document.write( "Question 437: Let p1 and p2 be two odd primes. Show that there is a prime q such that q is not in {p1,p2} and q divides the sum p1 + p2. \n" ); document.write( "

Algebra.Com's Answer #169 by AnlytcPhil(1810) $\"\"$ $\"About$

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Let p1 and p2 be two odd primes. Show that there is a prime q such that q is
\n" ); document.write( "not in {p1,p2} and q divides the sum p1 + p2
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\n" ); document.write( "Example to illustrate, not a proof: 3 and 5 are two odd primes. We have to
\n" ); document.write( "show that there is a prime q, not between 3 and 5 such that q divides 3+5, or
\n" ); document.write( "8. Such a prime is q = 2.
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\n" ); document.write( "The sum of two odd primes must be even, and since the smallest odd prime is 3,
\n" ); document.write( "the sum of any two odd primes must be greater than 2. We also know that 2 will
\n" ); document.write( "divide any even number, and 2 is never between two odd primes. Thus the
\n" ); document.write( "theorem is proved with q = 2
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\n" ); document.write( "Edwin\r
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