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## Find the Sum

Math brain teasers require computations to solve.

 Puzzle ID: #39976 Fun: (2.1) Difficulty: (2.61) Category: Math Submitted By: shenqiang

Find the sum of all prime numbers between 1 and 100 that are simultaneously 1 greater than a multiple of 4 and 1 less than a multiple of 5.

Numbers that are 1 greater than a multiple of 4 are 5, 9, 13, 17, 21... where 9 is 1 less than a multiple of 5. lcm(4, 5)=20, therefore the pattern repeats in each 20 numbers.

9 (composite) 29 (prime) 49 (composite) 69 (composite) 89 (prime)

Therefore, the sum of all such numbers is 29+89=118.

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 javaguru Jan 13, 2009 I did it a little different. The numbers on either side must be even. The number below is 2 x an even number, so the number above is 2 x 5 x an odd number. That gives the odd multiples of 10 as the number above the prime, leaving just the 5 numbers to check.

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