**4. Conclusion**

We notice theorem 1 that shows us the relationship between the numbers in the form *am* <sup>þ</sup> *<sup>b</sup>* and *ma<sup>m</sup>* <sup>þ</sup> *bm* <sup>þ</sup> 1. This is represented by a polynomial that combines these two numbers. One of the benefits of this relationship is that polynomial can be used as a primitive test, as well as clarifying the properties that those numbers have. But from an abstract arithmetic point of view, we find that theorem 3 is in fact more general than the theorem 1, and this is due to theorem 3 combining all the prime numbers. These results are in Cullen numbers and those in 5, 6 ½ � we note that these results are more generalized and differ from those in the form of a gem, and this appears and ideas used differ from those in 5, 6 7, ½ � … *::*12,13 . In general, we studied all numbers in from *p* ¼ *ba* þ 1 where *a*, *b*>1∈ , as well as Mersnne numbers and Cullen numbers, Fermat numbers. We showed about these numbers that have properties and a relationship between them. We proved this relationship in the form of a polynomial that combines two types of prime number or more. We note that only prime numbers in form *p* ¼ *ba* þ 1 *where a*, *b*>1∈ have been studied no more prime numbers in form *p* ¼ *ba* þ *m where a*, *b*, *m* >1∈ have not been studied.
