Fifty first-order non-consecutive prime generating polynomials with sequence distances superior to five v1.2

This paper discusses the mathematical Number Theory field of first order Prime-Generating Polynomials (P-GP) also referenced as Arithmetic progressions (AP). In regards to the Green-Tao theorem, it emphasizes “the primes contain arbitrarily long polynomial progressions” by exploring specifically the primorial p29# co-linear space.本文探讨了一阶素数生成多项式（Prime-Generating Polynomials，下称P-GP）所属的数论领域，该类多项式所构成的序列亦被称为算术级数（Arithmetic progressions，下称AP）。针对格林-陶定理（Green-Tao theorem），本文通过专门探究素数阶乘p29#对应的共线空间，着重论证了"素数集合中包含任意长的多项式级数"这一核心结论。