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MATH / The set of integers {2,4,10,x} has the property that the sum of any three members of the set plus 1 yields a prime number. What is the smallest possible value of x greater than 10?

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problem

The set of integers {2,4,10,x}\{2,4,10,x\} has the property that the sum of any three members of the set plus 1 yields a prime number. What is the smallest possible value of xx greater than 10?
Plain-text mathematical notation (without MathML)
The set of integers {2,4,10,x} has the property that the sum of any three members of the set plus 1 yields a prime number. What is the smallest possible value of x greater than 10?
Original LaTeX notation
The set of integers $\{2,4,10,x\}$ has the property that the sum of any three members of the set plus 1 yields a prime number. What is the smallest possible value of $x$ greater than 10?

level

Level 3

type

Number Theory

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Source and history

task_id
7ab46402-cbf6-534b-869d-da0392a8007f
task_key
number~5ftheory--test--7ab46402-cbf6-534b-869d-da0392a8007f
task_revision_id
1
config / split
number_theory / test

Official source

initial import