12 can be made into a prime by changing the 2 to 3; likewise, 63 can be changed into a prime by changing the 6 to 7.
What is the smallest number that cannot changed into a prime by changing a single digit?
Are there infinitely many such numbers?
There are infinite numbers such as 200. For example, 19!+10 es one of
them -- it ends in 0, and if you change that zero to other number, you
get 19!+11, 19!+12, ... , up to 19!+19 -- all composite. For all
N>19, N!+10 also satisfies the "never prime" condition.
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Posted by e.g.
on 2004-04-29 14:58:54 |
A simple solution for the 2nd part
