Try this beautiful Problem based on Number theory from AMC 10A, 2002 Problem 15.
Using the digits $1,2,3,4,5,6,7$, and 9 , form 4 two-digit prime numbers, using each digit only once. What is the sum of the 4 prime numbers?
Arithmetic
Divisibility
Prime Number
Elementary Number Theory by David M. Burton.
AMC 10A 2002 Problem 15
190
First try to find the probable digits for the unit place of the prime number.
The two digit prime number should end with $1, 3, 7, 9$ since it is prime and should not divisible by $2$ or $5$.
So now try to find which two digit primes will work here.
So, the primes should be $23, 41, 59, 67$.
Now find the sum of them.
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