# 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:** 3
**Author:** ![Filbert](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/filbert/32/3433_2.png) [@Filbert](https://boards.straightdope.com/u/Filbert)\ **Post date:** [March 23, 2013, 12:24am UTC](https://boards.straightdope.com/t/in-school-were-you-taught-that-1-is-a-prime-number/653655/41 "2013-03-23T00:24:32Z")
I’m 30, so am I between 20-30 or 30-40? Not that it matters, because I was taught that it wasn’t prime anyway. Bananana pudding it is. ---
**Author:** ![cochrane](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/cochrane/32/10441_2.png) [@cochrane](https://boards.straightdope.com/u/cochrane)\ **Post date:** [March 23, 2013, 1:07am UTC](https://boards.straightdope.com/t/in-school-were-you-taught-that-1-is-a-prime-number/653655/42 "2013-03-23T01:07:54Z")
I’m sure I was taught that 1 is prime. But I was also taught that Pluto was a planet. ---
**Author:** ![RealityChuck](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/realitychuck/32/195_2.png) [@RealityChuck](https://boards.straightdope.com/u/RealityChuck)\ **Post date:** [March 23, 2013, 1:15am UTC](https://boards.straightdope.com/t/in-school-were-you-taught-that-1-is-a-prime-number/653655/43 "2013-03-23T01:15:27Z")
We were taught in junior high (or earlier) that one was not prime, though the reason was not closely explained: a prime number was a number that was divisible by two numbers: itself and one, and one was only divisible by a single number. ---
**Author:** ![Ethilrist](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/ethilrist/32/4604_2.png) [@Ethilrist](https://boards.straightdope.com/u/Ethilrist)\ **Post date:** [March 23, 2013, 1:38am UTC](https://boards.straightdope.com/t/in-school-were-you-taught-that-1-is-a-prime-number/653655/44 "2013-03-23T01:38:17Z")
> [@cochrane](#): > > I’m sure I was taught that 1 is prime. But I was also taught that Pluto was a planet. Great, if they keep this up, 1 won’t even be a number any more, and we’ll have to reprint all the clocks. ---
**Author:** ![truthSeeker2](https://avatars.discourse-cdn.com/v4/letter/t/7cd45c/32.png) [@truthSeeker2](https://boards.straightdope.com/u/truthSeeker2)\ **Post date:** [March 23, 2013, 2:08am UTC](https://boards.straightdope.com/t/in-school-were-you-taught-that-1-is-a-prime-number/653655/45 "2013-03-23T02:08:55Z")
when we were taught abt primes , we were not told anything abt 1. Though in the text book, it was mentioned that its not . In the later years we were taught in the higher class that 1 is not prime, when we were using prime numbers for something else. most of indians learn tables like this: 2 2 ja 4 2 3 ja 6 2 4 ja 8 You even ask most of the older people, they will tell the table using ja. It was much later when I though wth is this ‘ja’, then it came to me tht Ohh…it must be 's are . Like 2 2’s are 4… ---
**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\ **Post date:** [March 23, 2013, 2:45am UTC](https://boards.straightdope.com/t/in-school-were-you-taught-that-1-is-a-prime-number/653655/46 "2013-03-23T02:45:18Z")
> [@delphica](#): > > I notice in the wikipedia article, the ancient Greeks did not even consider one to be a _number._ What’s up with that? Well, there are a number of reasons. ---
**Author:** ![ZenBeam](https://avatars.discourse-cdn.com/v4/letter/z/3ab097/32.png) [@ZenBeam](https://boards.straightdope.com/u/ZenBeam)\ **Post date:** [March 23, 2013, 2:51am UTC](https://boards.straightdope.com/t/in-school-were-you-taught-that-1-is-a-prime-number/653655/47 "2013-03-23T02:51:52Z")
> [@kunilou](#): > > Which is why I voted for banana pudding. I’m over 40 and was taught one was not prime nor will ever be prime. Some of us are watching our weight… ---
**Author:** ![Nava](https://avatars.discourse-cdn.com/v4/letter/n/da6949/32.png) [@Nava](https://boards.straightdope.com/u/Nava)\ **Post date:** [March 23, 2013, 2:53am UTC](https://boards.straightdope.com/t/in-school-were-you-taught-that-1-is-a-prime-number/653655/48 "2013-03-23T02:53:24Z")
I was taught that “a prime number can be divided only by 1 or by itself” and that you would never write 1 as a factor when performing factorization because it’s unnecessary, but the issue of whether 1 was itself prime or not didn’t come up. ---
