A curious mathematical principle
by dogpatch from LinuxQuestions.org on (#56KAT)
Caveat: This is not a programming question per se, but am posting here for LQ minds attuned to logic and mathematics.
Recently wanted to generate a 6-digit prime number from the set of digits {0,1,2,3,4,5} or {1,2,3,4,5,6}. Goal: Generate a six digit prime number using each digit in the set exactly once, in any order. After a few failed attempts, I started puzzling and soon remembered a mathematical principle via which I knew, without having to write a program or trying all possible combinations, that my goal was impossible given either of the above two sets of six digits.
Rules: Assume normal base-10 integers. Use each of the six digits in the set in any order. Leading zero OK. Obviously, the final digit may not be an even number or a five, so only numbers ending in a 1 or 3 need be tried. This leaves 240 possible combinations of digits for each 6-digit set. None of which are prime.
Other sets such as {1,4,6,7,8,9} or {3,6,7,1,8,4} might yield one or more prime numbers (e.g. 417869 and 186437). But there are no prime numbers containing the six digits {0,1,2,3,4,5} or {1,2,3,4,5,6}
I can explain why. Can you?
Am confident someone in LQ land is already aware of the mathematical principle involved, which can also lead to a neat number trick to play on friends. Possibly more to follow.
Recently wanted to generate a 6-digit prime number from the set of digits {0,1,2,3,4,5} or {1,2,3,4,5,6}. Goal: Generate a six digit prime number using each digit in the set exactly once, in any order. After a few failed attempts, I started puzzling and soon remembered a mathematical principle via which I knew, without having to write a program or trying all possible combinations, that my goal was impossible given either of the above two sets of six digits.
Rules: Assume normal base-10 integers. Use each of the six digits in the set in any order. Leading zero OK. Obviously, the final digit may not be an even number or a five, so only numbers ending in a 1 or 3 need be tried. This leaves 240 possible combinations of digits for each 6-digit set. None of which are prime.
Other sets such as {1,4,6,7,8,9} or {3,6,7,1,8,4} might yield one or more prime numbers (e.g. 417869 and 186437). But there are no prime numbers containing the six digits {0,1,2,3,4,5} or {1,2,3,4,5,6}
I can explain why. Can you?
Am confident someone in LQ land is already aware of the mathematical principle involved, which can also lead to a neat number trick to play on friends. Possibly more to follow.