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Can you pick the prime numbers?
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Prime Number Shooting Gallery Quiz
Created Mar 28, 2012 in
Featured Mar 1, 2013
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Comment below threshold:
Mar 29th, 2012 at 01:19 GMT
No one has ever done this before? lol. You should do the same thing, but for even numbers.
Comment below threshold:
Mar 29th, 2012 at 19:53 GMT
Since when is 1 not a prime number???
Mar 30th, 2012 at 16:22 GMT
Since prime numbers were defined.
Jan 18th, 2013 at 15:13 GMT
This is probably a good time to advertise
, my favorite game on the internet:
Game published: Mar 1st, 2013 at 04:00 GMT
Mar 1st, 2013 at 04:09 GMT
A prime example of a great quiz.
Mar 1st, 2013 at 04:30 GMT
missing 2 makes me doubt my entire existence
Mar 1st, 2013 at 05:17 GMT
i also tried 1, not sue why, i know its not prime... but why isnt it a prime?? the definition of a prime number is its only divisible by 1 and itself.. well what other number is it divisible by?? it really should be considered prime
Mar 1st, 2013 at 05:33 GMT
@EmYanks2001: Including 1 messes up pretty much every application prime numbers have.
Mar 1st, 2013 at 06:28 GMT
Related to Syzygy's comment, a very good example of why we don't want 1 to be prime is the Fundamental Theorem of Arithmetic: Every positive integer larger than one can be expressed uniquely as the product of primes. But if 1 is taken to be prime, there can be more than one prime factorization of a number. (21=3*7=1*3*7=1*1*3*7). "Every application prime numbers have" is a bit of an exaggeration, but the existence of a unique prime factorization is key to much of number theory. It is best, therefore, to define prime numbers as natural numbers with *exactly* two factors: one and itself. Alternatively, call a number p>1 prime whenever if p=a*b then a=1 or b=1.
Mar 1st, 2013 at 11:29 GMT
Great video series about numbers on YouTube is Numberphile. Here's their episode on 1 not being a prime: http://www.youtube.com/watch?v=IQofiPqhJ_s
Mar 1st, 2013 at 12:11 GMT
i bet 91 is the most common mistake
Mar 1st, 2013 at 12:41 GMT
@antoniobroto I have decided I do not deserve my Masters in Mathematics after that mistake.
Mar 1st, 2013 at 12:47 GMT
Simple explanation for the 1 problem: as EmYanks said, a prime number is only divisible by itself and 1, meaning it has two and only two distinct factors. (For example, 2 is prime because its only two factors are 2 and 1.) However, the number 1 only has one factor - 1 - so it is considered a "unit" number, not prime or composite.
Mar 1st, 2013 at 13:39 GMT
@SpeedyJohn: Okay, maybe I'm missing something here. The claim "Every positive integer larger than one can be expressed uniquely as the product of primes" would seem to be counterindicated by prime numbers themselves. For example, what primes is 7 a product of? I assume that a product is defined as the multiplication of 2 or more numbers. I don't think a single number can be a product.
Mar 1st, 2013 at 14:15 GMT
Mar 1st, 2013 at 14:18 GMT
@rockgolf, I see your point. When I learned the theorem it was worded a little differently, something like this: "All positive integers are either prime, or can be expressed as a unique product of primes." This version of the theorem also take into account that the "empty product" (the product of no numbers) = 1.
Mar 1st, 2013 at 14:59 GMT
I'm a kid and I missed all but two. And both of those were stupid mistakes.
Mar 1st, 2013 at 19:13 GMT
@rockgolf 7 is the product of 7, as with all prime numbers their unique product of primes is just itself.
Mar 1st, 2013 at 19:29 GMT
@rockgolf: A single number is a product of one prime. Anyway, the definition of prime has got nothing to do with multiplication, as it's "a positive integer that is divisible by exactly two positive integers"
Mar 1st, 2013 at 20:04 GMT
The only one I missed was 5, because everyone knows multiples of 5 are not primes. Oops.
Mar 1st, 2013 at 22:49 GMT
@Jactor- I'm currently a math major. Mistakes like that are how you know you ARE studying math.
