The norm of a partition is defined as the product of its parts. This paper aims to conduct a thorough study of norms of prime partitions which are partitions with all prime parts. The analysis begins by defining $r_p(i,n)$, called the primal norm counting function, which refers to number of times i appears as a norm to the prime partitions of n. The generating function for this function is deduced, using which a wealth of intriguing relations are proved like series, product, integral representations, and recursive relations, etc. The special cases of these results bear resemblance to other results known in classical partition theory. An analogue of the Goldbach conjecture in the theory of norms is presented, and it is stressed that an explicit formula for $r_p(i,n)$ must be extracted. Two approaches are discussed for this purpose, and the paper is concluded with a potential scope for future work.

分区的范数定义为其部分的乘积。本文旨在深入研究素数分区的范数，素数分区是所有素数部分的分区。分析从定义开始$r_{磷}(\mathrm{一世},n)$，称为原始范数计数函数，它指的是i作为n的素数分区的范数出现的次数。推导出该函数的生成函数，使用它证明了大量有趣的关系，如级数、乘积、积分表示和递归关系等。这些结果的特殊情况与经典划分理论中已知的其他结果相似。提出了范数理论中哥德巴赫猜想的类似物，并强调了一个明确的公式$r_{磷}(\mathrm{一世},n)$必须提取。为此目的讨论了两种方法，本文的结论是对未来工作的潜在范围。