QQuestionMathematics
QuestionMathematics
What is the smallest prime number that can be made from the sum of three different prime numbers?
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Answer
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Step 1:I'll solve this systematically using the guidelines you specified:
Step 2:: Identify the smallest prime numbers
• The smallest prime numbers are 2, 3, 5, 7, 11, 13, etc. • We need to find three different primes that sum to a prime number
Step 3:: Start systematically checking combinations
• Sum: $$2 + 3 + 5 = 10$$ (not prime)
• Let's start with the smallest primes: 2, 3, 5
Step 4:: Try next combination
• Sum: $$2 + 3 + 7 = 12$$ (not prime)
• Next combination: 2, 3, 7
Step 5:: Continue searching
• Sum: $$2 + 5 + 7 = 14$$ (not prime)
• Next combination: 2, 5, 7
Step 6:: Next combination
• Sum: $$3 + 5 + 7 = 15$$ (not prime)
• Try: 3, 5, 7
Step 7:: Continue searching
• Sum: $$2 + 3 + 11 = 16$$ (not prime)
• Next: 2, 3, 11
Step 8:: Final successful combination
• Sum: $$3 + 5 + 11 = 19$$ (prime!)
• Combination: 3, 5, 11
Final Answer
19 is the smallest prime number that can be made from the sum of three different prime numbers.
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