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I have lost the original post. Who was looking for a project

in computer science? In any case, shall I just post the idea

here? Contact me offlist for questions if you wish.

Prime numbers are very much a phenomenon of nature, or

rather meta-nature for the primes are the same for every

intelligent species that has discovered them, regardless

of what noxious fumes they respire or what number base

they may use. Primes are universal.

This idea is related to a function I have been toying with

since the publication of this month's Scientific American.

The Mathematical Recreations column describes the

gaps between primes, then defines the most common

interval as the "jumping champion".

The first several primes are: 2, 3, 5, 7, 11, 13, 17, 19, 23,

29, 31, 37, 41... so the intervals in those first twelve primes

would be 1, 2, 2, 4, 2, 4, 2, 4, 6, 2, 6, 4. In that interval, the

most common jump is 2, so the jumping champion for the

first 13 primes is 2, so J(13) = 2.

Nowthen, this function as defined in the SA article is

rather dull. You go out very far and the J(n) = 6 for a

looooong long time, until you get way out into the jillions.

But if you define the J function with two parameters, a

lower and an upper limit, interesting things happen. For

instance if we wished to calc J(7, 13), the jumping champion

between the 7th and the thirteenth primes, then the primes

are 17, 19, 23, 29, 31, 37, 41, the jumps are 2, 4, 6, 2, 6, 4

and the jumping champion is a threeway tie between 2,

4 and 6. For greater interest, let all ties go to the

largest, so J(7, 13) = 6.

Nowthen, heres the trick. Make a plot, the x axis is lower

limit, the Y axis is the upper limit minus the lower limit. At

each X,Y coordinate is the jumping champion in that

interval J(X,Y). So on our map, at the coordinates (7,[13-7])

is a column 6 high.

Nowthen, if you write an algorithm to create a map of

all the jumping champions in all intervals, you create

a universal landscape of sorts, one that would be recognized

by mathematicians from the planet Ork as well as here.

It is a fascinating primescape. As I said before, the most

common jumping champion is 6, so let 6 be identified

as "sea level" on the primescape. You form a coastline,

where the upper limit minus the lower limit = 1. Along

this coastline are towers and mountains of various heights.

It really is a marvelous sight. There are islands, isolated

"land masses" in a sea of 6. There are lakes, which are

closed areas of 6 within areas of raised areas. The

primescape contains lagoons, inlets, rivers, mesas,

islands, everything. Again, that map that you create

is truly *universal* in that it is the same map as can

be created anywhere in the universe.

Computer science student, you project will be to

write a piece of code that you can distribute over

email to volunteers, who will pool their computer

resources to map out the primescape by each taking

a range of X and Y to map. Then you

will need some means of storing all the findings.

I have some ideas on how this could be done,

and I have already written the code to create the

map. With enough volunteers, perhaps 30, you

should be able to create a map between 1 and

about 1 million, and about 200 pixels out to sea.

The extropian list alone should get ya 10 or 20

volunteers. Then answer the following questions

about the primescape:

1) what is the largest island below X=1E6?

2) what is the island farthest from the coast?

3) what is the largest landlocked lake?

4) if volume is defined as area times altitude,

what is the landmass with the greatest volume

below X=1E6?

5) where is the steepest cliff?

6) where is the landmass with the greatest

number of different altitudes?

7) Are there any examples of an island within

a lake? [answer = yes] How many are there

of these below X = 1E6.

All of these answers may be known to some

extraterrestrial beast, but no human knows them.

It would make a wicked cool computer science

project. spike

**Next message:**Russell Whitaker: "Re: Launch Technology"**Previous message:**my inner geek: "Fw: The Numbers Just Don't Ad Up"**In reply to:**J. R. Molloy: "Re: 11 questions about the Universe"**Next in thread:**Spike Jones: "new puzzle"**Reply:**Spike Jones: "new puzzle"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]

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