Monday, August 17, 2009

Is 151 a prime number? Hmm... Let's check

Let X and n be natural numbers. If X has no factors less than n, and X is less than n squared, then X is a prime number.

69 comments:

  1. your point? is that oh so clear chicago air getting to you?

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  2. Duh. It’s like saying “If I have no brothers and my mom had no daughters, I am the only child”.

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  3. not if your father has daughters.

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  4. The only child of my mother. Whatever. My point was: what e wrote is bloody obvious.

    If b has no factors <a, then, if a>b, b has no factors, which makes it a prime number. If a<b, then the only possible factor of b is a itself or a number c (if such exists) between a and b, but since a²>b (and, therefore, c²>b), it’s not the case, so, again, b has no factors and is, by definition, a prime number.

    (a, b and c are natural numbers, obviously.)

    This has nothing to do with being able to tell if a number is a prime number just by looking at it which is one of the paths to proving Fermat’s theorem.

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  5. oh wow, and i understand it SO much better when u explain it!!

    i don't think e had a point.

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  6. Well, read what i said and think about it. It’s not even algebra, it’s just one-dimensional arithmetic. Just draw a number line, put numbers a, b and k there and see what I mean.

    Unless you are trying to prove Aristotle right.

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  7. what did aristotle say? that im stupid? (or was that directed at e)

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  8. Aristotle hypothesized that the function of brain is to cool blood. In some people this is indeed the main function of their brains.

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  9. ok i get it. so he has no point then.

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  10. u mean they dont use their brains to think.

    i can think if i want to. i just dont bother to sometimes. that doesnt make me stupid. just lazy.

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  11. As far as the result is concerned it’s the same thing. Plus, use it or lose it.

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  12. why thank you kind sir. i shall keep that in mind at all times, as it is a good thing to remember for life.

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  13. It’s like that joke with an Old Jew who just came off the boat and a vending machine.

    “Reb Yid, why do you need so many cans of Coke?”
    “What do you care that I keep winning?”

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  14. unfortunatly, your advice is no victory for me, since i can certainly do without it. thanks anyway.

    now who's blogstalking whom?

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  15. Not only naive (that I would tell you who is stalking me) but with illusions of grandeur (that I meant you).

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  16. ok a) i am not niave, and yes i mistakenly assumed you meant me. but no, i really dont give a (fill in the blank) who is stalking you.

    good luck with that. i hate stalkers.

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  17. Too bad. I like mine a lot.

    Yeah, and that was very lady-like. Sure.

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  18. excuse me, i did not curse. and shame on you if u actually filled in the blank.

    correct me if i'm wrong, but generally people don't like stalkers. so if u are strange enough that u actually LIKE your stalker- then isn't that not considered a stalker?

    of course i may be totally wrong, and u are completely sane. (probably not though.)

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  19. Sane? Me? That’s the silliest thing you’ve suggested the whole night.

    There are all kinds of stalkers.

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  20. that was said in a sarcastic tone of voice. i dont actually think u are sane.

    ok then. i hope u and your stalker are happy together.

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  21. ok i have to say, u are weird. u dont actually have a stalker...

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  22. and are we gonna have another blogger 'mazal tov' soon?

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  23. If “somebody” actually listens to the stalked and starts a blog already. But even then it would not be the same.

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  24. ok dont speak to imaginary ppl on blogs. or muse aloud. it hurts the rest of our concentrations.

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  25. Aurgh! I didn't subscribe to comments on the post and missed this fascinating conversation.

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  26. u didnt subscribe to your own post? thats dumb. i get responses automatically.

    thats ok. your input wasnt necessary as u can see.

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  27. CA: I didn't think it was a huge chiddush. I often do prime factorization in my head just for fun or as a mnemonic to help me remember a number. This idea bounced around in my head many times, and today I finally sat down and thought about it, until I had it all worked out.

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  28. If you get the updates automatically, comments from different people are grouped into different conversations.

    I usually subscribe as soon as I post, but I made this post by sending a text message from my phone (hence no fancy symbols) so I couldn't subscribe.

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  29. aha. and if u have a fancy phone like u do, then it makes sense the way you do it.

    i am a slave to my computer, to i do it the smartest way.

    oh well. your loss.

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  30. new title? wow the cooliest. it makes the post so much more sophisticated.

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  31. Altie, the person you said should speak her mind says “hi”. She also says you should start loving the term “ba’alei teshuva” (in plural) — at least as long as you’re being snappy about grammar.

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  32. 151 is not divisible by 2, 3, 5, 7, or 11. Now, is it divisble by 13? we could use long division by find out. But that would be a pain. Instead we note that 151 has no factors less than 13 and is less than 13 squared.

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  33. CA: Are you about to get engaged to your stalker? Oh, that would be so nice.

