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A “Sophie Germain” prime is any positive prime number p for which 2p +
[#permalink]
21 Apr 2021, 15:58
21 Apr 2021, 15:58
11
Expert Reply
27
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00:00
Question Stats:
30% (03:05) correct
69% (02:36) wrong based on 184 sessions
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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. 3
B. 7
C. 21
D. 27
E. 189
Re: A “Sophie Germain” prime is any positive prime number p for which 2p +
[#permalink]
05 Jul 2021, 04:42
05 Jul 2021, 04:42
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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.
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.
General Discussion
Re: A Sophie Germain prime is any positive prime number p for which 2p +
[#permalink]
15 May 2022, 16:02
15 May 2022, 16:02
can this question type appear on the exam?
