Journal of Advances in Mathematics and Computer Science

An innovative approach that treats prime numbers as raw experimental data and as elements of larger and larger finite sequences {P_m}≡{P(m_p)} is shown in the present report. The modified chi-square function X_k²(A,m_p/x_o) with its three parameters A, k and x_o=x_o(k) is the best-fit function of the finite sequences {ρ_m}≡{l_gP_m/l_gm_p} from the analytical viewpoint thus showing that the property of scale invariance does not hold for the finite sequences of this prime variable and so for primes themselves. In addition an injective map can be set between these {ρ_m} sequences and the {m^α} progressions with domain N and co-domain R⁺ being α∈(–1,0)⊂R^– through the parameter k=2+2α of their common fit function X_k²(A,m_p/x_o). All that leads to induction algorithms and to relationships of the kind P_m≈P(m_p), though within the precisions of the calculations and holding locally.