Question 1209417
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Some prime numbers are of the form {{{2^n-1}}}. For example, the prime number 7 is equal to {{{2^3-1}}}. 
Make a list of the first seven exponents (n<20) that produce prime numbers of this type 
(include the number 3 as one of the seven in your list).
CC11F #5
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<U>ANSWER</U>.  The first seven exponents n < 20 that produce prime numbers of the form {{{2^n-1}}} are 2, 3, 5, 7, 13, 17, and 19.


For the solution, see the link


https://www.google.com/search?q=.+Some+prime+numbers+are+of+the+form+%7B%7B%7B2%5En-1%7D%7D%7D.+For+example%2C+the+prime+number+7+is+equal+to+%7B%7B%7B2%5E3-1%7D%7D%7D.+Make+a+list+of+the+first+seven+exponents+(n%3C20)+that+produce+prime+numbers+of+this+type+(include+the+number+3+as+one+of+the+seven+in+your+list).+CC11F+%235&rlz=1C1CHBF_enUS1071US1071&oq=.+Some+prime+numbers+are+of+the+form+%7B%7B%7B2%5En-1%7D%7D%7D.+For+example%2C+the+prime+number+7+is+equal+to+%7B%7B%7B2%5E3-1%7D%7D%7D.++Make+a+list+of+the+first+seven+exponents+(n%3C20)+that+produce+prime+numbers+of+this+type++(include+the+number+3+as+one+of+the+seven+in+your+list).+CC11F+%235&gs_lcrp=EgZjaHJvbWUyBggAEEUYOdIBCTQwNjdqMGoxNagCCLACAQ&sourceid=chrome&ie=UTF-8


This solution is provided by artificial intelligence (AI) by my request.



Among the obvious facts that are useful to know,  &nbsp;in order for &nbsp;{{{2^n-1}}} &nbsp;be 
a prime integer number, &nbsp;the exponents n must be an odd integer number.


The even exponents n, higher than 2, produce composite numbers.



Among other useful facts to know is THIS: 


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;if the exponent n is a composite number,

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;then  &nbsp;{{{2^n-1}}} &nbsp;is a composite number, &nbsp;too.


So, &nbsp;for such a search as in this problem, &nbsp;you should look among prime exponents n,
rejecting composite exponents n.



Enjoy (!)