Prime number support

[zak]

i have tried it for 15 minutes,
Timing[PrimeQ[33759183*2^123459-1]]
and when my cpu begins to heat more than 50 Cel. degree i stopped the program, because i have a previous experience of another pc damaged from heating the cpu. and the 50 degree indeed more than that, and my pc begins to slow down. someone may said 50 C. degree is normal, but this heating is specific to every pc alone, when i got 50 or more i have problems. also this heating does not refer to the ram memory which can be heated to the damaging point since there is no Fan over the ram memory.
if you zipped or rared the txt file it may be uploaded, try it as an experiment.
the curent modern i7-... cpu's are more efficient.
that number discovered in 2009, they may used universities super computers.
mathImpossible.PNG

[Johannes]

Doing this for all primes up to 1,000,000 results in a prime of 433,637 digits. I've just started the script to see what the result is for primes up to 10 million...

If you multiply all primes smaller than 10 million and add one you get a prime of 4,340,852 digits. The last 23 digits are 12222286177766366668971. Don't know how long it took exactly. Less than two hours, obviously.

Up to 100 million should finish in a couple of days. My guess is that the result would have more than the (almost) 13 million digits in the currently largest prime known. The problem is that I would have to mathematically prove my program (as well as the PowerBASIC compiler) for anybody to accept such a number as prime.

[danbaron]

Sorry, Johannes, I was wrong.

2 * 3 * 5 * 7 * 11 * .., + 1, is not necessarily prime.

Stop your calculation.

See this reference.

http://primes.utm.edu/notes/proofs/i...e/euclids.html



(If you never do anything, then, you'll never make a mistake, right?)

[danbaron]

Zipping the file only reduced it by 48%, zak.

Anyway, if you did the calculation, your computer would melt.

[Johannes]

Sorry, Johannes, I was wrong.

2 * 3 * 5 * 7 * 11 * .., + 1, is not necessarily prime.

Stop your calculation.

See this reference.

http://primes.utm.edu/notes/proofs/i...e/euclids.html



(If you never do anything, then, you'll never make a mistake, right?)

I should have checked this myself.

2 * 3 * 5 * 7 * 11 * 13 + 1 = 30031 = 59 * 509

Duh.

[danbaron]

I went to zak's site,

http://www.wolframalpha.com/ ,

and tested the 14th Wagstaff prime,

56713727820156410577229101238628035243,

http://en.wikipedia.org/wiki/List_of_prime_numbers

for primality,

"PrimeQ[56713727820156410577229101238628035243]".

Super-Mathematica didn't hesitate, it immediately verified that the number is prime.

(I call it Super-Mathematica, because, my suspicion is that the calculations are not being performed by computers like ours.)

[Johannes]

"PrimeQ[56713727820156410577229101238628035243]".

Super-Mathematica didn't hesitate, it immediately verified that the number is prime.

(I call it Super-Mathematica, because, my suspicion is that the calculations are not being performed by computers like ours.)

Sounds to me like they maintain a database of extremely large (non-)primes. That's what I would do. If you haven't encountered the number before do the calculations and store the result, otherwise return the result.

Sure, it'll take up some storage, but that's what terabyte-drives are for.

[danbaron]

If they're doing that, then, I don't think they should.

It seems like a deception to me.

Anyone could just make a list of big primes, using the internet.

But, that's not doing any mathematics.

Their main goal is to sell Mathematica.

I think, the web page,

http://www.wolframalpha.com/ ,

is basically an advertisement for Mathematica.

If a person enters a big prime there, and immediately receives verification, he might think that Mathematica is super-powered; when actually, it just looked up the number. I would classify that as a form of false advertising.

But, I can't stop them - (or, can I ?!?!!!)

[zak]

i don't think they use pre built tables, i have desconnected from the web so local mathematica installed in my hard disk will not consult the main site, then i run the PrimeQ[56713727820156410577229101238628035243]
and it gives the result immediately. i asked next prime , and the same .

[Johannes]

Zak,

I'm a little suspicious of the execution time given for the NextPrime. The first time, zero seconds, is logical if the internal timer hasn't had time to progress. But a time in the order of 10^-17 seconds? That's impossible. Clock speeds these days are in GHz which would give a resolution of 10^-9 seconds. Even if the internal clock runs ten times as fast we're still seven orders of magnitude away from the time given by Mathematica.

On this page people say Mathematica has certain limits for prime calculations.

How big is the installation of Mathematica on your hard drive?