School-Safe Puzzle Games

## 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”

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

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

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

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