Prime Cell Phone Numbers: Oddity or Probability?

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SUMMARY

The discussion centers around the concept of prime cell phone numbers, initiated by a user who discovered their own ten-digit phone number is prime using Wolfram|Alpha. Participants explore the probability of ten-digit phone numbers being prime, estimating it at approximately 4.04204977% based on the distribution of primes. They discuss methods to check for prime numbers, including generating random numbers and using the Pari/GP tool for verification. The conversation also touches on the implications of number properties, such as the fact that no ten-digit number can end in 0 and be prime.

PREREQUISITES
  • Understanding of prime numbers and their properties
  • Familiarity with the Wolfram|Alpha tool
  • Basic knowledge of the Pari/GP software for prime checking
  • Awareness of the NANPA (North American Numbering Plan Administration) phone number structure
NEXT STEPS
  • Research the distribution of prime numbers using the Prime Number Theorem
  • Learn how to use the Pari/GP software for prime number verification
  • Explore algorithms for generating random ten-digit numbers and checking their primality
  • Investigate the implications of number properties in telecommunications, particularly in NANPA regulations
USEFUL FOR

Mathematicians, computer scientists, and anyone interested in number theory, particularly those exploring the intersection of mathematics and telecommunications.

  • #31
Char. Limit said:
Except I don't live in Canada...

Its not nice tricking people into thinking that you live in Canada.
 
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  • #32
Tangentially related: both my birthday and month of birth are prime and together they form a http://en.wikipedia.org/wiki/Sexy_prime" pair. Yay.

None of my phone numbers are prime though.
 
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  • #33
Vasara said:
Tangentially related: both my birthday and month of birth are prime and together they form a http://en.wikipedia.org/wiki/Sexy_prime" pair.

May 11th, July 13th, November 5th, or November 17th, then.
 
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  • #34
Kajahtava said:
Okay, I've got an algorithm running right now which should give me the amount of ten digit primes, if anyone has a faster computer than I and runs scheme, or has some pointers on reducing complexity:

http://codepad.org/pD8jMxnp

I have no idea how long this will take, I made the algorithm to compute the list of primes a while ago, hence it has comments. In theory it should compute a list of all primes smaller than 999999999 and then count the the amount that are higher than 1000000000.

I have that number already -- 404204977. But I don't have the number that excludes area codes starting with 1, certain numbers with connection 555, etc.

Borek said:
7 = (\sqrt 7)^2

so 7 is a square.

"Square" is surely used in its number theory sense here, as Kajahtava suggests.
 
  • #35
What if where you live they don't have 10 digit phone numbers?
Well anyway, this 8 digit number of mine is even so... I'm one of the special ones that has a composite phone number.
 
  • #36
When did I say I was in Canada?

I've aleady mentioned in the Member Photo Thread that the lake behind me was Lake Coeur d'Alene... in Idaho.
 
  • #37
CRGreathouse said:
I have that number already -- 404204977. But I don't have the number that excludes area codes starting with 1, certain numbers with connection 555, etc.
Ah yes, good point.
"Square" is surely used in its number theory sense here, as Kajahtava suggests.
Even better point.
 
  • #38
Char. Limit said:
When did I say I was in Canada?

I've aleady mentioned in the Member Photo Thread that the lake behind me was Lake Coeur d'Alene... in Idaho.
If you don't remember I'm not going to remind you.





;-p
 
  • #39
Don't forget also, all numbers with the fourth through sixth digits "911" have to mostly cancel as well...
 
  • #40
CRGreathouse said:
May 11th, July 13th, November 5th, or November 17th, then.
Yup, November 5th is right. That's also the smallest sexy prime pair.
 
  • #41
Char. Limit said:
Don't forget also, all numbers with the fourth through sixth digits "911" have to mostly cancel as well...

I hadn't thought of that -- I wonder if this means the number I gave was too high, or if that rule is subsumed in another.

Vasara said:
Yup, November 5th is right. That's also the smallest sexy prime pair.

The 5th of November? Ominous.
 

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