任意整数能否修改O(1)位变成质数

数论爱好者

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