# In school, were you taught that 1 is a prime number? **URL:** \ **Category:** In My Humble Opinion\ **Created:** [March 22, 2013, 5:45pm UTC](https://boards.straightdope.com/t/in-school-were-you-taught-that-1-is-a-prime-number/653655 "2013-03-22T17:45:20Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![Skald\_the\_Rhymer](https://avatars.discourse-cdn.com/v4/letter/s/ecccb3/32.png) [@Skald\_the\_Rhymer](https://boards.straightdope.com/u/Skald_the_Rhymer)\ **Post date:** [March 22, 2013, 5:45pm UTC](https://boards.straightdope.com/t/in-school-were-you-taught-that-1-is-a-prime-number/653655/1 "2013-03-22T17:45:20Z")
I just had to disabuse my nephew (who is, I think, 14) of this notion, which was taught him by his math teacher (in explicit contradiction not only of the fundamental theorem of arithmetic, but also the textbook). So I thought I’d ask. Yes, I’m aware that 1 was formerly classified as a prime, but that hasn’t been true in about a hundred years. Poll in a moment, but don’t let that slow you down. I’m feeling cruel today so the results will be public. ---
**Author:** ![kayaker](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/kayaker/32/441_2.png) [@kayaker](https://boards.straightdope.com/u/kayaker)\ **Post date:** [March 22, 2013, 5:53pm UTC](https://boards.straightdope.com/t/in-school-were-you-taught-that-1-is-a-prime-number/653655/2 "2013-03-22T17:53:19Z")
One is the loneliest number that you’ll ever do. ---
**Author:** ![hogarth](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hogarth/32/1773_2.png) [@hogarth](https://boards.straightdope.com/u/hogarth)\ **Post date:** [March 22, 2013, 5:56pm UTC](https://boards.straightdope.com/t/in-school-were-you-taught-that-1-is-a-prime-number/653655/3 "2013-03-22T17:56:01Z")
The list of choices seems very strange. If I was taught that 1 is not prime, you only care if I’m under 20, am I understanding it correctly? ---
**Author:** ![AngelSoft](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/angelsoft/32/440_2.png) [@AngelSoft](https://boards.straightdope.com/u/AngelSoft)\ **Post date:** [March 22, 2013, 5:57pm UTC](https://boards.straightdope.com/t/in-school-were-you-taught-that-1-is-a-prime-number/653655/4 "2013-03-22T17:57:46Z")
I always assumed it was a prime number. I can’t explicitly remember being taught it, but I guess I must have been in order for me to think it’s one. I mean…why wouldn’t it be? I thought a prime number was any number that couldn’t be divided by any other number than one/itself? Is it that the rule is one AND itself? Is that what makes 1 not a prime number? ---
**Author:** ![tdn](https://avatars.discourse-cdn.com/v4/letter/t/94ad74/32.png) [@tdn](https://boards.straightdope.com/u/tdn)\ **Post date:** [March 22, 2013, 5:59pm UTC](https://boards.straightdope.com/t/in-school-were-you-taught-that-1-is-a-prime-number/653655/5 "2013-03-22T17:59:56Z")
College? College? We didn’t have math in college. As long as we could count to 4, we were good. I think I was taught that it was prime, though. Back in the 70s. ---
**Author:** ![hogarth](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hogarth/32/1773_2.png) [@hogarth](https://boards.straightdope.com/u/hogarth)\ **Post date:** [March 22, 2013, 6:02pm UTC](https://boards.straightdope.com/t/in-school-were-you-taught-that-1-is-a-prime-number/653655/6 "2013-03-22T18:02:23Z")
> [@AngelSoft](#): > > Is that what makes 1 not a prime number? If you assume that 1 is prime, then you don’t get unique prime factorizations for the integers (among other things). E.g. 6 = 1 \* 2 \* 3 = 1^2 \* 2 \* 3 = 1^3 \* 2 \* 3 = … ---
