Primeless Line
Number Theory
Level
3
What is the smallest value for such that there's no prime number above as a result?
The answer is 20.
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1 solution
I would phrase this question as "For what value of x are none of the numbers between 10x and 10(x+1) prime?"
My initial response to the question as phrased was "Well, that depends on what the value of a is." But you want none of {10x+1, 10x+3, 10x+7, 10x+9} to be prime.
Anyway, the answer is x = 2 0
2 0 1 = 3 ∗ 6 7
2 0 3 = 7 ∗ 2 9
2 0 7 = 3 ∗ 6 9
2 0 9 = 1 1 ∗ 1 9
Solution found using a Python program.
functions:
is.prime.number(x) - x integer, returns true if x is prime, called by...
any.prime.number(l) l - list of integers - returns true if at least one prime in list
generate.list(x) - returns list [10x+1,10x+3,10x+7,10x+9]
Then just iterate over x until any.prime.number returns false for a generated list