How many ten-digit phone numbers are possible in the North American Numbering Plan?

Question

Express your answer in scientific notation.

Answer 1

3628800

3.6288 x 10^6

Taking the fact that you can get number 0000000001 to 9999999999

Answer 2

1

Answer 3

Here are a few things to remember about NANP:
Area codes may not start with 0 or 1. Nor may they contain a 9 as the middle of the 3 digits.
Exchange Numbers (the first 3 digits, but not the area code) may not start with a 0 or 1.

Therefore, the whole series of number may be as follows
[2-9][0-8][0-9] [2-9][0-9][0-9] [0-9][0-9][0-9][0-9]


Ok, I was never great at math, so I had to think about this a bit more.
Your answer is combinations of area code multiplied by combinations of exchange (or central office code) mutiplied by combinations of Station code.

So, area code = [8 x 9 x 10] = 720
Exchange code = [8 x 10 x 10] = 800
Station Code = [10 x 10 x 10 x 10] = 10,000

Product of all that is 5,760,000,000.
Expressed in scientific notation, the result is 5.76 x 10^9

Answer 4

what about the hidden power of 2 be jumbled up? like 4888886? the hidden power is 64. is that a container or non-container? ok, read AD already. so 4888886 is non-container. nothing elegant comes to mind, though.

Answer 5

The NANP can assign exactly 5,480,570,800 possible numbers in its 25 countries under current restrictions.


Area Codes:
1st digit must be 2-9; 0 and 1 are special prefixes and are NOT allowed (8 possibilities)
2nd digit can be 0-8; the digit 9 is NOT allowed*** (e.g. 596, 891, 497 are NOT valid area codes) (9 possibilities)
3rd digit is 0-9 (10 possibilities)
MINUS the 8 special N11 numbers (211 through 911)
MINUS the 20 area codes that are reserved for special purposes: 10 from 37X and 10 from 96X
Total: (8 * 9 * 10) – 28 = 692 possible Area Codes

Exchange codes: (the first 3 digits of your 7-digit number
Same rules as above, except: the 20 reserved codes are allowed, and the second digit 9 is allowed.
1st digit is 2-9; 0 and 1 are special prefixes and are NOT allowed (8 possibilities)
2nd digit is 0-9; the digit 9 IS allowed*** (10 possibilities)
3rd digit is 0-9 (10 possibilities)
MINUS the 8 special N11 numbers (211 through 911)
Total: (8 * 10 * 10) – 8 = 792 possible exchange codes in each Area Code

Subscriber numbers: (the last 4 digits of your number)
All 10 digits are allowed for all 4 numbers
Total: (10 * 10 * 10 * 10) = 10,000 possible subscriber numbers in each exchange, in each Area Code.

Finally, there are 100 reserved numbers in each area code that can be used in fiction: (NXX) 555-01XX
There are 100 such numbers for EACH of the 692 area codes.
Total: –(100 * 692) = –69,200 (Negative, because we are subtracting these from the total available codes)

Grand Total: (692 area codes * 792 exchange codes * 10,000 subscriber numbers) – (100 fake numbers * 692 area codes) = 5,480,640,000 – 69,200 =
5,480,570,800 unique assignable numbers in all assignable area codes, all assignable switchboards, excluding all special N11 codes, 37X and 96X area codes, N9X area codes***, the reserved prefixes 0 and 1, and fictitious 555-01XX numbers.

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Exclusions explained:

The digit '1' is the long distance prefix, thus cannot be the first digit of the area code or switchboard.
Also, the prefix '11' is used on rotary phones without a star (*) key; e.g. '*69' is dialled as '1169'.
Also, the prefix '101' is used to select a different long distance carrier other than your default.
Also, the number '123' is used by certain carriers to reach your voicemail.
Also, the number '112' is used in CERTAIN countries, in CERTAIN states, by CERTAIN phone companies as an emergency number like '911'. This is NOT UNIVERSAL! IT WILL NOT WORK EVERYWHERE IN THE NANP!

The digit '0' is the prefix for long distance calls and to connect to an operator, thus cannot be the first digit of the area code or switchboard.
'0' is operator assistance.
'00' is Long Distance operator assistance.
'01' is International operator assistance.
'011' is the International dialling prefix.

N11 numbers (211, 311, 411, 511, 611, 711, 811, and 911) are used for emergencies, telephone company services, and various other government services. The most popular is 911.

***The second digit cannot be 9, A.K.A. N9X numbers are NOT allowed. This is because it is reserved for a transition from 3-digit area codes to 4-digit area codes in the future. Existing area codes will have a 9 inserted as the 2nd digit during the transition, e.g. Area Code 212 will become 2912, 313 will become 3913, etc. Having 9 as the second digit would confuse switchboards during the transition period (e.g. did you dial "1 (2912) 875 2145" or "1 [phone] 5"?) so they are not allowed at all under the current plan.

37X and 96X are reserved for no specific reason, but just in case. From the NANPA site: "Two blocks of 10 codes each have been set aside by the INC for unanticipated purposes where it may be important to have a full range of 10 contiguous codes available."

The reserved 555-01XX numbers are pretty self-explanatory; they allow for 100 fake, unassigned numbers in each area code for use in fiction.

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General Info:

NANP = North American Numbering Plan; the telephone number plan currently in use in the United States, Canada, and other countries on or near the North American continent. There are a total of 25 countries in the NANP. The international prefix is '+1' for the entire NANP.

NANPA = North American Numbering Plan Administration; the administrator of the NANP; it is operated by Neustar corporation.

N (as in 'N11' or 'N9X') = Any digit between 2 and 9; 0 and 1 are excluded because they are special prefixes (see above) and this digit may be dialled first.

X (as in '555-01XX' or 'N9X') = Any digit between 0 and 9–any digit at all; 0 and 1 are NOT excluded because this digit will never be dialled first.

N11 = The special codes explained above; does NOT include '011' (the International prefix) or '111' (unused, but can be confused with '11').

N9X = An Area Code with '9' as the second digit; the first digit is 'N' (can be anything 2-9) and the third digit is 'X' (can be anything 0-9). As explained above, these are unused, to avoid confusion with future transitional 4-digit area codes, as explained above.

REMEMBER: The NANP is NOT used solely in the United States! It is used in a total of 25 countries! The large 5-billion-and-change number I wrote includes all possible numbers in all possible area codes! This includes FOREIGN area codes! This includes UNASSIGNED area codes that MAY OR MAY NOT be assigned to FOREIGN countries! This includes NON-GEOGRAPHIC area codes such as '800' or '900' that are NOT A PART OF ANY SPECIFIC COUNTRY!

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TL;DR


5,480,570,800