**From New Scientist #2182, 17th April 1999** [link]

**Across:**

1. A prime which is also a square reversed. The first two digits form a square, and the last two a prime. The 1st, 3rd and 5th digits are all the same.

4. The square root of 7 across.

5. A palindromic square.

6. The square root of the reverse of 2 down.

7. A square which is prime when reversed.

**Down:**

1. A prime which is also a square reversed. The first three digits form a square which is also a square when reversed. The last two digits form a prime which is also a prime when reversed.

2. A prime which is also a square when reversed. All the digits are different. The first three digits form a square which is also a square when reversed: and the last digit is the same as that of 1 down.

3. A square which is a prime when reversed.

Find the answers for 1 across, 1 down, 3 down and 7 across.

[enigma1026]

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Several of the digits are equated with each other, either directly or by the use of palindromic numbers.

We can apply these and then use the [[

`SubstitutedExpression()`

]] solver from theenigma.pylibrary to solve the remaining conditions of the puzzle.The following run file executes in 142ms.

Run:[ @repl.it ]Solution:1 across = 16141; 1 down = 14437; 3 down = 18496; 7 across = 70756.