alchemist009 wrote:
A “Sophie Germain” prime is any positive prime number p for which 2p + 1 is also prime. The product of all the possible units digits of Sophie Germain primes greater than 5 is
A. 3
B. 7
C. 21
D. 27
E. 189
A prime number greater than 5 can have only the following four units digits: 1, 3, 7, or 9.
If the units digit of p is 1 then the units digit of 2p+1 would be 3, which is a possible units digit for a prime. For example consider p=11=prime --> 2p+1=23=prime;
If the units digit of p is 3 then the units digit of 2p+1 would be 7, which is a possible units digit for a prime. For example consider p=23=prime --> 2p+1=47=prime;
If the units digit of p is 7 then the units digit of 2p+1 would be 5, which is NOT a possible units digit for a prime;
If the units digit of p is 9 then the units digit of 2p+1 would be 9, which is a possible units digit for a prime. For example consider p=29=prime --> 2p+1=59=prime.
The product of all the possible units digits of Sophie Germain primes greater than 5 is 1*3*9=27.
Answer: D.
Hope it's clear.
Bunel from 23 we get 47. So both the condition of p & 2p+1 is met. Then why we are not taking 7 from 47 ? what is the logic of taking 7 from 47 and doing multiplication? do we have to take 2p+1 again as p and repeat the same process.