5 added 447 characters in body
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Jelly, 13 12 9 8 bytes

Æf×\D⁼U$

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How it works

Æf×\D⁼U$  Main link. Argument: n

Æf        Yield all prime factors of n, with multiplicities and in ascending order.
  ×\      Take the cumulative product.
    D     Decimal; convert each product into the array of its base 10 digits.
       $  Combine the two links to the left into a monadic chain.
      U     Upend; reverse all arrays of decimal digits.
     ⁼      Test for equality.

Jelly, 13 12 9 8 bytes

Æf×\D⁼U$

Try it online! or verify all test cases.

Jelly, 13 12 9 8 bytes

Æf×\D⁼U$

Try it online! or verify all test cases.

How it works

Æf×\D⁼U$  Main link. Argument: n

Æf        Yield all prime factors of n, with multiplicities and in ascending order.
  ×\      Take the cumulative product.
    D     Decimal; convert each product into the array of its base 10 digits.
       $  Combine the two links to the left into a monadic chain.
      U     Upend; reverse all arrays of decimal digits.
     ⁼      Test for equality.
4 added 1 character in body
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3 deleted 14 characters in body
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Jelly, 13 12 12 9 bytes

ṚḌ=a:ÆfṪßµḊ¡Æf×\µD⁼Ṛ€

Try it online!Try it online! or verify all test casesverify all test cases.

Jelly, 13 12 bytes

ṚḌ=a:ÆfṪßµḊ¡

Try it online! or verify all test cases.

Jelly, 13 12 9 bytes

Æf×\µD⁼Ṛ€

Try it online! or verify all test cases.

2 added 1 character in body
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1
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