Module:Factorization/sandbox

 local p = {}

 function p.factor(frame)
	-- Consider calling the parser function #expr
	-- to simplify a potential mathematical expression?
 number = tonumber(frame.args[1])
 if number == nil then
 	return '<strong class="error">Error: input not recognized as a number</strong>'
 end

 productSymbol = frame.args['product'] or '·'
 bold = frame.args['bold'] and true
 big = frame.args['big'] and true
 serif = frame.args['serif'] and true
 primeLink = frame.args['prime'] and true

 number = math.floor(number)
 if number < 2 or number > 1000000000 or number == math.huge then
 return '<strong class="error">Error: ' .. number .. ' out of range</strong>'
 end

 result = ""
 currentNumber = number
 power = 0
 divisor = 2

 -- Attempt factoring by the value of the divisor
 -- divisor increments by 2, except first iteration (2 to 3)
 while divisor <= math.sqrt(currentNumber) do
 power = 0
 while currentNumber % divisor == 0 do
 currentNumber = currentNumber / divisor
 power = power + 1
 end

		-- Concat result and increment divisor
		-- when divisor is 2, go to 3. All other times, add 2
		result = result .. powerformat(divisor, power, productSymbol)
 divisor = divisor + (divisor == 2 and 1 or 2)
 end

 if currentNumber ~= 1 then
 result = result .. currentNumber .. ' ' .. productSymbol .. ' '
 end

 if currentNumber == number and primeLink then
 return '[[prime number|prime]]'
 end

 result = string.sub(result,1,-4)

 return format(result)
 end

 function powerformat(divisor, power, productSymbol)
	if power < 1 then return ''
 elseif power == 1 then return divisor .. ' ' .. productSymbol .. ' '
 else return divisor .. '<sup>' .. power .. '</sup> ' .. productSymbol .. ' '
 end
 end

 function format(numString)
 if bold then
 	numString = '<b>'..numString..'</b>'
 end

	ret = (serif or big) and '<span ' or ''
	if serif then ret = ret .. 'class="texhtml" ' end
	if big then ret = ret .. 'style="font-size:165%" ' end
	ret = ret .. ((serif or big) and '>' or '') .. numString .. ((serif or big) and '</span>' or '')

 return ret
 end

 return p