math

You first.

You want that in numbers or letters?

Two odd numbers (or a factor of two odd numbers) adds to an even number therefore it is not prime.

Three odd numbers (or more than 3 odd numbers) requires than 1 of the odd numbers is more than one either side of a number divisible by six, therefore at best two are either side of a six and the third is 3 away from a six therefore it is divisible by 3.

qed

1) The sum of two consecutive odd integers is even.
let n be any even number
then (n+1) and (n+3) are two consecutive odd numbers.
(n+1)+(n+3)=2n+4=2(n+2)

2) The only even prime numer is two (2).

3) Two (2) cannot be expresses as the sum of two consecutive odd integers.
the smallest even/odd number is 0, so let n=0, then (n+1)=1 and (n+3)=3
1+3=4
4 is not equal to 2

4) The sum of two consecutive odd integers is not 2

5) The sum of any two consecutive odd integers cannot be prime.

Rap

wow rap you've really clobbered two odd numbers any chance of you addressing 3 or more odd numbers, that is the question?

i reckon my answer was as elegant as a mathematician on a bicycle

proving the sum of more than one consecutive odd numbers is not prime is somewhat trivial.

simply show that the sum of k consecutive odd itegers is

(n+1)+(n+3)+......+(n+1+(k-1)*2)=k*n+(1+3+...+(1+(k-1)*2)=k*n+k^2=k(n+k)

BTW one of my cycling buds has a phd in math---

Rap