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Sum of Primes

Big Thanks to Puzzle GrandMaster Shawn for submitting this!

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18 Comments to “Sum of Primes”


  1. virgolady85 | Profile

    X=61
    61=2+59
    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
    N=P*P*P*P
    M=reverse(N)
    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)


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


    125134417339:
    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 [...]


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