how many of the first 30 positive integers can be expressed as a sum of two distinct prime numbers?

Question

how many of the first 30 positive integers can be expressed as a sum of two distinct prime numbers?

Answer 1

The folllowing are ans
1 2 3 no. as 2 is the lowest prime, 11,17,23,27,29 also no rest yes so 22 numbers

4 = 2+2
5= 3+2
6= 3+3
7= 5+2
8= 5+3
9= 7+2
10 = 5+5
11 = no
12 = 7+5
13 = 11+2
14 = 7+7
15= 13+2
16= 11+5
17 = no
18 = 11+7
19 = 17+2
20 = 17+3
21 = 19+2
22= 11+11
23 = no
24 = 13+11
25 = 23+2
26 = 13+13
27 = no
28 = 17+11
29 no
30 \= 17+13

Answer 2

20 of 30 (remembering 2 is prime)

1 No
2 No
3 No
4=2+2 No, not distinct
5= 2+3
6=3+3 No, not distinct
7 =2+5
8=3+5
9=2+7
10=3+7=5+5
11 No
12=5+7
13=2+11
14=3+11=7+7
15=2+13
16=3+13=5+11
17 No
18=5+13=7+11
19 = 2+17
20=3+17=7+13
21=2+19
22=3+19=5+17=11+11
23 No
24=5+19=7+17=11+13
25=2+23
26=3+23=7+19=13+13
27 No
28=5+23=11+17
29 No
30= 7+23=11+19=13+17

Answer 3

4 (2+2)
5 (2+3)
6 (3+3)
7 (2+5)
8 (3+5)
9 (2+7)
10 (3+7)
12 (5+7)
13 (2+11)
14 (3+11)
15 (2+13)
16 (3+13)
20 (7+13)
21 (2+19)
22 (11+11)
24 (11+13)
26 (13+13)
28 (11+17)
30 (13+17)

19 in all... I think I got them all, but I could be wrong.

Answer 4

I'd write it out and just do it manually in my head;
1+3=4
1+5=6
1+7=8
and so on...but I suck at math!

Answer 5

Find out and get back to us with an answer... We'll be waiting... There aren't that many prime numbers anyway...

Answer 6

5,7,8,9,10,12,13,14,15,16,18,19,20,21,22,24,25,26,28,30
So 20 numbers however 16,18,20,22,26,28 can b written in 2 ways
& 24, 30 in 3 ways
[PLEASE NOTE THAT PRIMES SHOULD BE DIFFERENT]

Answer 7

It's one thing to ask for advice with your homework, it's another to post every question on your homework assignment. Do it yourself!!!!!!!!!