Another Look at Prime Numbers

Blog Articles
21

Hi, that was a another good post!..

heres some more stuff for your first example-‘guessing evenness’ .

you could also analyze even and odd powers in this manner …

odd^odd -> odd (There are no 2s at all)

even^even -> even (Lots of 2s!)

even^odd -> even (We are just multiplying even numbers with even numbers. Its just the number of times they are multiplired that is odd )

odd^even -> odd ( no 2’s at all again )

Primes can also help in finding the total no. of factors in a number and their sum …
e.g. 12 = 2^2*3

to get all factors… write this as
(2^0 + 2^1 + 2^2)(3^0 + 3^1)
= 1 + 2 + 4 + 3 + 6 + 12
sum = 28
no. of factors = 6.

notice that the number of factors is just the number of terms in the expansion…

so if you see a number as a^m * b^n with ‘a’ and ‘b’ being prime, then the number of prime factors is simply (1+m)*(1+n)

:slight_smile:

22

Nice as always, Kalid -

I have a tiny nitpick, only because I’m a chem major – the noble gases aren’t in group “18” they are in Group 8A. Carbon / Silicon are in Group 4A.

The reason this is important is due to valence shells (an elements group #, from the “A-Series” indicates the number of electrons in its outermost, or valence, shell). The B-Series (aka “transition metals”) are more or less completely irrelevant in an organic context. :slight_smile:

I did like your analogy to functional groups though – that’s a neat way to think about it. FG’s are generally expressed, formulaically as “R-OH” [alcohol] or “R-COOH” [carboxylic acid] implying that the R-group is unimportant / non-reactive.
In your example, the R-group would be whatever is added to the functional portion. So the 2 * 5 F.G. could be expressed, in an O-Chem context, as R(2*5).

Anyways… enough of my anal-retentiveness – very cool, as always.

23

@Aaron: Thanks for the comment (I just fixed up the groups)! Actually, I had wondered about that myself – I faintly remember chemistry from school, and never had a proper organic chemistry class, so it’s nice to have these ideas run by someone in the field. I enjoy finding these analogies as they pop up. Thanks again for the notes.

24

Your last link is dead.

25

Thanks Ryan, I just fixed it.

26

Hi, if anyone looks for a good algorithm to display any number by multiply prime numbers (recursive):

code start

void numWays(int num)
{

if ((num%2!=0) && (num%3!=0)){ // This is the simplest event and that means that the number is prime!
	if (num!=1)	cout
27

As a high school student desperately attempting to approach math as an acadamic subject as opposed to a scary monster, I’d like to thank you for this article. It’s really made prime numbers seem much more friendly than before. =)

28

@Shir: You need to be careful – try it with 25 :slight_smile:

@Mike: Glad you enjoyed it!

29

hi I m looking for parallel algoriths.
and a problem solve by using parallel algorith.

30

[…] Numbers: number systems, visual arithmetic, different bases, Prime numbers […]

31

Also, small addition here.

Any number with a 3 can have its digits tallied and they will also be divisible by 3. For example, 141 (473) = 1+4+1 = 6, also 196605 (655353) = 1+9+6+6+0+5 = 10+12+5 = 27 = 2+7 = 9. Etc.

Thank you for setting this site up. I have never studied Calculus, always considered it the Devil’s answer to real thought. Now I am heading back to school to get my degree in programming, and have found this site fantastic.

Many many thanks.

32

@Steve: Awesome, glad it is coming in handy! Yes, I like that trick about the digits adding up.

33

Thank you so much for making this site. It really made primes a lot easier. I’m doing a report on them (due this monday i’m afraid). It made them seem like they had a purpose and explained a lot.

34

@Lisa: You’re welcome, I’m glad it was helpful for you. Good luck with your report!

35

hey mate,
(Guessing evenness)
you say that to quote "Odd times odd is odd. We never put in a 2 the whole time, so we stay odd."
but what about 3x3= 6 EVEN

36

@Al: Make sure you double check that 3x3 :).

37

Hi yeah all it is Me Nobody and I painted the table for you all and let Me tell you you are just going to pee your self when you see it. Mind boggling I must say. So many of you are so close if it was a snake he has his fang up against your skin and is ready to bite. That guy with the 12 block Idea now he has been bitten already and the Hope mathematics people with there 180 system ,look out for them for they are getting bitten hard.

38

[…] because the integers themselves cycle even, odd, even odd… after all, a square keeps the “evenness” of the root number (even * even = even, odd * odd = […]

39

I really appreciate your article. I was searching for a way to make primes relevant to my 4th & 5th graders, not just naming them, so I am exceptionally interested in the aspect of relating it to nature and the cycles of nature. I will focus my studies in that direction for know and would love to have any more info you have on prime cycles in nature – saving me slogging through the animal kingdom, plant kingdom, etc…

40

The sequence of the prime numbers has not been explained yet. True, but let’s claasify them logically. The number two [2] is in one class by itself and the numbers [3, 5, 7, 11, … ] are in another categorically distinct class having an infinite number of members. I want to share an insight that recently occurred to me. The distribution rules of elementary algebra universally apply to multiplication over addition and subtraction. That gives us two rules. The other rule: the distribution of addition and subtraction over multiplication is generally untrue. The word " Generally " differentiates this situation from universally or categorically untrue. The assertion is that the latter rule is true - sometimes. Allowing addition and subtraction to be distributive over multiplication brings into existence relationships between the algebraic variables. This may prove to lead to very interesting consequences where the four rules of distribution are true altogether. Especially where the algbraic variables are uneven integers.