Husk, 11 bytes

^{I got ninja'd..}

§&tΛo€Ṗd1dp

Try it online!

Outputs truthy for a lobster number and falsy otherwise. This would be shorter if all returned 0 for empty lists.

Explanation

§&tΛo€Ṗd1dp
 p prime factorization of the input
§ fork:
 t is the list not composed of a single element?
 & and,
 Λo d are all the prime factors' digits
 € present in
 Ṗd1 the powerset of the input's digits?

Husk, 11 bytes

^{I got ninja'd..}

§&tΛo€Ṗd1dp

Try it online!

Outputs truthy for a lobster number and falsy otherwise. This would be shorter if all returned 0 for empty lists.

Explanation

§&tΛo€Ṗd1dp
 p prime factorization of the input
§ fork:
 t is the list not composed of a single element?
 & and,
 Λo d are all the prime factors' digits
 € present in
 Ṗd1 the powerset of the input's digits?

Husk, 11 bytes

§&tΛo€Ṗd1dp

Try it online!

Outputs truthy for a lobster number and falsy otherwise. This would be shorter if all returned 0 for empty lists.

Explanation

§&tΛo€Ṗd1dp
 p prime factorization of the input
§ fork:
 t is the list not composed of a single element?
 & and,
 Λo d are all the prime factors' digits
 € present in
 Ṗd1 the powerset of the input's digits?

Husk, 11 bytes

^{I got ninja'd..}

§&tΛo€Ṗd1dp

Try it online!

Outputs truthy for a lobster number and falsy otherwise. This would be shorter if all returned 0 for empty lists.

Explanation

§&tΛo€Ṗd1dp
 p prime factorization of the input
§ fork:
 t is the list not composed of a single element?
 & and,
 Λo d are all the prime factors' digits
 € present in
 Ṗd1 the powerset of the input's digits?