What is a Sophie Germain prime number? If you can multiply the prime by 2 and add 1, and the answer is prime, then it's a Sophie Germain prime. For example, take the prime 29. 29 * 2 = 58. 58 + 1 = 59. Quick trick to prove if a number is prime or not: square the number, add 17, then divide by 12. If their is a remainder of 6, or if the calculator you use has .5 after it, then it's prime. In this case, $\frac{{59}^{2}+17}{12}$ has a remainder of 6. So it's prime.

In the example above, 59 is called the safe prime. There's a good s&m joke there, but I'm too mature to make it. What's really cool about Sophie primes is this: 59 * 2 + 1 = 119. 119 is prime, so therefore 59 is a Sophie prime. 119 * 2 + 1 = 239. 119 is a Sophie prime. And so is 239. Same works for other Sophie Primes.

Like I said, I finished this yesterday. I didn't post it, because I also wrote this bash script for Sophie Primes. My month isn't going exactly as planned, but damn it I can at least attempt to try!

#!/bin/bash

echo "Please enter a number"

read NUMB

prime=$(($NUMB**2 + 17))

function e {

prime=$(($1**2 + 17))

if [ $(($NUMB)) -le 3 ]; then

test =$(($NUMB * 2 + 1))

echo "$NUMB is prime, and the safe prime is $test"

elif [ $(($prime % 12)) = 6 ]; then

echo "$NUMB is a prime number"

safe=$(($NUMB * 2 + 1))

sophie=$(($safe**2 + 17))

if [ $(($sophie % 12)) = 6 ]; then

echo "$NUMB is a Sophie prime! The safe prime is $safe"

exit

else

echo "$NUMB is prime, but it's not a Sophie prime."

exit

fi

else

echo "This number is not prime"

exit

fi

}

e $NUMB

It's fairly simple code, really. It uses the prime test I discussed early to test if a number is prime or not. If it is, then it multiplies it by 2 and adds one, then tests if that number is prime. Simple. Problem is this: the prime test does not work for numbers less than or equal to three. So there is a special case to check if the number entered is < 3. This is written in bash, which is not that powerful, so it does not like big numbers. If you give it 1000000000000066600000000000001, which is prime, it just says "Not prime". This is because the result of the prime test is too large to store in it's memory.

Questions, comments, thoughts? Leave them below.

ReplyDeleteBanned complain !! Complaining only causes life and mind become more severe. Enjoy the rhythm of the problems faced. No matter ga life, not a problem not learn, so enjoy it :)

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