Re: What do these primes have in common?

From: Ignacio Larrosa Cañestro (ilarrosaQUITARMAYUSCULAS_at_mundo-r.com)
Date: 12/29/04 

Date: Wed, 29 Dec 2004 12:22:43 +0100

En el mensaje:1104304597.703630.126650@z14g2000cwz.googlegroups.com,
30pack@sbcglobal.net <30pack@sbcglobal.net> escribió:
> Of little value, but ending with an interesting question !
>
> 23
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> --->oo
>
> Answer--
>
> Two consecutive primes grouped to form another larger prime.
> A large portion of the groupings that are not prime
> are congruant to 0(mod 3). Interesting.
> Will any consecutive twin ever form another larger prime?

Twin primes are of the form 6k +/- 1. I.e., one of then is a multiple of 3
minus 1, an the other is the same multiple of 3 plus 1. It is well known the
divisibility by 3 criterion: N is multiple of 3 iif the sum of the digits of
N is a multiple of 3. Then, if you concatene twin primes, you get a multiple
of three.

Roughly, the half of pairs of consecutive primes must be distincts modulo 3.
Then, its concatenation is multiple of three. 

-- 
Best regards,
Ignacio Larrosa Cañestro
A Coruña (España)
ilarrosaQUITARMAYUSCULAS@mundo-r.com

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