All numbers that end in 1 are prime numbers.? true or counterexample

False. As a counterexample, you can choose 21, which is 3*7

To generate other counterexamples, you can play with multiples of 3: we know that the sum of their digits is a multiple of 3.

So, for example, you may pick a number composed only by one 1, one 5 and as many zeroes as you like. So, numbers like 51, 501, 5001, 50001, 5000001, etc, will all be divisible by 3, because the sum of their digits is 6.

Similarly, you may compose numbers with three ones and as many zeroes as you like: numbers like 111, 1011, 11000001, 1000000001000001, etc, will all be divisible by 3, because the sum of their digits is 3.