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#1 2005-09-21 09:23:07

dean
Guest

Problem with prime numbers

I need to prove that if p is a prime number ending on 1 (like 11, 101), p+4 is a multiple of 15. It is obvious that it's a multiple of 5, so i just have to prove that it's also a multiple of 3. But how? I have really tried, but I just can't work it out.

dean

#2 2005-09-21 23:59:30

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,535

Re: Problem with prime numbers

Haven't worked it out for you yet, but you could try looking for a proof that p+1 is divisible by 3 (because if p+4 is, then p+1 is and vice versa)

Another thing: Prime Numbers are either 6n-1 or 6n+1 (n being an integer), because 6n is divisible by 6, 6n+3 is divisible by 3 and  6n+2 and 6n+4 are divisible by 2, leaving only 6n+1 or 6n+5 (which is a type of 6n-1)

So there is a fair chance that a prime plus one will be divisible by 6 (and hence 3) but not proven.

Umm ... let me see ... if the prime must end in 1 then the case p-1 is divisible by 10, right? That gets us close ...


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#3 2005-09-27 02:22:39

santhoshkumar
Guest

Re: Problem with prime numbers

respected sir im a guy form india. have question about the prime
number
,here is my question
when does the prime number comes after what type
of number does the prime
number come.if found in a web site that
primenumber expect 2,3 comes before
or after a number divisible by 6.
but some time it is right a many times its
wrong. and i have another
question when does the even number and odd number
come after what type
of number can we get the odd and even what are therules to find out the
next number.kindly do this as my kind request .i hope
u will help me.
this would me very usefull if u do this .
                           
your's faith full'
                              r.santhoshkumar

#4 2005-12-04 08:39:26

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,535

Re: Problem with prime numbers

Such a nice request, but noone answered it? It slipped under my radar.

Ummm ...


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#5 2005-12-04 08:42:11

Roraborealis
Member
Registered: 2005-03-17
Posts: 1,594

Re: Problem with prime numbers


School is practice for the future. Practice makes perfect. But - nobody's perfect, so why practice?

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