If `M & alpha` are twin prime `&alpha+M=7` then the greatest integral value of `N` is

Options

A. `25`
B. `32`
C. `52`
D. `61`

Answer

A, B, D

Explanation

`alpha_(1), m in {3, 4}, {2, 5}, {1, 6}`
`alpha = 3, m = 4 , log_(4)N = 3 + b , N in [4^(3), 4^(4)) = [64, 256)`
`alpha = 4, m= 3 , N in [81, 243)`
`alpha = 2, m = 5 , N in [25, 125)`
`alpha = 5, m = 3 , N in [32, 64)`
`alpha = 1, m = 6 , N in [6, 36)`
`alpha = 6, m = 1 , m ne 1 :. N_(max) = 6`