What number (1-31) is neither prime nor the sum of two distinct primes?

Question

This is for math homework, hard math homework.

Answer 1

primes from 0 to 31 are
1 2 3 5 7 11 13 17 19 23 29 31
test

4 = 3+1, no
6=5+1, no
8=5+3, no
9= 7+2
12 = 11+1, no
13=7+5, no
14=13+1, no
15 = 13 +2, no
16=11+5, no
18=13+5, no
20 = 19+1, no
21 =19+2, no
22 = 17+5, no
24=23+1, no
25 = 23+2, no
26=23+3, no
27 is the answer
30=29+1, no
31=29+2, no

Answer 2

Hmm...I think you guys got caught up in the question... It says "neither" prime nor the sum of two distinct primes.

1 or 2 are primes, so it does not satisfy condition #1 where it is not a prime.

Primes are: 1 2 3 5 7 11 13 17 19 23 29 31

So, the only answer is 27. It is NOT a prime nor the sume of two distinct primes. All other numbers can be a sum of two distinct primes:

1, prime
2, prime
3, prime
4, 1+3
5, prime
6, 1+5
7, prime
8, 1+7
9, 2+7
10, 3+7
11, prime
12, 1+11
13, prime
14, 1+13
15, 2+13
16, 3+13
17, prime
18, 1+17
19, prime
20, 1+19
21, 2+19
22, 3+19
23, prime
24, 1+23
25, 2+23
26, 3+23
27, THE ANSWER
28, 1+27
29, 2+27
30, 3+27
31, prime

Answer 3

a prime number is a number that has exactly two distinct natural number divisors, which are 1 and the prime number itself.

Primes for numbers 1 to 31 are

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31,

The number 4 is neither prime, nor is it the sum of two distinct primes

The number 6 is neither prime, nor is it the sum of two distinct primes

The number 27 is neither prime, nor is it the sum of two distinct primes

So I think there are three answers: 4,6 and 27

Answer 4

how about 27?

It's divisible by 9 and 3, so it's not a prime number; nor is it the sum of any two prime numbers.

PS: 9 does not work... 7 is a prime number, and so is 2.

Answer 5

9

Technically 1 as well, because 1 is technically not a prime nor a composite number.

Guy above also forgot 27 in his list of primes

Answer 6

and 4, 6, 14


1 is NOT prime!

Answer 7

zero or one.