*Spoiler for New Scientist Enigma 1740: “Sudoprime” *(Follow the link to see the puzzle.)

Label the squares:

A - - - B C D - E F - G H I - J K - L M N - - - O

*A* is 5 and *H* is 9. *C, D, F, I, K, L, M, N, *and *O* must be odd and not 5.

*AC* must be 53 or 59. Try 59 first:

Then C*D* must be 97. *K* cannot be 7 or 9 so must be 1 or 3. Then *DGK* is 743, 751, or 761. *L* cannot be 7 or 9 so must be 1 or 3. If *DGK* is 743 then *GHI* is 491 and *L* cannot be 1 or 3. Dead end. If *DGK *is 751 then *GHI* is 593 and again *L* cannot be 1 or 3. Dead end. So *DGK* is 761, *GHI* is 691, and *L* is 3. *EIL* must be 613. This means *O* must be 1. *F* cannot be 1 or 7 or 9 so must be 3; then *EF* can only be 63 which is not prime. Dead end.

So *AC* must be 53. *CD* can be 31 or 37. Try 37:

Same argument as above except we conclude *F* must be 9, so *EF* is 69 which is not prime. Dead end.

Then *CD* is 31. *N* cannot be 3 or 9 so must be 1 or 7. *K, L,* and *O* must be 3 or 7. So *LM* and *MO* are 31 and 17 or 71 and 13. Either way *M* is 1. Try 31 and 17:

Then *F* is 9. *I* is 1 or 7. The 3-digit primes ending in 13 or 73 are 113, 173, 313, 373, 613, 673, 773. None is legal for *EIL.*

So *LM* and *MO* are 71 and 13. Then *I* is 1 or 3. The 3-digit primes ending in 17 or 37 are 137, 317, 337, 617, 937. Only 617 is legal. Then *EF* is 67. *K* is 3. *GHI* is 491 or 691. But 143 is not prime so *DGK *is 163. *B* is 4. The only possibilities for *JN* are 41 and 47, but we already have *BF* = 47 so *JN* is 41.

The grid is:

5 - - - 4 3 1 - 6 7 - 6 9 1 - 4 3 - 7 1 1 - - - 3

and the answers required are 617 and 41.