How many of the prime numbers from 2 to 100 may be written in the form p = kx6 - 1 (multiple of 6 minus 1) ?
Multiples of 6 are even numbers that can not be prime. There are 5 numbers between any two multiples of 6. The ones in the middle are
multiples of 3 and can not be prime. The adjacents of the one in the middle are even numbers and can not be prime. This means if a number is prime, it should be either
in the form 2xk-1 or 2xk+1 .
n consecutive numbers do always have a greatest difference of n-1 .
4xA = 112 and A=? .
6xSubtrahend - 48 - Subtrahend = Difference .
The same shapes correspond to the same numbers, but they can also be any one of the numbers seen .
Let the number be in the form AB. Then we have AB - BA = ?6 where A and B are digits .
10xA + B - 10xB - A = 10x(A-B) + (B-A) = 10x(A-B) - (A-B) = 9x(A-B) = ?6 .
So the difference must be a multiple of 9 and it can only be 36 . 40 has reversed form 04 which is not used and therefore disclosed.
51, 62, ... ,95 ...
100000-1000 = 99000 ; 100000-100 = 99900 .
The number is 2009 .
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