# Question

• Jul 28th 2009, 11:52 PM
jgv115
Question
Three numbers p, q and r are all prime numbers less than 50 with the property that $p+q=r$. How many values of r are possible?

I would think this is 0 because prime numbers have to be odd and odd + odd always equals an even number. But the answer is not 0
• Jul 29th 2009, 12:21 AM
SENTINEL4
It's not all prime numbers odd. You forget 2 which is prime and even.
Then if p=2 and q=3 then p+q=2+3=5=r and p,q,r are all primes.
Same if p=2 and q=5 then r=7.
Check if there are any more...
• Jul 29th 2009, 12:25 AM
jgv115

ok

2,3
2,5
2,11
2,17
2,29
2,41

did i miss any?
• Jul 29th 2009, 12:28 AM
jgv115
OK I have another one.

When 1000^2008 is written as a numeral, the number of digits written is..

How do you go about doing this?
• Jul 29th 2009, 12:35 AM
SENTINEL4
I don't quite understand what you want for the last one you asked $1000^{2008}$
You want to know how many digits this number has?? Too many! (Rofl)
• Jul 29th 2009, 12:36 AM
songoku
1000^1 = 1000 ( 4 digits)

1000^2 = 1,000,000 (7 digits)

1000^3 = 1,000,000,000 (10 digits)

there is pattern ^^
• Jul 29th 2009, 01:11 AM
jgv115
oo alright! so if $1000^2$ has 7 digits (6 zeros) that means

$2008\div2 = 1004$

$1004* 6 = 6024 + 1$ (the extra 1) is 6025!