Problem 87: Prime power triples

The smallest number expressible as the sum of a prime square, prime cube, and prime fourth power is 28. In fact, there are exactly four numbers below fifty that can be expressed in such a way:

28 = 2² + 2³ + 2⁴
33 = 3² + 2³ + 2⁴
49 = 5² + 2³ + 2⁴
47 = 2² + 3³ + 2⁴

How many numbers below fifty million can be expressed as the sum of a prime square, prime cube, and prime fourth power?

Here is my solution in GoLang; it is a little more verbose than necessary but the extra checking of the upper limit of 50,000,000 and breaking loop logic. as well as caching products, expedited time to execute.

package main

import (
	"fmt"
)

func main() {
	primeList := sieveOfErastothenes(7071) // Sqrt of 50 million
	numberFound := make([]bool, 50000000)  // It's over 9 thousand!
	count := 0                             // Less than 9 thousand
	primeListLength := len(primeList)
	for i := 0; i < primeListLength; i++ {
		// calculate to prevent redundant calculations
		ipow := primeList[i] * primeList[i]
		// 2^3 + 2^4 = 8 + 16 = 24, i is too high
		if (ipow + 24) > 500000000 {
			break
		}
		for j := 0; j < primeListLength; j++ {
			jpow := primeList[j] * primeList[j] * primeList[j]
			if (ipow + jpow) > 50000000 {
				break
			}
			for k := 0; k < primeListLength; k++ {
				kpow := primeList[k] * primeList[k] * primeList[k] * primeList[k]
				l := ipow + jpow + kpow
				if l < 50000000 {
					// If false, number hasn't been marked
					if !numberFound[l] {
						// mark and increment counter
						numberFound[l] = true
						count++
					}
				} else {
					break
				}
			}
		}
	}
	fmt.Printf("The total number of numbers below 50 million that can be expressed as the sum of a prime square, prime cube, and prime fourth power is %d", count)
}

func sieveOfErastothenes(maxVal int) []int {
	sieve := make([]bool, maxVal)
	primeList := make([]int, 0)
	primeList = append(primeList, 2)
	for i := 3; i < maxVal; i += 2 {
		if sieve[i] == false {
			primeList = append(primeList, i)
		}
		for j := i * 2; j < maxVal; j += i {
			sieve[j] = true
		}
	}
	return primeList
}