Mar 1st, 2013 at 22:50 GMT
@rockgolf: We learn in school that a "product" is the result of multiplying two numbers (and by extension of multiplying any amount of numers, so we would consider 2*3*3 a product). But as with many of mathematics, consistency for a lot of rules made it easier to also allow for only one number to be multiplied, or even no number at all (Noisewater's "empty product"). This way in some theorems or problems we can say "just multiply all the numbers thrown at you" even if there is only one or no number at all - this way we don't have to make exceptions like "except if there is only one number then it will be our result or no number, when our result will be 1". It's basically the same reason why 3^0=1. 3^2 (9) is a third of 2^3 (27), 3^1 (3) is a third of 3^2, so 3^0 (multiply 3 zero times with itself) should be a third of 3^1 - in essence, when you reduce the exponent by 1, you divide by three (this continues with 3^(-1) and so on).
This way the definitions are just way easier to handle and you can expand all kind of rules (like the ones of derivation) without making all kind of exceptions and additional rules.
By the way, the same holds for sums, only the "empty sum" equals 0.
But do not feel too bad for poor little one - it gets the moniker of "neutral element of multiplication" (because x*1=x - multiplying by 1 does not change anything), just as the 0 is the "neutral element of addition", making those two the most important numbers of them all in mathematics (runners up are e and pi, also i if you work with complex numbers). Actually, any set of elements for which we define some sort of "a and b combined gives us c" will always have something like the 1 and something like the 0 to be really useful (called a "field" in mathematics, but I guess now I digress).
Mar 1st, 2013 at 23:48 GMT
How is 1 not prime??
Mar 2nd, 2013 at 00:48 GMT
Thank you eab21. Thank you. That damn 1 messes me up on prime numbers everytime. Now I finally understand. Amazing what you forget from elementary math. Also, I can't believe I missed 2 though... Yikes...
Mar 2nd, 2013 at 01:41 GMT
@LICA98: A prime number must have the factors of 1 and itself. 1's factors are well... just 1, so yeah.
Mar 2nd, 2013 at 05:51 GMT
Maybe by far the easiest solution to the immediate quandary is just removing "1" from the shooting gallery; you don't have the wonderful 101-103-107-109 sequence at the other end, after all. It seems clear to me as a non-mathematician that the primeness or non-primeness of One is like many (as "Law & Order" might put it) parallel and equally valid systems, such Euclidean and non-Euclidean geometry, or choosing whether to accept the Axiom of Choice. Other analogies would be Russell's paradoxes or Goedel's Theorem of Undecidability. As secondary school maths teachers everywhere sometimes have to tell their unbelieving students, and as survey-takers often tell respondents, there is no "right" choice or "correct answer". It all depends on what you're asking One and the distinction between Prime and Compound Numbers to do.
Now that doesn't mean the preceding debate isn't interesting or useful; it just (almost
and by definition) will never reach a definitive or universally-conclusive yes/no answer.
Mar 2nd, 2013 at 18:16 GMT
I agree with the point you're trying to make, that even in mathematics you can change some parameters at will and see which results will, well, result (after all it is "only a brain exercise", not a natural science). Like your non Euklidian geometry. That being said however: while 1 may fit the definition some people are taught at school, it just is not used as a prime in formal mathematics. You could try to define number theory with 1 being prime, but unlike the geometry example, this will not yield different results, but only more complicated sentences. Bottom line: any definition of a prime number that includes 1 is possible but highly impractical, thus incomplete with regards to mathematics as they are used.
Mar 4th, 2013 at 21:59 GMT
I had 16/25 (64%), which happens to be the same as my grade-twelve math mark! I guess I'm doomed. Thank God I'm a writer.
Mar 6th, 2013 at 20:44 GMT
17/25 pretty good game
Mar 6th, 2013 at 22:03 GMT
The more or less official definition of a prime number is a positive interger that is divisible by exactly two numbers. Therefore, 1 is not prime.
Mar 16th, 2013 at 17:55 GMT
Someone should inform my fourth grade teacher that one is not prime because I have been lied to.
May 1st, 2013 at 17:49 GMT
May 11th, 2013 at 20:17 GMT
91 the classic stumper for middle school kids.
May 11th, 2013 at 20:22 GMT
A prime number is divisible by exactly TWO natural numbers. One is divisible by exactly ONE natural number. Composites are divisible by more than two natural numbers. 1 is a non-composite number, but it is not a prime number.
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