数论爱好者
发表于 2022-10-29 19:46:17
l4m2 发表于 2022-10-29 02:09
我的理解是他证明了存在前面补0的素数,任改一位都变合数,但是没有具体给出例子吗?
You can add any 1 extra digit on the left to 294001 without getting a prime but adding two digits would allow for the creation of a prime. For example 10294001 is prime but none of X294001 are.
Starting at 604171 you could add 3 extra digits to the left but not 4 without being able to produce a prime number.
X604171 is not prime
X0604171 is not prime
X00604171 is not prime
however 4000604171 is a prime number
For the largest one found so far
X142243533671
X0142243533671
X00142243533671
...
X0000000000000000000000000000000000000000000000142243533671 are all composite
but 900000000000000000000000000000000000000000000000142243533671 is prime