other Maths Puzzle Numerical Ability

Find the only such prime number lesser than 4000 which cam be represented as the sum of two prime numbers and the difference of two prime numbers.

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other Other Question

Which of the following is a counterexample for this conditional statement?

""""If the sum of two numbers is even, then those numbers are both odd.""""

Answers:

2&3

3&3

1&6

2&6

3&9

which of the above option is correct??

( you just have to write the correct option number)

Remember>.....

~~~~{{A counterexample is an example in which the hypothesis is true, but the conclusion is false. If you can find a counterexample to a conditional statement, then that conditional statement is false.}}~~~
The positive integers N and N+1 both have digit sums that are divisible by 7. What is the smallest possible value of N?