Question

Докажите что сумма четырех последовательных чисел не может быть простым числом

Answer 1

Возьмем самые маленькие натуральные числа 1,2,3 и 4
1+2+3+4=10 - не является простым числом.
Следовательно сумма четырех последовательгых чисел не может быть простым числом.

Answer 2

Proof that the Sum of Four Consecutive Numbers Cannot Be a Prime Number

To prove that the sum of four consecutive numbers cannot be a prime number, we can use the concept of divisibility and the properties of consecutive numbers.

Let's consider four consecutive numbers represented by a, a+1, a+2, and a+3.

The sum of these consecutive numbers can be represented as: a + (a+1) + (a+2) + (a+3)

Expanding this expression, we get: 4a + 6

Now, let's analyze the possible scenarios for the sum of these consecutive numbers.

1. If a is even, then 4a is also even. In this case, the sum 4a + 6 would be even, and the only even prime number is 2. Therefore, the sum cannot be a prime number.

2. If a is odd, then 4a is also even. In this case, the sum 4a + 6 would be even, and the only even prime number is 2. Therefore, the sum cannot be a prime number.

Based on the above analysis, we can conclude that the sum of four consecutive numbers cannot be a prime number.