School-Safe Puzzle Games highly recommends Plexus Puzzles, try one free right now!

Sum of Primes

Big Thanks to Puzzle GrandMaster Shawn for submitting this!

Answers to this challenge can be entered into the section below; submissions will automatically be revealed when time is up!

18 Comments to “Sum of Primes”

  1. virgolady85 | Profile

    61 reversed is 16
    square root of 16 is 4
    square root of 4 is 2

  2. shaks | Profile

    1. 5 – 2+3=5

    2. 61, when reversed is 16 – root once is 4, twice gives 2 – so I guessed 61

  3. suineg | PUZZLE MASTER | Profile

    I think its 123031

    1) 123029+2
    2) reverse: 130321 ….. 361……19 its prime, cool man!

  4. suineg | PUZZLE MASTER | Profile

    61 is the answer man….. bad bad….. cool

  5. Bobo The Bear | PUZZLE MASTER | Profile

    Sorry I’m late to the party.

    61is prime, and equals 59 + 2, both prime.
    61 reversed is 16
    ?(?(16)) is 2, which is prime.

    Wonder what the next smallest one would be.

  6. Vik | Profile

    61=59+2 & sqrt(sqrt(16))=2

  7. Hex | PUZZLE MASTER | Profile

    I checked the website a little while ago and discovered this puzzle.

    The easiest way to proceed is to iterate through the prime numbers:
    P=prime number
    check if M is prime
    Check that M is a sum of 2 primes

    I was able to implement a program to do the above but the last step due to the short notice. I got the 1st 3 possibilities:
    61, 123031, 125329

  8. Shawn | PUZZLE GRANDMASTER | Profile

    Very good, everyone found 61, but that was the easy one!

    The followup question is the one Bobo asked – what is the next prime “X” for which this puzzle works?

    Hint: Unless I missed one, the next possible answer for “X” has 12 digits.

    Some patterns that you might have noticed:
    1- primes are always odd (2 is the only exception)
    2- adding 2 primes together always yields an even number, unless one of the two primes is the number 2
    3- therefore, for this puzzle, one of the two primes that are added together to form “X” must be the number 2

  9. Hex | PUZZLE MASTER | Profile

    I just completed the last step:
    123031, 125329 are ruled out.

    @suineg: 123029 = 17 x 7237

  10. Hex | PUZZLE MASTER | Profile

    146231183533 seems to be the 1st 12 digits solution:
    sqrt(sqrt(335381132641)) = 761 (prime)
    146231183533 = 146231183531 + 2 (both primes)

    sqrt(sqrt(357040905841)) = 773 (prime)
    148509040753 = 148509040751 + 2 (both primes)

    sqrt(sqrt(933714431521)) = 983 (prime)
    125134417339 = 125134417337 + 2 (both primes)

  11. Shawn | PUZZLE GRANDMASTER | Profile

    Good old Hex comes through again!

    146,231,183,533, with a reverse double square root of 761 is also the next prime I found that fits the bill.

    But wait, this solution has the lowest double square root prime at 761. However, it looks like Hex found a higher value for this prime, 983, that actually yields a lower value for “X”, so this would be the best solution.

    I must admit, I was solving the problem based on the double square prime, and I stopped when I found that 761 worked, but 983 just slips in under the wire in allowing a double square of 12 digits. Very nice!

  12. Hex | PUZZLE MASTER | Profile

    The next solutions are one with 13 digits, one with 15 digits, and 3 with 16 digits. Anybody?

    @Shawn, I’ll always be present whenever such challenging puzzles are posted.
    What method did you use to get your result? I was able to compute the 9 solutions (16 digits or less) in exactly 22 seconds :D

  13. Shawn | PUZZLE GRANDMASTER | Profile

    @Hex, 22 seconds to program or to compute? If that is your programming speed, I bow in your general direction :agape I used Excel, and it took me a quite a while to get it all set up and debugged ! (I am not a programmer by any definition of the word)

  14. Hex | PUZZLE MASTER | Profile

    @Shawn, 22 seconds to compute of course. How much time did Excel require?

    Programming is cool when it helps solving such numerical problems :)

  15. Shawn | PUZZLE GRANDMASTER | Profile

    If I really try to account for every minute, Excel probably took me 2-3 hours. A lot of that time was spent teaching myself how to use the particular formulas and subroutines. I’m trying to learn Excel a bit better every day. When I stumbled on a way to check for primes, I thought it would make a nifty puzzle, and this is what popped out.

  16. 33550336 | Profile

    X is 18

    18 = 11 + 7 (or 13 + 5)

    9 x 9 = 81
    3 x 3 = 9

  17. Square of the Primes | Smart-Kit Puzzles and Games | Guest

    […] Sum of Primes! « Best of Casual Puzzle Games […]

Enter an Answer/Comment/Reply

To comment log in or register for a free Smartkit account.

Recent Comments Sign In