Question

Which is a counterexample to this conjecture?

The sum of any two consecutive integers is a composite number.

A.
16 + 17 = 33

B.
10 + 11 = 21

C.
6 + 7 = 13

D.
7 + 8 = 15

Answer 1

@SolomonZelman

Answer 2

I am realy realy bad at math.

Answer 3

try to find two consecutive integers that add to a prime number

Answer 4

what is composite number?

Answer 5

A number that has one and itself.

Answer 6

what about 13?

Answer 7

Does 13 have one and itself as multiples.

Answer 8

33=1*3*11
21=1*3*7
13=1*13
15=1*3*5
1 is factor of every number.
so you can know.

Answer 9

\(\normalsize\color{blue}{ \rm Composite~~numbers }\), are the opposite of prime numbers.

\(\normalsize\color{blue}{ \rm Composite~~numbers }\):
\(\normalsize\color{blue}{ \rm 4 }\) (can be divisible by 2)
\(\normalsize\color{blue}{ \rm 6 }\) (can be divisible by 2 & 3)
\(\normalsize\color{blue}{ \rm 8 }\) (can be divisible by 2 & 4)
\(\normalsize\color{blue}{ \rm 9 }\) (can be divisible by 3)
\(\normalsize\color{blue}{ \rm 10 }\) (can be divisible by 2 & 5)

and etc.,

\(\normalsize\color{red}{ \rm Prime~~numbers }\) would be starting like:
\(\normalsize\color{red}{ \rm 2 }\), \(\normalsize\color{red}{ \rm 3 }\), \(\normalsize\color{red}{ \rm 7 }\), \(\normalsize\color{red}{ \rm 11 }\) and \(\normalsize\color{red}{ \rm on... }\)

Answer 10

yes 13 is a composite number.

Answer 11

I mean prime sorry.

Answer 12

yes, it prime

Answer 13

prime numbers have one and itself as multiples.

Answer 14

\(\normalsize\color{red}{ \rm prime~~number }\) can be only divided by \(\normalsize\color{red}{ \rm itself }\) and by \(\normalsize\color{red}{ \rm 1 }\).

Like, \(\normalsize\color{red}{ \rm 13 }\) can be only divided by \(\normalsize\color{red}{ \rm 13 }\) (itself), or by \(\normalsize\color{red}{ \rm 1 }\) .

Answer 15

do you understand the conjecture?

Answer 16

or not?

Answer 17

I understand.

Answer 18

just to make sure, which answer choice did you choose?