**Author:** ![AngelSoft](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/angelsoft/32/440_2.png) [@AngelSoft](https://boards.straightdope.com/u/AngelSoft)\ **Post date:** [March 22, 2013, 6:06pm UTC](https://boards.straightdope.com/t/in-school-were-you-taught-that-1-is-a-prime-number/653655/7 "2013-03-22T18:06:29Z")
> [@hogarth](#): > > If you assume that 1 is prime, then you don’t get unique prime factorizations for the integers (among other things). E.g. 6 = 1 \* 2 \* 3 = 1^2 \* 2 \* 3 = 1^3 \* 2 \* 3 = … …Uh…oh of course. How…silly of me to not realize that…😕 Says the person who has difficulty doing simple addition/subtraction in her head. ---
**Author:** ![Skald\_the\_Rhymer](https://avatars.discourse-cdn.com/v4/letter/s/ecccb3/32.png) [@Skald\_the\_Rhymer](https://boards.straightdope.com/u/Skald_the_Rhymer)\ **Post date:** [March 22, 2013, 6:07pm UTC](https://boards.straightdope.com/t/in-school-were-you-taught-that-1-is-a-prime-number/653655/8 "2013-03-22T18:07:47Z")
> [@hogarth](#): > > The list of choices seems very strange. If I was taught that 1 is not prime, you only care if I’m under 20, am I understanding it correctly? The poll is best ignored, except for the banana pudding recipe; it’s formatted badly. I was wondering how long ago the erroneous – no, let’s call it reconsidered – notion that 1 is prime stopped being taught, but I am trying to quit coffee again and thus have a no coffee headache and am having difficulty concentrating and so didn’t put the options up properly. I blame the Russians. > [@AngelSoft](#): > > I always assumed it was a prime number. I can’t explicitly remember being taught it, but I guess I must have been in order for me to think it’s one. I mean…why wouldn’t it be? I thought a prime number was any number that couldn’t be divided by any other number than one/itself? Is it that the rule is one AND itself? Is that what makes 1 not a prime number? Here you go, lad or lassie: [Fundamental theorem of arithmetic](http://en.wikipedia.org/wiki/Fundamental_theorem_of_arithmetic). It doesn’t hold if 1 is prime. Also consider [this section](http://en.wikipedia.org/wiki/Prime_number#Primality_of_one) in the Wiki on prime numbers. And yes, I’m perfectly aware that I’m abusing “Wiki” in the previous sentence, but I’m feeling contumacious today. ---
**Author:** ![Andy\_L](https://avatars.discourse-cdn.com/v4/letter/a/c67d28/32.png) [@Andy\_L](https://boards.straightdope.com/u/Andy_L)\ **Post date:** [March 22, 2013, 6:08pm UTC](https://boards.straightdope.com/t/in-school-were-you-taught-that-1-is-a-prime-number/653655/9 "2013-03-22T18:08:15Z")
I was never taught that 1 is prime, but I note that the idea that 1 is prime was once a respectable idea [Prime number - Wikipedia](http://en.wikipedia.org/wiki/Prime#Primality_of_one) ---
**Author:** ![Skald\_the\_Rhymer](https://avatars.discourse-cdn.com/v4/letter/s/ecccb3/32.png) [@Skald\_the\_Rhymer](https://boards.straightdope.com/u/Skald_the_Rhymer)\ **Post date:** [March 22, 2013, 6:11pm UTC](https://boards.straightdope.com/t/in-school-were-you-taught-that-1-is-a-prime-number/653655/10 "2013-03-22T18:11:37Z")
> [@Andy\_L](#): > > I was never taught that 1 is prime, but I note that the idea that 1 is prime was once a respectable idea [Prime number - Wikipedia](http://en.wikipedia.org/wiki/Prime#Primality_of_one) I realize that, and given that primality is a human concept I’m not willing to say the notion of one being prime is wrong, in the sense that the notion that the moon is made of green cheese is wrong. I brought it up because, as your cite mentions, mathematicians stopped considering 1 to be prime about sixty or seventy years ago. But as my OP mentions, my mid-teens nephew was told the contrary by a teacher recently, so I was wondering how current the misapprehension was. ---
