3 ms·

"1 is non-prime by definition." dammit!

by nosage 11y ago

delecti 11y ago
I froze when I saw 1, and ended up going the same way you did. That one feels cheap. :P
mediumdeviation 11y ago
It's mainly due to the Fundamental Theorem of Arithmetic (aka unique prime factorization) - https://en.wikipedia.org/wiki/Fundamental_theorem_of_arithmetic https://en.wikipedia.org/wiki/Fundamental_theorem_of_arithme...
- btilly 11y ago
  However this was not settled surprisingly late. I have seen tables of prime counts produced in the 1950s and 1960s that specified whether they counted 1 as a prime, and some did count it.
  - OJFord 11y ago
    Still the case for the natural numbers (with 0 instead of 1). Though perhaps more obvious why you would choose one or the other there. Going through school I'd be told 1 was/not prime differently by different teachers. Always seemed pretty arbitrary to me; like 'They' ought just to decide! What we seem to be hearing here is that They had, just another classic case of this information taking 50 years to filter down the education system.. (I wonder how many planets they teach there as being in our solar system?)
    - nonbel 11y ago
      >(I wonder how many planets they teach there as being in our solar system?) Your comment got me to look up the number of objects considered planets over the years, this has ranged from 5-23. Data since 1543 is available here: https://dx.doi.org/10.1038%2Fscientificamerican0107-34 https://dx.doi.org/10.1038%2Fscientificamerican0107-34 For fun I did a linear regression of year vs # planets and found that the while the slope was 1.8 planets/century, this was not significantly different from zero. The evidence appears to be consistent with a constant number of planets.
  - Someone 11y ago
    "The history of the primality of one: a selection of sources" (https://cs.uwaterloo.ca/journals/JIS/VOL15/Caldwell2/cald6.html https://cs.uwaterloo.ca/journals/JIS/VOL15/Caldwell2/cald6.h..., via https://primes.utm.edu/ https://primes.utm.edu/): "The way mathematicians have viewed the number one (unity, the monad) has changed throughout the years. Most of the early Greeks did not view one as a number, but rather as the origin, or generator, of number. Around the time of Simon Stevin (1548-1620), one (and zero) were first widely viewed as numbers. This created a period of confusion about whether or not the number one was prime. In this dynamic survey, we collect a cornucopia of sources which deal directly with the "question what is the smallest prime?" The goal is to create a source book for studying the history of the definition of prime, especially as applied to the number one."
baddox 11y ago
Yeah, that ended my run at 22 correct answers. Pretty annoying. I knew it was non-prime by definition, but I had no idea whether this quiz was aware of that, so I just made a quick gut decision.

"1 is non-prime by definition." dammit!

by nosage 11y ago

"1 is non-prime by definition." dammit!

delecti 11y ago

I froze when I saw 1, and ended up going the same way you did. That one feels cheap. :P

mediumdeviation 11y ago

It's mainly due to the Fundamental Theorem of Arithmetic (aka unique prime factorization) - https://en.wikipedia.org/wiki/Fundamental_theorem_of_arithmetic https://en.wikipedia.org/wiki/Fundamental_theorem_of_arithme...

btilly 11y ago
However this was not settled surprisingly late. I have seen tables of prime counts produced in the 1950s and 1960s that specified whether they counted 1 as a prime, and some did count it.
- OJFord 11y ago
  Still the case for the natural numbers (with 0 instead of 1). Though perhaps more obvious why you would choose one or the other there. Going through school I'd be told 1 was/not prime differently by different teachers. Always seemed pretty arbitrary to me; like 'They' ought just to decide! What we seem to be hearing here is that They had, just another classic case of this information taking 50 years to filter down the education system.. (I wonder how many planets they teach there as being in our solar system?)
  - nonbel 11y ago
    >(I wonder how many planets they teach there as being in our solar system?) Your comment got me to look up the number of objects considered planets over the years, this has ranged from 5-23. Data since 1543 is available here: https://dx.doi.org/10.1038%2Fscientificamerican0107-34 https://dx.doi.org/10.1038%2Fscientificamerican0107-34 For fun I did a linear regression of year vs # planets and found that the while the slope was 1.8 planets/century, this was not significantly different from zero. The evidence appears to be consistent with a constant number of planets.
- Someone 11y ago
  "The history of the primality of one: a selection of sources" (https://cs.uwaterloo.ca/journals/JIS/VOL15/Caldwell2/cald6.html https://cs.uwaterloo.ca/journals/JIS/VOL15/Caldwell2/cald6.h..., via https://primes.utm.edu/ https://primes.utm.edu/): "The way mathematicians have viewed the number one (unity, the monad) has changed throughout the years. Most of the early Greeks did not view one as a number, but rather as the origin, or generator, of number. Around the time of Simon Stevin (1548-1620), one (and zero) were first widely viewed as numbers. This created a period of confusion about whether or not the number one was prime. In this dynamic survey, we collect a cornucopia of sources which deal directly with the "question what is the smallest prime?" The goal is to create a source book for studying the history of the definition of prime, especially as applied to the number one."

baddox 11y ago

Yeah, that ended my run at 22 correct answers. Pretty annoying. I knew it was non-prime by definition, but I had no idea whether this quiz was aware of that, so I just made a quick gut decision.