primes by hand

[futurebird]

What is the fastest way to tell if a largish number is prime ***using only a a pencil and paper***?

Please find out if each of these is prime and explain the process you used.

a. 1,979

b. 3,127

c. 2,281

d. 42,499

e. 10,573

f. 847,313

g. 104,009

Comments

[chrismsx]

ahhhhhhhhhhhhhhh math... my brain !!!!!

[grayden]

Without Googling the answer, here's the approach I'd take

Much of this has already been said by <lj user=grayden>.

[dangerzooey]

I don't know of a systematic way to do it other than calculating the square root and then trying every prime number equal to or less than the square root.

An article I read a while back on an entirely different issue said that the current largest known prime number is 391,581 x 2^216,193 - 1, a number 65,087 digits long. Just thought you might find that interesting. (I don't know if another has been found since.)

Of course, you could always just get your hands on an idiot savant (I don't like the term, but I think its extension is clear) like the pair in one of the stories in Oliver Sacks' marvelous book The Man Who Mistook His Wife For a Hat and Other Clinical Tales.

Re: Much of this has already been said by <lj user=grayden>.

[futurebird]

The twins? I love that part of he Man Who Mistook His Wife For a Hat-- I have always admired people who can count/calculate/see numbers quickly.

Do you think you could factor numbers faster if you were given little square chips to place in rows? It should be pretty easy to sort the chips in such a way as to determine if a given number is prime.

I think I'm going to try this witha few hundered little squares and see if it makes me angry or not.

Re: Much of this has already been said by <lj user=grayden>.

[dangerzooey]

I'm not really sure I understand how the chips are supposed to help, but let me know how it goes for you. :)

Re: Much of this has already been said by <lj user=grayden>.

[futurebird]

It's not so complex....If you can make a rectangle out of it it ain't prime. :)

[hipstomp]

I have to confess I've no idea. But I've got a problem for you, which you may have already heard:

What is the next number in this series? 8, 14, 23, 28, 33.

[grayden]

The only number I can come up with that fits is -960.

My algorithm is rather convoluted and I'm sure that's not the right answer but my head hurts and I want to go eat some more turkey.

[futurebird]

do tell...

[grayden]

The numbers are 8, 14, 23, 28, 33.

A square series is 9, 16, 25, 36, 49

The difference between the series is:

1, 2, 2, 8, 16

oooohhhh! too cool to be a coincidence right? Now it's a powers of 2 game. The powers in question are:

0, 1, 1, 3, 4

Now that I'm looking at my calculation scribbles I have NO idea how I arrived at this conclusion, but I remember thinking about Fibonacci sequences. Somehow I decided that 10 was the next number in this series. No idea why anymore.

Now 2^10 must be subtracted from the next power in the first series. That comes out to 64 - 1024 = -960.

I blame it on lack of sleep.

[drjon]

I don't know :)

I also don't know why I've not seen you post on _koyaanisqatsi for almost two months, and I missed your voice, so...

[futurebird]

I'm a teacher and school is going full blast these days! I'll be back... promise.