AI 中文总结
研究找到对于任意非负整数$d$都是$d$-平移单位敏感的非负整数等差数列，构造出含$k$个连续素数的该数列，找到首个此类已知素数，还优化数列使其元素既是$d$-平移单位敏感的又是布赖尔数且含$k$个连续素数。
AI 中文摘要
一个非负整数$n$，当在其右侧附加$d$个零并将个位数字改变为任何可能的个位数字（只要得到的数不是$n$）时会产生一个合数，那么称$n$是$d$-平移单位敏感的。我们找到了对于任意非负整数$d$都是$d$-平移单位敏感的非负整数的等差数列。我们构造这个等差数列，使得对于任意正整数$k$，该数列中存在$k$个连续素数。由此找到了第一个对于任意非负整数$d$都是$d$-平移单位敏感的已知素数。我们还优化了这个等差数列，使得其中的整数对于任意非负整数$d$都是$d$-平移单位敏感的且是布赖尔数。优化后的等差数列对于任意正整数$k$的选择都包含$k$个连续素数。
英文摘要
A nonnegative integer $n$ is $d$-translated unit sensitive when appending $d$ zeros to the right of the number and changing the unit digit to any possible unit digit (so long as the resulting number is not $n$) results in a composite number. We find an arithmetic progression of nonnegative integers that are $d$-translated unit sensitive for any nonnegative integer $d$. We construct the arithmetic progression such that there exists $k$ consecutive primes in the progression for any positive integer $k$. The first known prime that is $d$-translated unit sensitive for any nonnegative integer $d$ is found as a consequence. We also refine the arithmetic progression such that the integers in the progression are $d$-translated unit sensitive for any nonnegative integer $d$ and are Brier numbers. The refined arithmetic progression contains $k$ consecutive primes for any choice of positive integer $k$.
Comments18 pages and 12 tables
