Weakly Prime

A prime number is said to be weakly prime if changing a single digit to every other possible digit produces a composite number when performed on each digit. The first few such numbers are 294001, 505447, 584141, 604171, 971767, 1062599, ... (OEIS A050249).

If the restriction that the initial digit may not be changed to a 0 is added, then the first few such numbers are instead 294001, 505447, 584141, 604171, 929573, 971767, 1062599, 1282529 1524181, 2017963, 2474431, 2690201, 3070663, 3085553, ... (OEIS A158124), namely the same sequence as before plus the additional terms 929573, 3070663, 5285767, ... (OEIS A158125).

REFERENCES:

"Problem #12." https://math.smsu.edu/~les/POW12.html.

Rivera, C. "Problems & Puzzles: Puzzle 017-Weakly Primes." https://www.primepuzzles.net/puzzles/puzz_017.htm.

Sloane, N. J. A. Sequences A050249, A158124, and A158125 in "The On-Line Encyclopedia of Integer Sequences."