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Minimal sum of a set of primes

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January 11, 2006
number theoryprime numbers

Problem Statement

Several sets of prime numbers, such as {7,83,421,659} \{ 7, 83, 421, 659\} use each of the nine nonzero digits exactly once. What is the smallest possible sum such a set of primes could have? <spanclass=latexbold>(A)</span> 193<spanclass=latexbold>(B)</span> 207<spanclass=latexbold>(C)</span> 225<spanclass=latexbold>(D)</span> 252<spanclass=latexbold>(E)</span> 447 <span class='latex-bold'>(A)</span>\ 193\qquad<span class='latex-bold'>(B)</span>\ 207\qquad<span class='latex-bold'>(C)</span>\ 225\qquad<span class='latex-bold'>(D)</span>\ 252\qquad<span class='latex-bold'>(E)</span>\ 447