In[1]:= n=10
        q=RandomPrime[{n^2,2n^2}]
        m=1.1*n*Log[q]
        α=1/(Sqrt[n]*Log[n]^2)
        σ=α * q
        Floor[q/2]
        q/4
Out[1]= 10
Out[2]= 131
Out[3]= 53.6272
Out[4]= 1/(Sqrt[10]*Log[10]^2)
Out[5]= 131/(Sqrt[10]*Log[10]^2)
Out[6]= 65
Out[7]= 131/4

In[323]:= (*Probability that sum is greater than q/4*)
          CDF[NormalDistribution[0,Sqrt[m]*α*q],-q/4]
Out[323]= 0.279785