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What is a two digit prime number whose digits add up to 5?

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it is 23 because 2+3 = 5
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A three digit number whose digits add up to 9?

900, 810, 801, 720, 711, 702, 630, 621, 612, 603, 540, 531, 522, 513, 504, 450, 441, 432, 423, 414, 405, 360, 351, 342, 333, 324, 315, 306, 270, 261, 252, 243, 234, 225, 216,

Why do no digits of a prime number add up to 9?

Because they're in multiples of three - a quick way to tell if a number is a multiple of three is to add up the digits and see if the digits add up to a multiple of three e.g