## 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!*

**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!*

virgolady85| Profile May 8th, 2012 - 2:47 amX=61

61=2+59

61 reversed is 16

square root of 16 is 4

square root of 4 is 2

.mau.| Profile May 8th, 2012 - 2:51 am61

shaks| Profile May 8th, 2012 - 11:29 am1. 5 – 2+3=5

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

suineg| PUZZLE MASTER | Profile May 8th, 2012 - 10:56 pmI think its 123031

1) 123029+2

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

suineg| PUZZLE MASTER | Profile May 9th, 2012 - 10:38 am61 is the answer man….. bad bad….. cool

Bobo The Bear| PUZZLE MASTER | Profile May 10th, 2012 - 8:16 pmSorry 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.

Vik| Profile May 11th, 2012 - 8:27 am61=59+2 & sqrt(sqrt(16))=2

Hex| PUZZLE MASTER | Profile May 11th, 2012 - 10:33 amI 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

Shawn| PUZZLE GRANDMASTER | Profile May 11th, 2012 - 10:41 amVery 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

Hex| PUZZLE MASTER | Profile May 11th, 2012 - 10:47 amI just completed the last step:

123031, 125329 are ruled out.

@suineg: 123029 = 17 x 7237

Hex| PUZZLE MASTER | Profile May 11th, 2012 - 12:30 pm146231183533 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)

Shawn| PUZZLE GRANDMASTER | Profile May 11th, 2012 - 1:41 pmGood 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!

Hex| PUZZLE MASTER | Profile May 11th, 2012 - 3:00 pmThe 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

Shawn| PUZZLE GRANDMASTER | Profile May 16th, 2012 - 9:50 am@Hex, 22 seconds to program or to compute? If that is your programming speed, I bow in your general direction 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)

Hex| PUZZLE MASTER | Profile May 24th, 2012 - 11:10 am@Shawn, 22 seconds to compute of course. How much time did Excel require?

Programming is cool when it helps solving such numerical problems

Shawn| PUZZLE GRANDMASTER | Profile June 5th, 2012 - 3:31 pmIf 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.

33550336| Profile September 3rd, 2012 - 8:16 amX is 18

18 = 11 + 7 (or 13 + 5)

9 x 9 = 81

3 x 3 = 9

Square of the Primes | Smart-Kit Puzzles and Games| Guest January 14th, 2013 - 11:38 pm[...] Sum of Primes! « Best of Casual Puzzle Games [...]