Problem 51
Prime digit replacements
By replacing the $1$st digit of the $2$-digit number $\text{*}3$, it turns out that six of the nine possible values: $13$, $23$, $43$, $53$, $73$, and $83$, are all prime.
By replacing the $3$rd and $4$th digits of $56\text{**}3$ with the same digit, this $5$-digit number is the first example having seven primes among the ten generated numbers, yielding the family: $56003$, $56113$, $56333$, $56443$, $56663$, $56773$, and $56993$. Consequently $56003$, being the first member of this family, is the smallest prime with this property.
Find the smallest prime which, by replacing part of the number (not necessarily adjacent digits) with the same digit, is part of an eight prime value family.
素数数字替换
将两位数$\text{*}3$的第一位数字替换为任意数字，在九个可能值中有六个是素数：$13$、$23$、$43$、$53$、$73$和$83$。
将五位数$56\text{**}3$的第三和第四位数字替换为相同的任意数字，在十个可能值中有七个是素数，这也是同类例子中最小的一个。这些素数分别是：$56003$、$56113$、$56333$、$56443$、$56663$、$56773$和$56993$。$56003$作为其中最小的数，也就是最小的满足这个性质的素数。
通过将部分数字（不一定相邻）替换为相同的任意数字，有时能够得到八个素数，求满足这一性质的最小素数。