**Author:** ![Andy\_L](https://avatars.discourse-cdn.com/v4/letter/a/c67d28/32.png) [@Andy\_L](https://boards.straightdope.com/u/Andy_L)\ **Post date:** [March 22, 2013, 6:15pm UTC](https://boards.straightdope.com/t/in-school-were-you-taught-that-1-is-a-prime-number/653655/11 "2013-03-22T18:15:03Z")
> [@Skald\_the\_Rhymer](#): > > But as my OP mentions, my mid-teens nephew was told the contrary by a teacher recently, so I was wondering how current the misapprehension was. Yeah, I agree that’s weird. ---
**Author:** ![leahcim](https://avatars.discourse-cdn.com/v4/letter/l/b4bc9f/32.png) [@leahcim](https://boards.straightdope.com/u/leahcim)\ **Post date:** [March 22, 2013, 6:15pm UTC](https://boards.straightdope.com/t/in-school-were-you-taught-that-1-is-a-prime-number/653655/12 "2013-03-22T18:15:10Z")
> [@Skald\_the\_Rhymer](#): > > I realize that, and given that primality is a human concept I’m not willing to say the notion of one being prime is wrong, in the sense that the notion that the moon is made of green cheese is wrong. I brought it up because, as your cite mentions, mathematicians stopped considering 1 to be prime about sixty or seventy years ago. But as my OP mentions, my mid-teens nephew was told the contrary by a teacher recently, so I was wondering how current the misapprehension was. Back when I used to TA calculus, I encountered some kids who were told that mathematical induction was an invalid proof mechanism because it “assumes at the outset what it is trying to prove” by their high-school teacher. That teacher got a call from the faculty. Nothing about 1 being prime, though. ---
**Author:** ![Skald\_the\_Rhymer](https://avatars.discourse-cdn.com/v4/letter/s/ecccb3/32.png) [@Skald\_the\_Rhymer](https://boards.straightdope.com/u/Skald_the_Rhymer)\ **Post date:** [March 22, 2013, 6:17pm UTC](https://boards.straightdope.com/t/in-school-were-you-taught-that-1-is-a-prime-number/653655/13 "2013-03-22T18:17:48Z")
> [@leahcim](#): > > Back when I used to TA calculus, I encountered some kids who were told that mathematical induction was an invalid proof mechanism because it “assumes at the outset what it is trying to prove” by their high-school teacher. That teacher got a call from the faculty. > > Nothing about 1 being prime, though. I can top that. I know of a chemistry teacher – scratch that, a person employed to teach chemistry – who, less than five years ago, insisted that there were only 92 elements. Not 92 naturally occurring elements: 92 elements total. Simply refused to acknowledge synthetic elements as _existing_, much less valid. I suspected there were religious reasons but there was nothing in it for me in confronting him. ---
**Author:** ![Ms.Pumpkin](https://avatars.discourse-cdn.com/v4/letter/m/a87d85/32.png) [@Ms.Pumpkin](https://boards.straightdope.com/u/Ms.Pumpkin)\ **Post date:** [March 22, 2013, 6:20pm UTC](https://boards.straightdope.com/t/in-school-were-you-taught-that-1-is-a-prime-number/653655/14 "2013-03-22T18:20:15Z")
Not prime. I’m 31. ---
**Author:** ![Sattua](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/sattua/32/11906_2.png) [@Sattua](https://boards.straightdope.com/u/Sattua)\ **Post date:** [March 22, 2013, 6:20pm UTC](https://boards.straightdope.com/t/in-school-were-you-taught-that-1-is-a-prime-number/653655/15 "2013-03-22T18:20:47Z")
There’s no option for me. I’m between 30 and 40 and was taught that one is NOT prime. In middle school. ---
**Author:** ![Procrustus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/procrustus/32/2994_2.png) [@Procrustus](https://boards.straightdope.com/u/Procrustus)\ **Post date:** [March 22, 2013, 6:22pm UTC](https://boards.straightdope.com/t/in-school-were-you-taught-that-1-is-a-prime-number/653655/16 "2013-03-22T18:22:14Z")
Don’t remember. I’m 51. Prime numbers is what, like 6th grade? I barely remember last week. ---