**Author:** ![Trinopus](https://avatars.discourse-cdn.com/v4/letter/t/2bfe46/32.png) [@Trinopus](https://boards.straightdope.com/u/Trinopus)\ **Post date:** [March 23, 2013, 3:29am UTC](https://boards.straightdope.com/t/in-school-were-you-taught-that-1-is-a-prime-number/653655/49 "2013-03-23T03:29:15Z")
And yet, when calculating “perfect numbers,” you include one. Six is a perfect number, and so is 28…but only when you include 1 as one of the divisors. ---
**Author:** ![Carnacki](https://avatars.discourse-cdn.com/v4/letter/c/b5e925/32.png) [@Carnacki](https://boards.straightdope.com/u/Carnacki)\ **Post date:** [March 23, 2013, 3:34am UTC](https://boards.straightdope.com/t/in-school-were-you-taught-that-1-is-a-prime-number/653655/50 "2013-03-23T03:34:52Z")
> [@Skald\_the\_Rhymer](#): > > How do you think the classification of 1 as non-prime is “gerrymandered”? I’m not **njtt** , but I have a similar “gut” feeling about 1 being prime (I’m 34 and I _think_ I was taught 1 was prime). Per the wikipedia definition, “a prime number is a natural number **greater than 1** that has no positive divisors other than 1 and itself”. If you strike the “greater than 1” line, then 1 is a prime. If not, it’s not. You don’t have to worry about any fundamental theorems or anything more complicated than the definition of prime. The longer definition that explicitly excludes 1 as prime means that 1 is not prime, and I’m savvy to that now. But when I learned prime numbers, I don’t remember learning that primes had to be larger than 1. ---
**Author:** ![njtt](https://avatars.discourse-cdn.com/v4/letter/n/ecd19e/32.png) [@njtt](https://boards.straightdope.com/u/njtt)\ **Post date:** [March 23, 2013, 4:03am UTC](https://boards.straightdope.com/t/in-school-were-you-taught-that-1-is-a-prime-number/653655/51 "2013-03-23T04:03:46Z")
> [@Skald\_the\_Rhymer](#): > > How do you think the classification of 1 as non-prime is “gerrymandered”? What **KidScruffy** said. One is specifically excluded in the standard definition. Without that clause, one would fall under the definition and be prime. What is that if not a gerrymander? ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [March 23, 2013, 4:18am UTC](https://boards.straightdope.com/t/in-school-were-you-taught-that-1-is-a-prime-number/653655/52 "2013-03-23T04:18:13Z")
It’s actually not that bad to let one be a prime in the integers. But when you try to move to [more general settings](http://en.wikipedia.org/wiki/Ring_(mathematics)), allowing things with multiplicative inverses to be primes would just complicate the hell out of everything. So we disallow one as a prime in the integers to make the general theory simpler. ---
**Author:** ![Johanna](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/johanna/32/8318_2.png) [@Johanna](https://boards.straightdope.com/u/Johanna)\ **Post date:** [March 23, 2013, 6:13am UTC](https://boards.straightdope.com/t/in-school-were-you-taught-that-1-is-a-prime-number/653655/53 "2013-03-23T06:13:49Z")
I’m over 40, and it was taught to me in grade school math that 1 is not a prime.\* That the smallest prime is 2. The concept uniquely for 1 was “identity.” There was no choice on the poll for being taught that 1 is not a prime. In college calculus, I don’t think the subject of primes ever came up. \*However, we were sometimes encouraged to lump 1 in with the primes for convenience’s sake, along with the caveat that it isn’t really prime. ---
**Author:** ![Malacandra](https://avatars.discourse-cdn.com/v4/letter/m/45deac/32.png) [@Malacandra](https://boards.straightdope.com/u/Malacandra)\ **Post date:** [March 23, 2013, 7:48am UTC](https://boards.straightdope.com/t/in-school-were-you-taught-that-1-is-a-prime-number/653655/54 "2013-03-23T07:48:59Z")
If you think that 1 is a prime and it’s “gerrymandering” to claim it isn’t, go run the Sieve of Eratosthenes algorithm starting from 1 = prime. Let me know how much use you get out of it. ---
