Please help me to do this 2 problems?

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1 Answer
May 16, 2017

See below.

Explanation:

5)
Let d(n) be the function which counts the number of digits of n then

5.1) n ge 10^(d(n)) ge g(n)
5.2) (n-6)^2=g(n)->n = sqrt(g(n))+6 then
g(n_k) = k^2, k = 1,2,3,cdots so the equation to obey is

n_k = k+6 so the only number observing this relationship is

n_1=7

6)
Let 4+p_1p_2 = m_1^2 and 4+p_1p_3=m_2^2
then

{(p_1p_2=(m_1-2)(m_1+2)),(p_1p_3=(m_2-2)(m_2+2)):}

but p_1,p_2,p_3 being prime numbers then

{(p_1=m_1-2),(p_2=m_1+2),(p_1=m_2+2 " otherwise " m_1=m_2),(p_3=m_2-2):}

so

m_1 = m_2+4 then

{(p_1=p_3+4),(p_2=p_1+4):}

and

p_2> p_1 > p_3

so the prime numbers are

p_1-4, p_1, p_1+4

or

p_3=3, p_1=7, p_2=11