**Author:** ![AngelSoft](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/angelsoft/32/440_2.png) [@AngelSoft](https://boards.straightdope.com/u/AngelSoft)\ **Post date:** [March 22, 2013, 6:24pm UTC](https://boards.straightdope.com/t/in-school-were-you-taught-that-1-is-a-prime-number/653655/17 "2013-03-22T18:24:07Z")
> [@Skald\_the\_Rhymer](#): > > Here you go, lad or lassie: > > [Fundamental theorem of arithmetic](http://en.wikipedia.org/wiki/Fundamental_theorem_of_arithmetic). > > It doesn’t hold if 1 is prime. > > Also consider [this section](http://en.wikipedia.org/wiki/Prime_number#Primality_of_one) in the Wiki on prime numbers. And yes, I’m perfectly aware that I’m abusing “Wiki” in the previous sentence, but I’m feeling contumacious today. Well…that just made my eyes go cross. Clearly this is well outside of my brain’s ability to process math stuff. I’ll just remember that 1 isn’t a prime number ‘just cause’ and leave it at that. XD ---
**Author:** ![delphica](https://avatars.discourse-cdn.com/v4/letter/d/e9a140/32.png) [@delphica](https://boards.straightdope.com/u/delphica)\ **Post date:** [March 22, 2013, 6:28pm UTC](https://boards.straightdope.com/t/in-school-were-you-taught-that-1-is-a-prime-number/653655/18 "2013-03-22T18:28:44Z")
I was taught that 1 is a prime\* number, with the asterisk being my middle school math teacher who essentially said “Kid, you’re in 7th grade, and your average in this class is about an 81. For any math you encounter, go ahead and consider 1 a prime number. I doubt you need to worry about it beyond that.” So there was some recognition that 1 wasn’t prime, I would have been about the right age that some of our older textbooks would have said yes, it’s prime and our newer textbooks said no, it isn’t. I notice in the wikipedia article, the ancient Greeks did not even consider one to be a _number._ What’s up with that? ---
**Author:** ![Skald\_the\_Rhymer](https://avatars.discourse-cdn.com/v4/letter/s/ecccb3/32.png) [@Skald\_the\_Rhymer](https://boards.straightdope.com/u/Skald_the_Rhymer)\ **Post date:** [March 22, 2013, 6:36pm UTC](https://boards.straightdope.com/t/in-school-were-you-taught-that-1-is-a-prime-number/653655/19 "2013-03-22T18:36:34Z")
> [@delphica](#): > > I was taught that 1 is a prime\* number, with the asterisk being my middle school math teacher who essentially said “Kid, you’re in 7th grade, and your average in this class is about an 81. For any math you encounter, go ahead and consider 1 a prime number. I doubt you need to worry about it beyond that.” > > So there was some recognition that 1 wasn’t prime, I would have been about the right age that some of our older textbooks would have said yes, it’s prime and our newer textbooks said no, it isn’t. > > I notice in the wikipedia article, the ancient Greeks did not even consider one to be a _number._ What’s up with that? Euclid’s definitions. [QUOTE=what did I just say? and why has no one brought me any coffee, damn it!] Def. 1. A unit is that by virtue of which each of the things that exist is called one. Def. 2. A number is a multitude composed of units. [/QUOTE] A lot of things that seem obvious to us today were not so to the ancients, because we’re standing on their shoulders. ---
**Author:** ![Left\_Hand\_of\_Dorkness](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/left_hand_of_dorkness/32/7156_2.png) [@Left\_Hand\_of\_Dorkness](https://boards.straightdope.com/u/Left_Hand_of_Dorkness)\ **Post date:** [March 22, 2013, 6:39pm UTC](https://boards.straightdope.com/t/in-school-were-you-taught-that-1-is-a-prime-number/653655/20 "2013-03-22T18:39:13Z")
> [@Ms.Pumpkin](#): > > Not prime. I’m 31. Uh, if you’re 31, yes you are. [Next page](https://boards.straightdope.com/t/in-school-were-you-taught-that-1-is-a-prime-number/653655.md?page=2)