Is this real?

The sum of any two odd primes is even, so $1001,$ being odd, cannot be the sum of two odd primes.

Since the only even prime is $2,$ the only remaining case is that $2 + p = 1001$ for some prime $p,$ but then solving for $p$ yields $p = 1001 - 2 = 999$ which isn't prime.

That is, we can conclude that $1001$ cannot be written as the sum of two primes, so there are $\boxed{0}$ ways.

since 2 is the only even prime number and 999 isn't prime then there is no way

A very simple solution Let x and y are 2 prime numbers such that x + y =1001 or. y = 1001 - x Now take any prime number. First even prime number 2 y = 1001 - 2 = 999 but here 999 is divisible by 3. So 2 , 999 can't be a solution. Now other prime numbers like 3, 5, 7, 11 etc So y =1001- odd number y = even. Since odd - odd =even And other than 2 all even numbers are composite numbers. So there will be no such prime numbers.

I was really confused, until I realised that the reason why 3, 5 and 7 weren't working was because an odd number plus an odd number is an even number. Simply stated, as all primes, except 2, (which gets all the credit literally for being the only prime that divides by 2-when it is 2 itself, so of course it divides!You may as well throw a party because 3 is the only prime that divides by 3) are odd and we need an odd prime plus an even prime or an even prime plus an even prime to get an odd number like 1001, we know 2 is the even prime. Obviously, 2 plus 2 is 4 (not 1001), so that doesn't work. Finally, the only option that remains is 2 plus an odd number (which is 1001 minus 2, 999). However, 999 is not a prime: It's 9 times 111 and 9 is 3 times 3. Not to mention 111 is actually 3 times 37, making 999 3 times 3 times 3 times 37. Therefore, we have no solutions

We can see that 1001 is odd. We also know that every prime number besides 2 is odd. That means that every prime number “x” will be odd and 1001-x is even (except when x=2). Given those conditions, we have a maximum if one possible sum of primes. 1001-2=999, and we can easily see that 999 is divisible by 3. Therefore, there are no sums of primes that add up to 1001

In order for the sum to be odd, one of the factors must be even (the sum of two odds is even, the sum of two evens is even). The only even prime number is two, since all other evens have 2 as a factor. 1001 - 2 = 999. 999 is not prime (since it has other factors than 1 and itself). Therefore no prime two sums can add to be 1001.

If $1001$ were the sum of two primes, one of the summands must be $2$ . The other summand must then be $999$ , which is composite; a contradiction.

Larger prime number always end with 1, 3, 7, 9. Adding any of the two digit from 1,3,7,9 doen't give 1 as last digit in the sum. Besides, the sum between prime number 5 to any 1,3,7,9 digit also doesn't give 1 as last digit. The only thing to consider is 2 + 999 and 999 is not prime number. Therefore, there is 0 ways that sum of two prime is 1001.

In this case 1001 can be obtained only by sum of odd and even number, 1001-2 wont work and there are no other even primes.

1001 is an odd number, and to get an odd number as a sum of two numbers, one of them is always an odd one, and the other, an even one, and even numbers are never prime numbers, so there is no way to get 1001 as a sum of 2 primes.

1001 is an odd number. So you need one odd and even number so that it's sum will be odd. We know that there is only one prime number 2 but with that we will need 999, which is not a prime number. And if we choose an odd prime number, the other number will be even which is obviously not prime(it will always be divisible by 2). Hence there are no ways.

2 primes added it always gives an even number, even if you write the primes in the first 1000 numbers and try to add them.

By far the easiest "AHA" problem that should be intuitively known since a year from your birth.

The answer becomes more obvious when you stop and think about it. 1001 is an odd number, and the only way to add two numbers to get an odd number is if one number is even and one number is odd. Since an even number is always divisible by two, and therefore not prime, 1001 is not decomposible into two prime numbers.

Prime numbers are almost exclusively odd numbers. 2, the only even prime number, needs 999 to add to 1001. 999 is a composite number.

There is no way to write 1001 as a sum of two primes , because if p and p' are primes ,so they are impairs , and the sum of two numbers impairs is pairs , but 1001 isn't pair

Being an odd number, 1,001 cannot be the sum of two odd numbers (that would be even). The only possible combination involving at least one prime is 2 (only even prime) + 999. 999 is very obviously divisible by 3 (actually full prime factorization is 3 x 3 x 3 x 37), therefore 999 is not prime, so there are no combinations of two prime numbers that add up to 1,001.

First of all, that problem is bogus, because 1 and 0 are not primes - 1 can only be divided by itself, unlike 41, a prime number, can also be divided by 41. 0 can't be divided by anything, so it would not work. Also, 1 + 1 is 2, which is an even number because odd + odd is even, but even + even is is even. So 0 + 0 doesn't equate to anything, but 1 + 1 equals 2, which is more than 1. So the answer is №.

All positive odd integers add to an even sum, the only even prime is 2.

I need perfect solution

1001 is an odd number. The sum of two odd numbers is necessarily even. Since all Prime numbers other than 2 are odd numbers , one cannot obtain an odd number by adding two primes (which are not equal to 2).

The only other case to be verified remaining are 2 + p = 1001 , this solves as p = 999 ; 999 is not a prime number as it divisible by 3, 9, 11 etc.,