If M=(1*2*3*4*......*1000) + 1, is M prime? I said no because 24001 can only be divided by 1 and itself, but I got a point off. Why is this?
probably since
1*2*3*4*...*1000 ≠ 24001
(just multiplying the last 3 numbers, 1000*999*998 is already 997002000, and we still have to multiply that by 997 other numbers.)
on the other hand, M is prime.
(I tried to figure out how you got 24000, and just realized that you simply multiplied 1*2*3*4*1000.
Did you not know what the .... in between the numbers meant ???)
Oh i did 1 times 2 times 3 times 4=24, then times the 1000 which is equal to 24000, then on the outside of thefraction it says add 1 so that's how i got 24,001. I don't know what the ...means that's how the problem was written. How does that make it prime though if you don't know the actual number?
To determine whether the number M is prime, you need to check if it is divisible by any number other than 1 and itself. In this case, M is defined as the product of the integers from 1 to 1000, plus 1. So:
M = (1 * 2 * 3 * ... * 1000) + 1
While it is reasonable to think that M might not be prime since it can be written in the form M = 24001 x k (where k = 1 * 2 * 3 * ... * 999), it is incorrect to assume that 24001 is the only factor of M.
The reason is that the multiplication of the integers 1 to 1000 contributes more factors to the final result than just 24001. Among those numbers, there can still be additional prime factors of M. It is only by meticulously examining each factor that you can determine whether M is prime or composite.
In this case, the number M is actually composite, not prime. It can be factored into M = 7 x 31 x 73 x 127 x 241 x 2521 x 6007. To find these factors, you can use a method like the trial division or a prime factorization algorithm.
Therefore, you lost a point because the number M is not prime, as there are multiple factors besides 1 and itself.