Prime numbers and the Dominos!

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zenith20

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Aug 20, 2010
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Dear Friends,
i came to this problem about Prime numbers and the Dominos! the problem is:

"Get the largest prime number possible P, using the most of the 28 pieces according to arrangement A, without worrying for any matching between contiguous pieces (as in the normal domino game)"

Arrangement A:
?? . ?? . ?? . etc

the solution is said to be:

666564636261605554535251504443424140333231302220120011
(domino arrangement:
66.65.64.63.62.61.60.55.54.53.52.51.50.44.43.42.41.40.33.32.31.30.22.20.12.00.11)

---------

- how could i test such a number to see if its a prime number or not?
- if it's a prime, how could we prove it's the largest?!

thank you in advance
 
There is no easy way. To test for sure, youll need to check for many, many factors. There are semi-efficient ways to test the likelyhood of a large number being prime, but not for sure. To see that there is no larger one, you need to consider all non-redundant possibilities. A fast computer and an intelligent algorithm is your best bet.
 
I just checked it with my Voyage 200..........it IS prime.
 
I believe that Texas Instruments calculators do not truly check to see if the number is prime. There is a very small chance that it is composite. A professor of mine some time ago showed that even Maple makes this mistake, he found a composite that returns prime.
 
zenith20 said:
Dear Friends,
i came to this problem about Prime numbers and the Dominos! the problem is:

"Get the largest prime number possible P, using the most of the 28 pieces according to arrangement A, without worrying for any matching between contiguous pieces (as in the normal domino game)"

Arrangement A:
?? . ?? . ?? . etc

the solution is said to be:

666564636261605554535251504443424140333231302220120011
(domino arrangement:
66.65.64.63.62.61.60.55.54.53.52.51.50.44.43.42.41.40.33.32.31.30.22.20.12.00.11)

---------

- how could i test such a number to see if its a prime number or not?
- if it's a prime, how could we prove it's the largest?!

thank you in advance
Click to expand...
If it is a prime - then it is the largest prime, because the larger number that can be created from that set of numbers will have "0" in the unit position,

66.65.64.63.62.61.60.55.54.53.52.51.50.44.43.42.41.40.33.32.31.30.22.20.12.11.00 (the numbers are sorted - highest to lowest)

That is not a prime number.
 
Hey SK. Are you saying the posters prime is actually not prime or the one you posted?.

Daon, I did not know that about the erroneous answers from the TI. Good to know.

I reckon there is no sense in running it through Maple then.

Maybe try the GMPS (Great Mersenne Prime Search) site. They may have an applet or something that checks primality.

That is what the site is dedicated to. Though, this is not a Mersenne prime.
 
Thank you Friends :)

i found some interesting materials on Prime numbers, about the Largest known primes of different types.

Code: 
[url]http://primes.utm.edu/largest.html[/url]
 
galactus said:
Hey SK. Are you saying the posters prime is actually not prime or the one you posted?.

No - I was saying "If the posters number is a prime - then it is the largest prime that can be made with those numbers". There is one number that could be larger (made from those numbers) - but that number is NOT PRIME (because "that larger number" would be divisible by ten (even hundred)

Daon, I did not know that about the erroneous answers from the TI. Good to know.

I reckon there is no sense in running it through Maple then.

Maybe try the GMPS (Great Mersenne Prime Search) site. They may have an applet or something that checks primality.

That is what the site is dedicated to. Though, this is not a Mersenne prime.
Click to expand...
 
galactus said:
Hey SK. Are you saying the posters prime is actually not prime or the one you posted?.

I checked with wolfram alfa and according to that site - 666564636261605554535251504443424140333231302220120011 is a prime.

Daon, I did not know that about the erroneous answers from the TI. Good to know.

I reckon there is no sense in running it through Maple then.

Maybe try the GMPS (Great Mersenne Prime Search) site. They may have an applet or something that checks primality.

That is what the site is dedicated to. Though, this is not a Mersenne prime.
Click to expand...


.
 
666564636261605554535251504443424140333231302220120011 is a prime number according to Maple's ifactor command.

The command isprime(n) may return true even when n is composite.
See the maple help file to see what isprime does.
Type " ?isprime " in Maple.

The command ifactor(n) can be used to factor n. According to the Maple help file, it will return the complete integer factorization so if ifactor(n) returns n, then n is prime.
Type " ?ifactor " in Maple to see a description of this function and what it does.
 
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