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?
(In reply to
Explanation to answer for part (a) by K Sengupta)
A(m) = 200+2310*m, for any positive integer m, provides an infinite family of solutions in consonance with the given conditions,.
The veracity of the foregoing are borne out by changing the last digit of 200 inclusive of A(m):
-> To 1, provides an infinite sequence of composite numbers given by 201+2310*m, each of whose members is divisible by 3.
-> To 3, provides an infinite sequence of composite numbers given by 203+2310*m, each of whose members is divisible ny7.
-> To 7, provides an infinite sequence of composite numbers given by
207+2310*m, each of whose members is divisible by3 3.
-> To 7, provides an infinite sequence given by: 209+2310*m, each of whose members is divisible by 11.
solution for part (b)