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  34. I will keep you updated on all aspects of my personal life, as usual.

    Prime numbers: interesting.

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  35. Now what about 846,753,746,876? Is that a prime number?

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  36. Intersting? Do I detect some mockey in your voice? Earlier you said that my oh-so-useful theorum is obvious to all those whose brain doesn't merely cool their blood.

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  37. Of course 846,753,746,876 is not prime. It's divisible by four, yielding 211,688,436,719.

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  38. No, I thought for a second it was genuinely interesting, but then realized that it doesn’t give you much for large numbers which you know not to be divisible by the small numbers. I.e., you’re lucky it was divisible by 4. I could have chosen something that’s divisible only by 151.

    It’s not an algebraic algorithm, that’s my problem.

    But I do find it interesting.

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  39. it's good for numbers less than 361 (19^2).

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  40. If X has no factors less than n-1 is slightly better.

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  41. CA- tell her hi back. :) I shall try to correct my speech next time. and if u do get engaged i shall be so happy for u. keep me informed too.

    once again, the math has flown right over my head. have fun, math geeks.

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  42. anon: What's this n-1 rule?

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  43. Let X and n be natural numbers. If X has no prime factors less than or equal to n-1, and X is less than n squared, then X is a prime number.

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  44. It’s like that joke:

    A mathematician is telling a story: “N birds flew up. No, wait: m birds flew up.”

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  45. is that joke supposed to be funny?

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  46. It’s not supposed to be. But it is.

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  47. Well, I, for example, find it funny. So, not necessarily.

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  48. And if I call you a shiksa (in response to you calling me a goy), I suppose you will act all offended?

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  49. i didnt say goy. there are many russian jews.

    cal me a shikse. all my friends do. and you would probably be right.

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  50. but what's funny about it? I see the funniness of a mathematician describing a bunch of birds as "n birds." But what's so funny about him changing it to "m birds"?

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  51. An attempt to explain a joke is an exercise of futility.

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  52. I guess I'll just need to remain in the dark.

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  53. i didnt say goy. there are many russian jews.

    Would you say that the Rebbe is a Russian?

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  54. yes, most Americans wouldn't see anything wrong with calling the Rebbe Russian.

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  55. CA- whats your point? I still didnt call u a 'goy'

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  56. e: the joke was certainly col worthy.

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  57. That’s because the word “American” means “American citizen”. Everywhere in the world, a member of a certain nationality is also a member of a certain ethnicity. In Russian language, there are even two different words: rossiyanin (Russian national) and russkiy (ethnic Russian).

    Neither of which the Rebbe was. I don’t really see in which way he was a Russian.

    But it goes deeper than that. We are Jews. Our ethnicity is Jewish (except geirim, whose grandchildren are already ethnically majorly Jewish).

    Our nationality and citizenship are Jewish: we are citizen of the Jewish state. Not the G-d know what kind of state of Israel of today, but of the theocracy ruled by a king and Sanhedrin. Sure, there is no such thing right now, but that’s because we are in exile — like there were Poles in exile during the WWII. So, we are dual citizens just like them. (Plus, in our everyday life we follow the laws enacted by that government, so even legally we are its subjects.)

    And of course, religiously. There is no such thing as a Mathematician Jew or a plumber Jew. No such thing as a Russian Jew or a French Jew. No such thing as a brunette or blond Jew. Of course, a Jew can have this or that profession or could be born in this or that country, but those characteristics are nullified by the essential characteristic of him: that he is a Jew.

    To the point that just like it doesn’t make sense to say that Hashem is wise — He possesses wisdom — it also does not make sense to say that a Jew is a certain professional or a certain national.

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  58. Okay, THAT was your point? That you are not Russian? Fine by me.

    I like this line:

    'we are citizen of the Jewish state. Not the G-d know what kind of state of Israel of today, but of the theocracy ruled by a king and Sanhedrin. Sure, there is no such thing right now, but that’s because we are in exile'

    Everyone asks me why i wont make Aliya, and thats the perfect answer.

    I get what you are saying. We are Jews 1st, and 2nd whatever we want to be.

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  59. Plus, culturally, he is a Jew to such a degree that whatever cultural influences living in a certain land may have had on him should be drowned out by the culture imposed on him by Jewish tradition. For instance, in European culture it is less proper for someone to wear shorts in a workplace. In American culture, there is no problem with that (except highly professional environments: corporate, law and medicine). But for a Jew these things don’t matter. He looks into what it says in mesoira, what the halacha and what the minhogim are concerning the specific question of wearing shorts.

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  60. 'whatever cultural influences living in a certain land may have had on him should be drowned out by the culture imposed on him by Jewish tradition.'

    Emphasis on the SHOULD BE. Lots of Jews these days would rather fit in with the Secular society.

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Forth shall ye all hold.