I was randomly thinking through some of the scenarios for the formulae (X ^ Y) - (Y ^ X) where one is odd and other is even. For eg. ( 4 ^ 7) - (7 ^ 4)
Surprisingly, most of the resultant answer is either prime or a number whose factors are predominantly prime numbers and odd as well
3 ^ 4 - 4 ^ 3= 17
2 ^ 7 - 7 ^ 2 = 79
2 ^ 9 - 9 ^ 2= 431
4 ^ 5 - 5 ^ 4 = 399 (19 x 7 x 3)
Is there any pattern others see? And any justification using a mathematical equation (I did try logarithms but don't think it helps)
Surprisingly, most of the resultant answer is either prime or a number whose factors are predominantly prime numbers and odd as well
3 ^ 4 - 4 ^ 3= 17
2 ^ 7 - 7 ^ 2 = 79
2 ^ 9 - 9 ^ 2= 431
4 ^ 5 - 5 ^ 4 = 399 (19 x 7 x 3)
Is there any pattern others see? And any justification using a mathematical equation (I did try logarithms but don't think it helps)
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