This paper introduces prime holdout problems, a problem class related to the Collatz conjecture. After applying a linear function, instead of removing a finite set of prime factors, a holdout problem specifies a set of primes to be retained. A proof that all positive integers converge to 1 is given for both a finite and an infinite holdout problem. It is conjectured that finite holdout problems cannot diverge for any starting value, which has implications for divergent sequences in the Collatz conjecture.

翻译：本文引入了初级缓冲问题, 即与 colatz 猜想相关的问题类别。 在应用线性函数之后, 而不是去掉一组有限的质因, 缓冲问题指定了要保留的一系列质因。 证明所有正数整数一致到 1 是针对一个有限和无限的缓冲问题。 推论, 有限的缓冲问题不能因任何起始值而产生差异, 这对Collatz 猜想的不同序列有影响 。