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Is 132 the sum of two odd primes?
No. Consider that every prime number except 2 is an odd number. Consider also that the sum of two odd numbers is always an even number. Thus, the only case in which an odd n…umber can be expressed as the sum of two primes is when it is 2 greater than a prime number, since it can take advantage of the only even prime number, 2. For example, 21 can be expressed as 2+19, both of which are primes. However, 27 has no such two primes, since 25 is not prime (5x5=25).
5 + 3 = 8 5 + 5 = 10 5 + 7 = 12 7 + 7 = 14 11 + 5 = 16 11 + 7 = 18 13 + 7 = 20
Sum of two odd numbers are always even, and the sum of 2 even numbers are also even. The sum of an odd number & an even number are always odd.
The sum of two odd numbers is always an even number, e.g. 3 + 5 =8. This can be proven as follows: Every even number can be expressed as 2m where m is a real number. Every odd… number can therefore be expressed as 2m+1 where m is a real number. For this proof, we will consider two different odd numbers: 2m+1 and 2k+1. 2m+1 + 2k+1 =2m + 2k + 2 =2(m + k + 1) As m+k+1 is a real number, the answer must be even. Therefore the sum of any two odd numbers is an even number.
If the sum of two prime numbers x and y is odd Then the product of x and y must be divisible by which number?
Prime numbers are usually odd.The only even prime number is 2.When two prime numbers are added say 3 and 5 the result wil be 8(even).So the question of ur answer is only appli…cable to the following set:2,3.The sum of an even prime and an odd prime will exhibit an odd number.2+3=5.When this two prime nos. are multiplied 2*3=6,it will be divisible by both 2 an 3.
The odd composite numbers between 50 and 60 are 51, 55, and 57. Because all the primes are odd except for 2 and adding two odd numbers will result in an even number, one of th…e two prime numbers must be 2, which when added to an odd number will result in an odd number. So, we subtract 2 from each of these numbers and check whether it is prime. 51 - 2 = 49, which is not prime. 55 - 2 = 53, which is prime. 57 - 2 = 55, which is not prime. Thus, the number is 55, which can be written as 2 + 53.
34 = 17+17 34 = 23 + 11 34 = 29 + 5 34 = 31 + 3
trial and error, also called guess and check, but not quite let x = 1st odd prime, and y = 2nd odd prime the y can be 1,3,5,7,11,13,17,19,23,29,31 then x+y = 36, or x = 36 - y…, by substitution x = 36 - 1 = 35 not prime so not a solution x = 36 - 3 = 33 not prime x = 36 - 5 = 31 prime x = 36 - 7 = 29 prime x = 36 - 11 = 25 not prime x = 36 - 13 = 23 prime x = 36 - 17 = 19 prime x = 36 - 19 = 17 prime (but a repeat of another solution) so (5+31), and (7+29), and (13+23), and (17+19) are all solutions For your question about the method, maybe it is called the method of exhaustion. List all possibilities for one number and exhaust (solve and check) for all other solutions.
This question cannot be answered because three odd primes always have an odd number for their sum.
The sum of any two odd numbers is always even. This is because (a) any odd number can always be expressed as an even number plus 1, and (b) the sum of two even numbers… is always even. So if X is even and Y is even then X+1 added to Y+1 will equal X+Y+2
44=41+3 46=41+5 24=11+13 18=11+7
7 & 29, 13 & 23, 17 & 19...
It could any odd prime number and 2 since 2 is the only even prime number and add whole numbers to an odd sum requires both odd and even.In other words, 2 and any other prime …will work.
11 and 12
What's a counterexample to the statement that all odd numbers can be expressed as the sum of two primes?
There is a simple counterexample: the number 1: 1 is an odd numberthe first prime is 2 (not 1, see below) which is bigger than 1 so 1 cannot possibly be the sum of two primes…. There are plenty of other counterexamples: The sum of two odd numbers is even;All prime numbers except 2 are odd;When adding two prime numbers together, to get an odd result one of them must be even, namely 2;So any odd number that is 2 more than a composite number will not be expressible as the sum of two primes. examples: 11, 17, 23, 27, 29, 35, 37, ... Another counterexample is the number 3: 3 is an odd number3 can only be made by 2 + 11 is not a prime (see below) A prime number is a number that has exactly 2 distinct (different) factors. The number 1 has only 1 distinct factor (the number 1) and so is not a prime number; the first prime number is 2.
-- The first odd number is some even number plus an extra ' 1 '. -- The second odd number is some even number plus an extra ' 1 '. -- Add them. You get (an even number) …+ (an even number) + ( 2 ). That's an even number. ==== Another mind-bending , brain-busting way to look at it : -- The first odd number is some even number plus an extra ' 1 '. -- The second odd number is some even number minus ' 1 '. -- Add them. You get (an even number) + (an even number) + ( [1 - 1] or zero ). That's an even number.