward the open window.  “Had a few drinks tonight?”  It comes across more as a demand; a demand for a confession of wrongdoing.

The man looks over to the passenger side seat of the car to a as of yet unseen occupant.  An accusatory look, but also a pleading one.

The camera cuts to the passenger.  The Samuel Adams guy sits in the passenger side seat.  You know the one from those commercials.  Wearing old-timey clothes and accompanied by a stein full of beer.  “Always a good decision.”  Yeah, that guy.  He’s sitting silently in the passenger side seat of this guy’s car.  Holding a stein full of beer.  He’s not saying anything, but he has a goofy smile that takes up most of his face.

The camera cuts to a blank screen.  A voiceover begins, “Drinking and driving is never a good decision.  Please drink responsibly.”  

The camera cuts back to Samuel Adams being handcuffed, the stein with contents spilled is tipped onto the ground.