anonymous
  • anonymous
prove there are no more than 9 primes whose decimal representation is a string of ones
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
PaxPolaris
  • PaxPolaris
Any hints on how to solve this.... All I got so far... If the length of the string is divisible by 3, then the number is divisible by 3 If the length of the string is even, then the number is divisible by 11
anonymous
  • anonymous
Hang on, I forgot - above 10 and below 10^29....
PaxPolaris
  • PaxPolaris
So strings of length 2 to 29... that's 28 numbers 11 is prime... Using the rules above we can eliminate strings of length: 3, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 26, 27, 28 We are left with: 2, 5, 7, 11, 13, 17, 19, 21, 23, 25, 29 that's 11 get rid of 2 more

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

KingGeorge
  • KingGeorge
While not the best method, now that we've reduced the possibilities to 11 a brute force attack might work.
KingGeorge
  • KingGeorge
Although, in that list, there are 9 primes and 2 composite numbers. I might also try to show that strings of length 21 and 25 are composite.
PaxPolaris
  • PaxPolaris
sorry 21 is already eliminated ... that's 10
anonymous
  • anonymous
multiples of 5 have 41 multiples of 7 have 239, 4649 11 has multiples of .... never mind 4 has 11, 101, 1111 6 has 7, 13, 21. Get rid of 3, 5, 7, 11 after some random working out, 19 and 23 are the only two that work. Thanks.
anonymous
  • anonymous
other than 2...
KingGeorge
  • KingGeorge
Then we're done. Now that we've eliminated at least 2 from the list, there can be no more than 9 primes whose decimal representation is a string of ones between 10 and \(10^{29}\)

Looking for something else?

Not the answer you are looking for? Search for more explanations.