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How Many Phone Numbers Are Prime?

About Prime Numbers

Remember doing middle school math? That was around the time we started learning about complex algorithms, multiplication, long division, and prime numbers. If you can recall, a prime number is a natural number (also called a whole number) that is greater than 1 and cannot be formed by multiplying two other smaller numbers together. This means that prime numbers cannot be decimals or fractions, either.

prime numbers

For example, the first ten prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29. Ten is not considered a prime number, for instance, because when you multiply two smaller numbers together, 5 and 2, you get ten. The number 1 is not a prime number, and two is the only even number in existence that is considered prime. 13 is a prime number because the only way to get this result through multiplication is 13 X 1. It takes some practice, but it’s easy to get the hang of it once you get started!

Though you may not inherently “know” a number is prime just by looking at it, there are larger prime numbers as well. Numbers such as 739, 853, and even 997 are all prime. In fact, it is calculated that billions of numbers are prime, so it’s impossible to list them all in a single place. It’s not just 3 digit numbers, 10 digit numbers are also included. This means that it’s very likely for a person’s telephone number to also be a prime number.

Calculating Prime Numbers

At times, a number can be so large that it is difficult to determine if it’s prime right away, just upon visual examination. However, there are some websites that allow you to enter a number of any size and see whether or not it’s prime. This is the easiest way to figure it out. If a number is not prime, this website resource will actually tell you which numbers it is divisible by.

If you would rather do things by hand, and tend to be fascinated by the process, prime factorization is a commonly known practice. This is another method taught in school to see which numbers multiply together to make the original number. All you need is a piece of paper and a pencil.

First, let’s take the number 24 as a simple example. 24 is divisible by 4 and 6. Neither of these numbers is prime, so you must branch this out even further:

2 X 2 = 4 and 2 X 3 = 6

The results, 2 and 3, cannot be broken down again, so we don’t need to add any more steps. Instead, we can conclude that the prime factorization of 24 is 2 X 2 X 2 X 3.

However, when working with large 10 digit numbers, prime factorization may not be the best route to take since this will require many more “breakdowns” and a longer amount of time to do the work. If you are privy to mathematics and have a knack for solving problems, you can also do the calculations yourself. While there is no complete “pattern” for discovering prime numbers, there are a few different formulas that can help.

First, there is a formula founded on Wilson’s theorem. This states that if integer p > 1, then (p – 1)! + 1 is divisible by p if p is prime. An integer is a whole number that is either positive (1, 2, 3) or negative (-1, -2, -3).

There are several other more complicated formulas for figuring out if a number is prime as well. One of these is Matiyasevich’s theorem, which explains: “Because the set of primes is a computably enumerable set, by, it can be obtained from a system of Diophantine equations.” In mathematics, a Diophantine equation contains two or more “unknowns.” Another individual, James Jones, discovered a set of 14 Diophantine equations which could work if a given number k + 2 is prime, if and only if the system produces a natural number. Check out this Wikipedia page to see each of these 14 formulas.

Prime Telephone Numbers

Once you start making calculations on your own, you might get curious enough to wonder if your own telephone number is a prime. Actually, it was a man named Michael Lugo who pointed out that the telephone number in the famous song “Jenny”, 867-5309, is a prime number (8,675,309). This song was on the Billboard Top Ten in the year 1982. This began a small trend of others wanting to see if they had a “famous” prime telephone number.

So just how many U.S. phone numbers are prime? The fastest method is to conduct a search online of all 10 digit prime numbers. However, this is not necessarily the most accurate way to do this. Ones of the reasons why is because not all 10 digit numbers in existence have been assigned to a landline or mobile number.

According to mathematics and applications writer Kevin Knudson, you can “denote by π(x) the number of primes less than or equal to x.” Again, you have to rule out some phone numbers from the equation. Not only for the reason listed above but also because not all 10 digit numbers are phone numbers. For example, the number 1 cannot begin an area code.

Knowing all of this information, the range we are actually looking at is 200-200-0000 and 999-999-9999.

According to Knudson, the equation is “π(9999999999) ≈ 434,294,481 and π(2002000000) ≈ 93,475,343.” It is a little difficult to solve on paper ourselves, so he did the math for us. This equals out to about 340,819,138 prime phone numbers. If you would rather read that figure as a percentage, that is 4.2% total of all American phone numbers or one out of 25.

For those who do not own a prime phone number, but want one, it’s possible to buy your own custom number from a vanity service. Either way, aren’t you glad we did the math for you?