All mersenne primes greater than 3 will end with either 1 or 7?
 

All mersenne primes greater than 3 will end with either 1 or 7.
Q1. Is the above statement true?
Q2. Why is it so?

Q1. Trivially, yes.
Q2. Because for any odd n, 2^n = 2 or 8 (mod 10):
2^1 = 2 (mod 10)
2^3 = 4*(previous value) = 8 (mod 10)
2^5 = 4*(previous value) = 2 (mod 10)
2^7 = 4*(previous value) = 8 (mod 10)
2^9 = 4*(previous value) = 2 (mod 10), etc, 2 and 8 will alternate.
Now, with the exception of 3 (which is 2[SUP]2[/SUP]-1), all other Mersenne primes are 2[SUP]odd n[/SUP] -1.

[QUOTE=soumya;335125]All mersenne primes greater than 3 will end with either 1 or 7.
Q1. Is the above statement true?
Q2. Why is it so?[/QUOTE]
@soumya: Are you being aware that in addition to this thing,
[COLOR=White]and then stuff matters,[/COLOR]
every prime factor for the Mersenne number with an odd exponent[COLOR=White] into this,[/COLOR]
i.e. a number of the form 2[SUP]2x-1[/SUP]-1, x ≥ 2, 2x - 1 ≥ 3[COLOR=White], it [/COLOR]is being of the form congruent to 1 or 7 (mod 8)?

In addition to it, each prime factor for the part [COLOR=White]afterwards [/COLOR]
after algebraic factors being removed for the Mersenne number 2[SUP]x[/SUP]-1, are always being of the form 2kx+1, i.e. it is being congruent to 1 (mod 2x).

[COLOR=White]and then certainly that always that[/COLOR]
[COLOR=Black]and then[/COLOR] therefore, so, thus, that way,
it is being true enough statement for the Cunningham numbers b[SUP]x[/SUP]±1, as well[COLOR=White] as,[/COLOR]

[COLOR=White]as follows as

Why so, thus?

[/COLOR][COLOR=Black][COLOR=White]and then

also too[/COLOR]
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