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26 Apr 2019, 01:29
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
62% (02:13) correct
38%
(02:27)
wrong
based on 205
sessions
History
Date
Time
Result
Not Attempted Yet
What is the sum of all the possible prime numbers p such that \(p^2 +8\) is also a prime number?
A. 3
B. 47
C. 32
D. 12
E. 21
A. 3
B. 47
C. 32
D. 12
E. 21
20 Sep 2024, 04:29
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1. Every Prime number is of the form 4n+1 and 4n-1 where n>2
2. Every Prime number is of the form 6n+1 and 6n-1 where n>3
let's try (6n+1)^2 +8= 36n^2+12n+9= 3(12n^2+4n+3) ==> definitely not a prime number
let's check 2 and 3, so,
for 2,
p^2+8 = 12 (not a prime number)
for 3,
p^2+8= 17 ( a prime number)
so, sum of all the possible prime numbers p is 3
2. Every Prime number is of the form 6n+1 and 6n-1 where n>3
let's try (6n+1)^2 +8= 36n^2+12n+9= 3(12n^2+4n+3) ==> definitely not a prime number
let's check 2 and 3, so,
for 2,
p^2+8 = 12 (not a prime number)
for 3,
p^2+8= 17 ( a prime number)
so, sum of all the possible prime numbers p is 3
General Discussion
26 Apr 2019, 02:25
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1. For any prime number p in the form of 3k+1
P^2 +8= 9k^2+6K+9 can never be prime, as it is multiple of 3
2. For any prime number p in the form of 3k+2
p^2+8=9k^2+6k+12, again multiple of 3
3. For any prime number p in the form of 3k
p^2+8= 9k^2+8 can be prime number
Only prime number which is multiple of 3 is 3 itself
sum of all the possible prime numbers p=3
P^2 +8= 9k^2+6K+9 can never be prime, as it is multiple of 3
2. For any prime number p in the form of 3k+2
p^2+8=9k^2+6k+12, again multiple of 3
3. For any prime number p in the form of 3k
p^2+8= 9k^2+8 can be prime number
Only prime number which is multiple of 3 is 3 itself
sum of all the possible prime numbers p=3