**Author:** ![Carnacki](https://avatars.discourse-cdn.com/v4/letter/c/b5e925/32.png) [@Carnacki](https://boards.straightdope.com/u/Carnacki)\ **Post date:** [March 23, 2013, 8:20am UTC](https://boards.straightdope.com/t/in-school-were-you-taught-that-1-is-a-prime-number/653655/55 "2013-03-23T08:20:36Z")
> [@Malacandra](#): > > If you think that 1 is a prime and it’s “gerrymandering” to claim it isn’t, go run the Sieve of Eratosthenes algorithm starting from 1 = prime. Let me know how much use you get out of it. I don’t think anyone’s arguing that 1 is a prime. All I was trying to say is that if someone asks me if 1 is a prime, I don’t say “let me brush up on my fundamental theorems” and I don’t say “let me refresh my memory on the sieve of eratosthenes” – all I say is “what is the definition of prime?” If the definition of prime includes the words “…greater than 1”, then 1 is not a prime. If the definition is just “a number that is only divisible by itself and one”, then 1 is a prime. I think everyone knows by now what the actual definition of prime is, but I was taught wrong in junior high school. ---
**Author:** ![Malacandra](https://avatars.discourse-cdn.com/v4/letter/m/45deac/32.png) [@Malacandra](https://boards.straightdope.com/u/Malacandra)\ **Post date:** [March 23, 2013, 8:28am UTC](https://boards.straightdope.com/t/in-school-were-you-taught-that-1-is-a-prime-number/653655/56 "2013-03-23T08:28:22Z")
Very likely. And to my dismay I saw a high school math teacher, just a week ago, struggling to explain what 1/0 meant, and I actually saw her write up “1/0 = 0”. :smack: ---
**Author:** ![VunderBob](https://avatars.discourse-cdn.com/v4/letter/v/839c29/32.png) [@VunderBob](https://boards.straightdope.com/u/VunderBob)\ **Post date:** [March 23, 2013, 8:40am UTC](https://boards.straightdope.com/t/in-school-were-you-taught-that-1-is-a-prime-number/653655/57 "2013-03-23T08:40:10Z")
I don’t recall either way anything about 1 being prime, and I’m 52. I have a heavier than usual math education, too. ---
**Author:** ![Johanna](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/johanna/32/8318_2.png) [@Johanna](https://boards.straightdope.com/u/Johanna)\ **Post date:** [March 23, 2013, 4:39pm UTC](https://boards.straightdope.com/t/in-school-were-you-taught-that-1-is-a-prime-number/653655/58 "2013-03-23T16:39:10Z")
> [@delphica](#): > > the ancient Greeks did not even consider one to be a _number._ What’s up with that? For that matter, in the old days, it was taught that the thumb is not a finger. What’s up with that? In piano notation, the fingering is given with thumb=1, index=2, etc. up to 5 for the pinky. But if you see an old piano score edited with fingering from the 19th century, back then they started numbering with the index finger being 1, and the numbers only went up to 4. The thumb was relegated to X. 😕 I get why they would omit the left thumb from numbering in classical guitar fingering, because you’re not supposed to use it on the frets. But why do piano like that? Makes no sense. ---
**Author:** ![RaftPeople](https://avatars.discourse-cdn.com/v4/letter/r/6f9a4e/32.png) [@RaftPeople](https://boards.straightdope.com/u/RaftPeople)\ **Post date:** [March 23, 2013, 5:49pm UTC](https://boards.straightdope.com/t/in-school-were-you-taught-that-1-is-a-prime-number/653655/59 "2013-03-23T17:49:32Z")
> [@Malacandra](#): > > If you think that 1 is a prime and it’s “gerrymandering” to claim it isn’t, go run the Sieve of Eratosthenes algorithm starting from 1 = prime. Let me know how much use you get out of it. But the problem could be handled on either side of the issue. Either say 1 isn’t prime, or alter the definition of a composite number to only allow 1 if the other number is itself - but that is probably a more cumbersome work around. ---
**Author:** ![Bricker](https://avatars.discourse-cdn.com/v4/letter/b/977dab/32.png) [@Bricker](https://boards.straightdope.com/u/Bricker)\ **Post date:** [March 23, 2013, 6:12pm UTC](https://boards.straightdope.com/t/in-school-were-you-taught-that-1-is-a-prime-number/653655/60 "2013-03-23T18:12:09Z")
I’m over 40 and was taught in high school and onwards that 1 is neither prime nor composite. [Previous page](https://boards.straightdope.com/t/in-school-were-you-taught-that-1-is-a-prime-number/653655.md?page=2) [Next page](https://boards.straightdope.com/t/in-school-were-you-taught-that-1-is-a-prime-number/653655.md?page=4)