calculus – prove or disprove this problem

Problemlet $mathrm P$the set of prime numbers ; $forall(p,p+2)inmathrm P^2: ptimes(p+2)=A_1 ,quad Ainmathrm N$where$A_1$is written on the figure : $A_1=a_1^1a_2^1a_3^1….a_{n_0}^1$ where $(a_i^1)_{1leq ileq n_0}subsetmathrm N $So we put : $$g(n_0)=displaystylesum_{i=1}^{i=n_0}a_i^1=a_1^1..a_{n_0}^1=A_2quad…