An algebra problem by Mauren Mark Mediante

Algebra Level 3

Let AB and CD be the smallest possible two consecutive prime numbers with digits A, B, C and D, such that the value of A + B + C + D A+B+C+D is a prime number (A and C may be equal). Find the value of ( A + C ) 2 + ( B + D ) 2 + A + D (A+C)^2 + (B+D)^2 + A + D .


The answer is 188.

Mauren Mark Mediante by Mauren Mark Mediante , 26, Philippines

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1 solution

Barr Shiv
Sep 28, 2018

If AB and CD are prime numbers it means that,B and D are not even numbers so B+D= an even Number. if we want the sum of their digits to be a prime number it must be a non even number. therefore A+C=non even. which means A can not be equal C. so we look at the two smallest prime numbers which agree with these terms: 47,53. A=4,B=7,C=5,D=3

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