Unescapable Sets |
Prime number 1597 contains the following prime numbers in its decimal representation: 17, 19, 59, 97, 157, 197
A set of prime numbers {P1,P2, ...} is said unescapable if any prime contains one of the Pi in its decimal representation.
Such a set is said minimal if we cannot remove any of its element.
Obviously, the set of all prime numbers is unescapable.
It is not minimal: if we remove 13, the remaining set is still unescapable: 13 contains 3
Quite unexpectedly (for me anyway), it has been proved that there exists a finite minimal unescapable set of prime numbers.
Can you find it?
You are given that its largest element is less than 70,000,000.
Answer format: Count,Sum
[My timing: 13 sec]
| All Submission |
Problem Maintainer : Philippe_57721
You need to be logged in to submit answer
Comments / Explanation
Show Comments
Thanks Robert.
In fact the wording was totally unintelligible for me.
Could someone answer my questions please?
I\'d like some clarifications.
1)\"
Prime number 1597 contains the following prime numbers in its decimal representation: 17, 19, 59, 97, 157, 197
\"
Why does 1597 not contain 5 or 7?
2)
\"It is not minimal: if we remove 13, the remaining set is still unescapable: 13 contains 3\"
Shouldn\'t this read:
It is not minimal: if we remove 3, the remaining set is still unescapable: 13 contains 3