### Brain Teasers

# Find the Sum

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.

### Answer

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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