A sketch of a prime monomial search.

prime _monomial_search_sketch.swift

extension BinaryInteger {
	// Let’s assume we have `BinaryInteger.isPrime()` implemented.
	func isPrime() -> Bool { /* … */ }
}

let possiblePrimeLastDigits = ["1", "3", "7", "9"] // Primes greater than five can’t have
// 0, 2, 4, 6, 8, or 5 in its one’s position. If it did, we’d have an even or a multiple
// of five in hand (assuming the prime is greater than five and we’re squarely in this
// territory since 5 _isn’t_ monomial).

let ms = (3...9).reversed() // The possible “m”s in the problem statement. We can
// safely ignore 2 since neither 12 or 21 are prime and we reverse the range
// since any prime in the upper end of the length range will be greater than monomial
// primes with a shorter length.

var largestPrimeMonomial: UInt?

outerLoop: for m in ms {
	let mLengthMonomials = (1...m)
		.reversed()
		.map(String.init)
		.permutations() // Let’s assume we have `Collection.permutations()` at hand.
		// `mLengthMonomials` will contain single-digit strings, up to the current monomial
		// length being considered. e.g. `[["1", "2", "3", "4"], ["2", "1", "3", "4"], …]`.

	for monomial in mLengthMonomials {
		guard
			possiblePrimeLastDigits.contains(monomial.last!), // Last digit check.
			let intMonomial = UInt(monomial.joined()), // Join the `String` digits
			// and cast to an unsigned integer.
			intMonomial > (largestPrimeMonomial ?? 0),
			intMonomial.isPrime()
		else { continue }

		largestPrimeMonomial = intMonomial
		break outerLoop // Once we’ve found a candidate prime, we can break out
		// of the outer loop since we’re searching in decreasing order.
	}
}

print(largestPrimeMonomial)